Of tljS (KnUjerj&Ug of Moxib :nbo&*& bv %%t SDf alec tic ano fM?il8fii!'C0pfe &0i(etieiS PERMANENT RESERVF THE LIBRARY OF THE UNIVERSITY OF NORTH CAROLINA ENDOWED BY THE DIALECTIC AND PHILANTHROPIC SOCIETIES MUSIC IfflMW VAULT MT50 .A2 R172 1779 ' *1 R>7 '779 This booh must not be taken from the Library building. - j^a » a [SB Digitized by the Internet Archive in 2012 with funding from University of North Carolina at Chapel Hil http://archive.org/details/treatiseofmusiccOOrame TREATISE of MUSIC, CONTAINING THE PRINCIPLES O F COMPOSITION. WHEREIN The feveral Parts thereof are fully explained, and made ufeful both to the Profeflbrs and Students of that Science. By Mr. R A M E A U, Principal Compofer to his Moft Chriftian Majefty, and to the \ Opera at Paris. Tranflated into Englifti from the Original in the French. Language. SECOND EDITION. LONDON, Printed for J.Murray, N°. 32, Fleet-Street 5 and Luke White, Dublin. mdcclxxix. B OF THE CONTENT CHAP. I. Page iMroduftion to Practical Mujic — — ■ i 1 C H A P. II. Of the fundamental Bafs — — ■ , i j CHAP. III. Of the perfect Chord, by which begins Compofition in four Parts . . ■ — ; I2 CHAP. IV. Of the Succejfion or Sequence of Chords • 1 3 C H A P. V. Of feme Rules that muji be obferved — — — • 1 7 C H A P. VI. Of the Chord of the Seventh . — — 18 CHAP. VII. Remarks touching the Difcord . 2 z CHAP. VIII. Of the Key, and of its Denomination of Flat and Sharp ib. CHAP. IX. Of the Marnier of Modulating harmonically, when a , diatonic ProgreJ/ton is given to the Bafs 25 C H A P. X. 13— Of the continued Bafs • — „ _- o 1 !? a CHAP. ro A TABLE of the CONTENTS. CHAP. XI. Page Of the Vrogrefiion of the Bafs, which fixes at the fame Time that of the Chords, and of the Manner of reducing a derivative Chord to its fundamental Chord 31 CHAP. XII. Offome other Rules taken from the laji Example — 39 CHAP. XIII. Of the perfeul Cadence — 1 ■ > ■ 4 1 C H A P. XIV. Of the Leading Note, or Jliarp Seventh, and of the Man- ner of ' ref diving all DiJ cords * ■ — * 42. CHAP. XV. Of the Eleventh, otherwife called the Fourth > 44 CHAP. XVI. Of the irregular Cadence • ~- 46 CHAP. XVII. Of the different Vrogreffions of a Bafs that bear a Relation to each other, wherein the Harmony doth not alter in, the upper Parts —, •— — — • 50 CHAP. XVIII. Of the Manner of preparing all Di fiords — • » 53 CHAP. XIX. Skews where Difccrds cannot be prepared • 57 CHAP. XX. An exacl Enumeration of all the different Vrogreffims of the Bafs, according to the different DiJ cords therein ufed — ' — i 60 CHAP. XXI. Of the Chord of the Second — - . 6$ CHAP. XXII. Of Kejs and Modes in general ■■ < 1 ■■ 67 ARTICLES 1. Of Jliarp Keys ■ ib. 2. Of fiat Keys 69 CHAP. XXIII. Of Modulation, or the Manner of removing from one Key into another — -, — ■ 7 a CHAP. XXIV. Some further Rules on the foregoing Chapter ■ » 74 CHAP. A TABLE of the CONTENTS. CHAP. XXV. Page Shews what Chords are to be given to the Notes of a Bafs in all Progrejions ■ 78 ARTICLES 1. Of Cadences, and of all that hath a Relation to a Clcfe of a Song or Melody — — ib. 2. Of imperfecl Cadences — — — 80 3. How the Key may be diftinguiflied, wherein the Progreffion of the imperfetl Cadences are ufed — 82 4. How to dijiinguijh, in a diatonic ProgrtJJion y whether the Melody rejts or jiofs upon the Key-note, or upon its Governing-note ■ £7 CHAP. XXVI. Of the Manner of praflijing the Seventh upon every Note of a Key in a diatonic Progrefjion — — 89 CHAP. XXVII. How one and the fame Difcord may be ufed in fever at Chords fuccejjively following upon different Notes ; and how it may be refolved by Notes that feem to be foreign to that Purpofe — •*— — — — ■ - 90 CHAP. XXVIII. Of Licences, and firft of the felfe or flying Cadence — 94 CHAP. XXIX. Of the Chord of the extreme Jliarp Fijth >■ 99 CHAP. XXX. Of the Chord of the Ninth — — — 101 CHAP. XXXI. Of the Chord of the Eleventh, otherwife called the Fourth 104. CHAP. XXXII. Of the Chord of the extreme Jliarp Seventh ■ 106 CHAP. XXXIII. Of the*Chord of the extreme Jliarp Second, and of its De- rivatives 1 108 CHAP. XXXIV. Of Chromatic -— — ■ ■ 1 1 1 ARTICLES 1. Of Chromatic defending * ■ 112 2. Of Chromatic afcendhig ■ 1 1 4 a 2 CHAP* J TABLE of ' the CONTENTS. CHAP. XXXV. Page Of the Manner of praSlifmg ail that hath been hHherto (aid — - — ■ ' — — — 117 ARTICLES i. Of the ProgreJJion of the Bafs • — ■ — ib. 2. How confonant and dljfondnt Chords, Concords and Dif cords are to be ufed 1 1 £ 3-. Of major Difcords proceeding from the Leading--. note, and of thofe Notes on which they are ufed 119 4. Of minor Difcords — — — 12a 5. Of thofe Concords or confonant Notes that are to be preferred when they are to be doubled — 121 6. Of the Meafure or Time — — ib. 7. Of Sincopation, or of a driving Note — — ib. CHAP. XXXVI. Of Compofition in two Parts » ■ - - 124 CHAP. XXXVII. Of falje Relations — - — — ■ ■ 127 CHAP. XXXVIII. Of the Manner ofcompofwg a Treble or an Air to a Bajs 12& CHAP. XXXIX. Of figurative Melody, or of Suppofition and pajfiyig- Notes 133 ARTICLES 1. Of figurative Melody by confonant Intervals — 134 2. Of figurative Melody by diatomic Intervals -—" 137 C H AP. XL. Of the Manner of compofmg a fundamental Bafs to a Treble 139 CHAP. XLI. Of the Manner ofcompofing a continued Bafs under a Treble 149 C HA P. XLII. Ufeful Remarks upon the foregoing Chapter ■ 153 C H A*" P.' XLIIL Rules to be obferved in a Compofition of two, three, or four Parts — U , 1^4 X H A P. XLIV. Of Defign, Imitation, Fugues, and Canons - 157 The Reader is defired to correcY fome fmall Miftakes that- have inadvertently happened in the Impreffion, according to the Errata at the End of the Book, P R I N C I- SBgpc PRINCIPLES O F COMPOSITION. CHAP I. Introduction to Vradiical Mujic, Of the Gamut. AS there are but feven Diatonic Sounds, that is to fay, feven Degrees, fucceffively in a natural Voice, fo like- wife in Mufic there are but feven Notes, C, D, £, F, G 9 A y B, which is called the Gamut ; and, if we proceed farther, it can be but by repeating the firft Note, and fo on, according to the above Order. Thefe fame Notes repeated, and which are but the Replicates of the one or the other, are called Oftaves. It is proper to add the O&ave t© the firft Note at the End of the Gamut, for better diftinguifhing this O&ave ; thus, C, D, E, P, G, J, 6, C. If we begin and end this Gamut by any other Note (which is proper to be pra&ifed, though it be contrary to the Diatonic Order) it is plain by this O&ave added, that the like may be- done to the other Notes ; fo that, if we begin by G, we mult then fay, G, J y B, C, D> E> F, G, in afcending ; and G f F, E y D, C9 &y ^i &» in defcending ; fo of the other Notes. Of Intervals. The Gamut may be repeated as well afcending as defcending, and by different Notes; but the Diflance from one Note to tho other mult alfo be ©bferved, and this only in afcending. A 2 i It $' frlncipla of " ComfioJUfov. It is from this Diftancc, that all Intervals in Muifc are formed ; and tbefe Intervals take their Denomination from Arithmetical Numbers, and are called,,^, T ^ rdj F o^h, FIfrb, six*, Seventh, «n4. Oftave' we nave P^ ce d the Figures over the -Names of each In- terval, becaufe we ill all hereafter ufe thefc Numbers for denoting* the Intervals we ftiall ipeak of ; fo that it nraft be remembered, tha 2 denotes the Second,. 3 the Third, 4 the Fourth, iff-. . until the Odlave 8 ; and when we mall fay the Third, the Fourth, &c. thole Intervals are to be taken in the Gamut, by afcending from the Note chofen for the firft Degree, that Note being deemed the loweft. The Intervals in the Gamut defcending are alfo to be obferved, wherein it will be found, that the Fourth below C is G, as the Fourth above C is C~, which is not difficult to comprehend, and* .may be very ufeful upon Occafion. Of Interval* irfmim. The two notes that create the Octave, are in the Main but one, and ferve as Limits or Bounds' to all the Intervals, fince all the Notes in the Gamut are inciuded in an O&ave. Thus by deeming the two C's, bv which the Gamut begins, unci ends, as one and the fame Note, it may eafc y be apprehend- ed that, whatever other Note be compared to each of thofe (vv© C's, it w\\) not produce two different Intervals ; but by obferv- ing, that the firffc C is below the Note compared, and that the Second is above, there ieeros to be a Difference; this, Difference in Appearance is proper to be explained, f. c\ Upon viewing the Gamut in this Shape, : that having compared a Note with this firft Decree, it mufl afterwards bis compared with the O&ave, from whence will ariie two Intervals, the Firft of which is called Fundamen- tal or Principal, and the Second, Inverted, as it is in Effect ; for if we compare C to '., and E to C, we find but a Companion Inverted, in the fame Manner as it is in Numbers, by fuppofing that 3 and i reprefent the fame Note, and this Compariion is firft made from I to 3, and afterwards front £ to 8. Of all Intervals, there are but Three that are Fundamental, and which ought confequently to be remembered ; they are the 3, the 5, and the 7, which may be placed in this Manner ; each firft f Note anfwers to 1, and their 3, 5, and 7, anfwer to the Numbers which ' . . 3 . , 5 . . 7 C . . E . . IG 4 , g D. . F . . J ,'. C E , . G . . B . . 15 ^ F . , A . . C , . £> G , . B . . D . , FJ A . . C . . E .. e! B , . D , . F . ■< ^ denote thofe Intervals ; and when pnee there three Intervals are known > in Relation to one of the feven Kotes, takefi for the firft Degree, we need only to add the O&ave to that firft Degree, in order to find that the Third becomes a Sixth, that the Fifth becomes a Fourth, and that the Seventh becomes a Second ; thefe Three laft Intervals,, viz the Sixth, the Fourth, and the Second, being then inverted from the three firft Fundamental Intervals. This Article ought to be carefully confidered, for the better i* fee underftoQcl, the readier will the reft be comprehended. 3L m Of CliiTs. There are thrc e Sorts of Cliffs in Mufic, the Bafs, or F Cliff* the Tepor, or C Cliff; and the Treble, or G Cliff. The Bafs, or F Cliff, which is the Low- eft, is generally placed yuan the fourth, or the third Line. The T^nor, or C Cliff, which is a Fifth above F t is placed upon all the Lines, exa centing the Fifth, The Treble, or G Cliff, which is a Fifth above the Tenor, or C Cliff, is generally ulaced upon the Second, or upon the firft Line, Of Principles of Compqfitiw. Of Parts. , As ftarmony confifts in the agreeable Union of feveral different Sounds, and as thefe Sounds cannot be produced but from a Voice or an Inftrument, each Voice or Inftrument is called a Part, and each Part hath its particular Name, which is not al- ways mentioned, but is known by the different Situation of the Cliflfc. *- Firffc Treble. EXAMPLES, 1 i—oj± I Thefe two Parts arc adapted Y to Female Voices* Second Treble. Counter Tenor, the highefl: of Male Voices.. ~ Tenor, a mean Part, the neareft tft the Lafl, i .-__- Bafs or Concordant, a mean Part between the **■ ■ — - m preceding and following Part. — 0- **(• ~-w Connter Bafs, the inoft grave, or loweH of Male ■ Voices. -— Q AV-- This Principles of Compofitiot}. 7 This Mark, or Guide *f, fhews that one may exceed the Note until that Mark, at the Difcretion of the Compofer, who is to keep his Voices within a proper Compafs, by Reafon that they arc always {trained or forced, when at the extreme Parts. As to Inrtruments, they have their different Compafs ; the Violin, for Example, is limited to an Oftave below its Cliff", but it is not fo limited above. As the Violin and the Harpfi- chord, or Organ, are fufficient to execute all Sorts of Muiic in General, we fhall paf6 over in Silence the other Instruments, the Knowledge of which may be acquired by thole who practice them. Of Unifoa, Unifon is two Notes in the fame Degree, «tr the fame Note repeated ; the Example fhews where the Notes of each Part are to be placed fo as to fee at the Unifon. mr: Ji IZZZ As Variety of Parte conMs in different _q_™J Sounds, and not in the Quantity, we may fay, -— — that all thefe Parts are but one ; from hence . L. the Unifon is forbidden in Compofition, yet IqZZI Beginners may ufe it uatil they tttYe ijijide a ZZZZ further Progrefs, n= e- Q~ -e* Of t Principles if Com f> oft '/ ion. ^ Of ftkmforf) Vip Tirr.ev Meafure is divided by Bars,, and each Bar obtains either tj 3, or 4 Parts, and is diftinpiifned by. Common Time am! Triple Time. Common Time is when there are ?,, or 4 eqitaj Notes, ©r Parts m a Bar ; and Triple Time is when there are out thrt* equal Notes, or Parts in a Bar. The floweft Movement in Common Time is known by this Mark^, by a $n when it is foniewhat fafter, 'and the ^uickeft of all by £nb or ^2« or — • 3- ? 4 Triple Time is diftinguifhed by this Mark — , Which Is the floweS Movement, and contains three Minims in a Bar; By "~-, which is fafter, and contains three Crotchets in a Bar-; and 8 3 by g , which is the quickeft of all* and coritains three Quavers in a Bar, There is another Kind of Triple' Time marked thus "7"* or g which is compofed of the former, and contains; a Crotches, or nine Quavers in a Bar, There is alfo another Kind of commonTime, compdled of Triple Time, marked thu s ~, and contains iix Crdtchets in a Bar; or 12 thus Yf which then conlifts of twelve Quavers in a Bar. Cf Notes and their Lengths, and ef Slurs, Points, Retfs, Qr Paufcs. There are fix Notes moftly in Ufe, which are a Serriibreve Sf, a Minim P? a Crotchet, P? a Quaver P a Semiquaver G> and a Dernifemiquaver g ; their Proportions to each other are thefe^ a Semibreve as long as two Minims, four Crotchets, eight Quavers, fix-teen. Semiquavers, ©r thirty-two Demifemiqua- Vers, EXAMPLE. Principles of CompofiAOiu E X AM? Z E. i Semibrere. 2 Minims. 4 Crotchets. 8 Quavers. 1 6 Semiquavers, J2 Demifemiquavers. The Characters for denoting Silence, called Refls, or Paufes, • are thefe. A Semibreve, A Minim, A Crotchet, A Quaver, A Semiquaver, Demifemiquaver, -4— Four Semibreves, Two Semibreves. --w— " ^ The laft Cha ' rafter is ufed as a Guide or Directory to the next Note. A Point or a Dot, added to any Note, makes it half as long again. EXAMPLE. o. T J. h 1 6 A Slu? to Principles of CompoJtion< A Slur is marked thus"""^. A Repeat is made thus :s:, and is ufed to fignify, that fuch jl Part of a Tune lijuft be played over again (torn the Note over whjch it i§ placed. A {ingle Bar lerves to divide the Meafure, and a double Bar js fet tQ divide the Strains, of Songs or Tunes, as The leaft Interval we have taken Notice of at the Beginning of this Chapter, was under the Denomination of a Second, and this Second may be ajfo diftinguifhed by a whole Tone or a Semitone. The Semitone is found between E and F 9 and be- tween B and C • whereas a whole Tone is found between all the other Notes of the Gamut, that make a Second. And although this Semitone, by which the imalleft Interval is formed, be not found between all the Notes of the Gamut, it may neverthelefs be ufed by Means of certain Signs, or Marks, which, being added to any Note, either increale or leffen it a Semitone. Thefe Signs are called Sharp, or 3g, Natural, or fej, and Flat, or ij. A Mi or Sharp, increafes a Semitone that Note againft which it is placed, whereas a jj, or Flat, leffon it a Semitone ; and a fc}, or Natural, which fometimes bears the Property of a 3$, is tiled to contradidi: thofe Flats and Sharps, in Order to replace the. Notes in their natural Order. EXAMPLE. C incrcafed Semitone. The lame Note replaced. B lefi'ened a Semitone. The fame Note replaced. Thofe Intervals whofe Difference confifts but of a whole Tone, or a Semitone (provided that the Name of the Interval be not thereby altered) are diftinguifhed by Major and Minor, or Sharp and Flat ; for Example, the Third from C to E is called Major, or S,l}arp, becaufe it exceeds that from D \o F, which is confer quently Minor, or Flat ; fo iikewife the Sixth from E to C is Minor, or Flat, becaufe it contains a Semitone lels than that from F to D ; fo of the other Intervals that bear the lame Name, the Difference cpnfifting only of a Semitone, more or lefs, and which may be aifo. diftinguifhed by extreme Sharp, or extreme Flat, as will be more fully explained hereafter. It Principles of Compofiiion. 21 tt is generally by Means of a % or fe, that tV Difference from the Major to the Minor, or a iharp or flat Interval, is known ; a Sharp ^ added to the lowermoft Note (F) generally makes a Minor Interval, and added to the uppermoft Note (G) makes it Major ; on the contrary, a ix, or Flat, added to the low- ermoft Note (H) makes a Major Interval, and placed againft the upper Note (ij makes it Minor. EXAMPLE, jj^g;_l :-^g_ _i_ _g— :zzj^— JSZ -ur— bQ- ' 3d Minor, 3d Major ^ 6th Major, 6th Minor, jtb, Falfe 5th, or flat 5th, is: Q H tt is by comparing trie tipper Note toitfi the cdrrefponding Note irl the Bafs, that the Major and Minor Intervals in the Example will be found. When a If, a iq, or a fe, is placed over or under a Note in the Bafs, it does not alter that Note, but denotes only Major or Mi- nor Iatervals, CHAP II. Of the Fundamental Bafs. THE grand Art or Myftery in Composition, either for Har- mony or Melody, principally confifts, and elpecially at prefent, in the Bafs, which we call Fundamental, and as fuch -jnuft proceed by Conionant Intervals, which ate the Third, the £ 2, Fourth, 12 Principles of Compo/ition. Fourth, the Fifth, and the Sixth; fo that of the Notes of the Fundamental Bafs to only by one of thofe Intervals, the leaft ferred to the greater!:, that is to fay, that, make that Bafs afcend or defcend a Sixth, make it defcend or afcend a Third ; for it to afcend a Third, or defcend a Sixth, is likewife to afcend a Sixth, or defcend a Thi or defcend a Fourth; to afcend a Fourth, the following Example fheweth. we cannot make any afcend or defcend, but of which is to be pre- lf we had a Mind to it would be better to is to be obferved, that the fame Thing ; fo rd ; to afcend a Fifth, or defcend a P lfth, as EXAMPLE. To afcend a 3d, a "4th, a ;th, a 6th. f* -cr- e ""- " . . 0, : r G ~ ' *■ " " *J* r =- s = — ^— _^_ - To defcend a 6th, a 5th, a 4th, a 3d. The Name of the Note being fufficient for determining a pro- . pofed Interval, and knowing that the Third to C is E, it matters not in the ProgrcfTion of that Bafs, whether E be placed above or below C ; fo of the others ; and this ought to be well remem-r bered ; for when we fhall hereafter fay, to afcend a Third, a Fourth, a Fifth, or a Sixth, it is to be underftood to defcend a Sixth, a Fifth, a Fourth, or a Third ; or if we fay, to defcend a Third, it is to be underftood to afcend a Sixth, &c. obferving that this only regards" the Progrefhon of the Bafs. We have not included the Octave among the Confonants, be- caufe that the Oclave being the Replicate of 1, it is as well for the Bafs to remain upon 1, as to afcend or defcend upon the Oc- tave ; yet we are fometimes obliged to_ make the Bafs defcend an Octave, for a greater Liberty to the other Parts, which are to be placed always above the Bafs. CHAP III. Of the perfect Chord, by which begins Compo/ition in four Parts. A CHORD is the Difpofition of feveral Sounds heard to- gether, which Sounds are marked by a Nete in each of the Parts p ropofed* The Pri?icip!es of Compqfitkn. 13 The only Chord we have at prefent need for, is the perfect, which is compofed of one Note placed in the Bafs, and of its Third, Fifth, and Ottave, placed in the other Parts, The Gamut will ferve to find thefe Intervals, and this Bafs may be reprefented by the Number i, as thus : C, E, G, C, Gk i» 3> 5> T > or 8 * i, *fe, 3, 4, 5, 6, 7, 8. We have marked i, or 8, be- caufe the O&ave is always reprefented by the fame Note that was taken for the Bafs. The Third, the Fifth, or the O&ave, may be placed indif- ferently in any of the Parts, being at Liberty to place the Third above the Fifth, or the Oclave, and the Fifth above the O&ave, provided that thofe Intervals are found to be always above the Bafs ; and each Part is to be kept within its natural Bounds, and,, fo contrived, that the Tenor may be above the Bafs, the Coun- ter-Tenor above the Tenor, and the Treble above the Counter*. Tenor. CHAP. IV. Of the SucceJJion or Sequence of Chords* IF the Bafs is to proceed by confonant Intervals, the other Parts on the Contrary are to proceed by diatonic Intervals; lo that in thefe laft Parts we cannot fkip from one Note to ano- ther, but to that which is the neareft ; as thus : C can go but to D, or to E, if it does not keep on the fame Degree, as it often happens; lb of the others; and here follows the Manner of doing it. i . We chufe a Note which is called the Key-note, by which the JBafs is to begin and end : This Note fixes the Progreffion of all thofe contained within the Compafs of its O&ave : If then we take C for the Key, we can ufe as well in the Bafs as in the other Parts, but the Notes C, D> E, F, G 9 J, and B without it, it being permitted to alter them by any Sharp or Flat. This Note C being placed in the Bafs, you difpofe the Chord in the other Parts, obferving that which makes the Oftave to C 9 that which makes the Fifth, and that which makes the Third. 2. If after C the Bafs afcends a Third A y or a Fourth B (fee the Example) the Teaor— that made the Q&ave to C 9 which U the 14 Principles tsf Compojlti6tti the Bafs, ought afterwards to make the Fifth to the Note whicri in that Bafs afcends a Third or a Fourth after C. The Counter-Tenor, which made , trie Third to C, ought a f-' terwards to make the Odtave to the Note which afcends a Third; or a Fourth; and the upper Party or Treble, which made the Fifth to C, ought afterwards to make the Third to the Note fO afcending a Third or a Fourth. 3. If after C the Bafs afcends a Fifth C, or a Sixth D (fee the Example) the Tenor— winch made the O&ave, ought, after- wards, to make the Third ; the Gounter-Tenor— that made the Third, ought afterwards to make the Fifthy and the upper Part or Treble that made the Fifth,* ought to make the 0£iave. 4. and Laftly, Thofe that will not burthen! their Memory* by retaining the Progreffion of each upper Part, iri reipeft to* the Bafs, need only to remember, that each of thofe Parts cart make but one of the three Intervals that compofe the perfeft Chord, and only in three different Manners, either by keeping on the fame Note, or on the fame Degree, or by afcending or defcending diatonically whatever Road the Bafs may take; fof that if a Note of one of the Parts can make the Third , the Fifth, or the O&ave, without altering its Pofition, it muft ab- solutely remain ; but if by this Manner you cannot find any one of thofe Intervals, you will infallibly find it by making it af- cend or defcend diatonically. If two Parts mould, by Chance, happen to meet upon the fame Note or Degree, whereby one of the Intervals in the per-* feci: Chord fhould be wanting, it would proceed from one of thofe two Parts having made one of the three Intervals of that perfeft Chord, either by afcending or defcending : So that, having made it to afcend, it muft afterwards defcend, or having made it to defcend, it muft afterwards afcend ; which is natural to that Part that makes the Fifth to a Note in the Bafs followed by another afcending a Fourth, to which Note, fo afcended^ this Part can make the Oftave by defcending, or the Third by afcending, to which Degree this Part ought then to afcend ;J this is alio natural to that Part that makes the O&ave to 3 Note of the Bafs followed by another afcending a Fifth, and, in that Cafe, that Part muft defcend upon the Third, to the Not* which afcends a Fifth in the Bafs. EXAMPLE* Principles of CompofJien* EXAMPLE. 5.J3.H5J3.H }.Lft. E5.L8.E5. *5 Treble. Counter Tenor. Tenor. Fundamental B&if, ' ^* ' fks-e-Or- n 2_ n S 3 . VJ 3G8. F 3 . G8. rr\ /-s r"\ ^\ ^~\ F3.H5. j 3.H5.J 3. n ° oH u °'0 ■ "V Or .- h * 1 . 1 i " . r~\ r-°\ rs — n ^->» "-n ^-n E 5. L8.E5. L 8.F3. G8.F3.G8. Mz g rgrjgrg; -&-B- eF=" A B D ^ , o 1- -e- Afcend a 3d, or de- fcenda6th. D c *s fe5 r?i B 1 Afcend ,a 4th, or de fcend a 5 :h Afcend a 5th, or de- fcend a 4th. Afcend a 6th, orde- fcenda3d Afcend a 6th, or de- fcend a 3d. Afcend a 5th, or de- fcend 84th Afcend a 4th, or de- fcend 85th. Afcend a 3d, or de- fcend a 6rh The Progrefiron of the upper Parts in this Example may be «afily remembered, fince you will find in all but 8, 5, and 8, 3, E>Fi 3> 8 > and 3> 5> g , H; 5> 3> and 5> 8 > 7> L I when the Bafs afcends a Third J, or a Fourth B, it is found that 8 leads to 5 E ; 5 to 3 J ; and 3 to 8 G : And when the Bafs afcends a Fifth C, or a Sixth £>, it is found that 8 leads to 3 F; 3 to 5 H; and 5 to 8 L : So that, whatever Road the Bafs takes, wc may know by the firft Interval (be it a Third, Fifth, or Eighth) that which mull be the next to the following Note in the Bafs ; and fo on until the End, by following the fame Method, for each Part feparately, and oblerving that the 3, 5, and 8 be al- ways contained in the three upper Parts, being at Liberty to give to any one of the Parts th&3, 5, or 8, to the firft Not* of the Bafs; but in a Succeffion of Sequence of Chords, onlr cannot help following the Method above prefcribedj to each Part that fhall haye made the 3, 5; or 8th, i£ Frlnciples of Compofitlon. It appears alfo by this Example, that this Order prefcribed dotli dot only happen, between the firft and fecond Note of each Bar, but likewife between the fecond Notes of a Bar and the firft of the next ; fo that, wherever the Progreffion of the Bafs is the fame, that of the other Parts will be fo likewife. Therefore, the Interval marked J, between the two Notes of the firft Bar, and between the two laft Notes of the Example, being the fame, the Progreffion of the upper Parts muft likewife be the fame ; fo of the other Intervals of the Bafs marked by a B, a C, or «i D. as well above as under the Bafs : Neverthelefs, one muft not ftri&ly feek the like Uniformity in one upper Part only, by Reafon that the SuccefBon of Chords will oblige it to make fometimes the Third, fometimes the Fifth, &c. but it will always be found, that that Part which hath made the Third, the Fifth, or the Oftave, will always follow the Progreflion which is affigned to it by that of the Bafs. From hence it is to be concluded that, after having fixed and determined the Chords of the Parts according to the Progreffion of the two firft Notes of the Bafs, we muft alfo fix and determine the Succeifion by that of the fecond Note of the Bafs to the Third, from this to the Fourth, and from this to the Fifth, and fo on to the End, each Note of the Bafs always making one ,of the cenfonant Intervals prefcribed to its Progreffion with that that follows or precedes it ; and each Interval of that Bafs fixes or determines the Progreflion of the upper Parts. We have placed the Number i, either above or below each Note of the Bafs, to fhew that in each Chord there will be found but the Numbers I, 3, 5, 8. You may at prefent compofe a Bafs after what Manner you will, neverthelefs, by making it begin and end by the Note C, being at Liberty to make it proceed by all the confonant Intervals, without altering the feven Notes, 6', D, E, F, G, A, B 9 by any Sharp or Flat, and obferving to avoid the Note B, in the Bafs only, and after having dilpofed the firft Chord in each Part, the Progreffion of thole Parts that make the 3, 5, or 8th— will J>e fixed by that of the Bafs,. EXAMPLE. Principles of Compqfition. n Treble. Counter Tenor. Tenor. E X A M P L F. _ Lb t 8 ' 5 ' **- 5 * 8 - ? * 3 '- 5 ' 3 ' *' 3 '- s ' 8 - * 8 ' * 223 3^ Q22 0-9 3-3 3-3 3-3-3-- 3.5.8.5.8.3.8.5.3.8.3.8.5.8.3.5.3.5. 3 IS ■fJT^O 3-3 33 e-e — QI£ ±2 3-o 31 4 „ ,; 8. 3. 5. 3 5- s - 5- 3- & <■ 8- ?- 8. 5- 8. 3. 8. 3. S Fund a men- tal Buis. §3 :§5 :_xl — e — -- To afcend a 5. 6.4. 6. 6. 4. 4. 4. 3. 5. 3. 5. 3. 5. 5. 4. 5. 4. Remember that to afcend a Sixth, or defcend a Third, is the fame Thing ; likewife to afcend a 4th, or defcend a 5th. It is proper at firft to begin by Common Time, and you may ufe either a Minim or a Crotchet for each Part ok the Meaiure or Bar, in the fame Manner as we have ufed a Semibreve* It is eafily perceived, that the Difpofition of this Bafs depends only upon Fancy or Tafte ; yet one may keep to it in the Be- ginning, to fee if the Parts that will be placed above it be agreeable to ours ; after which you may compofe other Baffes at Pteafure, obferving that the laft Note of the Bafs ought always to be preceded by another of the Diftance of a Fourth below, or a Fifth above it : that is to fay, that the Note C ought to be preceded bv the Note G, at the Conclusion, or final End of the Piece. CHAP. V. 0/ feme Rules which mufi be cbferved. TWO O&avea, or two Fifths, are never to follow one another immediately; yet it may be pracYifed in Pieces pf four Parts, provided that the Progreffion of the two Parts that make two O&aves, or two Fifths, moves by a contrary Motion, that is to fay, that if one of the O Saves afcends, th; 1. other ought to defcend. Examplt l H Principles of Compofition. Example of two Ofiava, and two Fifths, moving by a eon-? trarv Amotion. ~~ — © — , p 8. 8. a ±=z 2. Yen miift avoid afcending from a Minor, or flat Third, to the Octave, which cannot be found in the foregoing Examples, by Reafon that the Major or Minor, or fharp or flat Third, was not as yet in Queftion; but the Difcord we are going to treat of, will eafily make us obierve this Rule. CHAP VI. Of the Chord of the Seventh. ARTICLE I. SUppofing that you are arrived at a fufficient Knowledge of the conibnant Intervals, of which the perfect Chord and the Progreffion of the Bafs are compofed ; the Relation, which thefe Intervals bear together, is now to be examined ; and without taking any Notice of the Octave, which may be looked upon but as the Replicate of the Bafs, reprefented by the Number i', it will be found, that the perfect Chord is compofed of three different Sounds, theDiflance of which, from the firft to the Second, is equal to that from the Second to the Third, as appears by thefe three Numbers, i, 3, 5, a Third from 1 to 3, and another from 3 to 5. Now, to find the Chord of the Seventh, one need only to add another Sound in the fame Proportion thus, 1, 3, 5, 7, which makes another Third from 5 to 7 ; and this laft Chord differs from the perfect, only by the 7th, which is added to it. This Interval added to the perfect Chord, being Diffonant or a Difcord ; the Chord wherein it takes place is called Difibnant, am! the Octave may be added to it, as in the perfect Chord, either for compofing in five Parts, or for giving a better diatonic Progrefiion to the upper Parts ; in which Caie it is to be ob- icrved, that \h c Octave oftentimes takes the Place of the Fifth, which is indifferent, there, being, in that Calc, only to let tliQ Parts follow their natural CourJe, which .is to .proceed diatoni- " call 7 Principles of Compof.:ion. 19 tallVj whether the Oftave, or the Fifth, happens to be in this Chord of the Seventh, or not ; as to the Third, it cannot pro- perly be left out. This Chord of the Seventh muft not at prefent be ufed, but only upon iuch Notes of the Bafs as are preceded and followed by a Fourth afcending, or a Fifth defcending. The diflbnant Interval of this Chord, which is the Seventh, ought to be prepared and refolved by a confonant Interval ; that is to fay, that the Note which made the Seventh to the Bafs muft be prepared and refolved by a Third. The Third which prepares or precedes the Seventh muft be upon the fame Degree, or upon the fame Space or Line with the Seventh that follows it ; and the fubiequent Third, by which the Seventh is refolved, is to defcend diatonically. It muft befo contrived, that the firft Seventh be heard upon the lirft Note, or Part of the Bat, and confequently prepared upon the fecond Note, or Part- of the preceding Bar; the firft Seventh being that which is not immediately preceded by another Se- venth. As foon as a Seventh hath been taken upon a Note of the Bafs that hath been preceded by a Fourth afcending, or a Fifth defcending, the Bafs muft always proceed by the like In- tervals, until the Key-note, which at prefent is that of C, by- giving the Chord of the Seventh to each Note, excepting the Key-note and its Fourth, which are C and F. C 9 or the Key- note, is excepted, becaufe the Key-note cannot be deemed as fuch, but with the perfett Chord ; and F, or the Fourth, is excepted, becaufe, it being forbidden to ufe the Note B in the Bafs, if the Fourth, or F, carried the Chord of the Seventh, it would in that Cafe be obliged to afcend a Fourth, or defcend a Fifth up- on B. E is likewife to be excepted, lince one could not give it the Chord of the Seventh, without its being preceded by B, by reafon of the Progreffion limited to the bafs of this Chord ; fo that this Chord of the Seventh is not for the prefent to be ufed, but upon the Notes A> D } and G % EXAM- 23 Vrtncip'es of Compo/ltion. E X A M P L E. Treble. Counter Tenor. Tenor. Fundamen- tal Bafs. .<• 3* 7- 3- 7- 3- 8. 3- ?• 8. J. 3- 8. |. 3. 7. 3. 5. 3. ©Z2'pie:|sx 3-6 c :& 2^ ©-crl-e-i —zlzzz'zz: ,„ ,7*., : — — \~~~z ,. 8. 5. 3- 7- 3- 8. ?. 8. 3. jj 3. 8. jf. 3- 7- 5- 8. 3 e^ DIE §35 ±e: 8. -6 = c 7 7 7 |PI —9 3IZ zis: e- -—19- as zx c 7 7 oizhi§Iz:e z:s 2:z: 9 zs: To afcend a 3. 4. 4. 4- 4- 4- &• 5. 5. 3. 4 4. 3. 4. 4. 4. 5. 4. In the upper Parts, the Seventh is found always between two Thirds, thus : 3, 7, 3 ; and the firft Seventh is always prepared in the fecond Part of the Bar C. The Ncceffitv we are under to make the Seventh defcend upon the Third, by which it is refolved, alters the Progremofi of that Part, which, as we have laid before, ought to afcend from the Fifth to the Third, when the Bafs aicends a Fourth ; but as that fame Part may alio fall upon the Ottave, we muft abfolutely give it that Progreffion, when the Seventh happens to take Place; becaufe, that the Seventh is obliged to fall upon the Third: therefore, fince we cannot alter the Progreffion of the Seventh, that of the Fifth A muft be altered according to what we have already faid, that we were fometimes obliged to ufe the O&ave inftead of the Fifth, in the Chord of the Seventh, by Reafon of the diatonic Progreffion of the upper Parts ; and in Chap. IV. tliat when two Parts happen to meet upon the fame Degree, that Part that can make one of the three Intervals muft be aU tered, either by afcending or defcendmg. The fame Part that made the Fifth, can alfo make another Fifth i>, provided that its Progreffion, and that of the Bafs, be contrary, as was faid in the foregoing Chapter, which is done in order to complete the Chords, or to put the parts in their na- tural Place ; fee the Guide at £, which ihews the Octave, which we have avoided in this Place, becaufe it is found in another Part L. ARTICLE Principles of Compofithn. ARTICLE II. 21 THE Seventh, which is the firft, and we might fay the Prin- cipal of all Difcords, may be prepared and reiblved by all the Concords ; but as its feveral Refolutions are derived from the preceding Manner, we fhall not as yet ipeak of it, but only fay, that it may alio be prepared by the Fifth, and by the Octave, and in that Cafe the Bafs muft defcend a Third ; in order that the Seventh may be heard prepared by the Fifth, and afcend dia- tonically, when the Seventh is prepared by the Octave; obferving that all the upper Parts defcend, when that Bafs afcends diato- nically, excepting that Part which makes the Seventh, and which remains upon the lame Degree, in order. to fall upon the Third. The Seventh may be alio prepared by the Sixth, but it is not vet Time to fpeak of it, becaufe at prefent we are only talking of the Fundamental Harmony, compofed only of the Bals, of its Third, Fifth, and Seventh, as thus, i, 3, 5, 7. N. B, That the Progreffion we have prefcribed to the Bafs for the Chords of Sevenths, in the firft Article, cannot alter but only in refpect to the firft Seventh, and it is only in that Cafe that that Seventh may be prepared by the Octave, or by the Fifth ; for after the firft Seventh, you will always find the Se- • venth between two Thirds, and by whatever Manner it be pre- pared, it will always be refolved by the Third. EXAMPLE. Treble. Co\i titer- Tenor. Tenor. Fundamen- ' tal Bafs. 7. 3. 8. 8 5 . 8. 3. 7. 3. 3. 8. 5. 8. S . s=e szo o~c o-e 3Z2 e-e 5. 3. 5. 8. 5. 5. 3. 5. 7. 3. 8. 8. 7. 3. 7. 3. e-e & -w- -vf- 3- %£• U 3- i- 8. 3- £• 8.V. S . 3. 7. 3. 8. To afcend a 4. 6. 4. 4. 4. 5. 6. 6. 4* 4. QZZ — — -vf- 2. 4. 4. 4. 22 Principles of Compofition. __; 7 7 _7_7 7 7 - — n: zu — — -e- -A Q- — e- -e — - rg ZQZ E "O" This Example fhews how the Seventh may be taken upon the four Notes, E, J, D i and G ; by the liberty of making the Ba/s to fall a Third, in order to prepare the Seventh by the Fifth, or to make it afcend a Second for preparing the Seventh by the Oc- tave. We find, in this Example, two Parts that afcend together, an Octave (C t ) which may be done in order to put the Parts in their natural Place, provided that thofe Parts do not make to- gether two O&aves, or two Fifths following ; for what we have laid in refpe£t to the Bafs, mult likewife be understood of any two Parts taken feparately. If two Parts can afcend an O&ave, the like rule holds for one fingle Part, as appears by the Bafs (J) inftead of remaining upon the fame Degree ; yet an upper Part could not do the like, where a Difcord happens to be prepared, and it muft in that Cafe keep on the fame Degree. It is not yet neceffary to take any Notice of the Sharp placed before F } as Beginners are not obliged to ufe any Sharp or Flat, until they are better inftru&ed. ' If the Bafs exceeds its natural Bounds, and if the Tenor happens to be above the Counter-Tehor, it is by reafon that we would not alter the diatonic Order ©f the upper Parts, to which we muft fubjeft ourfelves, efpecially in this Cafe. We have nothing more to fay, but what depends upon thefe firft Principles ; the better they are understood, the lefs Diffi- culty there will be in comprehending the reft. CHAP. Principles of Composition* 23 CHAP. VII. Remarks touching the Difcord. A DISCORD, inftead of being troublefome t© a Compofer, on the contrary, it gives him a greater Liberty, for in all Progreffions of a Bafs afcending a Second, a Fourth, or a Sixth, there will always be found one Note in the upper Parts, which having made a Confonant Interval with the firft Note of the Bafs, may, without altering it, make the Seventh to the fecond Note of that Bafs, which ought to be praftifed as often as pofii- ble, and by that Means the Fault of afcending from the flat Third to the Octave, or from the flat Sixth to the Octave, will be avoided ; but at the fame Time it muft be confidered, Whe- ther the Note in the Bafs upon which you would take the Se- venth, be followed by another, that can refolve it by the Third, otherwife the common, or perfect Chord muft be taken.. E XA M P L E. A B C D 3E~ f: . , — . — — ■ I cannot take the Seventh upon the Note at (BJ though it be prepared by the Fifth to the Note at (A,) becaufe that it cannot be reiolved by the Third to the Note at (C'J but by putting the Note at (D) in the Place of the Note at (C) I then can take the Seventh to the Note at (B) fince it will be naturally re-* folved by the Third to the Note at (DJ fo of the reft, taking Notice that the Key-note cannot as fuch carry the Chord of the Seventh, and that we fpeak here only of the fundamental har- mony. CHAP- VIII. Of the Key, and of its denomination of Flat and Sharp. WE have called the Key-note, that by which the Bafs is; to begin and end ; and we have mentioned that that lame Key-note fixed the Progreffion of the other Notes con- tained in its Octave ; confecruently, if we take C for the Key- note. 24 Principles of Compofthn. note, we cannot alter the Notes C, £>, E r F, G, A, and B, by any Sharp or Flat ; for it is thus that the Gamut reprefents it in the O&ave of C ; from whence we conclude, that the Worcl Key is adapted to one Note, chofen as Principal to compofe a Piece of Mufic in, and for that Reafon is called the principal Key-note; -this Note -having the Privilege to determine all the diatonick Intervals, wherein all the Tones or whole Notes and Semitones, or half Notes, which ought to follow each other from ' the Key-note to its Oftave, take Place, and which is called Mo- dulating ; and the Difference of the Mode or Key is this : The Mode (from whence Modulation is derived) confifts in the Third to the Key note ; and as the Third can be but either Major or Minor, or Sharp or Flat; fo likewife the Mode is diftinguifhed but by tkofe two Sorts, and for that Reafon the Word Mode is generally comprehended or underftood in that of Key, faying only a fharp key, or flat Key. If we give the fharp Third to C, we fay that we are in the Key of C Sharp, or C Major ; and if w x e give it a flat Third, we fay, that we are in the Key of C Flat, or C Minor ; Modulation conlifting only in thefe two Species of Major and Minor, which depends upon the Third given to the Key-note. The Note C, within the Compafs of its Oftave, contains all the Tones Major that can be ufed ; and there being but a fmall Difference between the Major and the Minor, we fhall not fhew the Difference until we have fully examined and explained the. Major. The Key of C will ferve as an Example for all fharp Keys, for £), E, F y G, &c, may be taken as Key-notes, as well as C; but when once a Note hath been chofen for the Key-note, one cannot fpeak of the others, but. comparatively to that fame Key- note ; therefore the fecond Note, the Third, the Fourth, the Fifth, &c. will be fuch, but comparatively to the Note fuppofed for the Key-note ; and confequently, in the Key of C, the fe- cond Note js D } the Third £, the Fourth F, &c, and here fol- low the Names of the feveral Notes or Tones in the Key of C. (C Oaave,T B - - Sharp Seventh, or leading Note, A The Sixth, G The Fifth, or Governing Note of the Key, F,----"- - The Fourth, £ , The Third, D---~- - The Second, C - - - - ->' The Key-note, j Obferve two Notes, which, bdiJes the Key-note, have a pro- per Netnj to diftingiulh them from the others ; the one is the I governing Principles of Conipo/i.icn. 2 A governing Note of the Key, or the Fifth, and is thus called ; becaufe, in all final Cadences, this Note always precedes the Key-note, as may be ieen in the foregoing Examples, where G, which is the governing Note of C, always precedes it, and efpe- cially at the End or Ciofe. The other is the leading Note, or fharp Seventh, and is thus called, becaufe, in whatever Part this Note is heard, the Key-note immediately follows it; therefore it may very properly be called the leading Note of the Key ; and in the Key of C, the fharp Third is E, the governing Note is G, and the leading Note is B, and the governing and leading Notes, and the fharp Third, do in all Keys make the fame Intervals as E, G, and B, make in the Key of C, excepting in fiat Keys, in which the Third is flat. CHAP. IX, Of the Manner of modulating Harmonically, ivhen a diatonic Progreffion is given to the Bafs. A LL Notes that carry the perfeci: or common Chords may be Jf%^ deemed Key notes, and all thole that carry the Chord of the Seventh, may be deemed governing Notes, with this Dif- ference, that the governing Note of the Key is diftinguifhed from that which is but fingly a governing Note, by reafon that the Third to the governing Note of the Key muft always be fharp ; whereas the Third to thofe Notes which are but fingly governing Notes, is oftentimes flat; and there being no other Key-note in the Key of C, but C itfelf, the perfect Chord muft be given but to that fame Note C ; there being no other govern- ing Note of the Key, in that fame Key of C, but G y consequent- ly one cannot give the Chord of the Seventh with the fharp Third, but to that fame Note G. Thefe two Chords, the Perfect and that of the Seventh, are as it were the only Chords in Harmony, for all other Chords pro- ceed from them ; and thefe are only affefted to a Progreffion o£ the Bafs, fuch as we have hitherto treated of; and if we are go- ing to alter that Progreffion, we fhall not thereby alter their Chords, but only the Difpofition, by placing the octave, either above or below one of the Sounds, or Notes, comprized in the Chord ; which obliges us to give them another Name, in order to diftinguifh thoie from which they are derived. D Confonant 26 Pri?icqJes of Compqfition. Confondni Chords derived from th? V^rfeSi. It mutt be obferved, that the Number i reprefents the Bafs, and that the other Numbers fhew the Diftance from one Sound, or Note, to that of the Bais ; and that the Numbers 8, 10, 12, &c. are but the Replicates, or Octaves, of 1, 3, 5, &c. and as 8 is the Replicate of 1, jfp 10, and 12 are the Replicates of 3 and of 5 : Alio, that all Numbers may be reduced to a meaner or lower Term, the Intervals whereof will be equal : For Example, 4, 5, 6, may be reduced to 1, 2. 3 ; becaufe the Diftance from 4 to 5 is not greater than from 1 to 2. Therefore, the Numbers 6, 8, .10, 12, may be reduced to 1, 3, 5, 7, by reafon that there is not a greater Diftance from 6 to 8, . than from 1 to 3 ; fo of the others, it being neceffary to reduce to a Unity the firft Number of each Chord ; becaule that Unity reprefents the Bais to the perfedl Chord, and that of the Seventh, from whence all Concords and Difcorcls are derived. We lhall not take Notice of the 8 in the Chords, becaufe that K umber is the Replicate of the Bafs 1. Cj E, G. Figures which are pla-") TheperfeftChordiscompofedof 1, 3, 5, ced over or under the j This Chord is always taken Bafs, to fhew all the ]>upon the Key-note, and fome- Sounds the Chord is | times upon its Governing-note, compoied of. J or Fifth. Chords inverted, derived from the perfect Chord. F. y C, Cj C-, jGj G, 6. The Chord of 6 is compofed of 1, 3, 6, inverted ] 5 g IO from J h 3> 5- This Chord is always ufed upon the Third of the Key. * v ' 6 6 ' \ &» c -> E> . C 3 E, G. -. The Chord of - is compoied of 1, a, 6, inverted 1 ] 4 4 L 4j 6 , • 8. from • j *> 3> 5- This Chord is ufed but upon the Governing-note or Fifth of the Key, but not fo often as the perfect Chord, or that of the Seventh. Enumeration Principles of Compefitkn. 27 Enumeration of Difcords, cr Diffonaitt Chords, derived /rem the Chord of the Seventh. G, B, D, F. note, or Fifth of the Key, is compofed of j ' 3» 5? 7* Chords inverted, derived from the Chord of the Seventh. 7. The Chord of the Seventh to a Governing- 1 , G, B, D 9 F. -&, or St. The Chord of the fiat or falfe Fifth is ^ 5 B, D 9 F, G, U, 8, 10, 12. compofed of 1, 3, 56, 6, inverted from J 1, g, 5, 7. « ^ . This Chord is never uied but upon the Leading-note or fnarp Seventh of the Key. 6^. This Chord is called the fmall Sixth, and is^l G, B, D y F. A F, G, B, l 4 , 6, 8, to. compofed of 1, 3, 4, 6, inverted from J 1, 3, 5, 7. This Chord is generally ufed upon the fecond Note of the Key. 4Jg. This Chord is called the Tritonus, and is~]G, B, Z>, F a F 9 G,B%D 9 ^ U, 4, 6, 8. compofed of 1, 2, 4E, 6, inverted from J 1, 3, 5, 7. This Chord is never ufed but upon the fourth Note. It is to be obferved, that the Key-note lends its perfect Chord but to its Third and Fifth; the Third under the Name of 6 Sixth, and the Fifth under that of - ; fo that, when you can in 4 all Keys diftinguifh the Third and Fifth, you may at the fame Time know what Chords are to be taken, though the perfect Chord more properly belongs to the Fifth or Governing-note than the Chord of - ; and even the Chord of the Seventh feems 4 to belong only to the Fifth, efpecially" when it immediately pre- cedes the Key-note ; but let not the Difference between the per- fect Chord, and that of the Seventh, puzzle you, fince this laft Chord confifts only in a Note or Sound added to the perfect Chord, which the Compofer is at Liberty to leave out ; fo that, wherever the Chord of the Seventh might be ufed, you may take only the perfect or common Chords ; yet, as it is proper to know what we are about, it muil not be left out without a Rea- fon, efpecially as this Chord of the Seventh is the Origin of al D 2 Difcords £ 8 Principles of Compojiiion. Difcords ; she Knowledge of its Progreflion, that is to fay, of the Chord that is to fucceed it, being as neceffary, as that of its Con(b:uction ; l, e. of the Sounds or Notes of which it is com- po fed, fince it is upon its ConftrucYicn and its Progreflion that ail ether Difcords, or Chords diilbnant, are regulated. If we have faid, that the Fifth of the Key carried the Chord of the Seventh, only when it preceded the Key-note, it is to be at the fame Time underflood of all the Notes which compofe the perfect Chord of that fame Key-note ; tha* is to fay, of the Third, and even of that fame Fifth, when thofe two Notes bear the Chords derived from the Perfect, the Fifth may carry the Chord of Six and Four, after that of the Seventh, when its Length may permit it, at the Will and Pleafure of the Compofer ; and, as the Notes derived from the Key-note are to be preceded in the fame Manner as the Key-note, lb likewife the Deriva- tives of the Fifth of the Key cannot be deemed as fuch, nnlefs they immediately precede that fame Key-note, or its Derivatives;, and one muff, not only confider a Chord in its Confrru&io'n, and in its natural Progreflion, but alio in the different Difpofition that may be given to the Notes that compofe it, by placing in the upper Parts thofe that are found in the Bafs, or by placing in the Bafs thofe that are in the upper Parts ; which obliges us to give different Names to one and the fame Chord, according to its different Difpofition, and in order to know, at the fame Time, thofe Notes which ought in that Cafe to accompany the Bafs; and as it is known that the Third and the Fifth (which compofe the perfect Chord of the Key-note) may reprefent the Key-note, by bearing a Chord derived from the Perfect, when thofe Notes happen to be in the Bafs ; fo likewife the Notes which compofe the Chord of the Seventh, to the Fifth of the Key, cannot immediately appear preceding the Key-note, or its Derivatives, without bearing a Chord derived from the Seventh ; and, therefore, it muft be remembered, that if, in the Key of C, one of thefe Notes 6', B, D, or P\ fhould immediately precede C, or E, in the Bafs (we omit G, becaufe it is our chief Subject in the Chord of the Seventh) the three other Notes are to ac- company it. We have faid that the Fifth or Governing-note might carrv the perfeel Chord as w T ell as the Seventh, and be- fides, that the perfeel; Chord always fubfifted in that of the Se- venth ; therefore, the Chord of the Seventh muft be preceded in the fame Manner as the Perfeel: ; which obliges us to attri- bute a Govcrning>note to all thofe Notes that bear the Chord of the Seventh ; and as a Governing-note is always a Fifth above, or a Fourth below the Note governed, it is not difficult to comprehend that G can have but D for its Governing-note; and as a Note is c ed a Governing-Note, but by realon only of its being a Fourth below, or a .fifth above, it can carry in that Principles of Compcfitioru 29 that Cafe but the Chord of the Seventh ; fo that, by following the fame Difpofition that we have given to the Chord of the Seventh to the Note G, we (hall find that of the NoteD between thefe Notes D, F, A, C; from whence we conclude, that the Note _D, or tho'e comprehended in its Chord, cannot appear in the Bafs immediately before the Note G, without their Chord being compoied of any other Notes than D, F, J, C, in the fame Manner as G, B, £>, F ought to compofe the Chord to each of thole fame Notes, when the Note C follows them ; the harmonic ProgreiBon of Difcords being but a Succeffion or Se- quence of Governing-notes, or Fifths, which is not difficult to comprehend in its Bottom, as the Examples of Sevenths prove to us ; and it is by the Relation there is between the fundamen- tal Chord and its various Progreffion, that arifes the Liberty we have of ufing indifferently any one of the Notes contained in the fundamental Chords, which are the Perfect and the Seventh ; and it is in this Relation that all our Attention is hardly fuffi- cient ; neverthelefs, by keeping it within the Coropafs of an Octave, it is only neceffary to know the Manner how a Concord, or a confonant Chord, is to be preceded, having given to under- ftand, that a Difcord is not preceded by any other Manner ; and thus we fay, without making ufe of the Names of the Notes, but only of the Interval which each of thole Notes makes with the Key-note, in order that it may ferve for all Keys in general ; for when it is neceffary but to know how to diilinguifh the Key- note, you will then have got over moll Difficulties. The Key-note carries the perfect Chord ; its Third always carries that of the Sixth ; and its Governing-note, or Fifth, al- ways carries the Perfect, when it doth not immediately precede the Key-note ; otherwise the Seventh F mull be added to its perfeft Chord G, B, D. The lecond Note, which, in a diatonic Progreffion, is between the Key-note, and its Third, can carry, in that Cafe, but the Chord of the fmall Sixth D, F, G, B. The Leading-note, or (harp Seventh, which in afcending pre- cedes the Key-note, mull carry the Chord of the falfe or flat Fifth B, _D, F 9 G ; but when in defcending it precedes another, which is not contained in the Chord to the Key-note, then it is deemed but as the Third to the Governing-note, or Fifth cf the Key ; and in that Cafe mull carry the Chord of the Sixth B, .D, G, inverted from G, B, £>, The fourth Note, which in afcending precedes the Governing- note, mull in that Cafe carry a Chord like unto that of the Leading-note, when the Leading-note afcends to the Key-note, lince the Key-note and its Fifth mull be preceded alike ; fo that, as the Leading-note or fharp Seventh hath carried in that Cafe a Chord derived from the Fifth, fo likewife the Fourth will carry a %o Trine; pies of Compojition. a Chord derived from that Note, which is the Governing-note, or Fifth, to that Fifth . So that, if G governs C, D for the fame Reafon governs G ; and as, in the Key of C> F is the fourth Note, it will then carry the Chord of -, or the great Sixth F, s A, C and D, derived from that of the Seventh D, F, J, C. This Chord of the great Sixth differs from that of the falfe Fifth, but in refpect to the Fifth Avhich is perfect one Way, and flat or falfe the other ; which proceeds from the different Species of Thirds, which is fharp between C and E, and flat or minor between D and F; for it may be obferved, that the Difpofition of thefe two Chords is the fame, and they are taken equally upon the Third to the fundamental Note, on which the Chord of the Seventh is ufed ; we fhall in its proper Place fhew the Reafon why this Diftinftion is made upon the derivative Chords, and not upon the Fundamental. This fame fourth Note, which in defcending, precedes the Third, muff carry the Chord of the Tritonus F t G, B, D. The fixth Note, which one Way or other precedes the Fifth and its Third, muft carry the Chord of the fmall Sixth A> C, D, F y inverted, or derived from that of the Seventh to D 3 which governs G in the fame Manner as the Second, in the like Cafe, carries the like Chord, when it precedes the Key-note or its Third. If thefe Particulars be examined with the Enumeration of Chords, it will give a better and a clearer Idea of the Wholey obferving that the Fifth, or Governing-note, may be deemed or looked upon as a Key-note, by reafon that thofe two Notes ane equally preceded by the fame Chords, which fixes the Object ; and obferving alfo, in a diatonic Progreffion, thofe Notes which derive from the Chords affected, or adapted to the Key-note and its Fifth, and the Notes that follow them ; becaufe that one and the fame Note may happen to belong to two different funda- mental Chords, in which Cafe, in order to fix the Chord that it ought to carry, we muft be be guided by the next Note that follows it, taking Notice of the three or four Notes that com-' pofe the perfect Chord, or that of the Seventh, and with which the Note in the Bafs ought to be accompanied in the upper Parts. CHAP, Principles of Compofition. 31 CHAP. X. Of the continued Bafs. "E mufl not confound the diatonic Progreffion of a Bafs, which we now fpeak of, with the confonant Progreffion, of which we have given fome Examples upon the perfect Chord, and that of the Seventh ; -thefe two Chords are the Fundamental,, and as a Proof of it, we fliall hereafter, under our Examples, place that Bafs which we call Fundamental, the Notes of which will carry but perfect Chords, or of Sevenths, whilft the Notes of the ufual Bafs, which we call continued, will carry Chords of all Species, the Whole making together a complete Harmony ; fo that this fundamental Bafs will ferve as a Proof to all our Works and Examples, whereby it will be evident, that the feve- ral* different Chords which will be therein ufed, will proceed only, from an oppofite Progreffion to that of the fundamental Bafs," according to what we have juft no*/ explained, though the Chords, compared to one or the other Bafs, will be always the' fame in the main, their Difference proceeding from the Liberty of placing in the Bafs any one of the Notes contained in the fundamental Chords ; but all the Notes of the Chord taken to- gether will always be the fame, and the Progreffion, fixed to them by the fundamental Chords, will not be thereby al- tered. CHAP. XI. Of the Progreffion of the Bafs, which fixes at the fame Time that of the Chords, and of the Manner of reducing a deriva- tive Chord to its Fundamental, THE Progreffion of the Notes of a Bafs that carry confo- nant Chords, fuch as the Key-note, its .Third, and its Governing-note, or Fifth, is not limited, provided that that Progreffion be not foreign to the Key compofed in ; but, as at prefent the Queftion is only of one Key, one cannot be miftaken, by ufing only the Notes C, D, E, F, G, A y B. The Progreffion of the Notes of a Bafs that carry Difcords are limited, fuch as the Governing-note, when it carries the Chord of the Seventh, and all its Derivatives, or rather thofe which do not carry the perfect Chord, or any of its Derivatives ; becaufe, as loon as a Note carries a Difcord, it is certain that it governs another ; and if the Difcord is not that of the Se- venth, 32 Principles of Compqfition. venth, it is certain that it proceeds from -it ; it will then he only by reducing it to its original or fundamental Chord, that you may furely know the Chord that mult follow, whatever Note happens to be in .the ,Bafs. In order to reduce a Difcord to its original- fundamental- Chord, it rauft be obferved, that there are always two Notes, or F, G, C, D, two Numbers together, as 3, 4, 5, b i £sV. which is likewife found in the Seventh, by placing the Note of the Bafs at its' F 9 G, C, A O&ave, thus : 7, 8 ; fo likewife of the Second, 1,2. 1 his being, the Cafe, the uppermoft Note, or the higheft Number, rauft be placed at the fundamental Bafs, and it will be found that the lowermoft Note, or the leaft Number, always makes the Seventh to the other, by thus reducing derivative Chords to their original fundamental Chords t, 3, 5, 7, as we have enu- merated at Page 27. So that, if the Note G fliould be found in the Bafs after the Redu&ion, it is certain that the Note C will follow it ; and if you mould not meet with it in the Bafs, you will certainly find one of thofe that compofe its perfeft Chord, ©r that of the Seventh, fuppofing that you was in another Key; fo likewife, if the Note D Ihould be found in the fundamental Bafs, the Note G, or its Derivatives, will follow ; fo of the others ; obferving that, after a Chord of the Seventh, the funda- mental Bafs muft always deicend a Fifth. What we have faid of a Bafs already compofed, muft be alfo underftood of the Manner of compofing it ; and if this rule Ihould meet with fome Exceptions, as in the falfe and irregular Cadences, &c. one muft not as yet think of it. Before we give an Example of what we have already menti- oned, it muft be obfervedj, that the Chord of the Notes, which,, in a natural Progreflion, leads to thofe that ought to carry a perfeft Chord, is to be fuited to the Note that follows it, and not to that which precedes it ; and that this Progreflion is gene- rally made from, the Key-note to its Fifth, or vice verfa y from the Fifth to the Key-note, by fuppofing the Filth to be a Key- note, as we have before mentioned ; fo that in a diatonic Pro- greflion, by knowing the Chords that lead you to one of thofe Notes, you will certainly know thofe that lead to the other ; from hence we give for a general Rule. i. That all Notes that precede by afcending a whole Tone, or a Semitone, that Note on which the perfect Chord is taken, 6 are to carry the Chord of - , or the great Sixth, or the Chord ®f the flat or falfe Fifth. EXAMPLE. Principles of Compofuhn. EXAMPLE* Great Sixth. Perfect Chord. r\ /\ O r~\ f n\ Jj %i ^~o — 5- — Falfe Fifth. Perfect Chord. - (**• O >£ *■» "o O 5 s- 5b ~s c J. M _ Fourth Note. Fifth or Governing- note. Leading-note, or (harp Seventh Key-note. Obferve that the Difference of thefe two Chords is only in the Bafs ; for, whether you afcend a whole Tone, or a Semitone, upon a Note that bears common Chords, the Chord of the upper Parts will always be the fame ; the Compofer being at Liberty to caufe his Bafs to proceed by a whole Tone, or a Semitone, even though he fhould be in a Key wherein the Semitone did not properly belong, by reafon that as the Fifth, or Govern- ing-note, may be taken for a Key-note, we may introduce all the Sounds that naturally precede a Key-note, by adding (as the Example fhews) a Sharp to the fourth Note, which in that Cale is changed, and becomes a Leading-note, or iharp Seventh i and it is by this Progreffion of a whole Tone, or a Semitone, af- cending upon a perfeft Chord, that a Governing-note may be difiinguifhed from a Key-note, the Bafs afcending a whole Tone upon a Governing-note, and a Semitone upon a Key-note ; kad though, by this Progreffion of a Semitone, the Attributes of a Key-note are given to a Governing-note, yet we may afterwards continue in the original Key, notwithftanding that fame Go- verning-note appeared as a Key-note, for after a perfect Chord, we may remove into any other Key. 2. All Notes that precede in defcending thofe that carry common or perfeft Chords,, are to carry the Chard of the imali Sixth. EX4MPLE. 34 Principles of Compqfitioii. EXAMPLE. ££_ — . _ «_>"•_ <-s ../?•"■ • • u Q . . r O " X Second ' Note. Key- note. Sixth Note. Key- note. The Guides fhew that the Bafs may afcend upon the Third to each of thofe Notes that carry common Chords, without al- tering the upper Parts, and of Courfe, thofe Thirds will then carry the Chord of the Sixth. We cannot well in this Place perceive the Difference between a fecond Note and a Sixth, and from a Key-note and its Fifth,, by reafon that the perfect Chord, which the Fifth, or Governing- .ote, carries, requires to be preceded alike, which doth not give us Room to diftinguifh them in a fharp Key ; for in a flat Key,, ;iie iixth Note, which falls upon the Fifth, is but a Semitone higher, whereas the fecond Note is always a whole Tone above .the Key-note ; moreover, the Governing-note, or Fifth, always : mh its fharp Third, whereas the Key-note hath only a flat Third in a flat Key; but, if a Governing-Note cannot be dif- tircguifhed in a fharp Key, let it not puzzle you, becaufe in that Cafe you may ufe it as a Key-note, by fuiting to its Key the Chords of the Notes which precede it ; and by what follows, it (nay be eaiily known, whether it be truly a Governing-note, or a Key-note. EXAMPLE. -e- r^zzztz zsz§z zzzzz z§zoz z©zzz -q=£z :az zs; The Pfogreffion of the firft Note to the Note at (A) doth not rive any Room to difcover whether the Note at (A) be a Key- .-.ote, or a Governing-note; which is of no Signification, by reafofl that the Chords afligned to either of thole Progreffions are the lame; but it is obvious that the Progreffion from (A) to m Principles of Compofrficn. 35 (B) leads to a Key-note, therefore (A) is the Governing- note. If the Progreffion from (B) to (C) leaves us doubtful, the Note at fDJ fhews that the Note at fCJ is the Governing-note ; in like Manner, that at (F) fhews that fame Governing-note at (G,) becaufe, in all Keys, the Note immediately below the Key- note is but a Semitone ; whereas there is a whole Tone between a Governing-note and that which is immediately below it. If in a fiat Key, defcending from the Key-note to its Fifth, or at lead to its Sixth, the Note immediately below the Key- note is a whole Tone, the fiat Third to the Note diftinguifhes it, becaufe the Governing-note, or Fifth, muft always have its fharp Third. 3. All Notes that are a Third above, or below the Key-note, or the Governing- note, muft carry the Chord of the Sixth, when the Progreffion of the Bafs leads to one of thole two Notes. EXAMPLE, — Ogrr- G— 6 6 6 6 5 50 6 A -©- Q /" \p-fim T5~ Q — 2 a*i4^ _ : .;._ a - — — — The Progreffion of the Bafs which leads to the Notes at (B) (D) (G) and (L), where the perfect Chord is taken, obliges; us to give the Chord of the Sixth to the Notes at (A) (C) (F) and/j;. 4. The Third, reprefenting the Key-note, by reafon that the Chord of the Sixth upon the Third is the fame as the common or perfect Chord upon the Key-note ; we muft give the Chord of the Tritonus to the fourth Note defcending upon the Third, though one may give it alio the Chord of the great Sixth : but we ihall fpeak of it elfcwhere. E 2 EXM4PLE, 3« Principles of Compofition< EXAMPLE. A B (A) the fourth Note defcending upon the Third at (B). By thefe five lafl Examples, we can draw very ufeful Infe- rences, by qhferving the different Difpolition of the Sounds of which a fundamental Chord is compofed, according to the dif- ferent Progreffion of the Bafs ; for if the Fourth bears the Chord of the great Sixth attending upon the Governing-note, or Fifth ; if it carrv the Chord of the Tritonus defcending upon the Third ; if the Leading-note, or fharp Seventh, bears the Chord of the flat or falfe Fifth ; and if the Second and the Sixth carry the Chord of the final I Sixth defcending upon the Key, or upon the Governing-note, or Fifth, it is vifible that tliefe different Chords are but one and the fame Chord, and de- rived from that of the Seventh upon the Notes which in that Cafe govern thofe that follow ; which will be more clearly ex- plaincd, 4 by placing a fundamental Bafs under a general Example of all we have hitherto laid ; wherein it will be obferved, that the Leading- note, or fharp Seventh, is fuch but in afcending to the Key-note: for, if it defcends, then it becomes but a Third to the Fifth, or Governing-note of the Key ; though this laft Note may in that Cafe be looked upon hs a Key-note, in order that we may not be miftaken. General Principles of Compofitioru 37 General Example of the O&ave afcending and defending. ffro o pszst ie=s: :§zc: 3=©: -e-e- :^T2z :§rs: y — 1 — — . — Tgr-e-e- _e_Q- =EE|5EE ^z§:fe=§z — e—e— -o.z§z jQi 1 1 ' o o J. R. L. B. Continued Bafs. 7 . 7 . gj| „ io D. Z. Y. A. B. Fundamental Bafs. izza: -9 — D. M. N. T. K. -s — - e — e- 1 e- -9— zzzs: -9 — p. As the fundamental Bafs is placed under the other Parts, only as a Proof that all their Harmony is included and comprehended in the perfect Chord and that of the Seventh, one muft not ex- amine, if the Rules are ftri&ly obferved between the Parts and the fundamental Bafs ; but only whether there be found any other Chords than thole that are figured over each Bafs ; for the Sequence of the Sounds are to be examined but with the con- tinued Bafs, fince the Queftion at prefent is of a diatonic Pro- greffion given to the Bafs. i. After having obferved in the continued Bafs the fame Suc- ceffion, or Sequence of Chords, from J to L, and from B to Af y afcending to the Governing-note, or to the Key-note, as from N to K y and O to V, defcending to the Fifth,, or to the Key- note, it may be thereby inferred that the Whole is relative to each of thofe two Notes which are the only Notes that can na- turally bear the perfect Chord in any Key whatever, remem- bering that thole Notes, which are a Third above, are deemed Thirds, when the Bafs defcends from thefe to the Firft, though the 38 Principles of Competition. the Third to the Key-note will always be fuch, whatever Road it takes ; and that a perfect Chord cannot be preceded by a Dif- cord, but by that which governs it ; thus it appears that the Chords of the (mall and great Sixth, of the falfe or flat Fifth, and Tritonus, are no other but that of the Seventh to the Notes, in the fundamental Bafs, which naturally govern thofe that follow. The iinall Sixth to the fecond Note, the flat or falfe Fifth to the Leading-note, or fharp Seventh, and the Tritonus to the Fourth, derive from the Chord of the Seventh upon the Governing-note of the Key D, after which immediately follows the Key-note ; the great Sixth to the fourth Note, and the fiaall Sixth to the fixth Note, alio derive from the Chord of the Seventh to the fecond Note at A and C, which governs in that Cafe the Fifth, or Governing-note of the Key, and which laid Fifth immediately follows ; and the Chord of the Sixth is given to the Third, the Sixth, and the Leading-note, or fharp Se- venth, only becaufe that thofe Notes are a Third above or be- low the Key-note, or the Fifth, to which the Progreffion of the Bafs leads us immediately afterwards. 2. It would-be imagined, that the fixth Note ^X(B) ought to carry the Chord of the finall Sixth, agreeable to that of the Seventh, which is figured over the Note at (B) in the funda- mental Bafs ; but we leave out one of the Sounds that make the Difcord for divers Realbns ; firft, becaufe it is indifferent ; fe- condly, becaufe, the next following Note in the Bafs being the Leader, or fharp Seventh, and as fuch creating a Difcord Major (as we fhall hereafter explain) and as Difcords ought not to be doubled, we could not for that Reafon, and in this Cafe, give the Chord of the fmall Sixth to the fixth Note, without caufing the Third to that Sixth to defcend upon the Difcord Major ; and the laft Reafon is, that our Rule for taking the Chord of the Sixth, upon all fuch Notes that precede thofe that are a Third above or below thofe on whicn the perfect Chord is taken, fubiifh. 3. If the fourth Note R had not been placed in the continued Bais, and the fecond Note A or C, or the Sixth T y had been taken in its Stead, immediately preceding the Governing-note % or A', we fhould then have been obliged to fharpen the Fourth, as we have done it at S, by reafon that the Note on which the Common or perfect Chord is taken, chufes to be preceded by its fharp Seventh, or Leading-note, excepting in fiat Keys, wherein the Sixth never deicends but a Semitone upon J.ne Fifth ; and the iharp Seventh in that Cafe cannot then be heard, whatever Note in the Bafs precedes that Fifth ; for, if it was preceded by the fharp Seventh, it would then be deemed tnc Key-no:e, and the true Key we then intended to compote in Principles of Compofition. 39 in could not be difcovered but by the Notes that followed that Fifth; which is very plainly feen by our Example, where the Governing-note may be taken for a Key-note, it not appearing whether it be a Governing-note, or a Key-note, but by the Note that follows it ; confequently the Chord of the Tritonus derives from that of the Seventh to that fame Governing-note which is found to be under it in the fundamental Bafs at D. 4. The diatonic Progreffion of the continued Bafs alters that of the Parts at (FJ (G,) and at (H;) which cannot be other- wife, either to avoid two Oftaves, or two Fifths, following each other, or for replacing one Part in its natural Pofition, and above the Bafs, or in order that all the Sounds of the Chord, may be heard. If the upper Parts are to follow a diatonic Progreffion, it is only when the Bafs follows a Confonant, and Vice verfa ; be- lides, it is fometimes proper to alter the diatonic Order of one Part, in order to diveriify the Melody ; one could even alter the Order and Progreffion of thofe Parts that are above the Bafs, without committing any Fault, but that is not at prefent our Subject. 5. There happen to be in our Example feveral Sevenths, without being prepared, which feems to contradict our firft Rule ; but of this we fhall treat hereafter, and fhall now keep only to the Progreffion fixed to the Chords, according to the Order of thjs Oclave ; and we fhall alio hereafter fliew, that, after a confonant Chord, we are at Liberty to remove any where, provided we at the fame Time obferve the Rules of Modulation. If it be permitted to make the fundamental Bafs to afcend a whole Note, or a Semitone, the Progreffion of a Third, and of a Fourth, is thereby always understood, as appears between the Notes at (Zj (X\) and (A 3 ) where the Note (T) is added; the Seventh to that Note being prepared by the Fifth (ZJ ana the Third preparing the Seventh to the Note (A,) which doth not alter the Foundation of the Chords. CHAP. XII. Of fome other Rules taken from the laft Example, TAKE Notice, that when a Note in the Bafs ought to carry the Chord of the Seventh, you may always leave cut that Note which makes the Seventh, unlels it was found prepared 4o Principles of Coffipq/ithrt. prepared by a Concord in the preceding Chord ; though if that Concord was a Major, or a Sharp, as the Third and the Sixth may be, it will be better to make that Third, or Sixth, afcend a Semitone ; but if the Note of the Bafs carries only a Chord derived from the Seventh, you may ftrike out of that Chord one of the two Sounds that makes the Difcord ; thofe two Sounds being eafily difcovered, by reafon that they are always joined together, according to what we have laid in Chap. XI. The fame Note in the Bafs may be repeated, by giving it the fame Chord, or by giving it different Chords, as we increafe in Knowledge how to do it. You may ikip from one Note to another, where the Chord differs but in the Name, by going from the Chord of the Seventh to that of the flat or falfe Fifth, upon the Third to that Note, on which the Seventh hath been taken ; and, upon the Fifth to it, one may give it the Chord of the fmall Sixth, and in like Manner one may give the Chord of the Tritonus to that which makes the Seventh ; becaufe all thefe Chords are, in the Main, but one and the fame Chord ; io of the Others in the like Cale ; fee the following Example. Thofe Notes, that are a Third above the Note which imme- diately afterwards bears common Chords, ought, generally fpeak- ing, to bear a Chord derived from that which follows ; fee at (JJ where it is feeh that the Chord of Sixth derives from the Perfett that follows it ; and at (B,J where the Chord of the great Sixth, or the falfe Fifth, derives from that of the Seventh, which follows it. When the Notes in the Bafs alter their Pofition, and the fun- damental Chord fubfifts ; all the other Parts may remain as they were, without altering them, as to what concerns confonant Chords, or Concords ; but, as to Difcords, it ought to be con- trived, that all the four Notes, or Sounds of which they arc compofed, be heard together, which may be done by adding the O&avc Principles of CompoJiHin. 4i Oftave of the Note you quit (D,) if it had not a Place in the Chord, to that fame Note in the fundamental Bais, or by leaving out the Oftave to the Note" (J,) in order to place in its Stead the 0£tave of the Note you quit (C.) CH A P. XIII. Of the perfect Cadence. WE call a perfeft Cadence, all Conclusions made upon a Key-note, preceded by its Fifth, or Govern ing- note ; and this Key-note muft always be heard upon the firft Part, or Divifion of the Meafure, or Bar, in order that the Conclufion may be the better difcerned ; and in that Cafe its Governing-note which precedes it, ought to carry the Chord of the Seventh, or the Perfedt, becaufe the Seventh may be therein underftood ; fee the following Example. _Q__Q_ is I r Fourth Note, 1 Minor Difcord. ZZ= Third. Leading-note, or I {harp Seventh, ^ Major Difcord. Continued Baft. Continued Bafs. Fundamental Baft. 3EE 3£ &EEl= — 0- -e- It is by the Means of this perfect Ca- dence that we can judge what. Notes of a Bafs are to bear perfe£t Chords ; be- caufe, wherever we feel the Melody to reft, it is certain that inthatPlace theper- fett Chord muft be heard ; and this Reft doth not only make itfelf felt in the moft natural Progreffion of this Cadence, but likewi'fe in the Pro- greffion arifing by the Sounds ufed for its Accompaniment, the Difpofition of which is on the other Side, each Part being figured according to the Chord it fhould bear if it was placed in the Bafs, remembering that the perfeft Chord may be heard af- ter the great Sixth, as well as after the falfe Fifth; fo that, pro- 42 Principles of Compofition. vided we do not go out of the Key, it is hut upon the Key- note and its Fifth, that the Melody may reft, which fixes the Object in fuch a Manner, that whatever ProgrefRon is given to a continued Bafs, we may feel and know, at the fame Time, thofe Notes on which the Melody may reft, and the Chords that arc to precede it, according to the different Progreftions of that Bafs, as it is marked in each Part ; for whatever Part is chofen for Bafs, the other Parts will always accompany it in the like Cafe. In order to give a better and clearer Idea of it, we fhall fliew the Power of the Leading-note, or fharp Seventh, in this Cafe ; how by its Means we diftinguifh the Difcords, and the Obligation it lays us- under in the Order and Diftribution of the Chords. CHAP. XIV. Of the Leading-note, or fliarp Seventh, and of the Manner of refolving all Difco;ds. AS foon as the Leading-note appears in a Chord diffonant, it is certain that it determines a Conclusion of Melody, and therefore it muft be followed by the perfect Chord upon the Key-note, or its Derivatives ; whereas, if the Leading-note, or fnarp Seventh, doth not appear in a Chord diffonant, the Con- cluficn is not determined, and this diffonant Chord muft be fol- lowed by another, and fo on fucceflively from one Chord to another, until the Leading-note, or fliarp Seventh, be heard, which then determines a Conclufion, or at leaft an Imitation of it, as when we fall upon the Third, inftead of the Key-note. The Examples we have given of the Seventh prove what we here advance, fince, after the firft Chord of the Seventh, there always follows another, and fo on until the Governing Note of the Key, where the Leading-note, or lharp Seventh, is then heard. Remember that, notwithftanding the Rule we have juft now given, the Common or perfect Chord, to a Fifth, or Governing- note, may follow that of the great Sixth to a fourth Note, though the fliarp Seventh doth not take Place in this laft Chord, which notwithftanding is a Difcord. To diftinguifh at prefent the Leading-note, or fharp Seventh; in a diffonant Chord, there muft abiblutcly be found therein an Interval of a falfe Fifth, or of a Tritonus, either betwixt the Parts, or betwixt one Part and the Bafs ; and thofe Intervals muft be made up of the fharp Third and of the Seventh to the fundamental Principles of ttimpofoicrt. 43 fundamental Note of a Chord of the Seventh, this Note being always the Governing-note of the Key, otherwiie the Rule would. be falfe ; fo that, in the Key of C\ the falfe Fifth, or the Tri- tonus, will be found to be betwixt the Notes B and F, accord- ing to their different Difpofkion, the one making the fharp Third, and the other the Seventh to G, which is the Governing-note- of the Key. EXAMPLE. X Leading-note. Tritonus. "-^— Leading-note, ItolteKftiu The fame Tiling will be found in the Example of the perfect Cadence ; fo that, whatever Part of this Cadence is choien for Bafs, the other Parts being to accompany it, one of thele two Intervals will always be found ; becaufe their Difference arife? only from the different Difpofkion or Tranfpofkion of the two Notes that compofe one or the other of thofe Intervals. The Guides a-S- fhew the natural Progreffion of thofe Inter- vals, as it is marked in the perfect Cadence, from whence a lure and certain Rule is taken for the Progreffion of Difcords, which is called the Refolution. As we have diftinguifhed the Third by Major and Minor, fo likewife we diftinguifh all Difcords by Major and Minor. All Major Difcords are thofe that arile from the Leading- note, or fharp Seventh ; and as this Note ought naturally to afcend a Semitone to the Key-note (which is obvious by the preceding Examples) all Major Difcords are to do the like. In order to diftinguifh a Major Difcord, you muft know the Key you are in, and you will find that every Time that a Note which is but a Semitone below the Key-note, happens to be in a diffonant Chord, that fame Note will be the Major Difcord ; otherwife, by reducing a Chord to its Fundamental, you will find, that it will always be the fharp Third to the Governing-, note of the Key, bearing the Chord of the Seventh : therefore the fharp Third to the Governing-note of the Key, bearing a Chord of a Seventh, may be deemed a Major Difcord, and con- fequently the Leading-note, on which the falfe Fifth it taken ; the fharp Sixth to the lecond Note of the Key, and the Tritonus to the Fourth, are likewife Major Difcords. All Minor Difcords are thofe which arile from that Note that makes the Seventh to the fundamental Bafs ; and thele Difcords F 2, are 44 Principles of Compofition. are to be refolved by defcending diatonically ; fuch arc the Se- venth and the falfe Fifth. When you do not meet with the Major Difcord in a diffonant Chord, it is certain that the Minor Difcord only takes Place ; but this laft always meets with the Major, which doth not alter their fixed Progreffion. Thus it is that one may at once be inftrufted in the various Ways of refolving Difcords, which doth not confift in their dif- ferent Progreffion, but only in that of the Bafs, where it is per- mitted to pais to each of the Notes of the Chord that is to be naturally heard ; which may be always known by reducing it to its Fundamental. CHAP XV. Of the Eleventh, ctheruife called the Fourth. THE perfeft Cadence is generally preceded by a diflbnant Chord, hitherto called the Fourth, but which ought rather to be cnlled the Eleventh ; this Chord, on this Occafion, differs from the Pcrfc£t, only by taking the Fourth inftead of the Third, and therefore is never ufed but upon fuch Notes as ought naturally to bear the perfect Chord, or that of the Seventh, one of which two Chords always follows it upon the fame Note that the Fourth was taken ; the Difcord which the Fourth creates being by this means relolved by defcending diatonically upon the Third, and therefore muft be reckoned and admitted among the Minor' Difcords ; we fhall more fully explain it, when we fhall fpeak of Difcords by Suppofition. Here follows only an Ex- ample of all the different Ways of preparing it, and of its Re- faction, E X AM- Principles of Compofition. EXAMPLE. 45 The Eleventh, ' or Fourth, prepared. zsz -Q- ^4 3 :o: -e- 32: ^e 1 •^e-a-'-o-a - by the 3 I by the4. Baft. £E*§ ■ s n 'Q>_ ^©^ p 32: by the ^. 4. 3. -e- 202: :_: :E? D3 e 1 © ss: 5&^4 3 Bafs. -e- -e- -crn- :or "CT" -e-e- Bafs. The Eleventh, which to follow the Cuftom we figure by 2, 4, is prepared (as appears by the Example) by all the Concords, and even by the falfe Fifth, and by the Seventh ; which may be obferved at all thofe two Notes bound by a Semicircle ' s > and is always prepared at the fecond or laft Part of the Bar, and heard upon the firft Part of the next fucceeding Bar. One muft ftick clofely to the Key of C, in order to know all thefe different Preparations, which proceed from the different Progreffions of the Bafs, by reafon that it is the fame Thing in all other Keys ; this was not ftri&ly the proper Place to fpeak of this Difcord, but as the perfeft Cadence is feldom ufed with- out its being preceded by it, and even feveral Authors not having feparated it from that Cadence, we thought it not improper to follow them on this Occafion. CHAP. 4^ Principles of Compojiiioii, CHAP XVI. Of tht irregular Cadence. THE irregular Cadence is ufed upon the Governing-note, or Fifth, preceded by its Key-note ; whereas the perfect Cadence is ufed upon the Key-note, preceded by its Fifth ; and this laft Cadence is by defcending a Fifth, and the other is by 'afcending a Fifth, in iuch a Manner, that this laft may be made, upon the Key-note, preceded by its Fourth, fince to defcend a Fourth, or to afcend a Fifth, is the fame Thing ; the two Notes which .terminate this Cadence are naturally to carry the perfect Chord, but, by adding the Sixth thereto, the Conclufion is there- by more fenfibly felt, and befides we may thereby draw an agreea- ble Connexion of Harmony and Melody, This Sixth, added to the perfeft Chord, makes the Chord of the great Sixth, which the Fourth naturally carries, when it immedi- ately precedes the Governing-note of the Key ; fo that by pairing from the Fourth to the Key-note, by the fame Chords that this Fourth ought to carry afcending to the Fifth, and which the Key- note ought naturally to carry, this creates an irregular Cadence, ifl like Manner as by palling from the Key-note to its Fifth, by adding a Sixth to the perfeft Chord of the Key-note, EXAMPLE, (J) An irregular Cadence from, the Key-note to its Fifth. (B) An irregular Cadence from the Fourth to the Key-note. We find, in this Example, a Difcord between the Fifth and the Sixth, which Difcord proceeds by the Addition of the Sixth ; and, as this Sixth cannot defcetid upon the Fifth, it muft of Courfe af- cend upon the Third ; fee the Example where that Progreffion is marked by a Stroke /. This Sixth, added to the perfect Chord, gives us, in an inverted Manner, an cafy Way of making four or five Parts tp feveral Notes following Principles of Qompofititiu 4] following the Bafs, with which one of the Parts always proceed? by a Sixth, without committing any Fault agalnft the Rules, which is proved by the fundamental Bafs. EXAMPLE. -G-CL -CU 3P :d:§:£:z£: .q„z^±. e- 3EE 3CR ■ ij *5 3E§: ieslieo: 22 -e- ::2£ =E§ HgE^ HE i^id: -e-G- fe. :o:: -9-rrS- - c -e 1 II n° J^~ -\ -e- LW | ^-v n ° •""g' -OO. s fll o* a O -6-6- -6-6- -6-6- -6 6- -6- -6-6- -6- -6- -6-6- 6 — Part which always makes the 6th with the continued Bafs. 6 6 6 6 4 66466 4 36543 4 £ 6 3 322 szg -e- 6 6 6 4 4* 6 4-5 4* 6 pa^: :o: is: -e-e F. C. H. D. I. D. H. C. Continued Bafs. ' F. D. G. C. D. H. G. C. A. B. — 9- -e- — 9- 321 zee 7 7 ■9- -9-- A. B. ^Fundamental Bafs. A. B. A, B, irregular Cadences where the Sixth is added to the perfect Chord of the Note A* Thefe fix Parts might be heard together, excepting where trie fundamental Bafs afcends a Sacond to the Note that bears a Seventh, 4$ Principles of Compqfition. Seventh, at which Place one of the Parts that makes two Fifths, together with that Bafs, ought to be altered : Obferve thofe two Parts that proceed always by Sixes, as well afcending as de- fcending, which with the Sixth, added to the perfect Chord, procures an eafy Manner of making three other Parts, notwith- standing that this Progreffion be compofed but of three different Chords. You will find at C the perfeft Chord to the Key-note, which caufes that of the Sixth upon its Third ; and at Z>, that of Six and Four upon its Governing-note, or Fifth. At F you will find the Chord of the Seventh to the Governing-note of the Key, which caufes that of the fmall Sixth to the fecond Note ; and at G, that of the Tritonus to the fourth Note. And laftly, at H, you will find the perfeft Chord upon the Fourth, to which the Sixth is added, which creates that of the fmall Sixth to the fixth Note L ; but, as this fame Chord is not always affe&ed to an irregular Cadence, it then proceeds from that of the Seventh upon the fecond Note ' J 9 where it follows its natural Progref- fion. Before we had a Knowledge of thefe fmall and great Sixes, it was almoft impoffible to add two Parts with thefe Sixes ; where- as we can eafily add three Parts, and even the fundamental Bafs may be added to it, which pi'oceeds from an inverted Har- mony, and by making the Harmony always fuitable to one of the two Cadences we have fpoken of, or to the natural Pro- greffion of the fundamental Bafs, which will be found in our firft Examples ; for, if the Progreffion of the Bafs is not limited after a confonant Chord, yet the Chord that ought to be heard after it is limited, according to the Progreffion of that Bafs ; and, fuppoling that one could not eafily reduce a certain Pro- greffion of the Bafs to its Fundamental, you need only to ob- ferve the Place occupied by the Notes of the Key you are in, and the Key of C being only at prefent in Queftion, and know- ing that fuch and fuch Notes ought to bear fuch and fuch Chords, according to their different Progreffion, you can never fail by giving to thofe Notes the Chord that belongs to them in the like Cafe ; and, Experience increafing by Pra&ice, you will become Matter of the Choice of two different Chords, that may be heard upon one and the fame Note ; as may be obferved in the laft Example, where the Tritonus may be heard upon the fourth Note, inftead of the great Sixth, or this laft inftead of the other, and even one after the other, by placing the great Sixth the firft, all which may be prattifed when the fourth Note falls upon the Third, or the Key-note, having divided * ' •' .. the Principles of Ccmpofition, the Bars where that happens by Strokes / 49 over or under the Parts as thus, HC; G C; H G. When the Progreffion of the Bafs is like unto the Fundamen- tal, you muft give to each Note of that Progreffion fundamental Chords, excepting when you go from the fixth Note to the Third, in which Cafe the Harmony inverted from the irregular Cadence is extremely proper. zs: EXAMPLE. 32=©; 6 S& 7 7 + 4«r 6 fi -fcr- :oz: zzre: 5 7 .4 _7_ _w :£r S : A. B. C. D. F. G. L. M. N. Fundamental Bafs to the upper Part. H. J. zzzsg We give the Chord of the Seventh to the fecond Note J, be- caufe the Progreffion from ^ to B is fundamental. We give the Chord of the Seventh to B, becaufe the Seventh is found to be prepared by the flat Third to the Note A\ fo that it is better to keep on that flat Third, than to make it af- cend upon the Octave, which is abfolutely forbidden, excepting that it be found to be doubled in a Compofition of more than three Parts, in which Cafe we may make it to afcend, whilft the Rule holds in the other Parts that keep on. The iharp Third being heard at B, we cannot avoid making it afcend upon the Key-note, on which the perfect Chord is to be heard ; but as this Key-note doth not appear in the Bafs, and there being but its Governing-note^ or Fifth in its Stead, we are obliged to reprefent the Key-note, by giving to that Fitth of C> the Chord of Six and Four. We could have given the Chord of the great Sixth, as well as that of the Tritonus to the Fourth Note D, which, defcends upon the Third. We cannot help giving the Chord of the Sixth to the Third F, by reafon that the Difcord to the preceding Note cannot be refolved but by that Chord, though the Progreffion of that Third to the fixth Note G be fundamental ; the Difcord, which, in this Cafe, abfolutely requires to be refolved, being our prin- cipal object. G Bitvrssi 50 Principles of Compojilion. Between the Notes IT,' J, you will- find an irregular Cadence inverted ; fee the fundamental Bafs underneath it. The Note L mull carry the Chord of the .great, Sixth, which is the fame as that of the Seventh, which the Note at M bears, and which is found to be a Third below, according to what we have before faid at Chap. XII. The Note M bears the Chord of the Seventh for the like E.ea- fon as the Note J. ' The Eleventh prepared by M, N, this Eleventh preparing the perfect Cadence that follows* CHAP XVII. Of the different Progreffiom of. a Bafs which bear a Relation to each other, ztherein the Harmony doth not alter in the upper Parts. A S the Key-note, its Third, and its Fifth may each carry _XJt a Chord compofed of the fame Sounds, wherever the na- tural Progrefiion of a Bafs leads to the principal Note, which is the Key-note, we may place in its Stead one of the two other Sounds ; fo likewife if the Progrefiion leads to the Third, we may place the Key-note in its Stead ; for the fame Reafon we may place, in Lieu of the Fifth,., its Third, its Fifth, and its Seventh, when it carries the Chord of the Seventh, or its Third and Fifth, when it carries the perfect Chord ; fee the following Example. E X A M P L E. rzz zzzzizz zai=zcz zs:®:az za:®:^: *sr&\ -e-e-s- -e-e-e- — e-e-a- « 1. vV w e — s-^-e— L- Fall up On the Kty- notc. ~rtw" ZQ W Or upon itsThird. Sg-^-0Tg-P- Or upon theFiith. 51:oz Upon the Kcv-note. -\xf~Q~'vf' Or upon its Third. ~^s~oz "ozsz^r Upon the Third. Principles cf Compofiticn. _:gc§zg: Or upon the Key-note. The four lafl Falls and the Four following are not proper to the Governing-note or Fifth, becaufe they would, in that Cafe, pais for a Key-note. E X A M P L E. J2Z©ZSZ zdz^zsz ~~o. o o - zdz^zoz -s-e-e- zoz§zsz{:|:: o o - o 4r c ZjZ§Z5Z?Z Z^ZZZ®Z -Q-g-9- •g d: ^~ ' ~- g r* I — ?■*. to 1 A. The Key-note preceded by its Fifth J. J5. or of its fourth Note B. zzzlzzz c. or of the fharp Seventh C. D. or of the fecond NoteZ). Although in the above Examples we have begun by the Key- note, we might have equally begun by the Third or by' the Fifth ; fee the Guide M£. We do not pretend to fpeak of the Beginning of a Piece, which is the proper Place for .the Key-note, though one may trefpafs upon this Rule in refpeft to Fuges, but we are not yet come to them. When the fecond Note immediately precedes the Governing- note, or Fifth, in that Cafe the Second governs that Fifth, and mull carry the Chord of the Seventh ; fo that its Third and its Fifth may be placed in its Stead, and but fparingly the Seventh becaufe it is but the Key-note that can appear as fuch in this Cafe with the perfect Chord, E X A Mr 5* Principles of Compofition. E X A M V L E. The Fifth of the Kev, pre- ceded by the feeond Note, which in that Cafe is its Go- verning-note F. G. Or by the fourth Note G, which is the Third to the fe- condNote F. H. Or by the fixthNote H, which istheFifth to the fe- condNote F. You may place all thefe Notes in the Room of each other, provided the Suit of the Harmony be not changed, to know which, you mull reduce it to its Fundamental j fee the following Example. EXAMPLE. I ^f -n — e— — cf- t ng . ._, .,__ ._Q_ ThefecondNote whichinthisCafe governs the Fifth j of the I£ey, and which ferves as a fundamental Bafs | to the others. £S ioz -&- Q„ — A©- -e- vQ — 6: Ti 00- — _6 — fourth The feeond | Note^,in Lieu Note.5, inLieu of the Govern- I of the Second, ing-note of the j whilft the Se- Key. j cond C is in j Lieu of the 1 Fifth. -Q- ,,©- ._Q. - fG— : 7«- -w — 6—; The fourth Note D, in Lieu of the Second, and at F y in Lieu of theGovern- ing - note of the Key. Principles of Compofitibn 53 The Leading- note or fharp Seventh G, which, after the fourth Note, is in Lieu of the Fifth. G0- The fame Thing in a different Pro- grefiion. The fixth Note //, in | Lieu of the Second, J when this laft governs ■ the Fifth of the Key, I that Fifth being alio re I prefented by its fnarp Third, which is the Leading-note, or fnarp Seventh G. The Chord of Six and Four is oftentimes more proper to' the Fifth, than the Perfect, in a diatonick Progreffion, and efpecially when it happens on the unaccented Part of the Bar. Thefe different Progreffions of a Bafs, together with thofe we have hitherto mentioned, include all the Progreffions of a Bafs that can be practifed in the rnoft natural Harmony ; for, as to fome other Difcords that we have not as yet taken Notice of, their Progreffions are lb limited that there can be no Difficulty in knowing the Ufe of them, as foon as what we have hitherto mentioned be thoroughly underftood. CHAP. XVIII, Of the Manner of preparing all Difcords. WHEN we explained the Manner of preparing and refolv- ing the Seventh, we intended at the lame Time to ex- tend it to all Difcords, fince they all proceed therefrom. It is true that as we have diftinguifhed them into Major and Minor, it is but the minor Difcords that are to follow intirely the Rule of the Seventh ; for the major Difcords are derived from the Leading-note, or fharp Seventh, which neverthelefs makes a Part of the Chord of the Seventh. Now, if the Lead- ing-note is not to be prepared, we mail from thence conclude, that 54 •Principles of Compqfition. that all major Difcords do not require it ; but, if the Seventh is to be prepared by any one of the Confonants, fo muft all minor Difcords be; and, provided we do, not go out of the Key, we may eafily eaufe a Difcord to he heard, by repeating one of the cpnfonant Notes in the preceding Chord-j: the like- may be done by removing from one Key into another, when you are aci qoainted with the Manner of doing it fo as to create an agree- able Continuance of Harmony,. We have already mentioned, that one Note may fer've in different Difcords following, when the Chords wherein it is ufed are in the Main bat one and the fame Chord, and that the Eleventh might be prepared by the Seventh or by the falfe Fifth, although they be Difcords ; it muft therefore be eafily comprehended, that the fame Note that made the Difcord, may caufe another in a Chord which in fome Shape will appear to be different, provided that, in this Cafe, you do not go out of the Key. When we mention that the Seventh could not be prepared but by the Third, the Fifth, and the Octave,' it muft be under- floocl only when the fundamental Bafs follows -its mod natural Progreffion, which is to defcend a Third, a Fifth, or a Seventh ; taking Notice, that to afcend a Second, or' defcend a Seventh,, is the fame Thing; fo of the other Intervals that bear a like Relation ; and that from thofe Intervals that bear a like Rela- tion, the Leaft ought to be generally chofen for the Progreffion of the Bafs, as being more proper and better to afcend a Se- cond, than to defcend a Seventh, &c. But, if you keep to the inverted Chords (as you may introduce in the BaiTes any of the Notes of a fundamental Cho:d, upon which the faid Chord changes its Name, by Means of the different Intervals that the Sounds cf winch it is compofed will make, in refpect to the Note of the Bafs) you will then find, that, inflead of the Third or the Fifth, the Sixth or the Fourth will prepare the Seventh; in the like Cafe you will find, that the Third, the Fourth, the Fifth, the Sixth, "and even the Octave will prepare a falle Fifth, by reafon that the Chord of the Seventh is reprefented by, and included in, the Chord of the falfe Fifth, as well as in all other dii'fonant Chords ; fo that, by whatever confonant Note a Dif- cord is prepared, you can never be miftaken, provided you en- deavour to avoid what is not natural : For Example, if in the Bafs, inffead of the Key-note, I had a Mind to place its Third, or its Fifth, each bearing a Chord derived from the Perfect to that Key-note ; and that I would caufe a Seventh to be heard, prepared by the Octave, by the Fifth, or by the Third to the Key-note ; that Octave will then become a Sixth to the Third, and a Fourth to the Fifth ; fo of the Fifth and of the Third, Principles of Ccmpcfdiw. 65 Third, by obferving the fame Proportion. Arid, by this Rela- tion, our iiril Rule, as to Sevenths, is general for all minor Difcords; likewife if, after a perfect Chord upon the Key-note, its Third, or its Fifth, inftead of caviling a Seventh to be heard (which any one of the confonant Notes of that perfeft Chord may prepare) I had a Mind to hear a falfe Fifth, a Tritonus, a great or fmall Sixth, &c. that would proceed by my having placed in the Bafs one of the Notes belonging to the Chord of the Seventh, in Lieu of the fundamental Note. EXAMPLE. iznz te e- 6 7.4-7 — e- 333 D. F. Continued Bafs. 6 lour: G. EE5 , -2.- 13313: H. .Q_Q. 6 5 hacsr] L. -Q_Q- 6 -W 35332: 323 _ 4 2 23ZQZ ___ — — _»_ M. N. 333®; - -e- pBEftlpsSfc; 53 33 :_z£l iEE £. Fundamental Bafs. 7 c - 7 Fundamental Bafs; I. J, 56 Principles of Cm\ofition. i. J, the Seventh prepared by the 0£!ave, according to the fundamental Harmonv. -D, the Third upon which the Octave to the fundamental Bafs becomes a Sixth. F, the Governing- note upon which the Oclave to the fundamental Bafs becomes a Fourth ; by this Means the Seventh is found to be prepared by the Octave, the Sixth, and the Fourth. G, in the Chord of the great Sixth, the Fifth which repre- fe,nts the Seventh, is prepared by the Oftave ; and the Guides that are upon the Third and the Fifth fhcw, that the fame Fifth may be equally prepared by the Sixth, and by the Fourth of thofe two Notes ; io of the other Places where there are Guides. H, in tjie Chord of the frnall Sixth, the Third which repre- sents, the Seventh, is prepared by the Ociave, by the Sixth, and iby the Fourth. J y the Second, which is prepared in the Bafs, is preceded by its Third in the upper Part. %. By the Seventh prepared by the Fifth, according, to the | fund am e nt a 1 Ha r m p ny . L y In the Chord of the great Sixth, the Fifth which repre- -le-nts-the Seventh, is prepared by the Fifth, by the Third, and by the Qc^ave. My in the Chord of the fmall Sixth, the Third which repre- fents the Seventh, is prepared by the Fifth, by the Third, and- by the Odtaye. JY, The Second ["prepared by the Oftave, or by the Fourth •marked by a Guide. 3. C, the Seventh prepared by the Third aecording to the fundamental Harmony. O, In the Chord of the great Sixth, the Fifth is prepared by the Third to the fundamental Note to which the Seventh is added, P, that. fame Fifth prepared by the. .Fourth to the Note that makes the Seventh to the fundamental Bafs, which Note mull bear the Chord of the Second. M.", the Second, prepared in the fame Manner as at J. IE that fame Fifth prepared by the Sixth to the Note which governs that in the fundamental Bafs. Gbferve in this Place, that all Notes that govern another may be reprefentpd, by bear- ing a Chord inverted from the Perfect, or that of the Seventh .which the other . fhauld carry ; and that this Chord inverted is that of Six, Four, or the fmall Sixth. _S, that fame Fifth, is here prepared by the G£tave to the Note, which makes the Third to that in the fundamental Bafs. T, In the Chord of the fmall Sixth, the Third is prepared by the Third, by the Sixth, or by the Ottave ; and the Seventh that Principles of Compofition, £*] that precedes is refo!ved by the Sixth, to the fame Note on Which that fame Seventh hath been heard We have not hitherto taken Notice of the Second, but, before ttef fay any Thing concerning it, obierve, that it ihould be pre- pared but in the preceding Manner. It hath been fuffiojently fhewn, that all the feveral and differ^ ent Ways of preparing Difccrds proceed from that of preparing the Seventh • and that the only Difficulty confifts, how to know, by the Bafs, the Notes that compefe the Chord to that which is the Fundamental. In order thereto, you mud obferve, that the firft diflonant Chord muff be preceded by a confonant Chord ; and that this confonant Chord can be but the Perfeft to the Kev-note, its Fifth, or its Fourth; which perfect Chord may be represented by that of the Sixth, upon the Third of each of thofe Notes, and by that of Six and Four upon the Governing- note of the Key only. In Compofirjbn of two or three Parts only, we often chufe but the confonant Notes in a diflonant Chord, fo that, if we do not know the Key we are in, and have not a particular Regard to the Progreffion of the Bafs, all our Rules will be ufe'efs ; therefore you cannot too clofely apply yourfelf to underftand perfectly thefe Rules, which we have given in the Key of C, and are fufficient for all other Keys. As we ought not to begin a piece of mufic but by a confonant Chord, we cannot of Courfe ufe a Difcord, but after a confonant Chord ; but oftentimes, after a Difcord there follows another ; for as we have already faid, that a confonant Chord cannot ap- pear after a Difcord, unlefs the Leading-note, or fharp Seventh, be ufed in this laft Chord, otherwife you pafs on from one Dif- cord to another, as appears by our Rules of the Seventh ; and as this is a little difficult to difcover in Pieces of two or three Parts, becaufe that thefe diffonant Chords take in at leaft two confonant Notes, which are the Third and Fifth, and, in an in- verted Manner, the Sixth and Fourth, without mentioning the Odrave that may be found therein ; fo that one may often pais from a diffonant Chord to another, without knowing it : There- fore you muft endeavour to underftand thefe firft Principles, if you intend with Certainty to know ^what you are about. I CHAP. XIX. Shews where Difcords cannot be prepared. F, inftead of making the fundamental Bafs to defcend a Third, a Fifth, and a Seventh, we make it afcen.d in the H fame 5* Principles of Compofiiion. fame Manner, we fhall find that the Seventh cannot be prepared; yet in thole Progreffions we find foiifeth-ing that obliges us to caufe that Seventh to foe heard, as the Oftave in a diatonic ProgrdTion, in Chap. XI. proves it, when we proceed from the. Key-note to its Fifth; and that this 'aft retrogrades or defcends to the Key-note, the Ear is not in the leaf! fhocked thereby, according to the Opinion of all Matters. If the Bafs afcencls a Third, in order to defcend a Fifth im- mediately afterwards, the Seventh which is heard upon the Note fo aicending, cannot likewife be prepared. -e- E X A M P L E. - Q — ©- -e «z_q_ _~_ r»c- E£zo: i-zizsz zzl=ZzizQZ A. Fundamental Bafs. B. The Example A fhews a Progreffion of. a Fifth afcending,' finee it begins by the Third, which reprefents the Key-note . But the Example B proves that the Seventh cannot be prepared when the fundamental Bafs afcends a Third, fince the; Note that makes the Seventh to the fecond Note of the Bafs, cannot make a con- fonant Note with the Firir.. One might give a fharp Third to the fecond. Note at B, in which Cafe the Key would then be changed : And this is often pracufed, efpecially in an inverted Harmony ; as may be feen in the following Example. EXAMPLE. -4- rfi—w- . 63fc 6 4 6-:& — Ezrzrr: This fart may pafs upon the- Nore,or upon the Guides. I 6 u EZQZ^QZCZ^Z zzzzzz=zzz| : 6 5& ■-©- 7 m m 7 m SZ Z3Z ZSSZZSSZ Z3S 6 43% &.i.r... SSZZqZ SSL _1 zs: za: _©_ W W W -e- Fundamentai Buis. EDE Each Principles of CompofJion S9 Each Part may ferve reciprocally as an upper Part or a Bafs ; and you may fee how the falie Fifth, the Tritonus, and the Se- venth may not be prepared. If the Bafs afcends a Seventh, the Difcord cannot be pre- pared. EXAMPLE. Fundamental Bafs. The Seventh unprepared at J, when the Fundamental Bafs afcends a Third ; and at L, when it afcends a Seventh or dc{- eends a Second. N. B. It is but after a confonant Chord that a Difcord may be taken unprepared, for after a cliflbnant Chord the Difcord muff ablolutely be prepared, "according to our Rules. We muft obferve, that we do not intend to include the fharp Seventh or Leading-note, in the different Difcords prepared or unprepared ; by reafon that we here fpeak but of minor Dif- cords, and thefe Rules do not concern major Difcords which pro- ceed from the fharp Seventh, in Favour of which a Minor Dif- cord is often heard unprepared, as in a Progreflion of the funda- mental Bafs afcending a Third or a Fifth, in order to defcend afterwards a. Fifth, wherein the perfect Cadence, which is formed by 6o Principles of Compofiiion. by this 1aft Progrcffion in defcending, cannot take Place, unlefs the fharp Seventh be heard in the Chord to the firft Note that descends a Fifth ; fo that from thence one may draw very ufefui Inferences, but we Ihall not fpeak of them, until we have ex- plained the Manner of removing from one Key into another. CHAP. XX, An exall Enumeration of all the different Progrejfions of the Bafs, according to the different Difcords therein ufed. IT is always from our fundamental Bafs, and the fundamental Chord of the Seventh, that we are to draw the Rules con- cerning Difcords ; and we {hall fhew that the Chord of the Se^ venth only is predominant in all difionant Chords. We do not in this Place intend to enlarge further upon our< firft Rule concerning the Seventh, only by giving that Chord to every Note in a Key, when the Bafs proceeds by Intervals of a Fourth afcending, or a Fifth defcending. i The firft Seventh may be prepared by. any of the Concords, or may be taken unprepared, according to what we have faid upon that Subject in the foregoing Chapters : But we fhall here- after be obliged to follow the Rule which requires it to be al- ways prepared and refolved by the Third : See the following Example. EXAMPLE. Treble Counter-tenor Tenor. Fundamental Bafs. q:q: p-D- * -■ — -e-e- -^ -~" 2 - -*- 2 -© CL 7-7 SjEl. - — -6- — a- 7-7- siec" ■e — /T7N :t^2: 7-e- 7 zqzzi _ 7 _ c ._ 7 z±zc ICC Obferve, that all the Parts move by defcending, and that thefe Sevenths are alternately accompanied by the 1 bird and Fifth, Or by the Third and Eighth, thus, i, 3, 5, 7, or 1, 3, 7, t. In order to render this Harmony more complete, there ought to be five Parts, as we ihall prefently fhew. You will find fome of thefe Sevenths not in their natural Pro- portion, as thofe-of C and F, which we had expreflly forbidden Principles of Ccmpofiiion. 61 t>y our fiifr. Rules; but that is. to be overlooked in trie like Succcffion or Sequence of Difcords, as they are caufed by the Modulation, where it is not permitted to add any Sharp or Flat to any of the Notes. You will alfo find, in what follows, other falfe Intervals which proceed from thefe ; fo that, as it K'appens by Accident that they are fuch, they mufr. be written as if they were right, by reafon that we cannot help caufing thofe Notes to intervene in Harmony, when we do not chufe to go wide from the Key. If we take for Bats that Part which makes the Tenor at A, we fhall find that the firft Note that aniwers to that on which the firil Seventh is figured, will bear the Chord of the i'mall Sixth ; and, by the following Note which bears the Chord of the Se- venth, a new Progreffion of the Bafs may be formed by new Chords in Appearance, as will be fhewn by the following Ex- ample, where that Part will be likewife marked by the fame Letter A. If we afterwards take the Counter-tenor B for Bafs, we fhalt find that the Note, anfwering to that on which is the firft Se- venth, will tarry the Chord of the Second ; and, by the follow- ing Note which bears the Chord of the great Sixth, a new Pro- greffion may alfo be formed ; as will appear by the following Example, where that Part is likewife marked with the Letter B. It may be obferved, that the Chords of the Second and the Tritonus are made up of the lame Intervals, faving in the one that the Fourth is perfeft, and in the other it is fharpened ; and for that Reafon this laft Chord is called the Tritonus, which contains three whole Tones, The like Difference is made between the great Sixth and the falfe Fifth. The Chord of the fmall Sixth, either Sharp or Flat, partakes of the like Difference ; the Whole arifing from the Chord o£ a Seventh, where the Third to the Bafs is one Way Major, and the other Minor; though that Difference is not diftinguifhed hy two different Names, unlefs it be that we appropriate to the Governing-note of the Key only a Chord,' the fiiarp Third of which creates the falfe Fifth, or the Tritonus, with the Seventh to that fame Governing-note; whereas to the other Notes, that are but merely Governing-notes, we give a Chord, w'herein the Third is Minor or Flat, and neither the falfe Fifth nor the Tri- tonus take Place between the Third and the Seventh, by reafon that thefe laft Chords are to follow each other, until the Go- verning-note of the Key appears. The following Example will fliew all the Chords that proceed from the different Progreffions of the Bafs, and each Part may ferve reciprocally as a Treble or upper Part, excepting the fun- damental Bafs and that underneath it, which can ferve but as a Eaf&. • • - 62 Frinc'pks of Gompojition. EXAMPLE. §■ 6 4 . 5 a 6 6 5 2 6. 6,-6 Q Q 2 a ! 5 * 5 4 ^ 6 lEZZOZO: -e-e- BE j Firft Bafs, which may ferve as a Treble. ~- - -ZDZDZZeZe": ■4 — ■3- Second Bafs, which may ferve as a Treble. 6 6 6 6 6 6 7 6 7 3 zszd; zlzlz 2z :a:H 4 *£ -e 2 5 2 5 zszzsz©: -9 zs: ::s: 5 2 5b- z®zd: ^2Z 3E Third Bafs, which may ferve as a Treble. 6 4 6 6737 6767 67 67674 ShrfqJbezpszeZ Fourth Bafs, which may ferve as a Treble. 6 6 6 6 6 6 4 7 5 5 5 5 5 r©zs: Z3:: 0- z§z;s: :ez©: 7 -9- :©ze: zsz§z ZqZSZ zdz©z Fifth Bafs, which may ferve as a Treble 6 6 6 6 6 BSSL -D-3-ZZ B ^4 ..Q . =irgr zoz — zzzoz _© 1 ---9- 6 z£z -©- Sixth Bafs, which may ferve as a Treble 7 7 7 7 5b ±=* zzoz e- — Fundamental Bals. 6 2_z_ JLJL^ 7 9 ©- i: iszs: ;zsz _qZSZ Q- -p 7 9 m 7 7 -be — e 7977 -e- © - -a-°~ -Q- -o- :©z Bafs by Suppofition, to which one muft not a,s yet give any Attention' Principles cf Compcfiiion. 63 1. Obferve that the Progreffion of the four firft Baffes is the moft natural, in refpect to the Fundamental ; and that the Pro- greffion of the fifth and fixth Baffes are borrowed from thofe firft Baffes The Progreffion of the fifth Bafs is taken from the Firfl and Fourth. The Progreffion of the fixth Bafs is taken from the Second and Third, and, if we have not figured with a 7 all the Notes in the fifth and fixth Baffes, that might carry the Chord of the Se- venth, it is to be underftood, that the perfect Chord can only be taken, without the Seventh, by leaving out the Octave in the Chord to thofe Notes that precede them, by reafon it is. tiiat Ociave that prepare* the Seventh. 2. In the n.itural Progreffion of the Four firft Baffes, it is- oblervable that the Firft and Second, and the Third and Fourth, arc difpofed by Thirds, and, whilft the two lafc defcend, the two firft remain upon the fame Degree, and fo on alternatively unto the End ; for, as it is more agreeable to the minor Third to defcend, we cannot help giving that Progreffion at lcaft to thofe Parts which make it ; and, in a like Continuance of Harmony, the confonant Note which is a Third below, muft follow that Progreliion, remembering that a Sixth above, or a Third below, ^_~© — is the fame Thing as C E, or E C, ry*~g 0r co~*jr It is true that the confonant Note is limited in this Place, *©nly by reafon of the fundamental Bafs; for a confonant Note may remain upon the fame Degree, in order to create -a Difccrd, if the Bais proceeds thus : 3Hd C. D. J, B, the Bafs, defcends a Third, ^Z.&~CZ\Zq~^~\~'^-IZ inftead of a Fifth ; and then the confonant Note at C, which happens to be a Third below the Dilcord at F y remains upon the fame De- L_JL_ gree, in order to create the Difcord ]r¥- 9—1— — — ^— at D. — rjTzz~\~s :: -^ In order to hear the EfFeft of all thefe Parts together, the fifth and the fixth Bafs muft be left out. 4. If the /ur firft Baffes only are taken apart, you will find that the phi ipper Parts contain all the Sounds, of which the Chords ftgu u on the Fourth are compofed ; likewife, if any one of the o arts is choleo for a Bafs, by tranfpoiing it an Oftavc 64 Principles of Compqfition. Oftavc lower, fo that it be below the other Parts, or by tranf- pofing the'fe an O&ave higher, the Chords figured upon any one of thofe Baffes will be found to be in the other Parts. If the fifth Bafs is choien, you muft place over it only the Second, the Third, and the Fourth, brcaufe the firft bears too great an Affinity to it : and, if the Sixth be choien for a Bafs, then the Fi-fl, the Second, and the Fourth only are to be placed over it, by altering only one Note, which in the firft Bar creates two O&aves together. „ Thus in one fingle Example we are inftru£led in the different Conftru&ion of all diffonant Chords, of the Progreffion of Dif* cords, and of the Difference of thole Chords, in refpeft to the different Progreffion of the Bafs, the Whole confifting by in- verting the Chords, or in an Harmony inverted* 5. The fifth and the fixth Baffes have a good EfFeft, being taken feparately, and one may even make them fyncope. Thus, Or inverted. \ It is pretty difficult to add two other Parts to thefe, by reafoa that an Harmony inverted introduceth a certain Suppofition, which requires 3 vaft Knowledge in Harmony ; fo that one muft not at prefent praftife them, but as they are pricked, that is to lay, in two Parts only. When any one of the Parts is chofen for a Bafs, it ought to begin and end by the Key-note, and be fo contrived, that the Key-note at the End be preceded by its Fifth ; which may be ealily done by altering die other jParts fuitable to their Pro- greffion, when they are to be heard above the fundamental, Bafs. CHAP. Principles of Compcfitionl 6$ CHAP. XXL Of the Chord of the Second. THE Second is an Interval inverted from that of the Se- venth, and confequently the Chord of the Second is in- verted from the Chord of the Seventh. EXAMPLE. Chord of the Seventh. Chord of the Second. This Inverfion caufes another of the fame Nature, when it is neceffary to prepare and refolve theie Difcords. If all minor Difcords are to be prepared and refolved in the Treble, or upper Part, the Second on the contrary, which caufes the minor Difcord to be heard in the Bafs, is to be prepared and refolved by that fame Bafs, according to the Progreffion fixed to a minor Dilcord ; fo that you muft caufe to be heard in the fe- cond, or laft Part of the Bar in the Bafs, that Note on which you are willing to make a Second upon the firft Note, or Part of the next fublequent Bar, and this Note muft afterwards de^ fcend ; fo that, whilft you make a Bafs to proceed in that Man- ner, you may give to each Note a Chord like thofe in the fol- lowing Example, until the major Dilcord appears, after which follows a confonant Chord. One muft alio take Notice, that in a Progreffion, or Succeffion of Harmony, like unto that in the Example, a major Dilcord may appear, when the Air or Melody of the Bafs. proceeds by the fame Degrees, paffing through the Third, without caufing a Conclufion which is relerved for the Key-note, or one of its De- rivatives, which appears but in one more Bar afterwards, as may- be feen in the following Example. The major Difcord, which in that Cafe doth not follow its natural Progreffion, is, for that Inftant, deemed a minor Difcord, which is allowed only in re- lpe£l to the Modulation, when we are minded to fufpend the Concluiion for fomc Bars ; though it will always be better to I conclude 66 Frincipks of Compofitiw. conclude upon the perfect Chord to the Key-note, or upon tha$ of 'the Sixth to the Third, after the Iharp Seventh, pr Leadings note. EXAMPLES. 33 Treble. 69: CO — ©— Continued Bafs. 7 777777 7777 2ZE~~ — — : *C> -<3 C2^ 5 § Ts — i, Fundctnental Bafs. 2 6 -5 a 6 — 5 s-e- 61 5 33: Continued Bafs 77 77 77 77 77 7"TT~ —ft- — rzs L" a: e- sr zs Q- Fundamental Bais, -e -e- By thefe Examples it is evident, that the Second is prepared and refoPved in the Bafs, in the lame Manner as the Seventh is prepared and refolvecl in the Treble J, B, and that the Chords in one and the other are made up of the fame Sounds, as ap- pears by the fundamental Bafs. in order to know at prefent the Choice that ought to be made of the Chords in either of the Examples, where the Bafs pro- ceeds almoil equally alike, iince it defcends diatonically each Way, and caufes the lame Note to be heard twice on the fame Degree, it mult be obferved, that on one Side thole two Notes are contained within the fame Bar, and that on the other Side, they are divided by the Bar ; lb that, when your Bafs is like unto one of thefe, you may always life the like Chords, and be certain that you will not then commit any Fault by following this Rule. If in the Example in the preceding Chapter there be fomc Baffes, whole Progreffion is not agreeable to thefe, in refpeft to. the Chords they bear, "it is becaufe they reprefent only Trebles ; but otherwife do not go from the Ivule, if you intend to com- pofc rightly and regularly. The Second absolutely requires to be prepared by the Third, though it may be prepared in the Treble by all the Concords, rir conibnant Notes, and the Bafs mull always fyncopc in that Cafe. , Obfervo Principles cf Compojiticn. 67 Obferve at prefent, that it is by the different Progreffion of the Bafs that Difcords are found to be prepared and refolved by all the Concords ; and, in order that you may not be miftakeri therein, always add a fundamental Bafs under your Composition, and you will thereby fee, that the minor Difccrd which makes the Seventh to that Bats is never prepared but by the Oftave, the Fifth, or the Third, and that it is never refolved but by the Third, otherwife your Competition will never be juft or re- gular. We again repeat that the firft Difcord preceded by a confonant Chord may be prepared by the Ottave, the Fifth, or the Third to the fundamental Bafs ; and that it is at the fame Time necef- Ary, that thofe that fuccefiively follow the firft Seventh be pre- pared by the Third to that Notej rather than by any other Con- cord, by reafon that the Sequence of Harmony that proceeds from it is the moft natural : — Yet, for Variety-fake, we are fometimes obliged to prepare the Seventh by the Fifth, or by the O&ave to the fundamental Note, though this Seventh be found in the Middle, or after feveral others : but this is done only, in order to vary or diveriify the Melody or Harmony, fo that you muft pra&ife it but feldofn, and with Judgment : And what is hereby faid of the Seventh equally comprehends ail other minor Difcords, by reducing it to its fundamental Note, wherein the Seventh always prefides. If the Seventh is never to be refolved but by the Third to the fundamental Note, it is not underftood but that it may alio be refolved by the Fifth, and even by the Oftave ; but thefe arc Licences which you muft not pta&iie until you are Mailer of the reft, fo that we fhall not as yet fpeak of it. I CHAP XXII. Of Keys and Modes in general, F What we' have faid touching Keys and Modes at Chip. VIIL be perfectly underftood, there remains but what follows-; ARTICLE h Of Jhatp Keys,- AS you inay take whatever Note you think proper for ■ T Key-note, provided yo$ give a Progreffion to us Oftav. T o in a I 2 like 68 Principles of Compofdien. like unto that of C, if the Key be fharp ; then Sharps and Flats arc to 'be ufed, in orch r to increafe or leffen, a Semitone, thole Intervals that might lefTbn that Conformity ; the Queftion is only to know t he Number of Sharps or Flats that are generally placed after the Cliff, in order to fhew . that all Notes on the fame Degree, or Space, with thefe Sharps or Flats, are to be in- creased or IcfTencd a Semitone; for Example, if we take D for a Key-note, and would make its Key agreeable to that of C, wc obferve that F makes the flat Third to D, which is not con- formable to the Third of G, which is fharp;. therefore we mull add a Sharp to F, to make it a fharp Third to D, as E is a ill arp Third to'C, &c. So likewife the Fourth to F is B flat- tened ; therefore a Flat rrjuft be added to the Note B t when you are in the Key of F, to conform it to the Key of C. Example of all fharp Keys, whofe Modulation of an O&ave is agreeable to that cf the O&ave of C. By Sharps. — ©. !» 3: ?-©- ec IS "O Key of G, of D, of J t of£, of B, of F fharp, of C fharp- By Flats Of 2? natural. Of B flat. FU b- Of E flat. 7-^p— fev— e- Of A flat. m Here are eleven fharp Keys, which, with that of C, make twelve, there being but twelve chromatic Notes in an O&ave. As to the Order and Pofition of Sharps, they are declined thus, F, C, G y Z>, A^ E, B, &c. which fhews that, when there is but one Sharp, it can be but that of F; if there are two Sharps, they are thole of F and C; if three, then F, C, and G 9 he. reckoning always by Fifths, attending, from the firft Sharp which is F, to the laft. In order to know how many Sharps there muft be for denoting any one particular Key, you muft obferve that it is always the Leading-note, or iharp Seventh, that determines the Number, becauie the laft Sharp is always placed upon it; fo that the Key of D lharp requires two Sharps prefixed to the Key, by reafon that, C fharp being the Leading-note, or fharp Seventh, we can- not put a Sharp to C, without placing another to F, which is always the firft Sharp : for the fame Reafon, the Key of E fharp requires four Sharps, fince D fharp is the Leading-note, or iharp Seventh ; fo of the others. Principles of CompofJion 6 9 The Order and Poiition of Flats are declined by Fourths af- cending, beginning by that of B, thus, B y E, J, D y G, he. it is the fourth Note that determines the Number in fharp Keys ; for Example, the Fourth to F is B flattened, therefore we muft place a Flat upon the Line of B, in the fharp Key of F, and fo of the other Keys, obferving that fharp Keys that require Flats, begin by that of F; fo that reckoning by Fourths, as we reckon by Fifths for Sharps, you will find the Number of Flats re- quired. ARTICLE II, Of flat Keys. The O&ave to D will ferve as an Example for all fiat Keys. EXAMPLE. \B \A If ID ■ ^— -— - O&ave, — — Leading- note, or fharp Seventh, h — — — . The" Sixth, — — Governing- note, or Fifth of the Key, p. The Fourth, - ■ 1. 1 . . . m i i The Third, * ■" ' ■■ «■ ■ The Second, ■ ■ Key-note. The Progreffion of a flat Key differs from a fharp Key in af- cending, but in the Third, which one Way is fiat and the other fharp ; but in defcending we muft make B flat, and leave out, the Sharp to C» EXAMPLE. SEE? £§o§±= — ¥e= -e :££=: — o- sse— You can never be mjftaken by following thefe Progreffions in all fiat Keys, Example 7* Trinciples of Compojition. Example of all flat Keys, whofe Modulation of an Octave anfwers to the above Odtave ofD> By Sharps ~e- £2„ Flat Key of A. z\m ^n Flat Key of jE, Oi\g, I Of F | Of C fharp, (harpy zr^!n — *e Of G i fharp, Of D fharp. By Flats. < s!jEZZ._Z -e- Flat Key of G, =^r -e- i OfC, Ofi?, Thefe twoKeyff _ are the fame. -b — e- Of B flat, Of E fl&. The Author in the Example of flat Keys by Flats, hath folf Towed the ancient Manner, by omitting the flat Sixth after the Cliff, and, in that Cafe the Key of D is not diftinguiihed from the Key of J; but, according to our Author, the Sixth in flat Keys muft be deemed flat and mull be of the fame Species as the 1 Third. We here give another Example of flat Keys by Flats, beginning by the Key of D> which, in this Cafe, bears the firft Flat EXAMPLE. ■Q -e~ Key of A g?F= ---9- OfG, OfC, Htr 5 : e- ■-« Of.fi SEE frfrr-9 Of B flat. 3 &taE ±ng: Of E flat. As Beginners may be under fome Difficulty in refpeci: to th© Chords in the Modulation of an O&ave in flat Keys, here fol- lows an Example of the Chords in the flat Key of D* E X A M Principles of Ccmpojition* EXAMPLE. 7* ZQZ Fundamental Bafs. 5 \y ri 5-&I— S»-l The Chords in the Treble 1 are to be exa- r mined but with the con- tinued Bafs. Fundamental Bafs Here are likewife twelve flat Keys, including that of D, which, with that of J, is marked without a Flat or Sharp. The firft Key that bears a Sharp before the Cliff, is that of E, and, in order to know the Number of Sharps proper to eack flat Key, you muft reckon by Fifths, beginning at £ thus, i, 2, 3, 4 Sharps. E, B y F%, Q%[. &c. confequently the flat Key of B> which is the, Second, muft have two Sharps ; lb of the other Keys ; it is alfa the fecond Note of the Key that denotes the Quantity, it being the laft Sharp. The firft flat Key that hath a b Flat before the Cliff, is that ij 2, 3, 4, 5 Flats - of G, fo that reckoning by Fourths, G, G, F, Bfo, E, you will find the Number of Flats proper to each Key ; the flat Third, which bears the laft Flat, alio denotes the Quantity. . . . • CHAP, 72 Principles of Compojitioni CHAP. XXIII. Of Modulation, or the Manner of removing from one Key int» another. l. A LL Notes that carry the perfect Chord are deemed Key- x\ notes, therefore one may fay, that all thofe Notes, which in our firft Examples carry perfect Chords, are like fo many different Key-notes ; thofe Examples will alfo ferve for what follows ; for we cannot naturally remove from a Key-note into another, otherwife than by a confonant Interval, in fuch a Manner that, after having begun a Piece in a certain Key, you may remove into another that is a Third, a Fourth, a Fifth, or a Sixth above or below, fo that the firft Key-note may become a third, a fourth, a fifth, or a fixth Note to that you remove into, and fo on from one Key into another. 2. Befides what We have already faid, the Key-note in a fharp Key may alio fometimes become a Seventh, and even a fecond Note, but never a Leading- note, or a iharp Seventh ; and a Key- note of a flat Key can become but a fecond Note. Obferve in this Place, that the Seventh, we here fpeak of, is that which is a whole tone below the O&ave, and not that which is but a Semitone below, otherwife called the Leading-note, or fharp Seventh. 3. If when in the Middle of a Piece you would remove into the Fifth, or Governing- note of the Key, the Key of that Go- verning note, or Fifth, muft be naturally fharp, though we may fometimes make it a flat Key, but this with Judgment ; and the Key of a Governing-note, or Fifth to a flat Kev, muft be Hat. Thefe Rules may be trefpaffed upon when you are capable pf judging rightly, but you muft always be very cautious in doing it. 4. By whatever Key you begin, it is proper to modulate in that Key, for three or four Ears at leaft, being at Liberty to exceed that Number, as far as your Genius and Tafte will permit. 5. It is better to remove into the Fifth of the Key, than into another; and in that Cafe the firft Key-note will become a Fourth, and this may be done by the Means of the irregular Cadence. '6. As the Ear will be cloyed by often hearing the fame Ke^, it is but into the principal Key that it may be allowed to re- turn ; but, in refpeft to the other Keys, it is not proper to re- turn into them again, prefejitly after you have left it ; for Inftance, Principles of Ccmpcfitun. j% f-nfhnfp, fuppofing we had begun by the Key of C, we may, 'after having removed into another, return into it back again; but i*: would not be proper to return into another Key, after having quitted it, to retake afterwards that of C, or to retake another; therefore it will he better to remove into a new Key, and thus from one Key into another with Difcretion, by return?- infg'ihfenfihly, as it were, into rhofe that are the neareft to the principal Key, in order to conclude therein, in fuch a Manner fhat it may lcem as if one had not quitted it; and for that Reafon, when you have removed into feveral Keys, you mull modulate towards the End in this principal Key, for fome Time longer than at the Beginning. 7. In fharp Keys it is better to remove into the Sixth, than into the Third ; whereas in flat Keys it is better to remove into the Third, than into the Sixth. 8. In order to know if the Key you remove into is to be Sharp or Flat, you muft obferve that the Kev-note that follows that which you quit, its Third. and its Fifth, be made up of the fame Notes contained in the Octave to that which immediately preceded it, and even alio (provided that the Length of a Piece doth not oblige us to the contrary) that the perfect Chord to the Key-notes, that may be ufed in the Continuance of the Piece, be made up of the Notes contained within the Octave of the firft and principal Key, without altering thole Notes by any new Sharp or Flat ; for Example, If I begin by the Key of C> it is plain that the Notes E, F, G, SJ, and fometimes 2), their Thirds and Fifths, are made up of the fame Notes that belong to the Modulation of the Key of C, fa that we may remove indifferently from a fharp to a flat Key, and from a flat into a iharp Key, according as the Thirds happen to be conformable to the diatonic Order of the firft original Key, or at leaft to the laft you quit. If, after the iharp Key of C, we remove into that of A, this laft will be flat, by reafon that the Note C makes the flat Third to A\ fo of the others. In order to follow this Modulation in flat Keys, you muft obferve the Modulation of their Octaves only in defcending, where the Leading-note, or fharp Seventh, quits its Sharp and becomes natural ; it is for that" Reafon one may do the like in fharp Keys, by adding a Flat to the Leading-note, or Iharp Seventh ; for, when we have laid the Key -note might become a Second, it is but where there always mould be an Interval of a whole Tone between the Key- note and its Second, having already taken Notice of this Mo- dulation in the fecond Article. 9. You muft contrive to remove as it were infenfibly from one Key into another, and in inch a Manner that the Ear mav K hardly 9.4 Principles of Compofition. hardly perceiye it, which may be done by following the above Method. 10. The laft Note of the Key you quit, muft always bear a conlbnant Chord, To that this laft Note will be either the JCey - note, its Third, or its Governing-note, or Fifth, or fometimes the Sixth, which may carry the Chord of the Sixth; though you mull at firft only ftick. to rempve from a Key-note to its Fifth, and, that Fifth becoming a Key-note, you may afterwards follow the Method prefcribed in the following Example, by mo-, dulating for forne Bars, in the Key to each pf thole Notes which. vve make the Bafs to remove. EXAMPLE. Firft, Second, :zzu, 35±t :2:z: -e- : -e- 32: ° r 01 Firft, Second. : :p_ sac - -e- 3? : :d: . - :rdkz: 3: — e- :££_: -e-— -e- 33: The Bafs may begin upon the firft or fecond Bar, and you ought not to dwell as long upon the fecond Key, as upon the firft ; and ftill lefs upon the others, by uling fometimes but one, two, three, or four Notes of thefe laft Keys, in order to remove into the other, which depends more chiefly upon Tafte than, on Rules. CHAP. XXIV. Some further Rules on the foregoing Chapter, T is by the Means of the Cadences, that you may learn to L change Keys; thefe Cadences introduce a Sort of a Stop or Reft, during a Piece, after which you may remove into whatever Key you will, by making another Cadence in this laft Key ; for after a perfedl Chord, which is the Conclufion of all Cadences, you are at Liberty to remove to whatever Chord you will. Sometimes the Key-note may be repeated after a Cadence, by giving to that Note repeated a Chord proper and fuitable to the Key you remove into. By Principles of Compoftlon 75 By giving it the Chord of the Seventh, or of Six and Four, it then becomes a Fifth, or a Governing- note A By giving it the Chord of the TritOnus, or the great Sixth, it becomes a fourth Note B. By giving it the Chord of the Sixth, it becomes a Third C, or a fixth Note afcending to the Leading-note, or iliarp Se- venth D. By giving 't the Chord of the fma'U Sixth, it becomes a fixth Note defcending upon the Governing-note of the Key F; and fometirnes you may aflfo caufe the Key-note to afcend a Semi- tone inftead of repeating it, by giving the Chord of the falfe Fifth to the Note fo afcended, which then becomes a Leading-note or fharp Seventh H. When, the Key-note bears a fharp Third, it may then be- come a Governing-note, or Fifth, without any Alteration J ; fee the following Example. EXAMPLE. ZZZZQZ ■ 4 7. ZQZZ2. — 3- :eq: B. 43? 6 •e-a-!-Q e-e- H. B. :s:s: 7 7 -9 — — L$L__ 6 2x2: 5 Key of C, of G, of D. of F, of C, ofZ), of A, D. B. 6 5-B- 4*6 7 7 zzzzz&z *K£ zuz ESS: 6 E. 6 -e-e : !-i4>- :sis: Of C, of G, e-9- B. 6 : ¥e : e- .0"0" of F, of C, of G, of B flat, of is T. 6 BP=f= «_6_ 4 _7 c, 6 7 J 6 j r£a: 6 .ifiY.Pi 1 ..-, Q O .-, f _s:a: :q:q: -U'-vJ I "■ ■-■"*■ e-e- ^-. ^J w ; :.a_o_ S»" -e-e- "— -' 4 7 o. 6« A. O. 7 6 A. 6 6 6 7-fe- 4X6 6 47 :a_:n —•-3M •e-e- -e-e- :©:s- ssn :ge:a: — 9- 2®: of £, of D, of C, of F t of C. K 3 You 7 6 Ptinciples. of-Compofition^ You may give the perfe& Chord only to all thofe .Notes? fi- 6 gured thus, — , and over which ,1s z B, by reafon that the irre- 5 gular Cadence, which- then takes Place, doth not abfolutely re- quire nny other Chord ; a third Note may become a Sixth, as a fixt'h Note ma) become a Third, as may be partly oblerved in the above Example at the Letter T. EXAMPLE. The Note at 5, which is the Sixth to~C, becomes the Third of the Key of F. The fame Note at T, which is the Third to the Note F, be- comes the Sixth to C, without altering the Chord ; that Note .which may be either a third or a fi'xth Note, is always between two Notes of the Diftanee of a Fifth, and which divides it into two Thirds, as from F to C' } wherein the Note A is the* middle Note. The Key may be alfo changed" by the MeanS of 7ths, _ 7 and 6 6, 2, £%, - , and 5 t[ ; fo that, having cauffid one or mbre Notes 5 . • ■; of ihe Bafs to pafs through this Sort of Chords, you need only to caufe an [nterval of a Trircmis, or of a .falie Fifth, to be heard, in order to decide the Key you remove into ; obferving that this Tritonu«, or falie b ifth, is to be made up of the ftiarp Third, and the Seventh to the Governing-note of the Key ;* lee the following Examples t X J M- Pfincipks of CGjnprJtiUn, E X A M P L E. 6 r-r-i '~ — ZF~ D~ * OT »- (_, Key of C, of G, < Continued Bufi. rN 1 - 5 6 L 6 4-*6 s-e- . 5 ', :®zs: of c, q:zz of G, -e- 35 77 7 :z:zt of z>, ^zzroza: 7 zsz: 7 7 5: :s:~ Fundamental Bafs. ? 7 ■ zzzz: ~gy-"|r — wbryd- -e- 3E _e -,i — q- -—— 7 7 ^ -9.-9- zzzc: -9— zaz: 5& 5& 6-b 5-b- zzzrP? rifG, of\F, ~oflV~ sra4 fc-s-. ft -*-? X- cri ^ 7 ■ 7-CV z§Z¥to: :z:s: _7_ iIzzeJc — o— 7-77 :qz ~ ^T^i 1 ZAZjS3^- -e- a - -v4*5 9 iee- ziis: 6 4-- -.2 5<-~-4^r 6 5 7 9^ 2 1 1 -£=>_ 1 1 of ^, ofD, oi 0. Lzrie 5-D &9 ^9= :dzz ISO 9 — -Q— zzs: -9 — -s- 7___7 ,. 7 _ |:zz|:^' l_sz_:-- Q :_ 7 7 -9 3 Obferve that the Difcord by which you remove into another Key, mui! always be prepared by a conibnant Note in the Chord that ends the laft Key. Tliele Examples are iufficie'nt for inftructing how to compote a Bafs, according to the Chords that are choien ; but We are going to give it another Shape, by allowing '^he Liberty to com- pote a Bafs at Pleafufe, the Pro^refhon or" which will teach us what Chords they are co cany. CHAP. )% Principles of Compojiildtt. * CHAP. XXV. thews what Chords are to he given to the Notes of a Bafs in ail Frogrejfions. ARTICLE I. Of Cadences, and- of all that Hatk a Relation to a Clofe of a Song or Melody. I. /^VNE rriufc cl'ofely ftick to alf the Cadences, and to" all that V/ hath an Affinity to the Clofe of an Air or Melody; Beginners -cannot well help making Ufe of them at every In- fant in their BafTes, efpecially when they intend to change Keys ; which is not difficult to obferve, becaufe thofe CofVc.luiions are always made upon the firft Part, or Divifioh of the Meafure' or Bar, (6 that thofe Notes that are found in the firft Part of the Bar upon which the Melody feems in fome Shape to reft, ought always to carry the perfect Chord, for which Reafon they may be deemed Key-notes. 2. If after a Key-note the Bafs proceeds by confonant Inter- vals, you may give the perfect Chord to' each of thofe "Notes, ■until that Note Which is followed by a diatonic Interval, ex- cepting that Note which happens to be a Third above or below another that bears the perfect Chord ; and in that Cafe the iirft Note may bear the Chord of a Sixth, as' well, and rather than the perfect Chord; and oh the contrary, if you find that the iirft Note ought to carry the perfect Chord, then that Note which happens afterwards' to be a Third above or below, ought to carry the Chord of a Sixth, provided that after the laft Note there doth not follow another in a confonant Progreffionj by reafon that Progreffion naturally requires the perfett Chord, or that of the Seventh, upon each Note (which will be better explained hereafter) and that Note, which on the above Occa- fion we have faid might bear the Chord of a Sixth, is always a Third, or a fixth Note, though you may give only the per- fect Chord t© each of thofe Notes, when you are afraid of being miftaken. EXAM- Principles of CempofcUon. EXAMPLE. >9 6 A* L , .*%, -e-e- — e-l z?.±=LjH--_ .-"T-J _e_ Sixth Second Note. Note. -3- Being in the Key of C, we fee that the next Note which is a Third above C, and below the Governing-note, or Fifth, ough? to carry the Chord of the Sixth J. B, the Note which is a Third above the Governing-note, or a Sixth below, which is the fame Thing, might carry the Chord of the Sixth ; but wc have already fhewn, that the Chord of the falfe Fifth is more proper, -by reafon that that Note is the Leading-note, or fliarp Seventh to the Key of C, which wc have not quitted, and which keeps on until the Note C. We find four Notes together that afcend by Thirds from the Key-note, the Third to which bears_the Chord of the Sixth, and the Governing- note, or Fifth, carries that of Six and Four C, rather than the perfect Chord ; becaufe the Flat againft the Note B denotes a new Key, which is eafily diftinguifhed in the Progreffion of the Bafs by the Interval of the falfe Fifth between that fame Note B flat and the Note E that follows ; therefore the Note E, which is the loweft Sound to the falfe Fifth, be- comes a Leading-note, or fharp Seventh, and confequently the Chord to the Note B flat muft be fuitable to the Key which that fharp Seventh leads, fince this B flat is not comprehended in the Key of C, which is then quitted, and the Governing-note to C fuits its Chord to that which fucceeds it; fo that, without going out of the Key of C, it then carries the Chord of Six and Four, which makes that of the Tritonus to that fame Note B flat ; tor, if that Governing-note had carried the perfect Chord, the Third muft then abfoluteiy have been flattened, in order to avoid a falfe R lation, which t aife Relation confifts in never ufing, in two different Parts, two Notes together, the Name ot which alters but by a Sharp or Flat's being annexed to it ; that is to fay, that having taken in one Part the Note B 9 which makes the fliarp Third to G, we cannot uie, in another Part, that fame t Note B, with a Sharp or Flat; we fhall here- after jSo Tri net pies of Compofitlon. after treat of it more fully ; fince then we give the Chord of Six and Four to the Note at the Letter C, it is in order to fujt the Harmony of this Chord to that of the Chord that follows it ; lor we might have given it the perfect? "Chord with the flat Third, or we mjglit even have given it jthe Chord of the fmall Sixth and the falfe Fifth to the Note that immediately precedes it, by reafon that there happens to be an Interval of a falfe Fifth be- tween E and 1$ flat that follows ; io that, whenever a like In- terval appears in the Bafs, the Key is then absolutely decided, the Sound grave to this falfe Fifth being always the Leadings note ; and what we here fpeak of concerning the falfe Fifth, eqS'alty regards the Tritonus, the acute Sound of which is then a Leading- note. Yet if the" bafs proceeded by afcending a Fourth, or defcending a Fifth, after a like Interval of a falfe Fifth, or a Tritonus, a Leading-note; might not pofTibly happen in the Chord, by reafon that each oi thole Notes in the Bafs might be deemed as paffing Fifths, feeking the Governing-note, or Fifth of the Key,- as appears at G, H, J. But this can take Place but between the fecond and the fixth Note in flat Keys, which make between themfelves thefe Intervals of a falfe Fifth, or a Tri- tonus. According to our foregoing Rule, the Note at D ought to ifcord. v55 I and that the other Parts may af- cend or defcend ; for the Note of the fundamental Bafs, which is in the three lowermoft Parts, may remain upon the fame Degree, or delcend a Third in the fame Man- ner as it naturally delcends a. Fifth, by obferving to leave the Seventh out of the Chord, when it defcends a Third A\ becaufe that would create, as it were, two Octaves together, though that might be tolerated, efpecially ia four Parts. All thefe Progreffiohs are to be found in the Example of the Octave, Chap. XL with the fame Chords that they bear in this Example, and for a greater Certainty you may take for a Bafs; any one of the Parts, provided you avoid placing over the other Parts the two loweft Baffes ; the reft will have together a good Effect, in whatever Manner it be difpofed, and the Chords fi- gured in one Part will be contained in the other Parts. In moft of our Examples one may have obferved this Sort of imperfect Cadences, but they do not always happen upon the firft Part of the Bar, by reafori that they are ufed but in a dia- tonic Progreffiohy without making a final Cohclufion; A. Fandamental Bafs. ARTI- ?2 Principles of Compofitidn. ARTICLE III. How the Key may ledijiinguiflied, wrier eiri . the Progrfjfion of the- imperfect Cadences are ujedi IT is certain that a diatonic Progreffiori leads us into feveral different Keys ; to diftinguifh the fame, there are feveral Things to be obferved. 1. The Leading- note decides it aft once, and here follows the Manner of difcovering it in the Bafs. The Key-note being known, you 1cnow at the fame Tiras its Leading- note., Or fharp Seventh; and as this- Key can* pro- ceed but only upon certain Notes contained in its Oftave, ac- cording to the fharp Key of C, or the flat Key of A\ if one of thofe Notes is altered by a Sharp or a Flat, it is certain that tEf Key changes. The fi'r'ft Sharp that appears, fhews a Leading-note, and, if there happens two or three together, the Lafl is always to be deemed the Leading-note ; therefore, a Sharp placed again-ft F . makes it to be a Leading-note, and denotes at the fame Time the Key of G ; if with this Sharp againft F we find another at G y F fharp is no longer the Leading-note, and it will be G r which at the fame Time denotes the Key of A\ fo that reckon- ing or counting according to the Order and Pofition of Sharps-, F, C, G, D } J, &c. we cannot be miftaken, and, whatever Flais> are found intermixed with thefe Sharps, it doth not alter.. the. Cafe. But, if there fhould not appear any Sharp, then a Flat denotes a new Key, and the Leading-note will be that Note againft which another Flat ought to be added, fuppoiing that we were obliged to it; for lnftance, if there be a Flat againft B, and no fharp appears, the Note E y which is the Note againlr. which a new Flat might be placed, will be the Leading-note ; likewife, if a Flat is placed againft E, ^will then be, the Lead- ing-note, fo that reckoning according to the Order and .Poiition of Flats, B y E y yf, D y &c. fuch of thefe Notes againft which no Flat is placed, and that immediately follows one that hath a Flat, will always be the Leading-note. Take Notice of what we have faid in the fir ft Article, that the Interval of a falfe Fifth, or a Tritonus, fhews it in the Progreflion of the Bafs, for that Note which could have a Flat againft it, makes the Tritonus above, or the falfe Fifth below that which ought to 1 have the laft Flat." 2. As the Bafs doth not always reach to the Leading- note', and the Key may nevertheless change, there often happening in the Bafs an Interval of a falfe Fifth, or a Tritonus, anting from' the Principles of Compofition, *3 the fecond Note of a flat Key and the Sixth, or rather from the Sixth to the Second, provided there be no Sharp, for this always decides it ; you ralift obferve if the Key which thefe Intervals, or fome other Marks, denote, bears a Relation with the Key that you quit ; and if after the Stop or Paufe, which in fomc Shape is felt in a diatonic ProgrefTion, there doth not follow a Note which bears a greater Relation to a particular Key, than to another, efpecially when after the laft Note in a diatonic ProgrefTion there follows another in a confonant ProgrefTion, which often leads to fome final Cadences, for then the Key is decided. EXAMPLE. SEE. Leading- note to C. L 3 After 84 Tnnclpks of Gofljfiofitkv. After the f!r£- Leading-note (which is eaiily diftinguifhed). we, find a diatonic prpgreffion from the Note A interrupted at 2? s where the Rule of Sevenths is to be followed ; and this Inter- ruption which leads us to a Cadence upon the Note C, obliges us to fuit to its Key the Notes in a diatonic Progreffion from the; Governing-note of the Key of A, after which Note nothing ap- pears to oblige us to keep within £hat fame Key of A; which is the Reafon why we have givpn the Chord of Six and Four to the Cioverning-npte repeated, the better to unite its Harmony with thofe Chords that fellow* befides, the Note G, which be- comes natural at the Letter B, fhews it to be no longer a Lead- ing-note, and, not finding any Sharp or Flat until the Cadence of C, we clearly fee. that the Key of C manifefts jtfelf from the Note at A ; becaufe you rouft always have a greater Regard to the Key that follows, than that which you are in, efpecially when, you may fuit the Chords to the following Key, there being nq Sharp or Flat, nor any confpnant Progreffion, or Stop or Paufe, that might induce you to follow another Road. As the Sharp to the Note G remains no longer, the Sharp to C which follows, denotes a new Key, and the Stop or Paufe which is made at the Letter C, after which follows a confonant Interval that requires a Seventh upon that fame Note at C t obliges us to return into the Key of A y fince it is at that fame Note that the Progreffion of a Fourth afcending finifheth. The Sharp at F denotes a new Key, fince there doth not ap- pear any other after it. The Flat at the Letter ^obliges. us to give a fiat Third to the Note that precedes it, for a greater Conformity of Harmony ; and, the Flats being upon the Notes B and M, we therefore judge the Note A to be a Leading-note, after which E quitting its Flat becomes a Leading-note, fince the Flat (till remains upon; B, there not appearing any Sharp againft it. The Interval of a falfe Fifth between the Notes at the Letter; J) might produce a Leading-note at that Place, fince that Note which one would deem as fuch, afcends a Semitone at J (which is the natural Progreffion of a Leading-note) but the confonant Intervals that are ufed from the Note at L, where the Key of $ ends, obliges us to give to the following Notes perfe£t Chords, or of Sevenths, according to the different Intervals of the Bafs, and engages us, at the fame Time, to fuit our Chords to the Key, denoted by the Leading-note that follows ; we do not fay But that, according to the Rules of a Progreffion by Thirds, one might do thus : 6& D - . 5-b I* =§=ie= zjcW_ _zz::_ —~- Principles of Compcjitim. 85 And in that Cafe the Key of F would be continued until the Note D, which is followed by its Leading-note C fharp, that is arbitrary, when good tafte directs us ; this Tafte, which de- lights in Variety, directs us to quit a Key that hath been heard too long. The falfe Fifth, which is taken upon the Leading-note to the Note Z>, is not immediately refolved by the Chord that follows ; but one may obferve that it makes alfo the Sixth to the Note at the Letter G, without altering the Chord ; and that it is re- folved immediately afterwards, by defcending upon the fharp Sixth to the next Note, where the diatonic Progreffion obliges us to make the harmony fuitable to the Key, which the follow- ing Leading-note denotes. As we have not hitherto taken Notice of the Chord of the extreme fharp Second, which the Note at G carries, it is needlefs. at pre lent to give any Attention to it. The Note at H becomes a Leading-note, as well by reafon of the Progreffion of a Semitone between it and the Note that follows in the next Bar, as by reafon that the Chord of the falfe Fifth which it carries, is the fame as the Seventh, which, the Note immediately following ought to carry, fince that next Note afcends a Fourth ; befides, there do not appear any mora Sharps, and the Flat remains upon the Note B ; confequently the Note at if is the Leading-note; after which the Flats and Sharps difappearing, there is no other Leading-note, but the Note B, which denotes the Key of C, being obliged to give to the Notes of its Key the Chords that are prefcribed to them, and thus until the End, notwithstanding the Progreffion of a Fourth afcending at M obliges us to give a Chord of a Seventh, \o the Note C, and to give the perfect Chord to the Note F 9 jince that Note is ftill followed by a confonant Interval ; fo that the perfect Chord which the Note F carries, makes it a Key- note, but the Flat at B, that ought to take Place in this Key, being left out, and there not appearing any Sharp or Flat, the Note B becomes a Leading-note, having interrupted the Key of C, for an inftant only for Variety; becaufe it could be done according to the confonant Progreffion of the Bafs. To end this Subject we fhall fay, that all confonant Progref- fions are to be our Guide, and that diatonic Progreffions are to be relative to the confonant Progreffion that follows, i-ather than to that which precedes. If the Leading-note cannot be diftin- guifhed, there appears a certain Succeffion of Chords in a dia- tonic Progreffion from the laft confonant Chord, and which the tall Note in a confonant Progreffion ought to carry, which we ought not to quit, according to, the Rule of the O&ave in Chap. XI. If the Bafs afcends a Semitone, whiqh, in that Caie, might B6. Principles of Compofition. inight.be taken for a L&ading-note, we muft examine if there do not follow fome Sharps, or forae Notes that quit their Flat, by •Kcafon that the Leading-note is thereby fooner diftinguifhed than by a Progreffion of a Semitone afcending ; which may be done, in (harp Keys, from a Third to the fourth Note, and, in flat Keys, from the Second to the Third, or from the Fifth to the Sixth, this Sixth neverthelefs defcending immediately afterwards. If, immediately after a diatonic Progreffion, there follows a confonant Progreffion, the Note that ends the diatonic and be- gins the confonant Prog-reffion, ought to bear the perfect Chord, or that of the Sixth ; if it ought to carry the perfect Chord, it will be preceded by its Leading-note by afcending a Semitone, or elfe it will be the Governing-note preceded by a whole Tone ; if it be the Third, in a flat Key, it will be preceded by afcend- ing a Semitone, and, in a fharp Key, by afcending a whole Tone : And if, on the contrary, thefe Notes are preceded in defcending, the Key-note will always be preceded a whole Tone, the Governing-note but a Semitone in fiat Keys, and a whole Tone in fharp Keys. Now it will be impoffible but that, by knowing thefe different Progreffions in the feveral Keys, you muft underftand fomething, fince you already know the Relation that a Key ought to bear to that you quit, its Difference, in refpect to the major and minor Third, being taken from its Third and its Fifth, which are to be made up of the Notes contained in the Key that you quit. Befides, it is ahnoft impoffible but that a Leading-note will appear either before or after, and that the confonant Progreffion that follows will lead to a certain Conclufion that may guide us ; for it is to be obferved, that all Conclufions are determined by the Progreffion of a Fourth or a Fifth, excepting that, after one of thefe Progreffions, there fol-f lows a diatonic Progreffion of two or three Notes, either by af-^ cending or defcending, upon the Laft of which the Air or Me-. lody refts, and makes, as it were, a Paufe, or a Stop, in refpeft to the new confonant Progreffion that begins again. EXAMPLE. 6 rs-iziA: :=3i 6 6 — e- zsz— _QI§- ■ 5£ 7 6# — e- -e-6 33: — ~o..o~ -e— - _—Q- — e— . o -9 r-. e ~ — ~— ^ ~^-TT- — — Although, Principles of Compofttion. 87 Although the Bafs defcends a Fjfth at J,.\vt are not to take the Seventh upon the firft Note, becaufe the feeond Note ought not to carry either the perfect Chord or the Seventh, becaufe we are to be guided by the diatonic Progreffion that follows, where the Melody refts. The Melody which refts upon the third Note after 2?, obliges us to fuit to its Key the Note at B ; conlequently the Note that precedes it, ought to carry but that Chord which is required by this Kev, and not by that which is required by a confonant Progreffion, becaufe the Note at B is not to carry either the peri eft Chord or the Seventh. We give a Chord to the Note at C, fuitable.to the Key of the following Note where the Melody refts ; and we give-the Chord of a Seventh to this Note at C, preferable to that of the fmall Sixth, by reafon that this Seventh is found prepared by, the pre- ceding Chord, and it is refolved by the Sixth to the fame Note. We fpeak of it again in the following Chapter. We obferve the Rule prefcribed to thofe Notes that proceed by Thirds at D and J 7 ,, and, for a better Certainty, as to the Choice vve are to make of the Chords in this Cafe, obferve, that the "Notes in the firft Part of the Bar are to carry perfect Chords, rather than thofe in the feeond or laft Part of the Bar, on which the Chord of the Sixth is then fuitable ; though one might give the perfect Chord to each of thofe Notes, as we have done at G. The Conclufion, which is felt by the confonant Interval at the End, obliges us to fuit to its Key the Chords of all the pre- ceding Notes in a diatonic Progreffion from H, ARTICLE IV» How to dijlingwjh in a diatonic Progreffion, whether the Me- lody refls or flops upon the Key-note, or its Governing- note. IN order to diftinguifh, in a diatonic Progreffion, if the Me- lody refts upon a Key-note or a Governing- note, you need only to remember, that, in order to pafs from a Key-note to its Governing-note, the Bafs afcends a Fifth or defcends a Fourth; and, from a Governing- note to the Key-note, the Bafs afcends a Fourth or defcends a Fifth. Now, if a diatonic Progreffion exceeds that Compafs, the Leading-note will then appear in the Bafs, or not ; if it ap- pears, it will fhevv, at the fame Time, the Key-note; if not, you may then be fure that the Melody refts upon the Govern- ing-note. EXAM- H Principles of Coiftfiofttion. E X A M P L t 6 6 6 5 J?A £i5i£gg %£k A. 6 6 4 5 zr^^igc: Progreffiotis that lead to the Governing- . not6j \Vhere tbe Leadins-ftote doth not appeSr. 4 *c 6 6 G 5 & '"6 5& 6 6& r&PW* ;• ,.B. , B. 1J. K Frogrefiions leading to the Key-note, wheie the Leading-note appeals. The Bafs, which afcends a whole Tone at A^ fhews you the Governing-note, arid the Key-note at B, where the Bafs afcends but ai 'Semitone.. , ,. Agaifi; by whatever Note of the Key a .diatonic Progreffion -'begins, the confbnant Interval between that Note and that which precedes it, the Paufe or Reft that immediately follows, the whole Tones and Semitones that happen" in a. diatonic Progreffion, and the Interruption of this laft Prdgreffion by a conibnant Pro- greffion, will certainly fhew you the Place : It is true, that the' confbnant Interval \vhich. precedes a diatonic, cloth not fo clearly determine it, as that which follows a diatonic Progreffion, as the' Example in the preceding Article proves ; but the whole Tones? and Semitones that make up each Interval, in a diatonic Pro-, £reffion, are fufficierit of themfelves to' put you in the Way of it: It is therefore proper to ob'fefve the Place which. the Se- mitones occupy in each Mode or Key, as well a'feending as de- scending, and to remember that the diatonic Progreffion is fel- dom interrupted but after a Key-note, a Third, or a Govern- ing-note ; and if it Ihould be otherwife, a ( s it fOmetimes happens, : certainly the eonfohant Progrefiion that follows, as well as the above Rules on this Subject, will be fufficient, fo as not to be miftaken. We already know what the Progreffion of a Third, a Fourth, and a Fifth requires, as well afcending as defceriding, and how the fame Chord may fometimes be reprefented by two Notes of the Diftarice of a Third; according to the Progrefiion' that follows-: In fhort, if you will but give due Attention to &11 that hath been faid on this Subject, and ffick td Modulation, which is always to be our firft Objett, and bbfetve the Relation* 6f the Chords with the Progreffion of the Bafs ; and, if you compare the Whole with a fundamental Bafs, and take Notice of the Leading-note, which is* a very great Help in this Cafe ; it Will be almofl impdffrble to be miftaken ; fince,- when once you have difcovered the Chord, which a certain Note ought to bear, ^ou have only to'fdllow the Rule of the O&ave from that Note, until that where the diatonic Progreffion is: interrupted. See Chap. XI. As to the Variety of Harmony which may be therein other- wife introduced, it will be learnt by what follows. CHAP. Principles of Compcfitton. 89 C H A P. XXVI. Of the Manner of praSiiJing the Seventh, Upon every Note of a Key, in a diatonic ProgreJ/ion. THE Key-note is tlie only one that ought always to appear with the perfect Chord, whereas that of the Seventh may be given to all the other Notes, with this Difference, that, in a Progreflion of a Fourth afcending to a perfect Chord, or of a Seventh, all the Notes may be deemed Governing-notes, and may, in that Cafe, carry the Chord of the Seventh; but, in a diatonic Progreflion, that Note which carries the Chord of a Seventh, muft be divided into two Parts, or rauft be repeated twice (which is very near the fame Thing) in order that, upon the fecond Part, it may carry that Chord of the Sixth which is fuitable to it, according to the next following Note : And, in that Cafe, the Seventh muft always be prepared, faving the Firfl, which cannot be prepared according to the Progreflion of the Bafs*. EXAM? L ft. *76 C. j4, B. I cOuld have fiiited the Chords of thefe Notes, in a diatonic Progreflion, to the Key which fhews itfelf by the Con- clufion that follows ; but I may alio continue in the Key that precedes it, and upon the fecond Part of the Key-note B I take the Chord fuitable to the Key that follows. The Note at C ought naturally to bear the Chord of the great Sixth, which may be heard after that of the Seventh ; but, inftead of refolving that Seventh upon the Sixth to the fame Note, we refolve it by the Fourth to the following Note, be- caufe the Chord of the fmall Sixth, which this laft Note bears, and that of the great Sixth, which the Note at C ought to bear, are, in the Main, but one and the fame Chord : From hence M proceeds 9 o Principles of Ccmpojition. proceeds tlifs Rule, that, when a Difcord is ufed, we muft not quit it without refolving it ; and, as the Note in the Bafs, by whicb this Difcord ought to be naturally reiblved, doth not always appear, you muft fee if the following Note in the Bafs cannot bear a Chord made up of the fame Sounds that would co.. >e the Chord by which the Difcord ought to have been refolved ; which we are going to explain. CHAP. XXVII. How ovp. and the fame Difcord may be ufed in feveral Chords fuccejfively following upon different Notes, and how it may be refolved by Notes that feem to be foreign to that Purpcfe, IT muft be obferved, that the Chord of the Seventh is com- pofed of four different Notes, and that thefe Notes may be ufed one after the other in the Bafs, and that each of thofe Notes will bear different Chords in Appearance, although they are but one and the fame Chord (fee Chap. XII.) fo that having ufed a certain Difcord in a Chord, which cannot be refolved by the following Chord, you muft fee whether that fame Difcord cannot be ufed in the Chord to the following Note, and fo on, until you find that it can be refolved. EXAMPLE. zszsz 6 % 5 J -e- -e- f 7 r§=e- i B. The Difference in the Examples A and B confifts in the ma- jor Difcord, which appears in the Firft, and only the minor in the other. In the Chord of the fmall Sixth A, which is natural to the fecond Note of the Key, there happens to be a Difcord between the Third and the Fourth, which ought to be refolved by making the Third to defcend, which cannot be done upon the next Note ; but the fame Chord makes that of the Tritonus to this laft Note, where the Difcwd cannot as yet be refolved, and thus Principles of Compofition. 91 thus until the Note C, where the Difcord is refolved by de- fcending upon the Third to C, and v. i:iere ;it may be obierved, that the Note G, which bears the Chord o f the Seventh, ferves as a fundamental Note to thefe Four different Chords; lb that, when you meet with a Diicoro, you mull always reduce it to its fundamental Chord, and feek afterwards in the Bafs that Note by whith this Difcord may be refolved ; for, whilft there appear in the Bafs but the fame Notes contained in the Chord wherein that Difcord is uied, it is certain that it cannot be thereby refolved, and one of the Notes of the Chord, whereby the Difcord may be refolved by defcending if it be a minor Difcord, or by afcending if it be a major Difcord, muft abfo- lutely appear in the Bafs, which is eafily diftinguifhed after having reduced a Chord diffonant to its fundamental Note ; which may be eafily done, by faying, If the fundamental Note to this fundamental Chord governs fuch a Note, which is a Fourth above it; confequently I muft find that Note in the Bafs, or at leaft one of the Notes that compofe its perfect Chord, or that of the Seventh, fuppofing that the Melody doth not reft there ; if you meet but with the Fifth, then that Fifth, or Governing- note, being the fundamental Note to the diffo- nant Chord that appeared, muft be divided into two Parts, if it be not repeated, in order that upon the fecond Part it may bear the Chord derived from the Note that it governs. There is fome fmall Exception to be made to this laft Rule, which tvill be explained elfewhere. From what hath been faid, it follows that if a Seventh is taken upon a Note that ought naturally to bear another Chord, in refpect to that which follows, or according to the Rule of the Octave, and that this Note hath not a fufficient Length, or Value, to caufe the Chord which is fuitable to it to be heard ; in that Cafe the next muft bear the fame Chord, according to the fundamental Note, that is to fay, that the Notes, contained in the Chord to that fame next Note, be thofe of which the natural Chord to the firft Note ought to have been compofed ; fee the following Example, M 2 EX A M- 9 2 ' rz&z Principles of Compofition*. E X A M P L E. L *3 :sz: 6 7 5 zuiz: 7 . 4 5. 4« 6 7 7 A. ^ Continued Bafs« 7 7 L e?; iozs: Fundamental Bafs, Bv 7 7 : © :::=: :aze: -e-rr c. -e-e- _ 7 ' 5zl: •e— -e— - — e- D. 7 7 ZOZ -e — — e-i- zsr The Chord of the fmall Sixth, which the fecond Note of the Key at A and D ought to bear, is found in that of the Tri tonus, on the next Note after A> and in that of the Seventh, on the next Note after £>. The Chord of the fmall Sixth, which the fixth Note at B ought naturally to bear in defcending, is found in that of the great Sixth to the following Note. The Seventh which is heard upon the Governing-note, is re- folved by the Sixth to that fame Governing-note repeated at C ; from hence arifes that a Difcord may be refolved by divers Con- fonants, by reafon that it is always regularly refolved, provided it be by defcending upon a Conlbnant to the fame Note that carried a Difcord, or to the next Note, if that Diicord be a Minor ; for, if it be a major Difcord, it will be refolved by af- tending upon a Concord, or a confonant Note. There is another observation to be made, which is, that if, according to the natural Sequence of Chords;, you find yourfel£ in a Manner obliged to give to a Note a Chord derived from the Chord to the next following Note, you ought in that Cafe to obferve whether that firft Note could not carry the Chord that governs the next Note ; if to, it would be much better to give it this governing Chord, than that which in the Main would be but the fame Chord to the next following Note, efpecially when the Difcord that is to be heard in this firft Governing-note, may- be prepared by a confonant Note in the preceding Chord. A Sequence, or SuccefTion of Harmonv, is nothing elfe but a Link or Chain of Keys and Governing-notes, the Derivatives of which you ought to know perfectly, in order.to contrive it fo, that one Chord may always govern the next ; for a perfect Chord and its Derivatives do not govern any Thing, for after a perfect Chord you may remove to any other Chord, provided you keep to the Rules of Modulation ; but a diflonant Chord always. Principles tf Compofition. 93 always governs the next Chord, according to our Examples of 6 7, 7 and 6, 2, 4if, — , and $b ; and it is upon thofe Occanons that we fhould be very careful to know and difHnguifh Deriva- tives, in order to give them a proper Sequence, though the fe- veral Rules we have given for each Chord, and for each Pro- greffion of the Bafs, are fufficient to overcome thefe Difficulties. Example of the V reference that ought to he given to a Chord, in refpecl to that which follows. The fecond Note A ought naturally to bear the Chord of the fmall Sixth, derived from that of the Seventh to the Governing- note of the Key, which appears immediately afterwards ; but, for a greater Variety, we fhall obferve that this fecond Note governs that fame Governing-note, and therefore we give it the proper Chord in that Cafe ; and, though that Governing-note doth not immediately appear after B, yet it is plain that the Note which is between them, can carry but a Chord, derived from that of the Seventh to the Note at B ; and coniequently the Note at B is to bear the Chord of the Seventh, efpecially as the Seventh is therein prepared by a confonant Note in the preceding Chord. Obferve that all our Rules have hitherto only regarded Har- mony, and that the Melody of each Part is therein limited, faving that of the Bafs, upon which this Harmony is grounded ; therefore it will be proper to wait until you have attained to a thorough and perfect Knowledge of Harmony, before you pro- ceed to Melody, fupon which we fhall treat, after having ex- plained thofe Licences that ferve as an Ornament to Harmony by the Variety they introduce. CHAP. 14 Trinci'pks of Comfio/ition. CHAP. XXVIII. Of Licences, and, firjl, of the falfe or flying Cadence. AFalfe or flying Cadence is a certain Progreffion of the Bafs, which interrupts the Conclufion of a perfect Ca- dence ', for if after the Chord of a Seventh upon the Govern- ing-note of the Key, inftead of falling naturally upon the Key- note, you caufe the Bafs to afcend a whole Tone, or a Semitone, in that Cafe the perfect Cadence is interrupted, and the Seventh is thereby refolved by the Fifth to that Note fo afcended, which in fharp Keys afcends a whole Tone, and in flat Keys, only- a Semitone. E X A M P L E. Falfe Cadence in a fliarp Key. Falfe Cadence in a flat Key. In the perfect Chord that ends this Cadence, the O&ave t* the Third is heard preferably to that of the Bafs, which is con- trary to the natural Order ; but that proceeds rather from the falfe Progreffion of the Bafs, than that of the Parts, whereiiv it is obfervable, that the minor Difcord is always refolved by defcending, and the major by afcending; and that this Third doubled reprefents the fundamental Sound that ought to have been naturally heard ; although, in fharp Keys, we might de- fcend upon the Oftave to the Bafs, inftead of afcending upon the Third, as we have marked it by the Guide w ; but, in flat Keys, the Example muft abfolutely be followed. We fhall now invert the Chords that compofe this falfe Ca- dence, in order to difcover the Advantages that may be takea from it. EXAM- Principles of Competition. 95 EXAMPLE. 33? e- sb m -a- 6 — 4. raz: 43S: 4 =oz=Ze 5&- 6-fe- JD Z ie= Each of thefe Bafles be- ing placed tinder the other, you will hear all the dif- ferent Chords that are fi- gured ; from whence may be deduced an agreeable Connexion of Harmony and Melody, in a diatonic Progreffion, of the Bate afcending and defcending. See the following Exam- ple. 6 — I— -8- Fundamental Bafs flurp Key. 6& -dr Flat Key. UK AM* Principles of Qompofdion, EXAMPLE-. D. F. 7 2 4* 6 J5_Q_ -Q-fe,- - Q - -e-e- ; e-e : | : e ; 4 6 I-Q--4 -©— J2_Q. 3EE . l, 6 6 6 32 ^ \. ** ■ ** - < G. 7 5-b- 4* 6 6 sees; -e- ContinuedBafs. s: 6 7 5 When this Part ferves for Bafs; the Part D is. to be left out, and the Part .Pis to be altered in the two laft Notes ; the fame Thing is to be done in this, when the Part .Fferves- for the Bafsi When this Part ferves for Bafs, it muft proceed in a diatonic Progref- lidii Until the End, and rather: by afcending thafi defcending. When this Part ferves for a Bafs, the Part D is to be left out, by rea- fon that the irregular Cadence, which the Part D makes againft the Notes B C of the fundamental Bafs, cannot be inverted by a Chord of a Seventh, or of a Second, upon that. Firft of thofe two Notes. -e-e- 3E — e- A. B. C. ~q" Fundamental Bafs. In "this Part the perfect Cadence is avoided from A to B, by the Sixth's being added to the perfect Chord at B ; which prepares an ir- regular Cadence, avoided by adding the Seventh, in order to conclude by the perfect Chord. If the Fifth is left out of the Chord to the Note at B, you will then hear a falfe Cadence from A to B, as well as at H J, in the Part G. The Progreffion of the upper Parts is limited by that of the continued Bafs ; but if you would ufe them as Baffes, by Turns, you may then give them whatever Progreffion you think proper, tkat is to fay, the conjbnant Progreffion may be changed into a diatonic Principles of Compofition. 97 diatonic Progreflion, without altering the fundamental Harmony, and you will then fuit to it the Progreffion of the Parts above it. The Sixth may be taken upon the Second of two Notes that afcend a whole Tone, or a Semitone, in a falfe Cadence ; but then the Chord of the Seventh muft not be ufed upon the Firfl of thofe two Notes, by reafon that Seventh could not be re- iblved. It appears by the Example, that the Concluflon of each Ca- dence may be interrupted by adding a Difcord to the Note that ends thefe Cadences, provided that Difcord be prepared and re- solved according to the Progreffion of the fundamental Bafs, to which you muft always have Recourfe, to prevent a Mi flake ; for it is plain, that this Difcord cannot be prepared at i?, though it be good, becaufe the fundamental Bafs delcends a Fourth, or afcends a Fifth, which is the fame Thing. The irregular Cadence may be reckoned amongft the Licences, as well as the Difcords that cannot be prepared; as when the fundamental Bafs afcends a Third, a Fifth, or a Seventh, with all that proceeds by inverting thefe different Progrefiions ; though what we call Licence, in this Cafe, is infeparable from good Harmony ; which is the Reafon why we have chofen this Place to fpeak of it, for the better inff. rutting Beginners. Befides the Licences that the falfe Cadence can produce, by- inverting it, there is a certain Succeffion of Sixths, which is at- tributed to Tafte, and which Zarlino, Ta-^a parte. Cap. 61. Fol. 291 and 292, ftri&ly forbids, faying that the feverai Fourths together, which are therein heard, make pretty near the fame Effe£t as feverai Fifths, if the Chords be inverted according to the Example which he gives,. Neverthelefs it is plain, that, ac- cording to our Rules, this Succeffion of Sixths proceeds from the falfe Cadence, and from the Liberty we have of not preparing a Difcord in fundamental Progreffions of the Bafs afcending a Third, a Fifth, or a Seventh, N BXAM- n Principles of Con pojtthn. EXAMPLE. — e —UZ Q Q_ -e< 6 6 6 6 * : B J-l , ..... u or, 1-9- ~^r~ -e— o- -* ! — .■ ._ .. - .. Fundamental Bafs. -e — — - -e— — A. B. -©- Each Bar reprefents a falle Cadence, excepting the Peivultima, which reprefents a perfect Cadence, avoided by adding a Sixth at A; this Sixth preparing an irregular Cadence, which is likewife avoided by adding the Seventh at B, where the perfect Cadence is prepared and concluded upon the laft Note. If the two upper Parts were inverted, you will then hear as many Fifths as there are Fourths ; but the Infipidity of" feveral Fifths is fo much diminifhed, by inverting them, that we arc not to attribute to the Fourths what concerns only the Fifth and the Odtave. The Seventh is fometimes by Licence joined with the Sixth, which creates a very harfh Chord ; and the only Reafon why it can be tolerated is, that it is ufed as a palling Chord, and the harfh Sounds therein are heard in the preceding and following Chords, and the Note oi the Bafs, in this Cafe, can be admitted" bat by Supposition. EXAMPLE. -e-rsy-reH: -e-3— i -a "CT' a Z ,_ £_ _J_7._i_ 6 , 4—7 -e— b Another Principles of Compofition. Another EXAMPLE. 99 CHAP. XXIX. Of the Chord of the extreme Jkarp Fifth. WE muft alfo treat of certain Chords that are introduced by Licence ; and, firft, of the extreme fharp Fifth, we fay that it can never be ufed but upon the Third in flat Keys. This Chord, properly fpeaking, is no other than the Seventh to the Governing-note of a Key, under which is added a fifth Sound, at the Diftance of a Third. EXAMPLE. "■"Zo_~ Governing-note P Sound added. Chord of the extreme fharp Fifth. It is not in the Sound added, that you muft feek the fundamental Note of this Chord, This Chord hath for its fundamental Note the Governing- note of the Key, and will always follow its ufual Progreffion ; the major Difcord will afcend, and. the minor will defcend, and the Whole will be refolved by the perfect Chord to the Key-note ; whilft the Sound added will afterwards make a Part in that perfect Chord, or will defcend upon that fame Key-note. E X A M- 10© Principles of CompO/lticn. s/^S only the Chord EXAMPLE. This Chord muft be prepared by that of the Seventh to the Note that governs the Governing-note of the Key, wherein it appears, that the fecond Note, which, in this Cafe, governs the Governing- note of the Key, alcencls but a Semi- tone, inftead of afcending a Fourth, whilft, in the other Parts, you will hear the Seventh to the Governing-note of the Key, which is afterwards refolved according to our Rules. This Chord is ibmetimes ufed, in order to avoid a Cadence, by caufing the Governing- note of the Key to afcend a Semitone upon this Sound added, which, from a fixth Note, becomes a Third, by reafon of the Alteration of the Key, and by the Means of a new Leading-note, which the extreme fharp Fifth creates. EXAMPLE. When you compofe in four Parte, you are at Liberty to place in the upper Part the Notes marked by the Guides in the Room of the others. This Chord is alfo prepared by that from which it is derived, EXAMPLE. There are fome who fometimes prepare it by the Fifth to the fame Note, or by the flat Sixth to the Note which is a Semi- tone below it, or by the Chords derived from that of the Seventh to the Note, which is but a Semitone below ; but that is taking to much Licence. CHAP. Principles of Compofition. 10 i CHAP. XXX. Of the Chord of the Ninth. THIS Chord differs from the preceding Chord, only in the Fifth, which was fharp in the other, and which in this Chord ought to be perfect ; or rather in the Third to the funda- mental Sound, which in this Chord is flat, and in the other fharp ; fo that, if we take a Chord of a Seventh to a Governing- note with a flat Third, we fhall make that of a Ninth by adding a Note, a Third below that Governing-note. EXAMPLE. Governing-note. Sound added. !-_3_Q.Za Governing-iv»tej i O * Sound added. Chord of the extreme fharp Fifth. Chord of a Ninth. It is neceffary to take Notice, that all Chords by Supposition, fuch as the extreme fharp Fifth, that of the Eleventh, and that of the extreme fharp Seventh (we fhall fpeak of thefe two laft Chords in the following Chapter) derive from the Chord of a Seventh to a Governing- note, becaufe, by this Manner, you immediately know how thefe Chords are to be prepared and re- folved ; fo that, by the Means of a fundamental Bafs, you will fee how the Whole anfwers to our Rules of Sevenths. See the following Example. EXAMPLE. Continued Bafs. 7 7 7 z§z±z jz±=grq 7 7 Fundamental Bafs. e — g— 1-@— ©- i<92 Principles of Compofiiion. ! Fundamental Bafs. -^j ©- All thofe Notes in the continued Bafs that carry Ninths, 0$ fliarp Fifths, are to be left out when the fundamental Bafs is .made ufe of, otherwife the Notes in the fundamental Bafs ought to be above thofe that are figured by a 9, or a 53: ; becaufe the Sound in the fundamental Bafs, which in that Cafe is fuppofed, cannot be heard but above that which fuppofes it, Thofe Notes that carry Ninths and fliarp Fifths, may either defcend a Third, as it is marked in the Guides, or remain upon the lame Degree ; for which Reafon the Ninth may be refolved two Ways, viz. by %he O&ave, when the Bafs remains upon the fame Degree, and by the Third, when it defcends a Third ; in which Cafe it may be obferved, that the Seventh is then refolved bj the Oftave, as we fhall fhew hereafter. There are fome that hold that the Ninth may be refolved by the Fifth, by caufing the Bafs to afcend a Fourth ; but the Har-? mony that proceeds from it feems improper : Therefore we fhall leave it to the Difcretion of Compofers of a good Tafte, Example ef the Ninth refolved by the Fifth. Q g' o ub j "*"* - ■ * — ?'" Q-4 he prepa It might rather be refolved by the Sixth, by caufmg the Bafs to afcend a Third ; by reafon that, in this Cafe, the fundamental Harmony would not be altered. See the Guides in the other Example. All minor Difcords by Sup,- polition absolutely require to you fee th^t; the Ninth can be prepare^ Principles of Compofition. t°3 prepared by a confonant Note in the preceding Chord (provided, in this Cafe the Ba£s afcends a Second or a Fourth) you may praftife it by refolving it afterwards according to the Method prefcribed by the Example, and without going wide df true Modulation. The Seventh, which may always accompany the Ninth, ought not to be added to it, unlefs it be prepared by a Concord oc confonant Note in the preceding Chord. -Obferve alfo in this Place that minor Difcords by Suppofition. may be prepared by another common Difcord, fuch as the Se- venth, or by the falfe Fifth ; and that proceeds by reafon that thefe laft Difcords are contained in the fame fundamental Chord, having already obferved at Chapter XII. that one and the fame Note may create feveral Difcords following, when they proceed from tlie fame fundamental Chord. -o- -73- zSt , , Fundamental Bafs. The Notes A of the continued Bafs carry Chords derived from the fundamental Bafs ; the like of the Notes '£ ; if then we may hear Difcords by Suppofition after another Difcord, and if it be true, that a Difcord is to be preceded and followed by a Con- cord, we mufl conclude, in order that this Rule may hold good, that feveral Difcords that are heard following upon the fame Degree, are not fuch in Effect, but that they all proceed from the firft Difcord which is the Seventh, the fundamental Chord of which doth not change until the Expiration of thefe feveral Difcords in Appearance upon a Concord, as it is oblervable in the Example, and as it really is ; fee Chap, XV. how the ele- venth Heterodite may alfo be prepared by the falfe Fifth. CHAP. 104 Principles of Compojitton, CHAR XXXL Of the Chord of the Eleventh, otherwife called the Fourth. THE Chord of the Eleventh is compofed of five Sounds, thus A A, C, E, ®< j j 5> 7> 9> J i> where it is feen, that the Sound added i'a a Fifth below that which ferves as a fundamental Note to the Chord of the Sevenths This Chord is feldom ufed, by reafon of its extreme Harfh- nefs, there being three minor Difeords in its ■^> A Ml G 9 -\ Conftruftion, as appears by the Numbers lh3> 5> 7 J 7, 9, ii. Yet the Practice of it is eafy, by reafon that three Concords, or conibnant Notes, in. the preceding Chord, prepare thcfe three Difeords, by keeping on the fame Degree ; but they mull not be refolved all three at once, by reafon that, as they are minor Difeords, and muft defcend, one could not avoid two Fifths to follow in the Parts ; fo that you muft firft refolve the moil harfh, which are the Eleventh and Ninth, and afterwards the Seventh. EXAMPLE. r _SCifi2.|_e=- —..wr jAi. — I Chordof the extreme iharpSeventh. | Chord of the Eleventh. j I- I — ' J This Chord is never ufed but upon the Key-note, and is to be preceded and followed by the perfedt Chord to that fame Note, EXAM- Principles of Compofuion. EXAMPLE, toy -©- SB *~e- 73?r sJ*-©-- -0 Continued Bafs. s-e- -£— -9- — e- Fundamental Bafs. The Sounds ^keep in Sufpence thofeofi?, and theie Strokes (7) fhew the natural Progreffion of the Sounds A. The Sound that makes the fharp Seventh is often left out of, this Chord, when the Bafs de- fcends a whole Tone, or a Semi- tone, EXAMPLE. -e-j-e- ( lody, that proceeds by Semitones, as well in afcending as defcending ; which produces a furprifing EfFeft in Harmony, by reafon the greateft Part of thefe Semitones, that are not. in ^a diatonic Order, caufe at every Infrant fome Difcords that fuf- pend or interrupt a Conclufion, and give a Facility of filling up the Chords with all their Sounds, without altering the diatonic Order of the upper Parts. Chromatic is chiefly ufed in flat Keys, and is more difficult "to comprehend, when the Parts defcend, than when they afcend. ARTI< I J 3 Principles of Compofttion, ARTICLE I. ■ Of Chromatic defcendlng. W HEN you have begun in a chromatic Manner in a certain Key, by 1 making any one pf the Parts to defcend by Semitones, you may continue it throughout the Key upon its Governing-note, and more particularly upon its Fourth, the Key-note becoming in this laft Cafe a Governing- note ; and thus, by a Sort of a Chain, each Key-note may become a Go- verning-note to the Key you remove into; neverthelefs, you niuft not go too wide of the firft Key, for, as foon as you find Room to return into it, it will be proper to do it. By Means of the Leading-notes, which become fucceffively Governing-notes, you may acquire the Knowledge of Chro- matic. After we have paffed from the Key-note to its Fifth, we return back again to the Key-note by making it a Governing- note; and thus by following the Rule of Sevenths (fee Chap. XXI.) and making the upper Parts to proceed by as many Se- mitones as poflible (each of thefe Semitones making againft the fundamental Bafs, the Third, or the Seventh, or fometimes the falfe Fifth to the Note, which neverthelefs bears a Chord of the Seventh) you will find that the Difference between the Chro- matic and our common Rules conlifts but in the Leading-note, which in this Cafe may defcend a Semitone, whereas it ought •always to alcend ; but the Note or Sound, to which it ought to afcend, is always underftood in the Chord, and it is but in refpedt of the Chromatic only, that, we may take this Li- berty. E X AM- Principles of Compofitm, nq EXAMPLE. sb , 4* s-b- -Q- safe— ^- e- _Q 2.Q- ^-t * 4» 121 *! £ ^ 5-b- -- — *e- _4£___5_fe_ -q- Q cT~ 6-fe- •* 5 / feszzsz 5^ Z©=X3Z -e- /^^N6 7 ^~S6 * -»— -f— ~ -a- w 22Z£i :sz Z2Z 4-S~\X % % & "lb 6 5^ 6 3£ 'V'° c — © o o rs o , 1 iJ. o o n - - ■ , — ... 1— . 7 7$ 7$ & ZZ ZQI 7-b- 7-fe- 7 -e- :sz 5-D- 3? -be -5- - Fundamental Bals of Sevenths. -Q- "O" If all thefe Parts, excepting the fundamental Bafs, are ufed as Baffes by Turns, you will find a Succefiion of Sevenths and Sixes, like thofe derived from a fundamental Progreffion of Sevenths, with the Difference of the Chromatic which is therein ufed ; you will alfo fee how the Tritonus and falfe Fifth take the Place of 2, 6 and — , and how thefe Intervals ferve for the Refolutica. of each 5 other, by Means of the Chromatic ; the Leading-note defcending every -where inftead of afcending, faving at the End. Here follows another Manner of praftifing the Chromatic upon a Key, or Holding-note, £ X JM 114 Principles of Compojition. EXAMPLE. rap! B- — CT"~S — :z?::sQz: -e— r e- ^ e- r^s jo, 5Z3£ -e- -e— — Eg=3S3" . .. ZE Q-_L_0__ -e- H- -e — e-i-Q :nz I: nieZZe— ,6 6-b- 1S8 8 6-b- 7X -e — e- -e- -e- -e- -©- The Leading-note being frequently ufed in Chromatic, confe- quently you may uie all the Chords wherein the Difcord major is heard, as thofe in the above Example ; as alio that of the extreme fharp Second, its Derivatives, and efpecially that of the extreme fharp Fifth, when you are minded to avoid a Cadence ; fee Chap. XXIX. where the Leading-note defcends a Semitone. As you ought at prefent to know the Compofition of all the ex- treme fharp and flat Chords, the borrowed Chords, and thofe by Suppofition, you mav make Uie of them, wherever you feel the Leading-nete may take Place; neverthelefs, ufing now. and then the perfe£l Chord, and that of the Seventh and their Derivatives, and keeping as much as may be a diatonic Order in the upper Parts. ARTICLE II. Of Chromatic afcending. r J ]»'^ |"7 H E Chromatic may alfo be pradifed by afcending, but then J^ it has not the Sorrowfulnefs of the firft, and the Harmony it pioduces, unites itieif ptrfeclly well with the Fundamental. E X A M- Principles of Compqfitiort. 115 2?, this Note, though it be fundamental, cannot take Place, whilft the Note at C borrows from its fundamental Chord A, a falle Cadence. P 2 EX A M- no Principles of CGinpofition. E X A M P L E, Of two Parts, afcending and defcending at the fame Time by Semitones. The three tipper Parts may be inverted, and ferve as BaiTes re» ciprocally one to the other. -© OyFr*, i3W~ > ^" 6,6 sb 6 5 5-b- •& 4* P_Q_ zozo: 6 7 6* 6 5-fc> ggT7-fe- 2 5-D- iU4«6 6 7 4 5 » I2Z 6766^ ^©— e- 4 zzzs ZQZZ 6& _6 * Z£ 6 :®z©sozs: •6 6-& •42 — sb- - j-Q-e „ 1 -q kilcsp el|_ZZ_ -s EMiz*: -e-e- Continued Eafs. he^~ zszzo: z*zS: -e-Z 6 5 7 7 7 7 7 7 7 5-& .** 7 zsz^: as zzzp: -e — Q— Fundamental Bafa. -q— ©- TCTO: ^iIzqAzzozs: -©- Obferve that all thefe Semitones that are ufed in Chromatic, confift but in the lixth and ieventh Note of the Key, by reafon that in flat Keys, the Leading-note being to be flattened a Semi- tone ; in order to defcend ; and the lixth Note to be fharpened a Semitone, in order to afcend ; we may make thofe Notes pals upon one and the other Interval, as well in afcending as defending. We lhall add that Chromatic may be pra£tifed in fharp Keys, upon the fharp Third to a Governing-note, which afterwards be- comes a Seventh to another Governing-note, by defcending a Se- «iuoiie ; or elfe by making the fourth Note to afcend a Semitone upon a Leading-note to a frefli Key, CHAP, Principles of Compojition. 1 17 CHAP. XXXV. Of the Manner of prafiifing all that hath been hitherto faid, ARTICLE I. Of the Trogrejjion of the Bafs. » YOU muft begin by compofing a Bafs in a familiar Key, from which you may remove to others equally familiar, ac- cording to what we have faid at Chap. XXIV. This Bafs is to be filled up with perfett Cadences, as often as may be ; for it is the natural Progreffion of the Bafs to proceed rather by confonant than diatonic Intervals ; the falfe Cadence and the irregular ought not to be ufed until you know how to ufe them properly, either to avoid too frequent perfect Cadences (which is a Variety very pro- per in this Cafe) or to reft the Melody or Air upon a Governing- note, or even upon a Key-note, by Means of the irregular Ca- dence, which is another Variety that keeps the Ear in an agreea- ble Sufpenfe. You muft alfo endeavour to introduce in your Bafs thofe Pro- greffions that create a Continuation of Harmony, derived from that of the different Cadences, according to the Examples we have given, not forgetting the Progreffions of 7, 7 and 6, 2 and 6, 5^ and bpg, 22: , 9, 11, 5^, and $g, As fome Compofers (being doubtful of their Capacity) will be afraid that their Baffes are not well compofed, we fhall obferve, that (if they have not that natural Tafte for immediately invent- ing divers Airs, or Melody, that are always agreeable) they will never err by making the Bafs to proceed indifferently upon all the Not£s of a Key, by preferring the fmalleft Intervals to the great- eft, that 4s- tofayyby afcending a Third, rather than to defcend a Sixth, &c. and remembering that the Leading-note muft alwavs be followed by the Key-note, excepting in Chromatic ; that you muft make a final Cadence, before you remove into another Key, and proceed in this new Key, pretty near in the fame Manner, as in the other, and thus from Key to Key, according to the In- flations in Chap. XIII. XIV. XV. XVI. XXIV. and XXV. Again, as the Note that ends the perfect, falfe, or irregular Cadence, is to be heard upon the firft Note, or Part of the Mea- fure or Bar, you muft compoie a Bafs in fuch a Manner, as this Regularity may be therein obferved ; and in cafe at the firft Ca- dence it jhould happen othervvife, and that you would not alter the Air ot the Bafs, you need only to begin it upon another Part of the Bar, that is to fay, that, if it was begun by the firft Parr, 1 1 8 Principles of Compq/ition. Part, you may begin it by the Second or Third ; or, if" it was begun by the Second, you need only to begin it by the Firft, &c. and, if this fhould happen in the middle of a Piece, you mull then either add or leave out one or two Notes, according as the Cafe is, and obferving that the Cadences be heard every two or four Bars ; though you may trefpafs upon this Rule when good Tafte directs you, or when you are obliged to it by the Words that you fet to Mufic, which then are to be our Guide. ARTICLE II. How confonant and dijfonant Chords, Concords, and Dif- cords are to be ufed. ! THE perfect Chord is to be ufed at the Beginning and ait the Conclufion, and for all middle Clofes or Cadences ; it may alio be ufed in a diatonic Progreffion of the Bafs, as well as its Derivatives, which are the Chords of the Sixth, and Six and Four, obferving in the like Progreffions, that the confonant and diffonant Chords are as it were interweaved one into the other ; fee the Example of the Octave, Chap. XI. and that of the Sixths, Chap. XVI. You muft alfo contrive it, that all Difcords be prepared and refolved according to the Rules, which do not re- quire a great Attention, when you fully poffefs the Succeffion of Chords; befides, vou already know that they ought not to be prepared after a perfect Chord to the Key-note only, or upon its Derivatives, provided that the Key doth not alter; though it might be done when the Bafs afcends a Third, in order to de- fcend a Fifth immediately afterwaisds. EXAMPLE. When the Bafs afcends a Third, in order to defcend a Fifth, and the Key changes, if the firft Key be fharp, that into which you remove is flat A\ and on the contrary, if the firft Key is fiat, then the Second is fharp B ; the Strokes that go from one Note to the other, fhew how the Difcord is not prepared, and the Progreffion of the upper Part in that Cafe ought to follow. You ' Principles of Ccmpofitlon. 119 You may invert thefe fundamental Progreffions, and ufe them with Difcretion. You ought not as yet to alter the diatonic Order of the upper Parts, unlets it be for the better completing a Chord, or for re- placing a Part above the Bafs, or in its natural Place ; and you mult in this Cafe avoid uling two Oclaves, or two Fifths, toge- ther, unlefs they be reverfed. Thofe Parts that afcend or defcend together, are to be difpofed by Thirds or Sixes, and as little as may be by Fourths, never by the Oftave or Fifth ; that is to fay, whatever Parts make toge- ther a Third, or a Sixth, may make the like again in the follow- ing Chord, and fo on. When one Part afcends or defcends diatonically, whilft another proceeds by a confonant Interval, that is always good, until wc give a fuller Explanation. Remember, that the Succeffion of Chords contained in a Key is the fame in all other Keys. ARTICLE III. Of major Difeords proceeding from the Leading-note, and of thofe Notes on which they are ufed. 1. ""THE Tritonus is never ufed but upon the fourth Note, wfeen that Note defcends upon the Third, or upon the Key- note. 2. The falfe Fifth is never ufed but upon the Leading-note, or fharp Seventh, when that Note afterwards afcends to the Key- note, or fometimes to its Third. 3. The fmall fixth Major is never ufed but upon the fecond Note of the Key ; and, when it is Minor, then it is generally ufed upon the fixth Note. 4. The fliarp Third cannot be ufed with the Seventh, making between themfelves an Interval of a Tritonus, or a falfe Fifth, but upon the Governing-note or Fifth of the Key. Thefe fou* Difeords are the moil in Ufe. 5. The extreme fharp Seventh is never ufed but upon the Key-note, which continues upon the fame Degree, in order to prepare and refolve this Difcord. 6. The extreme fharp Fifth is never ufed but upon the Third in flat Keys. 7. The extreme fharp Second is never ufed but only upon the fixth Note in flat Keys, and this Note muft afterwards defcend. 1 8. The 1 20 Principles of CompoJitioU. 8. The extreme flat Seventh is never ufed but upon the Lead- ing-note, or lharp Seventh, after which this Note is to afcend. 9. The other Difcords that derive from thefe two laftj are wfed upon the fame Notes, wherein the Chords differ from the Go- verning-note to the Sixth in flat Keys only. Sometimes the Tritonus happens upon another Note than the Fourth, and the falfe Fifth upon another Note than the Lead- ing-note ; but then, and in that Cafe,thofe Intervals are no longer the Object of the Chord, they ftrving only as an Accompani- ment ; and it is the Modulation that caufes that Alteration in the fame Manner, as in the Progreflion of Sevenths, where fomc are altered, and are not in their true and juft Proportion ; there-* fore you muft never take any Notice of this Alteration, when, you know the Chord that ought to be ufed, and the Key you are in ; for it is the fucceffive Degrees of a natural Voice, con- tained in the Compafs of the Oftave of the Key, or Mode that you are in, that decides the Juftnefs, or the Alteration of an In- terval that makes a Part of the Chord. ARTICLE IV. Of minor Difcords. 1. '"pHE eleventh Heteroclite, otherwife called the Fourth, ma^ ■* be ufed upon all fuch Notes as bear the perfect Chord, or the Seventh, provided that thefe laft do immediately follow,, faving out of this Rule the firft and laft Note of a Piece; and in. this Manner it will always be found prepared by obferving two Things. Firft, That if you fall upon a perfect Chord, after one of its Derivatives, thefe two Chords being but the fame, the Eleventh cannot then be heard. The Second is, To give always the Sixth to the Note that afcends a Third upon that on which you take the Eleventh. 2. The Seventh, where the Dilcord major is not heard, chufes to be prepared by the Octave, by the Fifth, by the Sixth, by the Third, and even by the Fourth, which is a Concord, or a con- fonant Note, proceeding from the Chord of the Sixth and Fourth to a Governing-note of a Key, according to the different Pro- greifions of the Bafs. 3. The Ninth muft always be prepared by the Third, or by the Fifth, according to the Progrcffion of the Bafs ; it may alio be prepared by the falfe Fifth. 4. The t> Principles of Compojitiort, " 121 4. The Eleventh muft likewlfe be prepared by the Fifth, and fbmetimes by the Seventh, but this fparingly ; when it is hetero- clite, it may be prepared' by all the Concords, or conibnan«t Notes, and even by the Seventh, and by the falle Fifth. 5. The Second which is prepared in the Bafs, may be prece- ded in the Treble by any one of the Concords, whilft the Bats remains upon the fame Degree. To conclude, all Diicords are to be refolved, as hath been faid ; you may leave out of the diffonant Chords ont of the two Sounds that create between themfelves the Difcord, and only take th« perfect. Chord, or one of its Derivatives. ARTICLE V. Oftkofe Concords, or conformant Notes, that are to be pre* f erred, when they are to be doubled. WE have only to take the Confonants in their Order of Perfection, thus, the Octave, the Fifth, the Fourth, the Third, and the Sixth, in order to know that the Octave is to be preferred to the Fifth, and fo on ; obferving that it is already a Replicate, and that, in the confonant Chord of the Sixth, the Octave to the Third, or to the Sixth, is as proper, and as good ? as that of the Bafs. ARTICLE VI. Of Meafure, or Time. MU S I C K without a Movement lofes all its Grace ; therefore it is not enough to apply to the Compofition of Chords only, but you muft alio endeavour to give to each Part a certain Movement, wherein may be diftinguifhed a Casfure, a Section, a Cadence, a Syllable, of the Length of a Breve, and. the Places where the Difcord is to be ufed ; the Whole to be made fenfible and obfervable, immediately upon the firft Part o£ the Bar (fee Chap. I.) ARTICLE VII. Of Syncopation, or of a Drhniig-note. I N order to follow the natural Order of the Meafure, it muir be fo contrived, that the Value of each Note do begin and Q, end, 122 Trine I pies of Ccmpofition. end, within the Space of each Part or Divifion of the Bar ; y-ei a Note that begins immediately upon the accented Part of the Bar, may remain upon the lame Degree, as long as Tafte will permit, whether the Sound be lafting or not ; but as foon as a Note begins upon the unaccented Part of the Bar, and one half of its Value is heard upon the firft Part or Divifion of the next Bar, that cauies a Shock to the Ear, and, in that Cafe, that Note is faid to be fyncoped, and is called a Driving-note. And there arc four feveral Ways of ufing it ; the firft Way is when the Note is divided by the Bar into two equal Parts, thus, ZJE — F- fci The fecond Way is, when two Notes togethef of art equat Value, and upon the fame Space or Degree, are bound by a Se- micircle thus /^"S, or v — x\ which fhews that the Sound of thofe two Notes is to be lafting. EXAMPLE. /*S y-S r~^ >?n The third Way is when a Note is preceded by another, which is but of the Value of a Moiety,- or half of one Part of the Bar, or when it is preceded by a Character which denotes a Reft of the like V.alue,. fuppofing that this Note Id preceded anticipates upon the naxt following Part of the Bar. E X A M P L E. — ^ The Notes A, B, C, D, F, G t H, J, are fyncoped. The fourth Way is when two Notes are repeated on the fame Degree of an equal Value., the firft whereof begins upon the uir- accentsd Partot the Bar, and the iecond upon .the accented Part,. without Principles of Ccmprjttlon. 123 without binding them, whether it be for the Sake of the Words, or for giving a quicker Movement to the air. EXAMPLE. £ b » w In order that a Note be fyncoped, it muft not only begin on the unaccented Part of the Bar, or upon the iecond Half of the firfl Diviiion ; but it muft alfo be contrived, that its Value may be di- vided into two equal Parts, the one in the firft Part of the Bar, and the other in the next following ; and, inftead of making Ufe but of one Note, you may make Ufe of two Notes, each repres- enting one Half, or Moiety of the Note fyncoped, being at Li- berty to repeat them, or to continue the Sound, by binding them with a Semicircle, or Slur, which caufes them to be expreffed as cne Note, the Value of which will be equal to thofe two Notes. Thefe are the various Ways of Syncopation, and are ufed as Well in Harmony as in Melody : in Harmony, by caufing the* Difcords to be prepared ; and in Melody, in order to render the Air more expreffive, without altering the Species of the Interval, in one or the other Note of the Syncope, or in the fame Note (o fyncoped. EXAMPLE, 67 6 7 36 j6 4 6 6| 3 687 -e^ -P-Cir-r f: -#-r—ffl : F : -P-^r- P— ttHcaSt 8 2 [igggisrigg^i ( «|7 TF— I — =~r— H +— 1 tar- 1 — r « — 1 w ^izS=EEcEEE Q.* The *24 Principles of Compofition. The Figures that denote Concords or Conipnant Notes only, thus, 3, 6, tec. fhevy that the Syncope is ufed for the lake of the Melody or Air only ; and thole that denote a Difcord, fhew that the Syncope is ufed for Harmony. The Bals may fyncope as well as the TreMe, together, or fe- parately, in refpe£l to Melody; but, as to Harmony, the Bafs cannot fyncope bat in the Chords of the Second, of the Tritonus, and of the extreme fharp Seventh. In order that the Syncope be ftri£tly obferved in Harmony, it mull be contrived that the Value of the Note or Concord that prepares and refolves, and the Difcord prepared, be equal, as much as can be ; this fuffers an Exception but in Triple Time, where the two taft Parts or Divifions of the Bar are unaccented, fo that the Concord which prepares and refolves the Difcord, may, in that Cafe, contain double or one half of the Value of the Dif* cord prepared. When there happen feveral Difcords together, it is but the Firft that -is fubiect to the Rule of being prepared on the unaccen- ted Part of the Bar, and to be heard on the accented Part. In Common Time, where there are two equal Notes -in a Bar, the Firft is accented, and the Second is unaccented ; and, when there are four Parts or Notes in a Bar, the Firft and the Third are accented, and the Second arid the Fourth are unaccented. In Triple Time, where there are three Parts or Notes in a Bar, the Firft: only of the three is accented, and the other Two are unaccented. As loan as a Difcord crm be prepared, the Syncope no longer fubfifh, and then a diatonick Progrcfhon from the Concord that precedes the Difcord, until the Concord that refolves it, ought to, be followed ;. though this is not to ieive as a general Rule, efpe-. dally in regard to the Seventh, the falfe Fifth, and all major. Difcords. C FI A P. XXXVI. Of Compofition (n two Parts, THE lefs the Parts are in. a Piece of Murk, the ftri&er are the Rules to be obferved ; fo that certain Licences allowed in four Parts may become Faults, when the Parts are lefTened. 1. We muft now diftinguifh the conlonant Notes, or Concords, in perfcc-i and imperfect. The Principles of Compofitinn, I2 5 The perfect Concords are the Oflave and the Fifth, it not being herein permitted to make two Octaves, or two Fifths, to- gether, even though they fhould be reverfed. The Fourth is alio a perfect Concord, but, as it is but feldom u fed in a Compofition of two Parts, we ihall only prefcribe the Manner how it may be ufed. The imperfect Concords are the Third and Sixth, and we may ufe feveral of them together and intermix them without any Fear of being miftaken, provided that we do not go out of true Mo- dulation. If we fkip from a Third to a Sixth, or from a Sixth to a Third, and the Progreflion of the Parts is confonant, then the Parts ought to move in a contrary Direction, the one afcending at the fame Time that the otheivdefcends. It is proper to ikip, as much as may be, from a perfect Con- cord to an imperfeel, and vice verfa. One cannot well fkip from a perfect Concord to an imperfect? and vice verfa, but when one of the Parts proceeds diatonically, and the other by a confonant Interval ; and, in that Cafe, it is Very proper that the contrary Motion be obferved. £ X 4 M P L E. Of a Sequence, or SucceJJion of 'perfect Concords. Doubtful. _0 Q 8 5 •ZQZZZ 5 3 IOZZZ — e- IDZZZ £2Z All oilier Progreffions of two perfect Concords immediately following are not proper. Thofe Bars marked with the Letter A are alike, as well as th'ofe witk a B. 2. Yoa 1-25 Principles of Compojition. 2. You may make a Part to move by as many confonant In- tervals as you think proper, whilft the other Part remains upon the fame Degree, provided there be a Concordance between the two Parts. 3. All PalTages or Skips from the O&ave to the Third, from the Fifth to the Third and to the Sixth, from the Sixth to the Third, and from the Third to the Sixth, are proper. 4. The Paffages or Skips from the Octave to the Fifth are pro^ per, provided that the contrary Motion be obferved j yet that, where the Bafs defcends diatonically, is not proper. 5. Thofe of the Octave to the Fifth are proper, provided that the Progveffion of the Parts be contrary, when the Parts make each a confonant Interval, though all is proper, when the Bafs defcends a Third. 6. Thofe of the Sixth to the Octave are proper, excepting when the Bafs afcends diatonically, when the upper Part defcends in the like Manner, or when each of the Parts makes a confonant Interval. 7. Thofe of the Sixth to the Fifth are proper, excepting when, the upper Part afcends diatonically, when the Bafs defcends in the like Manner, or when each Part makes a confonant Interval. 8. Thofe of the Fifth to the Octave are proper, excepting when the Bafs afcends diatonically, or when each of the Parts makes a confonant interval. 9. Thofe of the Third to the Octave are proper, excepting when the Bafs defcends diatonically, and obferving, at the fame Time, a contrary Dire&ion, when the Bafs afcends a Fifth. 10. Thofe of the Third to the Fifth are alfo proper, provided that the Parts move by a contrary Direction at thofe Places where the Bafs afcends a Second, a Third, and a Fourth; and even one muft rather make it afcend a, Fourth than defcend a Fifth, other- wife the Progreffion would not be proper. 11. As to the Fourth, here follows an Example of all the Con«» cords that may precede or follow it. EXAMPLE. -e : 9 : § : a : 9 : ! S 4 3 4 s A, :§:s:§w::= B. isg rswd 3 4 6 4* [._:=:--:=:!|Z^z2Z==: 6-6-6' 6 6 5 4* 6 4 6 6' 4 3 54- ^ 4 2 _5 2__J> {& The Principles of Ccmpofaibni 127 The Guides fhevv the feveral Concords, 3rd even the Di (cords that may follow the Fourth ; the Figures that are between the Parts (hew the like ; and thofe under and over the Bafs fhew the Chords to be ufed in this Cafe. Take Notice, that the Guides, in the Examples A and B> de- note two different Chords^ that of the Tritonus, or that of the great Sixth; the one cannot be ufed, vyhilft the other takes Place. All other Progreffiorts than thofe we have prefcribed, are not proper, and obferve that they are grounded upon the Preference that ought naturally to be given to the fmalkft Intervals; that is to fay, that as to afcend a Sixth, or defcend a Third, is the fame Thing; the Progreffion of a Third defcending ought to be preferred ; lb of the other Progreffions that bear a like Relation, excepting when Talle requires the contrary, to fuch PaiTao-es where you find that Our Rules are not to be infringed. Thefe Rules will equally hold good for all Keys, whether the Third, or the Sixth, be fiat or (harp. The other Rules that concern four Parts, as well in refpeft to the natural Progreffion of fharp and flat Thirds, as of Difcords, are to be equally obferved. When once a Knowledge of true Modulation hath been attained to, all tkele Rules are naturally obferved, without burthening the Memory, or Mind. CHAP. XXXVII. Of falfe Relations. IN order to avoid falfe Relations in the Progreilion of a (ingle Part, you need only to make it proceed by diatonic or confo- nant Intervals, thofe of the falfe Fifth, the extreme flat Seventh, and the extreme flat Fourth, being permitted and allowed in defcending, but not afcending ; yet, true Modulation being ob- ferved, we may make Ufe of all the known Intervals, provided they do not exceed the Compafs of the Oftave, neverthelefs with a little more Circumfpe£tion, in regard to thofe that we have not named, than to the others ; fome Authors make Ufe of the ex-r treme flat Third in defcending, as from Eiz } to CM) which is left to the Difcretion of Compofers. As to falfe Relations between two Parts, you can hardly fall into that Error, when you are thorough Mafter of Modulation. E X A M- "Principles' of Compqfithn* E X A M P L E. A. *&. 6r B. B. A. or B. A. -e- - ™=5= B. or. B. A. B. A. or B. A. I bo .bo 33TS3Z ~e , You fee by this Example, that the Notes at A reprefent a (harp iCey, and that the Notes at B reprelent a flat Key ; lb that you cannot modulate in one Key half Major and half Minor, nor go from the Major to the Minor upon the fame Key-note, but after a perfect. Cadence, and even this is not to be done without Judg- ment ;|io that true Modulation puts us above thefe Rules, which are almofi ufelefs, when we have attained to a perfect Knowledge ofit;| . CHAP. XXXVIII. Of the Manner of compofing a ^Treble, Or cm Air to & Bafs." IN order to compofe a Treble or an Air to a Bafs, you mull at firft only compofe it in that Key that you know the Mo- dulation of; and when you alfo know the Succeffion of Concords and Difcords (the Manner of preparing and reiblving which hath been fully explained) it will not be difficult to compofe, without any Fault, a Treble, or an Air over a Bafs. Neverthelefs, in order to give a greater Scope to one's Genius, when you know the Chord that each Note is to bear, you may chufe one of the Sounds in each Chord, in order to compofe an Air or a Treble at your Pleaiure. Thus in the perfect Chord, you may chufe the Third, the Fifth, or the Octave ; and, in that of the Seventh, you may chufe it among the others, if you can, for you cannot chufe the Seventh, unl'efs it be prepared, ex- cepting when the Bafs afcends a Third, or a Fifth, whjlft the Treble defcends diatonically, or afcends and defcends afterwards in a diatonic Manner (fee the Example at Chap. XIX.) If even the Seventh could not be refolVed by defcending diatoni.cally upon a Concord to the next following Chord, you muft either not ufe it, or alter the Bafs, except you find that the Notes of the Bats belonged Prirxiples of Compq/ttion, T29 belonged to the Chord of that Seventh, and a Note followed af- terwards, whereby that Seventh could be refolved; and in that Cafe the Seventh before its Refolution always remains upon the fame Decree, provided that one of thofe Notes contained in the fame Chord, and which is found in the Continuation of the Bats, doth not make an Oftave with that Seventh, for otherwife you would be obliged to make the Seventh defcend a Third ; and, making this laft Note afterwards to afcend upon the Concord that ought naturally to follow that Seventh, one might alfo, in the like Cafe, make the Seventh to fall upon the Leading-note, fup- pofing that this Leading-note be a Part of the fame Chord, fo that that Note on which we may defcend a Third after the Se- venth, will make the Sixth to that which in the Bafs will make the Octave to that Seventh, and the Leading-note will then make the Tritonus. E X A M P L E. e- zdz: -s- -e-e- e- :sz c. 4* or d. F. 4* 5 8FF 7 s-e- 6 2 6__ HSZI 3 £5 _7 J±_ 6 2 _ " 11 1 1 9 ... (_j jf, I begin by the Fifth, though I might have begun by the Octave, or by the Third ; but it is better to begin in this Man- in order that the Seventh may be heard unprepared, as we have juft now faid. B, the Seventh, remains upon the fame Degree until C, where its Octave appears in the Bafs ; and in that Cafe I make it de- fcend a Third, in order afterwards to afcend upon the Concord that ought naturally to have refolved it, though, ablblutely fpeak- ing, I might have made it to defcend upon the Guide -vA D, the Seventh, is here prepared by the Third, and remains until F, where its Octave appears in the Bafs ; and in that Cafe I can make it defcend upon the Leading-note F 3 which is a Part of the fame Chord. It is eafily perceived that a Seventh may remain upon the fame Degree, whilft the Bafs makes divers Intervals, becaufe thofe Intervals muft make the Third, the Fifth, the falfe Fifth, or the Octave to that Seventh ; or that the Seventh makes the Third, the Fifth, or the falie Fifth to one of thofe Notes on the R Bafs. i$6 Principles of Compojitlon, Bafs. The fame Thing maybe obfcrved in all the other Dif- cords, if you reduce them to their fundamental Note; if not, as the Bounds and Limits of the Progreffion of Concords and Dif- cords are known, you cannot be miftaken. If a Note may remain upon the fame Degree in the Treble, whilft the Bals proceeds through all the Intervals contained in the fame Chord, as we have juft now fhewn it ; fo likewife a Note in the Bafs may remain upon the fame Degree, whilft the Treble goes through all the Intervals contained in the Chord to that fame Note in the Bafs. If the fame Note in t,he Bafs can carry different Chords, and the Third, the Fifth, the Sixth, &c. be found in each Chord, we may caufe them to be heard indifferently in one or the other Chord. When you compofe only in two Parts, the Treble ought al- ways to end by the O&ave, feldom by the Third, and never by the Fifth. Here follows a general Example. General EXAMPLE. Fundamental Bafs, as a Irregular Proof onJy of the Harmony. Cadence. Continued. Principles ofCompofftimi. Continued. '3* f~\ The upper Part, which we have compofed only to the conti- nued Bats, is full of Faults with refpeft to the fundamental Bafs ; not that they are Faults againft the fundamental Harmony, but only in refpeft to the Progreffion of the Parts ; the fundamental Bafs having been put only as a Proof of the perfe£t Harmony, and from which are chofen thofe Notes that are proper and iuit- able to the Air. A, I fkip at Pleafure through all the Notes of the Chord : From the Fifth, I go to the Sixth JS, though I might have kept upon the Fourth without altering the Fifth that precede*, by rea- R a ion t%i Principles of Compqfition. fon that tliis Fourth is a Part of the Chord of the fmall Sixth £ : I could have gone alfo to the Third. B, C, D, Ey I take four Sixths following, becaufe they are Part of the Chords, though I might have choien any one of the other Intervals contained in each of thofe Chords. F, G y inftead of going from the Leading-note to the Key- note, I go to its Third, becaufe that is not againft the Rules of confonant Progreffion ; and, at the fame Time, that Third repre- fents the Key-note, and makes a Part of its Chord. i7, I take the Fourth, which makes a Part of the Chord of the Second : I proceed afterwards to the Sixth J, and I fall upon the Second, which is a Part of the Chord of the Tritonus K, The Sixth, which I afterwards take at L, prepares the Seventh at AT, which is refolved by defcending upon the Sixth N ; this Sixth, which is the Leading-note, attending" afterwards upon the Key-note O : I afterwards proceed upoa the Third to that" fame Key-note P, in order to prepare the Second Mj The Seconds that are prepared and refolved in the Bafs P, J3, R 9 S, Ty are preceded in the Treble by the Third at P, and by the Sixth atR; they mightequally havebeen preceded by the O&ave, the Fifth, or the Fourth, becaufe "the Second may be preceded and followed by any of the confonant Notes contained in the Chord ; and at !Tyou will find it followed by the Fourth, which makes a Part Of the Chord of the iinall Sixth; though it is to be underftood, in the like Cafe, that the -limited Progreffion of the Bafs -doth not alter. As the Third is the mod proper Conco'rd to prepare and re- folve the Second, it is proper to ufe it in that Cafe, as often as may be : The Fourth^ which we have placed in its ffead at 7", and which creates a Difcord with it, being to fall upon the Note which that Third ought to have'defcended," if it had taken Place with that Fourth, as we fhew it at V% for we are to take it for a general Rule, that when, in Lieu of the Note which ought na- turally to refolve the Difcord in the Treble, we place or fubfti- tute, in its Stead, another Note that makes with it a Seventh or a Second ; in that Cafe we muft make that Note, fo fubftituted, to proceed upon the Note that ought to have followed that Note which doth not appear, and which would have made a minor Difcord with the Note fubftituted ; which may happen in the Chord of the fmall Sixth, between the Third and the Fourth ; and in thofe of the great Sixth and falfe Fifth, between the Fifth and the Sixth; lb that if, in thofe Chords, the Third or the Fifth is ufed, in order to refolve the Difcord, and if they are afterwards to defcend diatonically, confequently, the Fourth or the Sixth, which are the Notes fubftituted, are to pais to or fall upon Principles of Compofition. 13$ upon thofe Notes that ought naturally to have followed tha. Third, or that Fifth. You will find in the other Parts of the Example a Connexion of all that we have faid, obferving that the Key changes at m 9 at which Place we give the Seventh to the Key-note, inftead ot making its Leading-note to afcend upon its Oftave, which then becomes its Seventh ; this~Key-note becoming a fourth Note, by the Chords of the great Sixth and of the Tritonus, at n and 0; after Which we return into the Key of C at J, by Means of the confonant Progreffion of the Bafs which ends at V, and by which we know that the Key-note is C ; and which obliges us to pre- pare this Key by leaving out the Sharp to F, after which the Flat againft the Note B } in the continued Bafs, denotes the Key of F; and afterwards the Key of C is denoted by the || Natural .placed againft the Note B. Thefe Observations, in refpeft to the continued Bafs, may more clearly appear by comparing, one after another, the upper Part and the continued Bafs, with the fundamental Bafs; where you will find that out of each perfect Chord, or of the Seventh, which the fundamental Bafs bears, the Third, the Fifth, the O&ave, or the Seventh is chofen for the continued Bafs and for the upper Part, by giving to thofe two Parts a Progreffion according to our foregoing Rules. Obferve, that when the Progreffion of the con- tinued Bafs is diatonic, as between G t H, J, K, L, &c. the upper Part is often like unto that of the fundamental Bafs : From hence we conclude, that the confonant Progreffion of one Part oftentimes, obliges the other to follow a diatonic Progreffion, in like Manner. that a diatonic Progreffion of one Part often obliges the other to follow a confonant Progreflioa. . CHAP. XXXIX. .... , • • . ..... Of figurative Melody, or of Suppojition and pajjing Notes, WE call figurative Melody what hath been hitherto called Suppofition ; and herein confift the Rules of this figura- tive Melody. It being of an abfolute Neceffity that a Perfection of the Har- mony be heard and manifested upon every Part of the Meafure or Bar, we may, between one Part of the Bar and the next, pafs as many Notes as Fancy and tafle will permit. ARTICLE 4^4 Principles of Composition, ARTICLE I. Of figurative Melody by confonant Intervals^ IN order to pa.fs feveral Notes between eacfy Part qf the Bar by confonant Intervals, we can make Ufe but of thofe Netes that are comprifed in the Chprd to the ftrfr. Part of the Bar, in order to fall afterwards, upon a Note of r.fre Qhord tQ the next Part of tkfr Bar, and fo ©jtw • J M X J M P L E Of a figurative Trebk. 1 i m -r* E3 -.- e- ^=^m=^==^ -— -W— W — — -J— — -fr— -Jjp-lTrr«» 76 5 +*£-». AfJ— •' You fee in the Treble that all the Notes pafs »pon thofe Sounds that are feitable to the Chord %ur§4 *f* tHe Baj$. EXAM- Principles of Compofitioiu EXAMPLE Of a figurative Bafs. *35 m -e- M 3 S83583 * 3 3 5 8 S J 5 35«a Figurative Bafs. 7 7 =zs: I Tj 1 I — _^__ Fundamental Bafs. *3r tr. =P= 5^ v^- 2Si W" :s: — A^- W-- 0—6 fi 5 4- 7 tlSS^S -I — h 7 4 5 :azz i *A- The Figures that are under the Notes of the figurative Bafs, mew the Intervals they make with the fundamental Bafs ; and thole that are over, mew the Chords that thofe Notes bear in the like Cafe. In order to make a figurative Bafs, you may begin by com- pofing only a fundamental Bafs, over which you will compofe a figurative Bafs pretty near in the fame Manner as a figurative Treble, obferving to ufe as much as may be the fundamental Sounds of the fundamental Bafs, efpecially'in the firft Part of the Bar, You Il( nnciples of Compojtion. You muft. always make the upper Part to agree with that which is to be heard with it ; and, if this upper Part was to be heard with the two BalTes, it muft in that Cafe be compofed according to the Rules, in reflect to one and the other of thofe BalTes ; and, in that Cafe, the upper Part ought to be altered at C, £>, where it makes two Fifths with the fundamental Bais, and place, in its Stead, the Notes marked by the Guides a\£. You may alfo compofe a figurative Bafs firft, and place under it a fundamental Bafs intirely, according to the Rules prefcribed for the Progreffion of this laft Bafs ; afterwards you may compofe a Treble more or lefs figurative than that fame figurative Bafs. You muft leek for Variety, by avoiding repeating too often the jame PaiTages; and you are at Liberty either to figurate, or not to figurate, all the Parts of a Bar ; fometimes you may figurate only one Half, fometimes in the Bais, at other Times in the Treble, or both, together according to the Rules. l^ppiiipilll You may make one of the Parts to begin firft, either for a Half, or three Fourths of a Bar, even for one or two Bars ; fo of the other Parts, in Cafe there be more than two. You may begin by whatever Part of the Bar you think proper, and you may caufe one of the Parts to reft for a While ; but, if it fhould be the Bafs, it can be but for a Bar or two at moil, for the continued Bafs muft always be underftoodj though you ihould be willing that one Part onlv fhould be heard. A i rinciplet of Compofit'mn, »37 A Dot placed after a Note is to be deemed as the fame Note, and is generally concordant with the other Parts, by reafon of its being commonly ufed upon the accented Part of the Bar. ARTICLE II. Of figurative Melody by diatonic Intervals. YO U may pafs as many Nates as you pleafe between each. Part of the Meafure or Bar, and, if they proceed bv dia- tonic Intervals, it matters net whether they be of thofe'eom- prifed in the Chord, provided that the fir ft be one of the Notes of the Chord; but if, after feveral Notes in a like Progreflion, you fhould proceed by a confonant Interval from the laft Note to the firft Note of the fubfequent Part of the Bar, then this laft Note rauft alfo be comprifed in the Chord. If the Parts of the Bar be of a flow Movement, fo that they jnay be divided into two equal Parts, you will always do well to divide thefe paffing Notes into an equal Value, obferving that the •firft Note of each Divifion, or Part of the Bar, be of thole com- prifed in the Chord. Tafte obliges us fometimes to deviate from this Rule in refpect that, in a diatonic Progreffion, the firft Note of the Divifion, or Part of the Bar, is not always comprifed in the Chord that ought to be heard ; but you may obferve that this firft Note is only- then admitted as a paffing Note to the very next, which makes a Part of the Chord, before its Time or Value is expired. JS X A M P L E \sm 33E5EH te E E?=iiEE Continued. Principles of Ccm-pojitton. Continued. ** ~c — TT' : X ■w- 4* 6 :&—.::: A«/ — . This Meafure, or Time, though in two Parts, is divided al- Dioft throughout into four Parts, and you may fee that the Firft of the two Crotchets is always comprifed in the Chord. In the Part A, the Firft of the two laft Crotchets is not com- prifed in the Chord, by reafon that the Melody proceeds diato- nically from one Part of the Bar to the other, and the two firft Crotchets, which do not follow this Progreffion, are comprifed in the Chord. Each Note in the Part of the Par B is to bear a Chord, by di- viding the Time into four; by reafon that, as foon as the Key-? note appears after its Leading-note, it muft bear its natural Chord : If that fame Key-note appeared immediately afterwards in the following Bar, and that the Melody refled there, the Time, or Part of the Ear B, ought not to be divided ; but the Melody which refts upon the Fifth or Governing-note, creates, as it were, in Principles of Compqfithft. 1:9 :n that Cafe, an irregular Cadence, from the laft Crotchet, at -the Time Z), to the fubfequent and next Note. The firft and Third Crotchets of the Time C are not of the fame Chord, but pais to the fecond and fourth Crotchets, which are Part of the Chord ; for it was abfolutely neceifary that this laft Crotchet fhould be comprifed in the Chord, fince it pafles from one Part of the Bar to the other by a conlonant Interval: You will find the like PafTages at F and D. The Dot at D reprefents the preceding Note, and the Chord of the Tritonus, figured over it, keeps on until the Expiration of the Dot, fo that the Tritonus is relalved but upon the next fol- lowing Part of the Bar. Thus we have endeavoured to explain what hath hitherto ap- peared but under very confuted, oblcure, and abftrafled Rules ; and it is by Means of this Facility and Liberty of figurative Me- lody, and by inverting the Chords, that proceeds that incompre- henfible Variety in Mufic. CHAP. XL. Of the Manner of compofing a fundamental Bafs to a Treble. THE fundamental Bafs is a fure Method for finding that which is proper to a Treble already compofed, efpecially for thofe Perfons who have not a natural Genius or Tafte to feel, as it were, that Bafs at the fame Time that the Treble is com- pofed ; for every Melody or Air hath its natural Bafs ; and, for ever fo little that we are fenfible of a perfect Harmony, we natu- rally fing the Bafs to all Cadences, when we hear the upper Part, which is fufficient to know the Key we fmg in ; and thus from one Cadence to another, whether it be a perfect or an irregular Cadence, for there is no Difference in the Treble between the falfe or flying Cadence and the perfect ; we know the Alteration of the Keys ; and the fundamental Bafs (which bears only the perfect Chord and of the Seventh) will more readily fliew it. EXAM- Principles of Comprjitrttt. EXAMPLE. Of the different Progrejfions of a Treble in Cadences. F.FhtKey. G. | J Perfect Cadencesj "* | {harp and flat Keys. Perfect or irregular Cadences. Sharp H. Key, Flat J. Key. I Sharp L. Key :qzzs:z: :sz=srr FlatM.Key. I Irregular Cadences. All thefe Cadences are in the Key of C only, though they bear an Affinity to other Keys. The perfect Cadence A afcends from the Leading-note to the Key-note, in fharp and flat Keys, although it might have af« cended from the fecond Note to the third, in flat Keys, accord- ing to the Example F. The perfect Cadence B defcends from the fecond Note to the Key-note, in fharp and flat Keys, though in flat Keys it might have defcended from the fourth Note to the third, according to the Example G ; fo that the fharp Key of C and the flat of A have a great Relation one to the other in thefe two firft Cadences ; and thefe two Cadences may equally take Place as well in a fharp as a flat Key, where the Diftance is but of a fiat Third, as tram," C to J, from F to JD, from G to £, &c. The Cadences 6", Z>, F, G, which are arbitrary between the perfect; and irregular, are not diftinguifhed but by the Progreffion given to the Bafs, either by afcending a Fourth upon the Key- note, in order to make a perfect Cadence, or by defcending a Fourth upon that fame Nate, or upon the Governing -note, m order to make an irregular Cadence : When we fay or upon the Governing-note, it ! is by fuppofing that thefe Cadences can repre- fent another Key than that of C; for thofe at Cand at D may be taken for irregular Cadences in the Key of D, and that at D may be alfo taken for an irregular Cadence in the Key of F; thole at F and G may be taken for perfect in the Key of Eh. ; but the true irregular Cadences, upon the Governing-note to C, are thoie in the Examples H 3 J, L 3 M s although the Example H may Principles of Compofiticn. 14 s: may reprcfent a perfect Cacknce, or an irregular, in the Key of £& ; that at J may reprefent an irregular in the flat Key of Ay that at L may represent a perfect Cadence in the Key of Z>, and, finally, that at M may reprefent an irregular in the iharp Key of £i[, in the flat Key of G, and in one and other of EJZ. The Ufe that may be gathered from thefe arbitrary Cadences in the Treble, is this : r. You mull compofe your upper Part, or Treble, but in the fh?rp Key of C, or in the flat Key of D, Supposing that the other Keys are not fo familiar to you, and in order to know whether this upper Part is truly compoied in, one of thofe two Keys, as you cannot begin it but by the O&ave, the Third, or the Fifth, you will obferve where the firft Cadence happens, which commonly is at the fecond or fourth Bar ; fo that having begun by C, E, or G, which are the Octave, the Third, and the Fifth to C, if your firft Cadence fails upon Z), you will not therefore be in the Key of D; for, if it was, you fhould have then begun by D, F, or A y which are the Oftave, the Third, and the Fifth to D. Again, if you are obliged to add fome ]g or fome jj to the Notes for the Sake of the Melody or^Air, thefe Signs will fhew you the Key at once, according to the Explanation we have given of it in Chap. XXIV. and XXV ; for, if you had begun by C, this C makes as well the flat Third to A and the Fifth to F, as it makes the Oftave to C ; and it can be but by fome ]g or JS, and alio by the Cadences, that we can diftinguifh the Key ; though, if the Air be compoied in a natural Manner, the laft Note will ihew it, for it ought naturally to be the Key-note. 2. As foon as you are certain of the Key you compofe in, youi muft ufe all the Cadences that are proper to it ; and, when there happen fome that are foreign, you muft then have Recourfe to the above Example, obferving what follows : 1. The upper Part muft always make the Third, the Fifth, the Oc\ave, or the Seventh to the fundamental Bafs. 2. In the fundamental Bafs the Preference muft be given to the Progreffions that are the moft perfect ; fo that the Fifth in de- fcending is to be preferred to that of the Fourth, this Laft to that of the Third, and this to that of the Seventh, obferving that to afcend a Second is the fame as to defcend a Seventh, £sV. If the upper Part could not agree with the Bafs by making it defcend a Fifth, you muft then feek this Chord in a Pro- greffion of a Fourth, a Third, or a Seventh, preferring the moft perfect. 3. If you intend to follow the Stile of the fundamental Bafs, you muft not figurate the Treble, becaule the figurative Melody doth 142 Principles of Compojltioii. doth but puzzle Beginners ; fo that in that Cafe every Note ought to be of the Value of one part of the Bar. 4. You muft at firft apply only in compofing Airs of Chara&er, fuch as Gavots, Courants, ijfc. becaufe the Cadences happen almoft every two Bars. 5. If in your Airs you fhould perceive fame Cadences foreign to the Key, you muft obferve whether they end the Melody or not ; if they do, then the Key changes generally to the fifth, the third, the fourth, or the fixth Note of the Key you quit; which may be known by comparing thofe Cadences with the preceding Example, wherein you will find that, if one of theie Cadences ends -7?—b-s- * e z Q : Thus, ffa <2Z. -e- *e- 2: *e zsz Key of F, ofG, ofD, of E, of A, it reprefents a perfect Cadence in one of thole Keys, in the fame Manner as this $£h3- s: reprefents a perfect Cadence in the Key of C; {6 of^the other Cadences that bear a like Relation ; but, if the Melody is not abfolutely ended, you muft let the Bafs follow its natural Road, by preferring (as we have faid) the more perfect Progreffions as much as poflible. 6. VVhilft the upper Part makes the Third, the Fifth, or Oc- tave to a Note already placed in the Bafs, you may let this Note remain without altering it, unlefs you difcovered that it could be done without interrupting the natural Progreflion of the Bafs ; and, in that Cafe, Variety (which is one of the principal Beauties in Harmony) requires it. As the firft Part of the Bar is the chief or principal, if you fhould perceive that the Note in the Bafs, which could have been placed in another Part of the Bar, agrees with the firft Part that precedes or follows it, it will be better either to advance or poft- pone this Note, in order that it may be heard upon the firft Part of the Bar, obferving two Things : Firft, that if the Note that follows the firft Part of the Bar can be ufed in this firft Part, it is then that you muft ufe, in this firft Part, that Note which you intended to place after it : The Second is, that if the Note which you place in the unaccented Part of the Bar is the fame as that which is heard in the next Part, without being able to place one or more Notes between them, it will be better to leave in the Bafs that Note that was heard in the firft preceding Part, if pof- fible ; Principles of Ccmpojltlon. M3 fible ; otherwife you muft feek for another that is not the fame as that which is to appear in the very next fucceeding Part. EXAMPLE. —Q- zoz _C. e- T. l=±± -— - 1 1 1 1 ©i i ©i j nous:: e-l "~D s The Example H is the beft, by reafon that, as the Note which is heard in the fecond Part of the fecond Bar might ferve in the firft Part of the fame Bar, it ought to be preferred. Mother E X AM? L E T e-l ~3— F- -e- Q. see: B. -_Q- D. -e- ^S— ^- F idzzizd: -e- 9- -e- zszsz -e- 1 can keep upon the fame Note of the Bafs in the firft Bar of the Example A, though I might alter it as in the Example B 9 be- caufe I can place another Note between that of the fecond Part of the firft Bar and that of the firft Part of the fecond Bar; whereas in the Example C and F I am not to make Ufe of the fecond Note of the firft Bar in the Bafs, becaufe it ought to be heard immediately upon the firft Part of the next Bar ; fo that I make Ufe of the Note that hath already been heard in the firft Part of the Bar D t becaufe it agrees with the fecond Part j and 144 Principles of Compq/iti&n. I clrufe another "at G, becaufe the fame firft Note cannot be con- cordant in this Place with the fecond Part. 8. It is oftentimes neceffary to divide a Note in the Treble into two equal Parts, in order that two different Notes in the Bafs may be heard and may agree with that fame Note in the tipper Fart ; and this is done for the better preferving the confonant Progreilion of the Bafs, and that the moft perfeft Progreflion may be heard between thefe two Notes of the Bafs ? and the next. EXAMPLE mrf^r =e=fe £ zs~ }z: mm -t-p 1 7 nzzziz — I— -e- znz: This Divifion is alfo imfed", in order that the moft fnitable Notes, to the Key 'may be heard on the principal Parts of the funda- mental Bafs ; which Notes are the Key-note, its Fifth, or Go- verning-note, its Fourth, its Sixth, and fometimes its Second : and thus, by Order of Perfection, its Third is feldom ufed, and never ks Seventh, in whatever Part of the Bar they happen to be ; for, when it cannot be avoided, it is certain that the Key changes, as may be known by fome % or J2, or by fome foreign Cadences. q. The principal Parts of the Meafure or Bar are thofe where the firft Difcord is to be heard, when it is prepared ; for, if there i>e found feveral Difcords following, you muft only take Notice of the Firft ; and a Difcord unprepared cannot be ufed but in a diatonic ProgrefSpn of the upper Part, by defcending three De- grees, or by afcending and defcending immediately afterwards, whilft the Bafs afcends a Third, or a Fifth, in order afterwards to defcend a Fifth j and then, the Difcord is found in the Middle, •f thefe three Degrees* £ X'A M- Principles of Ccmpofition. EXAMPLE *4i ._Q._e rs- — _ B 1 _3_ — , Inftead of making the Bafs to afcend a Fifth in the firft Bar of the Example, you may only make it afcend a Fourth, in which Cafe the Difcord will not appear ; and it is by this Manner that you may tranfpofe a perfect Cadence, into an irregular, and an ir- regular into a perfect ; fee the Notes A, B, where another Note may be placed upon the Guide a*c in Lieu of that marked with an A: The Notes A B making a perfect Cadence, and the Note Ji, placed in the Room of the Guide, making an irregular Ca- dence with the Note B. The Guides, placed over the firft Note of the Bar, fhew the Progreffion that the Bafs might alfo follow on the like Occafion, by putting this firft Note in the Place of either of the Guides. / You muft remember that there is no other Difcord but the Seventh in refpeft to the fundamental Bafs, and that the other Difcords arife by its being inverted, that is to fay, by chufing. for Bafs one of the Notes that make up the Chord of the Se- venth, which the fundamental Bafs ought to bear ; wherein muft be obferved all that we have faid concerning it in Chap. XVII, XVIII, XX, XXI, XXII, and XXVI. There are fome Paffasres where the Seventh has a s;ood Effe£t againft the fundamental Bafs without being prepared, even whilft the upper Part makes a disjointed Interval ; but then the Note in that Bafs, that hath been heard before the Seventh, remains upon the fame Degree ; fo that it will always be proper to ufe the Seventh in this Manner, provided that the upper Part de- fcends diatonically immediately afterwards, and that the Bafs may afcend, in this Cafe, a Fourth, in order to make the Third with the upper Part after the Seventh^ j E XA M- Principles of Comprjitim, EXAMPLE. [-^_|^_ D Q_ Q O Z§ZZZZ ZQZ 1 mj,w U-^— A. D. F. L: izozzs: zo: \~/ -e— 8- :sz The Treble proceeds by Skips or disjointed Degrees between the Notes y^ and B, where the Seventh might be heard upon the Note B, if we vyere willing to keep the firffc Note of the Bafs oh the fame Degree • but as the upper Part doth not defcend after this Note B, and, if the firft Note of the Bafs had remained, it could not have made the Third with the Note J by afcending a Fourth; the Bafs muft be altered, as we have done it, by pre- ferring its moll perfeft Progreffion ; and what you dp not find between thefe Notes A> B, J, yod will find it between the Notes C, D, F, according to the Explanation we have jull now given, of it. This is what was alfo called Suppofkion, or a Difcord for the Sake of the Melody or Air ; but this' Difcord takes £lace from the firft Note in the Treble, whilft that of the Bafs remains upon the fame Degree, in order to receive this Difcord*, which appears afterwards, as may be obferved, by making all the Sounds of the Chord of the Seventh to be heard together upon the firft Note of the Bafs that llrikes with the Note at C; con- sequently the Treble may again pais after this Seventh upon Other Notes of the fame Chord, but it will always return to a Note that fhall make the Third to that Note that afcends' a Fourth in the Bafs G } or, at leaft, to a Note that fhall make tliQ Oftave to it. E X 4 M P L E. — e- 7 3 78 :§z£Z =Dz||z^z|z§zgz zzz ] 7 7 7 G. i 3 7 7 7 H. 8' : ! ^1? 1 ^ M* n l-e- -Q-3- V — s-l-e-G- — Inftead of making the Bafs to afc«,nd a Fourth, we might make it to afccnd only one Degree^ which would then create a falfe or Principles of Compofitinn. '47 flying Cadence; but that can take Place but in a borrowed Bafs, dr inverted from the fundamental, which depends, in that Cafe, Upon the Fancy or Tafte of the Compofer in the Middle of a Piece only, provided that the Bafs did not make two Fifths toge- ther with the Treble. 10. When you perceive divers Cadences of the fame Species iri the fame Key, you muft fee if one of thole that are in the Middle of the Melody, and which doth not make an abfolute Conclufion, would not be fuitable to a Cadence in another Key, in which Cafe it would then be proper to give it this foreign Cadence for a greater Variety in Harmony ; for an Air becomes infipid, when the fame Cadences are too often heard : And, fup- pofing that your Tafte would not fuffer you to alter the upper fart, you muft at leaft endeavour to make this Variety in the Bafs in the Middle of the Air, and efpecially in thofe Cadences that do not declare an abfolute Conclufion, If you are in a fharp Key, the foreign Cadences that bear aa Affinity to it, can be taken but in a flat Key, the Key-note of Which being but a flat Third under that of the fharp Key you are in ; and, if you are in a fiat Key, they can only be taken in. a fharp Key, the Key-note of which being but a fiat Third above that of the flat Key ; and obferving that this Difference may only appear in the Bafs, fince the Melody, or upper Partj will not be thereby altered. See the following Example. EXAMPLE A. s e- I5ZZZ Perfect Cadences in the Key of C, B. A. -e zzszz n the flat Key of A t :hz=s: in the fharp Key of Q ■e- iszzt- in the flat Key Hi A. 321 :sz: zszzzzz- --~gzz c. D. C. D. Irregular Cadences in the fharp Key of C, ZZSZZ^ZZ in the flat Key of^, in the fharp in the flat Key SEE zzzo: Key of C, oi A. zizzs: I3ZZZZZ :cc i *4 ^ Principles of Compofition. The perfect Cadences A B, and the. irregular Cadences C D? in the upper Part, may be naturally found in the fharpTCey of C, or in the flat Key of ^; fo that, if you are in one of thofe Keys, you have the Choice of one of thefe Cadences for the other Key : If you are in the Key of C fharp, the fame Cadence may ferve for the flat Key of A\ and, if you are in this laft, the fame Cadence may ferve for the other Keys that, bear the like Relation ; fuch as the flat Key of D with the fharp Key of F t and the fharp Key of G with the flat Key of E. This Manner of tranfpofing a Cadence from one Key to an- other is a great Help, when you are abfolutely determined to change the Key* You may alfo make Ufe of the falfe or flying Cadence in either of the above Cafes. ii. The irregular Cadences are excellent in the Middle of an. Air; and, when the Air or Tune is divided into two Parts, they may ferve to end the firfh Part ; but you muft not make a con- ftant Practice of it, they being rather to be ufed in the fecond, fixth, and tenth Bars, than in the fourth, eighth, and twelfth, where the. perfecf Cadence is more iuitable and proper; and, when a perfect Cadence happens in the fixth or in the tenth. Bar, yott. may ufe in its Stead the falfe or flying Cadence. 12. When you tranfpofe a Cadence from one Key into another^ it is fometimes proper to prefer the leaf! perfect Progreffions of the fundamental Bats to the moil perfect ; but the Whole is to be done with Judgment and Dilcretion. J 13. All thofe that compofe an Air or Melody, as, their Fancy / leads them, make no Attention whether it be figurate, or whe- ther it proceeds by conjoint Degrees.; fo that, if it be figurate, they r. re not fufiicienlly {killed to diftinguifh thofe Notes that make Harmony with the Bafs, from thofe that are only for Tafte; and, if they proceed by disjoint Degrees, or by Skips, they are fearful of making two Fifths or two Octaves to be heard toge- ther with the fundamental Bafs, by not knowing that, in that Cafe, the Melody or Treble follows the Road which the funda- mental Bafs ought naturally to take ; and it is for this Reaibr! that we are obliged to compofe a Bafs different from the funda- mental that may intvrely agree with this Part already compofed : Therefore, knowing by the fundamental Bafs the Chords that are neceifary to be ufed in the Continuance of the Air, it is not difficult to chufe, out of thofe Chords, a Note for that other Bafs, that fhall agree,in Harmony and M.elody,with the Part already compofed ; for it is proper to know that two Octaves or Fifths following, do n6t deftroy the fundamental and real Harmony, but they are forbidden, in order to avoid falling into a dry, intipid, and tueibme Monotony in,, a- Succellion of. Chords j fo. that, after bavins Principles of Compofition. 14^ having eftablifhed the Rules of Harmony upon the moft natural Progreffion of the Bafs, and of the upper Part or Treble, finding the Impoflibility there is to keep that natural Progreffion to the Bafs, as foon as it can be permitted to borrow that Progreffion for the Treble, or upper Part, we are obliged to eftablifh other Rules for the reciprocal Progreffion of the Parts that are to be heard together, in order that the fame Part, which is to be corn- poled, may be fuitable and proper to that already compofed. Yet thefe new Rules are grounded upon our firft Rules, where, ac- cording to the natural Order and Dilpofition of the Parts, we do not find two Octaves nor two Fifths together : And we alfo find all the Difcords reiblved as they ought and fhould be, and pre- paredj or unprepared, according to the moft perfect Progreffion of the Bafs. Sometimes we may go wide from the natural Progreffion of the Bafs, in order to avoid thofe frequent Concluiions which we feel in its moft perfect Progreffion, by applying to the Bafs one of the Notes of each concluding Chord ; by this Means we keep in the Melody and Harmony that Sufpenfion which the Subject requires ; for an ablolute Conclufion is proper only to a final End of the Senfe 1 The following Chapter will more fully clear up this Article. CHAP. XU. The Manner of comppjing a continued Bafs under a Treble. THE true continued Bafs ought to be the fundamental ; but, as Cuftom gives another Name to that which is dictated to us by Tafte, we diftinguifh it therefrom by the Epithet conti- nued. We have already faid, at the Beginning of the preceding Chap- ter, that thofe who have a Tafte naturally felt that Bafs which, was the moft fuitable to all Sorts of Airs ; but, notwithstanding this natural Gift, it is difficult to keep up the Truth, when it is not fupported by Knowledge ; and this Knowledge is not fufficient to attain to a Perfection, if a true tafte is wanting ; for the Li- berty we have of chufing, among the Sounds of a Chord, thofe that we think proper for a Bafs to a Treble ; yet it doth not ftri&ly direct us to chufe thofe that are the moft proper ; and we have no other Rule for Tafte, but Variety in Compofition; which muft'be endeavoured to be obtained by obferving what follows : 1. We 1 r*e Principles of Compofition, i. We.muft endeavour to avoid two O&aves and two Fi together, by ftri£tly obferving the Rules we have given in Chap.' XIV. XVIII, XX, XXI, and XXX, for the Succeffion of Con- cords and Difcords. 2. The fundamental Bafs being compofed, you 1 muff obferve the Defign in your Treble, the Air it expreffes, its Movement, and every Thing in it that is lingular and remarkable ; and then you mull endeavour to give the fame Expreffion in your new Bafs : You m'uft avoid final Cadences where the Melody doth not require it, by chuling out of your fundamental Chord the Sounds you think proper, fo that they may agree with the Tre- ble, according to the Succeffion of Concords and Difcords. If you ufe fome Difcords, take Care that they be prepared as they ought to be, ana* regularly refolved, according to the fixed Progreffion of each Sound that the Chord of the Seventh confifls of; afterwards, for Variety, you muft endeavour to ufe (between your Parts) Concords or Difcords of different Species ; for the Treble being compofed in fuch a Manner, and it being left to your Choice to take for Bats what other Note of the Chord you think proper, you muft obferve, that in one Place you have taken the' Sixth, followed by another Concord or a Difcord ; and that in another Place, though you might do the fame Thing, yet you' might give another Turn to your Bafs, fometimes by ufing the 1 Tritonus refolved by the Sixth, fometimes the falfe Fifth re- folved by the Third, fometimes the Seventh refolved by the Sixth, the Third, or the Fifth, according to the different Progreffion that you may give to your Bafs ; or elle you may caultf to be heard, between the Parts, the confonant Notes only, of which the Chord of a Seventh is compofed, fuch as the O&ave, the Fifth, or the Third, or, in an inverted Manner, the Sixth, or the Fourth : You may alfo make Ufe of the Chords by Suppo-. lition or borrowed, when you feel that the diatonic Progreffion of your Bafs leads you to it ; for this Progreffion is always the moft finging, and is to be ufed as much as may be, efpecially where there appears no Conclufion. And you are to remember, that all minor Difcords of a Chord, by Suppofition, are to be prepared by the upper Part, which fyncopes whilft the Bafs af- cends ; and, if it defcends, it can be but by Degrees disjoint or by Skips ; that the Chord, where the major Difcord takes Place,* requires the Precaution that we have given it, either in the Succeffion of the Oftave, or in what we have laid in Chap. XI, XXII, XXXI, XXXIV, and XXXV, of the extreme fharp Fifth, of the extreme fharp Seventh, of the Tritonus, and of; the extreme fharp Second ; and that the Second is to be prepared' by the Bafs which fyncopes. Afterwards, when you perceive that your Melody can conclude in a certain Place, )ou will then follow Principles of Cempofitlon. 151 follow the Progreffion of the fundamental Bafs : Thus will your 'Bafs be compofed with Art and Tafte. EXAMPLE. Fundamental Bafs. Obferve, that in the fourth Bar I might have tranfpofed the perfect Cadence of the Key of C into an irregular Cadence in that of A, which, for Variety, would have been proper in this Cafe. In the firft and fecond Bar of the fundamental Bafs, there are two equal Progreffions A B ; therefore, I keep that which hath the neareft Relation to the Cadence for the -fecond Bar ; becaufe that is the Place where the Cadence is moft commonly felt, ob- ferving that it is an irregular Cadence in this Place, and that in the fourth Bar it is a perfeft. _Again ? to return to the firft Bar, I give a diatonic Progreffion to the continued E&fs which agrees in every refpedt with the Tre- ble,, *£$ Principles of Compofition. He; and, in order to continue that Progreffion in the fecond Bar, upon the fecond Part of the Bar, I take a Note that makes a Seventh with a fundamental Bafs, and which is refolved by the Third to that fame Bafs, and which agrees with the Treble ; and I continue it until the Place where the perfecl Cadence is felt, and then I follow the Progreflion of the fundamental Bafs : I again feek for this diatonic Progreifion in the following Bars, where I find that the laft Note of the fourth Bar may continue upon tile fame Degree, in order to make the Third with the fun- damental Bafs, and theOclave with the Treble ; and, afterwards, the Sixth in the fifth Bar with the Treble, and the Seventh with the fundamental Bafs; and again, I find the Ninth in the fixth. Bar, and I do not follow the Progreflion of my fundamental Bafs, but at the final Clofe only. Befides, what leads me to know the Chords which the Notes in the continued Bafs are to carry, are the Intervals they make with the fundamental Bafs ; for as I know that this laft Bafs can bear but per feci: Chords, or that of the Seventh, when it is truly compofed, confequently, thole Notes that make the Third, the Fifth, or the Seventh to thofe in the fundamental Bafs, cannot carry but thofe Chords that derive from the perfecl: Chord, or that of the Seventh. So that I could equally place Figures o^ver the Treble, if I was willing, that it fhould bt*. ufed, or ferve for a Bafs : It is alfo for that Reafon that I have figured the Ninth upon the firft Note of the fixth Bar, becaufe that Note is found to be a Third under or a Sixth above the Note in the fundamental Bafs, which, confequently, cannot be admitted in Harmony but by Supposition ; fb that by the Chord ©f the -Seventh, which the fundamental Bafs carries, I find that Note can bear but that of the Ninth, though the Ninth doth not appear in the Treble ; but you will obferve, that the Fifth which is found therein, makes a Part of the Chord of the Ninth, and that this fuppofed Ninth is prepared arid refblved according to the ftricleft Rules. It would be endlefs, if we were obliged to reafon in this Manner upon all the different Ways that a continued £afs can be diverfified ; but if you will make the proper and neceflary Re- marks upon the feveral Examples that are contained in this Book, by applying to each of thofe Examples thofe Things you would be inftrucled in; and if, for the like Purpofe, you confult the Works of the beft Mailers; you will fooa overcome all Diffi- culties. CHAP. Principles of Compojition. V55 CHAP. XLII. . VJeful Remarks upon the foregoing Chapter. J."\7"OUmay compofea Bafs, under another Part, witliout the j[ Help of the fundamental Bafs, by the Knowledge of the SuccefTion or Progreflion of the Concords or confonant Notes, (which Succefljon we have fixed in fuch a clear Manner, that it cannot admit of any Doubt) provided that you remember to pafs from a perfect Concord to an imperfect, and from this to the other, to avoid two perfeft Concords together, when it can be done ; whereas the imperfect Concords may follow each other (though you muft not make too frequent ufe of this Liberty, by reafon that it would be a Fault againft that Variety which ought to be ufed) and to give to that Bafs a diatonic Progreffion as often as may be, though a confonant Progreffion is to be fome- times ufed, efpecially in the chief or principal Cadences, where it is abfolutely neceffary. 2. You may compofe a Bafs upon the Succeffion of the Chords 6 fixed in the Rule of the Oc\ave of 7 and 2, — , of 9, and others. 5 See Chap. XI, XXI, XXII, XXVII, XXVIII, and XXIX. 3. For Varietv, you may make Ufe of the Examples where the feveral different Ways of making the Bafs to proceed under the fame Treble are fixed, fee Chap. XVII. obferving that, of the four Parts that are contained in thofe Examples, it may happen that one of thGfe Parts will always be like that which you mall have compofed ; but, left you fhould be miftaken, you muft ob- fexve whether thefe, Progreffions are in the fame Mode or Key ; and, for that Purpofe, you muft not confult the Notes by their Names, but by the Rank and Order they ftand in the Key you are in, and in that of the Examples. And, as thefe Examples are compofed in the Key of C, you will find that a Progreffion from the Third to the Fifth, or from the Sixth to the Fourth, &c. will always bear the fame Chords in any Key whatever. See Chap. XIV. and XVII, of the Manner of preparing and yefolving Difcords. See alio Chap. XXIV. and XXVI, Art. I, II, aqd III, of the Manner of removing from one Key to another ; how they may- be diftinguifhed, and how you may know what Chords are to. be given to the Notes of a Bafs in any Progreffion whatever ; be- cauie the Knowledge of all' thefe Things conne&ed, will free you from an infir.ite Number of Doubts that will ftart at every Inftant. U When I. '54' Principles of Comp'njiihn," "When once you are tolerably well grounded, and Mnfter- of Jill thefe Articles, you will easily difcover afterwards, the Manner of pracfifmg Licences ; You may figurate the Melody or Treble and that of the Bafs, if you think proper, by obfervin'g, the prin- cipal Parts of the Bar, and the Note that is to bear a Chord in each Part, in, order that you may rightly- and truly figure your Bafs ; and, when you doubt of the Chord, you mnft place a fun- damental Bafs under thofe two Parts compofed, by which you, will fee whether you have committed any Faults, and what Chords the Notes in the continued Bafs are to carry ; obfcrving that the Note which makes the Third, the Hfth, or the Seventh to tha$ in the fundamental Bafs, can carry, but a Chord derived from it; or, if that Note in the continued Bafs is a Third or a Fifth below- that of the fundamental, the Chord will then be by Suppofition, and in that Cafe you muff, examine whether it be ufed properly, and according to the Rules. As foon as your Bafs is well and rightly figured, nothing is more eafy than to add to it two or three Parts, unlefs the upper Part, being too far fought, fhould hinder you from ranging thofe. other Parts in all their Regularity ; which is the Reafon, that, the more there are Parts, the more we are obliged to follow in the Bafs a fundamental Progrefhon ; though we have given divert Examples of making a Bafs to proceed diatonically, or by conjoint Degrees, in the Progrefiion ot anOflave, as well amending as. descending, whether it be by the common Chords, by the feveral 6 Chords of Sixths, or by thofe of 7 and 6 X of 2 and — , of 9, &ci $ A We now fhall fhe\y you what is to obferved in a Compofitioi^ of feveral Parts. CHAP. XL1IL Rules to be obferved in a Compofuion oj two, three, or four- Parts. IT is difficult to fuxceed p.erfecfly in Pifcccs of two and three Parts, if all the Parts are not compofed together, by reafon, that each Part is to have an eafy Singing and gracious Melody * and a fkilful Man feldom compoles one Part, without feeling, at, the fame Time, theLfftCtof the other Parts that are to accom- pany it. 1. Although one Part is gene-rally chofeh for containing the fineft Melody which is called the Subject, yet, if the other Parts, are Principles of Ccmpofition. J 55 &re left naked, that diminifheth greatly the Beauty of the Sub- ject; and it can be tolerated only in what is called a Recitative, where the Bafs and the other Parts ierve only to fill up the Har- mony ; but, otherwife, the Melody in two or three Parts are to be pretty near alike. The Ids there are Parts, the mere Variety is required in the Chords ; it is, therefore, for Pieces in two Parts that this Rule requires a greater Striftnefs. 2. When you compofe in three Parts, the Chords muff, be filled pp and completed as much as may be ; and the bell Rule for that Purpofe is, always to uie Thirds and Sixes, at leaft in two Parts ; .the Oc\ave ought to be ufed therein but , fcldonij unlets the TJ>efign, the * Fugue, or the Melody, leads us to it, efpecially in perfect Cadences, where each Part generally ends upon the Key- note. * We fhall fpeak of Defign, and of a Fugue, in the laft Chapter. EXAMPLE _»._£._i — _«. — ,, 3EEEEE:E±=E SIllSgE M fczttitz 4' _p_t_:-i-:p-P-:~ ■I— i 6 -U - fcfife w~P-^-*- ' -H _».:-i.:^: JS^s SfES -p-P—- - I — I ~tZ TZTTJI '*-F- — I -J-r^H^-fe :^:z:^i:fzf:==z: 6 U z Continued. 1 46 Principles of Compofttiofi. Continued. _ w_ --ed thefe Observations, it will not be improper to difclofe what Experience hath taught us upon this Subject. iv" The Fifth muft always anfwer the Key^-note, and the Key- note to the Fifth in the firft and I a ft Notes of the Fugue ; and we cannot go from this Rule but in the Middle of the Air, where it is permitted to trie or borrow the fourth Note in Lieu of the Fifth, and the fecond Note in Lieu of the Key-note, in Order to make the Succeftion of Melody more equal and conformable one to another; there being, by this Means, but four Degrees from the fecond Note'to the Fifth afcending, or from the Fourth to the Key-note defcending, from which you may compofe an Air pretty near like that which is within the Compafs of the four Degrees, from, the Fifth to the Key-ipte afcending, or from this Iaft unto the other defcending : The fame Liberty will alfp furnifh us with five Degrees from the fecond Note to the Fifth, defcending, and from the fourth Note to the Key-note afcend- ing, according to the five Degrees frorn the Fifth to the Key cteiceading, or from this laft unto the other afcending ; and, when we lay that the Melody formed from thefe borrowed Notes will be pretty near alike that which is heard between the Key- not^and its Fifth, it is by reafon that it cannot abfolutely be the fame, on Account of the diatonic Degree of each Mode, the Notes of which cannot be altered by any new Sharp or Flat, faving in fiat Keys, where a Flat muft be added to the fixth ■■ Note, when it defcends ; and a Sharp to the Reading-note, when it afcends ; being at Liberty, alio, to add fometimes a Sharp to the Third of flat Keys, and to the Fourth of all Keys, when they anfwer the Leading-note ; as we have done it in the fixth Example, to the Notes marked with a T, provided that thofe Notes make the fharp Third, or Sharp Sixth, with the Bafs. 2. The Bafs of the Fugue being found,, you may feek, alfo, for the other Parts that might accompany the Melody and the Bafs ; wherein may be obferved, that that Bafs and the other Parts will follow pretty near the fame ProgrefT.on with the firft Melody and the Anfwer y and alio, that the £als will bear the fame Chords in Principles of CompofJinn. 161 in one as in the other, if it be truly imitated ; fo that by the Means of this Bafs, and of the other Parts, we may find that of making feveral Fugues to be heard together, or to compofe an- other Species of Fugue, called a Canon, of which we fhall fpenk hereafter. 3. The Melody of one Fugue may admit of feVeral different Baffes ; it may be fo compoied, that it may be more fuitable to the Bafs, than to any other Part; which is indifferent, for, by inverting the Chords, we can compole various Baffes, or caule one Part to ferve as a Bafs, though the Melody might be more proper for a Treble; but nothing is more pleafing than to ufe alternately thele different Ways of accompanying a Treble or a Bafs, cfpecialiy in a Fugue, where a Variety can only be dif- cerned in the Parts that accompany if : And, if we have laid that the Bafs of a Fugue might a'ways be pretty near the fame, it was only, in order to give the mod juft and true Idea of the Manner how the Melody of a Fugue ought to be imitated; for "this Likenefs in the Chords is, ofitfelf, a fufficient Proof thereof. 4. In order to know the Choice that ought to be made of the Notes contained within the Compafs of the Key-note to its Fifth afcending, and from this to the other defcending, ycu muft al- ways keep in View the Key-note and its Fifth, at which Notes the Meiody of each Fugue generally ends ; but they are not to hinder us from making the Intervals of the Anfwer to be con- formable to thofe of the Fugue inverted, eipecially in the Middle of the Air: So that, having made an Interval of a Third, Fourth, Fifthj Sixth, or Seventh, in the Midffc of the firft Me- lody, we are to make the like in the fame Part of the Melody that anfwers the Firft, and fo of the others. Yet this hit Rule is not fo general, but that one may deviate from it, in Favour of a diatonic Progrefiion, or in Favour of the principal Notes of a Mode, having Regard rather to what follows than to what pre- cedes ; and to the Key-note and its Fifth (which generally be- gins and ends the Fugue) than to this Uniformity of Intervals which we have propofed. So that the Interval of a Fourth is oftentimes to anfwer that of a Fifth, and this lafi to anfwer the other ; but, moreover, if, after a confonant Interval there appear one or more diatonic Intervals, we muft then have Re- courfe to thofe Places where the Key-note appears, in order that the diatonic Progreifion, which is found from the laft confonant Interval until'the Key-note, be regularly imitated in the anfwer- ing Part until the Fifth; or, if the Progrefiion leads to the Fifth, it muft be imitated in the anfwering Part towards the Key-note, cfpecialiy when a Progreffion (be it which it will) ends by a Cadence; for the final Cadence of a Fugue muft always be made X" J upon %6z Principles of CcmpofJion. Upon the Key-note and upon its Fifth : Though, if thai Oa» dence doth not abfolutely end the Fugue, then wte may ufe the Fourth inftead of the Fifth, and, fometimes, the Second inftead of the Key -note, A Fugue ought feldom to begin or end but by the Key-note, its Fifth° or Third; the Sixth or the Seventh anfwering.then to. that Third, as it appears in the fifth preceding Example : So that, by flicking to what follows, rather than to what precedes, and by the Conformity of the Chords that are to meet over the Bafs ufed to Melodies anfvvering one another in Fugue, you, will, ieldom be aiiftaken, E X A M P L E Fiift Melody. Anfwer. Firft Melody. Continued Bals, An Aver. 6 6 6 M 54* I 6 6 6 6 4— £ B— & 6» 6 4* 6 4 5 6 4 5+« 6 Continued iials. . i &. _1JZ£ I _ a._i — E_^ Th« Principles of Compofdion* * 6 3 The continued Bafs is placed only to fhew, that, whatever Bafs you may imagine under a Melody propofed, it may always have the fame Uniformity, by bearing the fame Chords, but the Fun-r damental is ftill better in this Cafe. 5. The Melody or Subject of a Fugue ought to contain, at Jeaft, half a Bar ; and, if it contains more than four, the Anfwer muft begin in the Fourth; and yet the Movement ought to be fomewhat quick, that fo long a Succeffion, of Melody, ftripped of Harmony, may pleafe. 6. A Fugue may begin by any one of the Parts, but it ought naturally to end upon the firft Part of the Meafure or Bar, when it is divided into two Parts; and upon the third Part of the Bar, when it is divided into four ; and, when it ends in any other Part, it is either for the Sake of the Words, or for Fancy only. Sometimes, for Novelty, we may trefpafs upon thefe Rules, which depend only upon a good Tafte ; and the Surprife which thefe Sort of Fugues that end contrary to the Rule create, can be but pleafing, when they are done with judgment and Difcretion ; the/ may alio end upon other Notes than the Key-note and its Fifth. EXAMPLE. Firft Melody. Anfwer. 1 " Firft Melody. ,-Q-p ,, 1 — * — ' — j — -e- 7. The Melody of the Fugue is to be imitated, in every Re- fpedt, as much as can be ; for the fame Quantity of Semibreves, Minums, isfc. contained in any Part of the Meafure, muft be ufed wherever the Fugue is heard. 8. You may begin each Part in the Unifon, or at the Octave pf the firft Part ; but, when thefe Parts follow each other at the Fifth or Fourth, it is more agreeable, and produces a better Effeft. 164 Principles of Compofition. A Fugue may begin, and be anfwered, by any of the Parts in trie whole Courfe of the Piece; and, when you change Keys, every Note of the Fugue muft be the fame in this new Key, as well in Refpeft to the Degree they occupy in the firft Key, as in their Quality, Quantity j and Meafure. 9. You may wait until the Melody or Subject of the Fugue be' entirely finifhed, fo that each Part may anfwer it one after an- other ; but, as it fomettmes happens, that, in the Mid ft of the De- fign, each Part may be made to anfwer, it has no bad Effect provided that nothing be thereby altered. See the fixth Example. 10. By Inverting, all that Variety that may be introduced iri Harmony, gives a new Grace to a Fugue; fo that, having framed a Defign or Subject, you may invert it in fuch a Manner, that the fame Inverfion which has been heard afcending, may be heard defcending ; and, vice verja, without any other Alteration. E X A M P L E. Firft Melody. -_Oi- Fugue Inverted. , iaA 1 "zzirzz'zzThiizH: — p Anfwer inverted. 11. Several Fugues may be heard together, or One after the other; and it ought to be contrived, as much as poffible, that they fhould not always begin at the fame Part of the Bar, or in the fame Bar, efpecially for the firft Time ; and that their Pro- greflions be inverted, and differently chara&erifed ; that is to fay* that, if the one contains fome Semibreves, the other ought to con- tain Minims, Crotchets, tic-t at the Will of the Compofer ; and, if they cannot be heard together, that a Part of the one may, at lcaft, be heard with a Part of the other, which will be better ex- plained by the following Example. Princifles of Comfofition, QUlNQUE. 165 rfrr m'n I m ■ — ■ •La-bo _ra cla - - - - IS ffiff^ ■- "■ — = EE SE Continued Bafs fe I ctz Fundamental uafs P? ■ crT' 1 ! r r rir^rclnir'rcrrj'i- m _ ^niaros, La-baJ^i £ ffiS z 1= La .bo -ra -. - - -VI cla - _ _ SB ,-£ 5H SB "P~T _i 1 6" pp 5 -a- # ip^P 3D: iSG Princ ivies of Comfojitioti, . i it rm-m Principles of Comj>oJitio n , 157 - „ — -mans, De.fe -ce-ruiit L°— — cu-li 1 11 1 r*f-f me ^ ae,Fac-t» fnnt fau-ces fau-ces me ae, = M I I 1 » ■ » Rati ^ cae fac — tae MA. 1$8 Principles of Compojttion. I i &=* rr* p Id #— ♦ feEsg; De-fe-ce-nmt o-cuJi P. CL § P nre-i>Dumfpe-ro in De — um , me-uin,ilum fpe — tf irw t 33 La-bo -ra _. _'_•-. «.vi g ZOZZQ 1 ■ firnt fau-ces me - .. -ac» cla _" _ J; _ a sM-fH^ Rau .-Cae-factiefuntfau-ces me - _ _ _ae £E 35 at * PPP1 I 31 "CT 1 tea 7^5" 5 '!*■ 7 % ^3 l S me-i, dum fpe - - -roi dum-fpe.ro in De ^ura cla _ _ ,-;"-. - - ~- ,-mans, cla „ ^matiSj cla - — mans, ^ US De-fe-cejrunt o-ciuli tne-i.dum Fzpm m ?5 9 8 2| r*r s- 1 -^ n Xt=S. i£9 Principles of CompoJitioTU • Kan _ _ c* fac -t:e Jjl. x r i i i w f^. _m*ns,cla-man», cla - -mans, ~~E^m B f De-fe -ce-runt o - - - cu-li ^^ jjjjgplll f l J JB L70 principles of Compofition. 5=55 ■ ■ 133 M4fW3 iticaj. ^ De r fe _ ce — runt o - cu li ^ me M e< 5 q / q f 5 utitfau-ces me _ _ * Jfe, fan/.- - - - ces, . 1 futitfau-ces me Pip I n ? q « mej, dum fpe _ " ro »• De _ — — nm _ ,i m m i i i q i ss 1 P I ! rpe-ro/ in De r=f^ fpe _ to in De _ um me-um, dum fpe-ro, fpe-ro, 7 7 ' x>. IS 1 rhiciples of ComvoTitioiL, 173 E i fpe-.ro, fpe-ro, fpe-ro,fpe-ro in De- — um, fpe wm & fcac i 1- r ■ m fpe-ro in De-um i"pe — Iro, dutn fpe or, fpe — :& mm ^M Dam fpe-ro, fpe-ro, fpe - ro,dum fpe _ .- *C r f I'Kr o,aum ipe mm m E Dutn fpe-ro,fpe-ro, fpe-rpin pas: £ ri:t f I J PC rza *rf it- Dum fpe-.ro, a 3=£ 1 £ 5 4^ ff | | A 7 7 TV ^^ 1 1 [T * fnp g | yiipj Sj j -» -or f fpe -ro in pe-um Me - -. um* i R B re I inj.ro in LDe - — — um me- -um. Br* ffr rftrrr n ° =gii — ro, fpe-ro in De-um met, -uj»« m De-um me-um, in pe-um me- - um. um, in De-ur — be £Pff ro in De-ur =a 3 fpe-ro, fpe-ro in De-um me- — um, r hi i ijimr X I y- ^ 7 " 7 7 ^r Aa 174 Principles of €or$poJitie inverted* which contributes greatly to the Perfection thereof. The Fugue of Raucafa£i#Junt> &c. which, for an Anfwer at the Fifth, ends almoft every- where upon the fecond Note, would be more perfect, if it ended upon the Key-note, as you will find it at that Part where the Bafs takes that Fugue. Yet this fecond Note, which is there taken, inftead of the Key-note, may be to- lerated, and more especially when we are tied up by other Fu- gues, which, by Beginning and Ending with this, cannot agree but with Jthis fecond Note. The Succeffion of the Chords, or even good Tafte, may alio oblige us, fometimes, to interrupt the true Melody of the Fugue; which often proceeds from the Au- thor's Skill, in order to throw a greater Variety in the Courfe of his Piece: Neverthelefs, this. is not allowed, but after all the Subjects of the Fugue have been Efficiently heard. To diftinguifh the feveral Notes which we have the liberty of pairing between feveral Parts of the Bar for the Sake of t,he Air, you -muft examine the fundamental Bafs, which in that; Cafe, doth not make Harmony with thofe Notes. The fundamental Bafs is added to the other Parts, only for the Sake of proving, that, in the whole Courfe of. the Piece, - there are found but perfect Chords, or that of the Seventh ; and that the whole is taken from the Rules we have eftablifhed upon thofe two Chords : Therefore, and for that Reafon, *t ntuft not be examined with the other Parts, in refpeft to the Order, or to the Progreffion of the Concords and Difcords, but only as to the real Harmony and Foundation of the Chords ; this Order Or Progreffion being obierved .and kept, only between the five upper Parts and the continued Bafs; and the Foundation or Ground of the Chords is found in that fundamental Bafs, which contains very near .411 the feveral and different Prbgrefficcts from whence bur Rules have been taken, whilft the other Parts riever make but the Octave, the Fifth, the Third, or the Seventh, excepting in the irregular Cadences, and in the Qhprcls by Sup- pofition or borrowed . As we may find as many different Fugues as there are. different Airs, it would be impoffible ' for us to give Examples- of all of them; therefore tlie Choice muft he lift -to the Compofer's Tafte, provided he oblerves, in' all other ■RefpeSs',' r vvhat we have faid as to th^ Beginning and Ending of them and their A'nfvvefs. ' ■-% — firr - "*" And if you are willing' that feveral Fugues fhould be heafd together, you muft pitch upon one, and in this Cafe you may chule "■'".. '" - i ; ;,; - f , Principles of Compofitiw. 17$ ehufe which you pleafe ; fo that, if the Melody of one Fugue be agreeable to you, you may add to it three or four Parts, and you may find in thefe Parts the other Fugues. Yet, as feveral different Fugues that mould begin and end at the fame Time, and wherein there fhould happen to be the fame Number and Value of Notes, would become infipid, by appearing to be only an Accompaniment one to the other, you muft endeavour to 1 avoid this Defe&, by obferving the Method we have mentioned 1 in the Paragraph preceding the laft Example. Words in Prole, which feldom bear the fame Quality amongft themfetves, na- turally lead us to this Variety, which ought always to be fought after; but Word? in Rhyme, equally meafured, require a parti- cular Care to begin and end one of thofe Fugues fooner or later than the other, and to infert fome Divifions in thofe that can bear it, in order to introduce a greater Variety, but the whole muft be done without Confufion ; for the Entries or coming in of each Fugue are t© be diftinftly heard, without clafhing with the other by properly ceafing, for fame Space, that Part which is to retake the Fugue, and this- Silence or Reft can be made but upon a -Concord or confonant Note. One Fugue, for the tirft Time that it is heard, muft not ferve as a Continuance to the Melody that precedes it, but the Contrary muft be practifed with Succets, provided that this Fugue hath been heard at leaft once in every part. All the Entries of the firft Fugue may be heard feparately from the others ; after which you pafs to the Second, to the Third, &c in which Cafe you intermix the firft Fugue with the new Fugues : You may alfo caule each of them to be heard ie- parately one from the other, and intermix them afterwards. If you wou|d ufe ieveral Fugues together, by placing one of thefe Fugues: in one Part, and the other in another Part, it is then difficult to avoid Confufion. Oftentimes one Subject or Defign makes us forget the other; yet the Cornpofer ought to have them equally in View, and in his Mind. It is, therefore, by the Va- riety of Defigns, or Subjects, by giving them oppofite Progref- fions-, by caufing them to enter into different Parts of the Bar, fefe that you. may caule each Fugue to be heard. It often hap- pens, that one Part may fing two Fugues fucceffively, which at tirft appeared but one, and which afterwards may be divided into two, which produces alfo a very agreeable Effect. ; but, in that Cafe, the fecond Part that retakes thefe Fugues, ought to begin immediately at the Place where they may be divided, though one may anticipate or poftpone that Entry for fome Parts of a Bar, and even for more than a Bar. A a 2 , The *?& Principle's of Co'mpojitlon. , .The fame" Number of Refts, or of Bars contained in the fir& Part that retakes the Fugue, muft be obferved ih the next Part, that is to fay, that, if the firft Part that retakes the Fugue hath reckoned one Bar, each of the other Parts are to reckon the like- Number of Bars after that which immediately precedes it. This Rule, neverthelefs, is not fo general, but that it may be trefpafled iipon fometimes ; and we think, that the third Part that retakes the Fuguej may be poftponed or advanced for a Bar : So that^ if the iecoiid Part hath reckoned two Bars, the third Part may- reckon but one, or three after the fecond Part, and fo of the fathers which repeat this Fugue in the Unifon, or at the Octave, after the third Part ; for as the Fifth is to anfwer the Key-note, and the fecond Note the Sixthj fcfr. what may agree one Way, after the End of one or two Bars, may poffibly not agree with' the other, after a like Number of Bars. It would be, therefore, reftraining too much the Genius of an Author, by keeping him within the Bounds of the firft Limits; and fuch as will not agree to this, will find a thoufand Defigns or Subjects where it may happen, that not one of them can be fubiefted to this ft rift Re- gularity. See, upon this Subject, the Fugues of Raucce fa£lne Junty and of Defecerunt ocuii mei, in the laft Example. When all the Parts ceafe together, in order that a new Fugue may appear in a better Light, the Subjeft muft never appear as if it was abfolutely ended, for we muft always make the Auditor to expeft as much as poffible wliat we intend for him, and^ to> that End, this Reft or Silence ought to be ufed but in falfe or ir- regular Cadences ; and, if they be perfect Cadences, it muft, at leaft, be in a foreign Key, as we have obferved it in all the like Cafes. A Fugue is an Ornament in Mufic, founded upon good Tafte; fo that the moft general Rules we have given, are hardly fufficient to fucceed perfectly in it. The various Sentiments and Events that can be expreffed in Mufic, introduce every Moment a No- velty which cannot be reduced to fixed Rules. It is true, that a perfeft .Knowledge of Harmony difcovers to us the Roads we fhould take in this Cafe ; but the Choice of thofe Roads depends upon our Tafte, and this Tafte requires an Experience, which cannot be attained to but by Practice, and by ftudying and hear- ing the" Works of the beft and moft fkilful Mafters in this Kind. There is another Species of Fugue, called Perpetual, or Canon, which confifts in an entire Air, the Subjeft of which is to be repeated regularly by all the Parts. The Principles rf Ccmpofition. The moll common arc taken in the Unifon, or at the Ocl 77 ave. according to the Extent of the Voices or Inftruments ; and for that Purpofe you may compofe a Subject at Pleafure, to which you add as many Parts as you think proper ; and, of all thefe Parts, you compofe an entire Air, which is fo con- trived, that the Melody of one Part may ferye as a Continuance to the other; after which this Air begins by one of thole Parts which is immediately followed by another, at the Time that the firft Subject is ended ; thus each Part follows the other, and, when the Firft is at an End, it begins again, being always followed by the others, as at firft, provided that each Part began at its proper place. See the Example at the Side. Suppofing that you had imagined one of the Subjects contained in each of thefe five Parts, you might eafily add the others, and from thence make an entire Air, in which coniiits ail the Difficulty of this Canon, of which this is the Air* SEE -P^-h- Da Capo, -i W— Re— veill ez vous dor— meur fans fm^Relindindin, Reiindindin, Relindindin, Re-— The Melody of thofe five Piirts is very obvious in this Canon ; w£ have only added fome Notes for the Sake of the Air; and each of thefe Parts is to begin the Air one after the other, when the preceding Part is at the Mark*. Mliis perpetual Fugue may alio be taken at the Fifth or at the Fourth; but then, in this Cafe, the entire Air muft be framed, and proper Sharps and «J7Jats (as the Cafe requires) are to be added to thofe Notes, of which the natural Degrees would hinder thofe Parts that repeat the Air to be entirely conformable to the firft Subject, without obferving any Modulation, but only the Melody, which makes it the more difficult ; for, every Time that a Part takes the Fugue, it goes into a new Key, which is at the Fifth, if the Fugue is taken at the Fifth ; and at the Fourth, if it be taken at the Fourth. It the Number of Parts is unli- B b mited 178 Principles of Compqfition. mited in the foregoing Canon, we believe that in this there can- not be ufed more than four Parts, (ince there hath not hitherto appeared any of this Sort in four Parts. Canon at the Fifth. - *% — - 2 2 — B p _z B- — . . . __^_; — _ Ah ! loin de rire. r^z~zzz zzzz: L*_2_.__| ._. f~\ =H2 — 1 — Ah ! loin de lpZZ2 zzz zrzj:|zqz: Ah ! loin de ri— -^fczp ^s^i^jz Ldz.d_ _:z:^zs. Ah ! loin de ri- zzo: Pleu- r-x-w&- Ah ! loin de ri — -ZZZOI t** ■-fee- _o__ f- f- re, Plenrons, Pletirons. Ah! zisz. ~t i*z — -w] — «, : — ^.[1 : — - n — re, Pleurons,Pleurons.Ah! -f-*e- « ZSSf. -re, Pleu-rons. Pku -rons. Ah! be zE:SzEE~: — rons, Pleuron^. Ah! fP -w- t If Principles of Compofttion. *79 If the Voice cannot reach the Note marked J, the Unifon of the preceding Note may be taken. When a Canon is faid to be at the Fifth, it is to be under- ftood above; fo that a Fifth above, or a Fourth below, is the fame Thing; and this is to be allowed, efpecially, for the Con- veniency of Voices. We have placed the four Parts together, becaufe it would have been difficult to have judged of it otherwife. Though we might only have given Notice, that each Part is to be taken at the Fifth of that which precedes it after two complete Bars ; and though the Guides -W- which (hew where it muft begin again, are not upon the Space or Line which refers you to the Markf , one muft, neverthelefs, follow and continue in the fame Key de- figned by the Guide a«/, by imagining a new Key, or, rather, imagining that the Key hath changed, as it really does ; but that the Modulation of the Melody which is found at the Markf, is always the fame : Thus you may continue as long as you think proper. Canon at the Fourth. r- ggg| E==E|r^s|Eg|EB^) cdu vin,endormons nous, en-dor- Avec du via,endormons nous, en-dor _I«._®-lt_. bB- «*\fc- vin, en-dor-mons nous, en-dor mons nous, endor-mons nous. zSzPz u pnr-f-r- ~ w ■i — i^-^—i-j. mons nous, en-dormons nous, Avec du. i=SE:=iE lHzz[z=z::tz 1 - -dor — —mons nous. i Bo Principles of Compofition. \ It is difficult to compofe thefe two Sorts of Canont-, unlefs vow nave a thorough Knowledge of inverted Chords ; and you maft avoid ufing (as much as you can) the Fifth, the Fourth, and the Eleventh. The beft Method to make a quick Progrefs in Compofition, is to apply and flick clofely to Modulation, and to the fundamental Harmony, which are the principal and only Caufe of all that "Variety that may be therein introduced, by inverting that fame fundamental Harmony, the Modulation whereof never changes* FINIS. E R R A T A, Page by the Direft in the Tenor at Bottom mould be on C. The CKSf in the firft Bafs muft be on the third Line. The Direct at Top F, an<$ at Bottom G. — Page 17, Counter Tenor, feventh Bar, a 3 over the firft Note.- — Page 21, Bafs feventh Bar B under the firft Note. — Page 62, eighth Stave the F Cliff on the fourth Line. Third Bar fecond Note, B on the fecond Line, not F. — Page 68, Example of A Flat muft have B, E, D and F Flat. — Page 77, the firft Stave, the 7 over the iecond Note in the feventh Bar muft be out, and 7 put over the firft Note in the eighth Bar. The fourth Stave, the firft Note in the ninth Bar muft be B on the fecond Line.— ^Page 96, the third, fourth, and fifth Stave, the F Cliff muft be on the fourth Line, not on the Third. — Page m, the fecond Note in the firft Bar ihould be D,-^— Page 122, the laft Example, the fourth Note D in the fecond Bar, mould be a Crotchet.— Page 123, the laft Example, the fecond Note E in the fecond Bar mult be a Quaver.— Page 125, the fixth Bat the fecond Note in the Bafs muft be B.— Page 13 J, the fecond Stave, the fecond Note in the feventh Bar muft have a 6 over it inftead of a £. — Page 136, the fecond Stave, the fifth Bar, the fecond Note muft be C in the fecond Space.— Vage 138, F over the fecond Note *n the iixth Bar, of the fecond Part ia the Treble^ C over the firft Note in the feventh Bar. M A L C O L M's TREATISE O F c, MUSI Speculative, Practical, and Hiftorical. CORRECTED AND ABRIDGED By an Eminent MUSICIAN. SECOND EDITION. Hail Sacred Art ! defcended from above, To crown our mortal Joys : Of thee we learn, How happy Souls communicate their Raptures ; For thour't the Language of the Blefl; in Heaven. Divum hominumque voluptas. LONDON, Printed for J. Murray, N n . 32, Fleet-Street ; and Luke White, Dublin. mdcclxxix, CONTENTS T O T H E TREATISE on MUSIC. /^\ F Sound: The Caufes of it; and the various ^^ Affections of it concerning Mufic, p. i A Definition and Divifion of Mufic, - 1 8 A general Account of the Method of writing Mufic, 20 A more particular Account of the Method ; where ; of the Nature and Ufe of Clefts, 24 Of the Reafon, Ufe, and Variety of the Signatures of Clefts, - - - - - 31 Of the Name and various Definitions and Divifions of the Science, - - - - -41 The Invention and Antiquity of Mufic, with the Ex- cellency of the Art in the various Ends and Ufes of it, - - - - - - 46 The Exeellency and various Ufes of Mufic, 55 A fhort Hiftory of the Improvements in Mufic, 69 Guido's Scale, - - - - 72 Modes, ._-_-- yy The ancient and modern Mufic compared, - 80 I prn ^^ ££ ew^J^ ML *)*( 3"! I I fc.j* 808 «C Q$m& W && &.j* I TREATISE O F MUSIC. Of S o u n d : the C a u s e of it ; and the various Affections of it concerned in Music. 3j&£rfesfe5!feXCU SIC is a fcience of founds, whofe end is yir -^"JS '^!fi h pleafure. Sound is the object in general ; ¥srft ty[ ffiw or > to fpealc with the philosophers, it is the *p|3^ rlif* materia! objecl:. But it is not the bufinefs of ]^:^h! j*-3*f?! mufic, taken in a ftricl and proper fenfe, to «SP^vPW¥»w confider every phenomenon and property of found; that belongs to a more univerfal philofophy : yet, that we may understand what it is in founds upon which the formality of mufic depends, i. e. whereby it is diftinguifhed frcrn other fciences, of which found may alfo be the object : or, what it is in founds that makes the particular and pro- per objecl of mufic, whereby it obtains its end j we muff, a little confider the nature of found. So undis a word that (lands for every perception that comes by the ear immediately. And for the nature of the thin^, it is now generally agreed upon among philofophers, and alfo confirmed by experience, to be the effect of the mutual collifion, and confequent tremulous motion in bodies com- A municated $ A TREATISE rnunicated to the circumambient fluid of air, and propagated through it to the organs of hearing. A treatife that were defigned for explaining the nature of (ound univerfally, in all its known and remarkable phaenomena, (hould, no doubt, examine very particularly every thing that belongs to the caufe of it; firfr, The nature of that kind of motion in bodies (excited by their mutual percuffion) which is communicated to the air; then, how the air receives and propagates that motion to certain diftances: And, laftly, How that motion is received by the ear, explaining the feveral parts of that organ, and their offices, that are employed in hearing. But as the nature and defign of what I propofe and have eflayed in this treatife, does not require to large an account of founds, I mult be content only to confider fuch phaenomena as belong pro- perly to mufic, or ferve for the better underftanding of it. In order to which I (hall a little farther enlarge the preced- ing general account of the caufe of found. And, Firft, That motion is neceflary in the production of found, is a conclufion drawn from all our experience. Again, that motion exifts, firft among the fmall and infen- fible parts of fuch bodies as are fonorous, or capable of found ; excited in them by mutual collifion and percuffion, one againft another, which produces that tremulous motion fo obfervable in bodies, efpecially that have a free and clear found, as bells, and the firings of mufical inftruments; then this motion is communicated to, or produces a like motion in the air, or fuch parts of it as are apt to re- ceive and propagate it: for no motion of bodies at diftance can affect our fenfes (or move the parts of our bodies) with- out the mediation of other bodies, which receive theie motions from the fonorous body, and communicate them to the organs of fenfe; and no other than a fluid can reafon- ably be fuppofcd. But w^know this alfo by experience; for a bell in the exhaufled receiver of an air-pump can fcarcely be heard, which was loud enough before the air was drawn out. In the lad place, this motion mull be communicated to thofe parts of the ear that are the proper and immediate inftruments of hearing. The mechanifm of this noble or- gan has ftill great difficulties, which all the induftry of the rnoft capable and curious enquirers has not furmounted : there are queftions all unfolved about the ufe of fome parts, and perhaps other neceffary parts never yet difcovered : but the O F M U S I C. 3 the moll important queftion among the learned is about the laft and immediate inftrument of hearing, or that part which laft receives the fonorous motion, and finifhes what is ne- cefTary on the part of the organ. Confdt thefe with the philosophers and anatomifts; I ftiall only tell you the com- mon opinion, in fuch general terms as my defign permits, thus : Next to the external vifible cavity or pafLge into the ear, there is a cavity, of another form, feparate from the former by a thin membrane, or fkin, which is called the tympan or drum of the ear, from the refembiance it has to that inftrument : within the cavity of this drum there is always air, like that external air which is the medium of found. Now, the external air makes its impreffion tirft on the membrane of the drum, and this communicates the motion to the internal air, by which it is again communi- cated to other parts, till it reaches at laft to the auditory nerve, and there the fenfation is finifhed, as far as matter and motion are concerned ; and then the mind, by the laws of its union with the body, has that idea we call found. It is a curious remark, that there are certain parts fitted for the bending and unbending of the drum of the ear, in or- der, very probably, to the perceiving founds that are raifed at greater or lelter diftances, or whofe motions have dif- ferent degrees of force, like what we are more fenfible of in the eye, which by proper mufcles (which are instruments of motion) we can move outwards or inwards, and change the very figure of, that we may better perceive very diUant or near objects. But I have gone far enough in this. Left what I have faid of the caufe of found be too general, particularly with rcfpecl to the motion of the fonorcus bedy, which I call the original caufe, let us go a little farther with it. That motion in any body, which is the immediate caufe of its founding, may be owing to two different caufes; one is, the mutual percufiion betwixt it and another body, which is the cafe of drums, bells, and the firings of mufical instruments, Sic. Another caufe is, the beating or dafhing of the fonorous body and the air immediately againlt one another, as in all kind of wind-initruments, flutes, trumpets, hautboys, Sec. Now in all thefe cafes, the motion which is the confequence of the mutual percufiion betwixt the whole bodies, apd is the immediate caufe of the fonorous motion which the air conveys to our ears, is an invisible A a tremulous 4 A TREATISE tremulous or undulating motion in the fmall and infenfrbld parts of the body. To explain this j All vifible bodies are fuppofed to be compofed of a num- ber of fmall and infenfible parts, which ate of the fame na» ture in every body, being perfectly hard and incompreffible: of thefe infinitely little bodies are compofed others that are fomething greater, but ftill infenfible, and thefe are dif- ferent, according to the different figures and union of their component parts : thefe are again fuppofed to conftitute other bodies greater (which have greater differences than the lad) whofe different combinations do, in the laft place, con- ftitute thofe grofs bodies that are vifible and touchable. The firft and fmalleft parts are abfolutely hard; the others are compreffible, and are united in fuch a manner, that be- ing, by a fufficient external impulfe, compreffed, they reftore themfelves to their natural, or ordinary ftate : this cdmpref- fion therefore happening upon the fhock or impulfe made by one body upon another, thefe fmall parts or particles, by their reftitutive power (which we alfo call elaftic faculty) move to and again with a very great velocity or fwiftnefs, in a tremulous and undulating manner, fomething like the vfible motions of groffer fprings, as the chord of a muficai indiument ; and this is what we may call the fonorous mo- tion which is propagated to the ear. But obferve that it is the infenfible motion of thefe particles next to the fmallefr, which is fuppofed to be the immediate caufe of found ; and of thefe, only thofe next the furface can communicate with the air ; their motion is performed in very fmall fpaces, and with extreme velocity; the motion of the whole, or of the greater parts being no further concerned than as they con- tribute to the other. And this is the hypothefis upon which Monfieur Perrault, of the Royal Society in France, explains the nature and phenomaena of found, in his curious treatife upon that fuh- jedt, " Eflais de Phyfique," torn. 2. Du Bruit. How this theory is fupported I fhall briefly fhew, while I confider a few applications of it. Of thofe hard bodies that found by percuffion of others, let us confider a bell : firilce it with any other hard body, and while it founds we can difcern a feniible tremor in the furface, which fpreads more fenfibly over the whole, as the fhock is greater. This motion is not only in the parts next the- furface, but in all the parts through the whole 3 folidity, O F M U S I C. folidity, becaufe we can perceive it alfo in the inner furface of the bell, which muft be by communication with thofe parts that are immediately touched by the ftriking body. And this is proved by the ceafing of the found when the bell is touched in any other part; for this flaews the eafy and actual communication of the motion. Now this is plainly a morion of the feveral Tmall and infenfible parts changing their ficuations with refpe£t to one another, which being fo many, and fo clofely united, we cannot perceive their mo- tions fcparately and diftindtly, but only that trembling which we reckon to be the effedt of the confufion of an infinite number of little particles fo clofely joined and moving in in- finitely fma'l fpaces. Thus far any body will eafily go with the hypothecs : but Monfieur Perrault carries it farther, and affirms, That that vifible motion of the parts is no otherwife the caufe of the found than as it caufes the invifible motion of the yet fmaller parts (which he calls particles, to diftin- guifh them from the other which he calls parts, the leaft of all being with him corpufcles) And this he endeavours to prove by other examples, as of chords and wind-inftruments. Let us confider them. Take a chord or firing of a mufical instrument, ftretched to a fufficient degree for founding, when it is fixt at both, ends, we make it found by drawing the chord from its ftrait pofuion, and then letting it go; (which has the fame effect as what we properly call percuflion) the parts by this drawing, whereby the whole is lengthned, being put out of of their natural ftate, or that which they had in the ftrait line, do by their elasticity reftore themfelves, which caufes that vibratory motion of the whole, whereby it moves to and again beyond the ftrait line, in vibrations gradually fmaller, till the motion ceafe and trfe chord recover its for- mer pofition. Now the fhorter the chord is, and the more it is ftretched in the ftrait line, the quicker thefe vibrations are: but however quick they are, Monfieur Perrault denies them to be the immediate caufe of the found ; becaufe, favs he, in a very long chord, and not very fmall, ftretched only (b far as that k may give a diftinct found, we can perceive with our eye, befides the vibrations of the whole chcrd, a more confuted tremor of the parts, which is more difcerni- ble towards the middle of the chord, where the par s vibrate in greater fpaces in the motion of the whole ; this latl motion of the parts which is caufed by the full vibrations of the 6 ATREATISE the whole, does again occafion a motion in the leflcr parts or particles, which is the immediate caufe of the found. And this he endeavours to confirm by this experiment, viz. Take a long chord (he fays, be made it with one of thirty foot) and make it found j then wait till the found quite ceafe, and then alfo the vifible undulations of the whole chord will ceafe: if immediately upon this ceafing of the found, you approach the chord very foftly with the nail of your finger, you will perceive a tremulous motion in it, which is the remaining fmall vibrations of the whole chord, and of the parts caufed by the vibrations of the whole. Now thefe vibrations of the parts, are not the immediate caufe of found ; elfe how comes it that while they are yet in motion they raife no found ? The anfwer perhaps is this, That the motion is become too weak to make the found to be heard at any great diftance, which might be heard were the tympan of the ear as near as the nail of the finger, by which we perceive the motion. But to carry off this, Mr. Perrault fays, That as foon as this fmall motion is perceived, we fhall hear it found ; which is not occafioned by renewing or augmenting the greater vibrations, bccaufethe finger is not fuppofed to ftrike againft the chord, but this againft the fin- ger, which ought rather to flop that motion ; the caufe of this renewed found therefore is probably, that this weak motion of the parts, which is not fufficient to move the par- ticles (whofe motion is the firft that ceafes) receives fome afliftance from the dafhing againft the nail, whereby they are enabled to give the particles that motion which is neceflary for producing the found. But left it fhould ftill be thought, that this encounter with the nail may as well be fuppofed to increafe the motion of the parts to a degree fit for founding, as to make them capable of moving the par- ticles ; we may confider, that the particles being at reft in the parts, and having each a common motion with the whole part, may very eafily be fuppofed to receive a proper and particular motion by that fhock ; in the fame manner that bodies which are relatively at reft in a fhip, will be fhaken and moved by the fhock of the fhip againft any body that can any thing confiderably oppofe its motion. Now for as fimple as this experiment appears to be, I am afraid it can- not be fo eafily made as to give perfect fatisfaclion, be- caufe we can hardly touch a ftring with our nail but it will found. But O F M U S I C. y 3ut Mr. Perrault finifhes the proof of his hypothesis by the phsenomena of wind-inftrumcnts. Take for example a flute; we make it found by blowing into a long, broad, and thin canal, which conveys the air thrown out of the lungs, till it is daftied againft that thin folid part which we call the tongue, or wind-cutter, that is oppofite to the lower orifice of the forefaid canal ; by which means the particles of that tongue are compreffed, and by their reftitutive motion, they communicate to the air a fonorous motion, which being im- mediately thrown againft the inner concave furface of the flute, and moving its particles, the motion communicated to the air, by all thefe particles both of the tongue and inner fur- face, makes up the whole found of the flute. Now to prove that only the very fmall particles of the inner furface and edge of the tongue are concerned in the found of the flute, we muft confider, that flutes of different matter, as metal, wood, or bone, being of the fame length and bore^have none, or very little fenfible difference in their found; nor is this fenfibly altered by the different thicknefs of the flute betwixt the outer and inner furface ; nor in the laft place, is the found any way changed by touching the flute, even though it be hard preffed, as it always happens in bells and other hard bodies that found by mutuarpercuffion. All this Mr. Perrault accounts for by his hypothefis, thus : he tells us, That as the corpufcles are the fame in all bodies, the particles which they immediately conftitute, have very fmall differences in their nature and form ; and that tfce fpecific differences of viiible bodies, depend on the differ- ences of the parts made up of thefe particles, and the various connection of thefe parts, which make them capable of dif~ ferent modifications of motion. Now, hard bodies that found by mutual percuffion one againft another, owe their founding to the vibrations of all their parts, and by thefe to the infenfible motions of their particles; but according to the differences of the parts and their connections, which make them, either filver, or brafs, or wood, &c. fo are the differences of their founds. But in wind-inftrumcnts (for example, flutes) as there are no fuch remarkable differences anfwering to their matter, their found can only be owing to the infenfxbie motion of the particles of the furface: for thefe being very little difference in all bodies, if we fuppofe tbs found is owing to their motions only, it can have none ? or very fmall differences: and becaufe we find this true in fa<£r, it makes the hypothefis extremely probable, I have never in- deed $ A T R E A T I S E deed Teen flutes of any matter but wood, except of the fma# kind we call flagellets, of which I have feen ivory ones* whofe found has no remarkable difference from a wooden one ; and therefore I muft leave fo much of this proof upon Monfieur Perrault's credit. As to the other part, which is no lefs confxderable, that no compreflion of the flute can fenfibly change its found, it is certain, and every body can eafily try it. To which we may add, That flutes of diffe- rent matter are founded with equal eafe, which could not well be if their parts were to be moved ; for in diff- erent bodies thefe are differently moveable. But I muft make an end of this part, in which I th nk it is made plain enough, that the motion of a body which caufes a founding motion in the air, is not any motion which we can poflibly give to the whole body, wherein all the parts are moved in one common direction and velocity j but it is the motion of the feveral fmall and undiftinguifhable parts, which being compreffed by an external force, do, by their elaftic power, reftore themfelves, each by a motion particular and proper to itfelf. But whether you will diftinguifh parts and particles as Mr. Perrault does, I leave to yourfelves, my defign not requiring any accurate determination of this matter. And now to come nearer to our fubject, I (hall next confider the differences and affe&ions of founds that are any way con- cerned in mufic. Sounds are as various, or have as many differences, as the infinite variety of things that concur in their production ; which may be reduced to thefe general heads : Firft, The quantity, conftitution, and figure of the fonorous body ; with the manner of percuifion, and the confequent velocity of the vibrations of the parts of the body and the air j alfo their equality and uniformity, or inequality and irregular- nefs. Secondly, The conftitution and ftate of the fluid me- dium through which the motion is propagated. Thirdlv, The difpofition of the ear that receives that motion. And, fourthly, The diftance of the ear from the fonorous body. To which we may add, laflly, The confederation of the obflacles that interpofe betwixt the fonorous body and the ear; with other adjacent bodies that, receiving an impreflion from the fluid fo moved, re-ad upon it, and give new modi- fication to the motion, and confequently to the found* Upon all thefe do our d.ffaent perceptions of found de- pend. The O # U US I C. \ The variety and differences of founds, owing fo the vari- ous degrees and combinations of the conditions mentioned, are innumerable; but to our prefent defign we are to consi- der the following diftin£ticns. I. Sounds, come under the fpeciflc diftinc~r.ion, according 5 to the kinds of bodies from which they proceed : thus metal is eafily diftinguifhed from other bodies by the found ; and among metals there is great difference of found, as is dis- cernible, for example, betwixt gold, filver and brafs. And for the purpofe in hand, a moft notable difference is that of ftringed and wind-inftruments of mufic, of which there are alfo fub-'divifions : thefe differences depend, as has been faid, upon the different conftitutions of thsfe bodies ; but they are not ftrietly within the cOhficieration of mufic, not the mathe- matical part of it at leaft, though they may be brought into the practical j of which afterwards. 2. Experience teaches us, that fome founds can be heard, by the fame ear, at greater diflances than others ; and when we are at the fame diftance from two founds, I mean from the fonorous body or the place where the found firft rifts, we can determine (for we learn it by experience and obfer- vation) which of the two will be heard fartheft : by this comparifon we have the idea of a difference whofe oppofite terms are called loud and low (or (trong and weak.) This difference depends both upon the nature of different bodies, and upon other accidental circumfiances, fuch as their figure; or the different force in the percufHon ; and fre- quently upon the nature of the circumjacent bodies, that contribute to the ftrengthening of the found, that is a con- junction of feveral founds fo united as to appear only as one found : but as the union of feveral founds gives occafion to another diftin&ion, it (hall be confidered again, and we have only to bbferve here that it is always the caufe of loudnefs ; yet this difference belongs not ftriclly to the theory of mufic, though it is brought into the practice, as that in the fLft article. 3. There is an affection or property of found, whereby it is diftinguifhed into acute, (harp or high ; and grave, flat or low. The idea of this difference you will get by com- paring feveral founds or notes of a mufical inftrument, or of a human voice finging. Obferve the term low, is fometimes oppofed to loud, and fometimes to acute, which yet are very different things; loudnefs is very well meafured by the B diftancs io A TREATISE diftance or fphere of aftdibility, which makes the notion of it very clear. Acutenefs, is fo far different, that a voice or found may afcend or rife in degree of acutenefs, and yet lofe nothing of its loudnefs, which can eafily be demonftrated upon any inftrument, or even in the voice ; and particularly if we compare the voice of a boy and a man. This relation of acutenefs and gravity is one of the prin- cipal things concerned in mufic, the nature of which fhall be particularly confidered afterwards ; and I fhall here obferve that it depends altogether upon the nature of the fonorous body itfeif, and the particular figure and quantity of it ; and in fome cafes upon the part of the body where it is flruck. So that, for example, the founds of two bells of different metals, and the fame fhape and dimenfions, being ftruck in the fame place, will differ as to acutenefs and gra- vity ; and two bells of the fame metal will differ in acute- nefs, if they differ in fhape or in magnitude, or be ftruck ia different parts: fo in chords, all other things being equal, if they differ either in matter, or dimenfions, or the degree of tenfion, as being ftretched by different weights, they will alfo differ in acutenefs. But we muft carefully remark, that acutenefs and gravity, alfo loudnefs ar.d lownefs are but relative things ; fo that we cannot call any found acute or loud, but with refpecT: to ano- ther which is grave or low in reference to the former; and therefore the fame found mr:y be acute or grave, alfo loud or low in different refpecls. Again, thefe relations are to be found not only between the founds of different bodies, but alfo between different founds of the fame body, for different force in the percuffion will caufe a louder or lower found, and ftriking the bndy in different parts will make an acuter or graver found, as we have remarkably de- monftrated in a bell, which as the firoke is greater gives a greater or louder found, and being ftruck nearer the open end, gives the graver found. How thefe degrees are mea- fured, we fhall learn again, only mind that thefe degrees of acutenefs and gravity are alfo called different and diftinguifh- able tones or tunes of a voice or found ; fo we fay one found is in tune with another when they are in the fame degree : acute and grave being but relations, we apply the name of tune to them both, to exprefs fomething that is conftant and ahfolute which is the ground of the relation'} in Jike mamicr a> we apply the name magnhuds both to the things we calj. great O F M U S I C. ii great and little, which are but relative ideas : each of them have a certain magnitude, but only one of them is great and the other little when they are compared ; fo of two founds each has a certain tune, but only one is acute and the other grave in comparifon. 4. There is a diftinction of founds, whereby they are de- nominated long or fhort ; which relates to the duration, or continued, and fenfibly uninterrupted exiftence of the found. This is a thing of very great importance in mufic ; but to know how far, and in what refpe£l it belongs to it, we muff, diftinguifti betwixt the natural and artificial duration of found. I call that the natural duration or continuity of found, which is lefs or more in different bodies, owing to their different conftitutions, whereby one retains the motion once received longer than another does ; and confequently the found continues longer (though gradually weaker) after the external impulfe ceafes ; fo bells of different metals, all other things being equal and alike, have different continuity of found after the ftroke: And the fame is very remarkable in firings of different matter : there is too a difference in the bell or ftring, according to the force of the percuffion.' This continuity is fometimes owing to the fudden reflection of the found from the furface of neighbouring bodies, which is not fo properly the fame found continued, as a new found fucceeding the firft fo quickly as to appear to be only its continuation : But this duration of found does not properly belong to mufic, wherefore let us confider the other. The artificial continuity of found is, fhat which depends upon the continued impulfe of the efficient caufe upon the fonorous body for a longer or fhorter time, fuch are the notes of a voice or any wind-inftrument, which are longer or fhorter as we continue to blow into them ; or, the notes of a violin and all ftringed inftruments that are ftruck with a bow, whofe notes are made longer or fhorter by ftrokes of different lengths or quicknefs of motion ; for a long ftroke, if it is quickly drawn, may make a fhorter note than a fhort ftroke drawn flowly. Now this kind of continuity is properly the fuccefficn of feverai founds, or the effedf of feveral diftincf. ftrokes, or repeated impulfes, upon the fonorous body, fo quick that we judge it to be one continued iound, efpecially if it is continued in one degree of ftrength and loudnefs ; but it alfo muft be continued in one degree of tune, elfe it cannot be called one note in mufic. And this B 2 leads H A TREATISE leads me naturally to confidcr the very old and notable di- stinction of a twofold motion of found, thus, Sound may move through various degrees of acutenefs ijj a continual flux, fo as not to reft on any degree for any affignable, or at leaft fenfible time ; which the ancients called the continuous motion of found, proper only to fpeaking and converfation. Or, 2do. it rpay pafs from degree to de- gree, and make a fenfible ftand at every pitch, fo as every degree mall bediftincl; this they called the difcrete or dis- continued motion of found, proper only to mufic or fmging. But there may be no obfeurity here, confider, that as the ideas of motion and difranoe are infeparably connected, fp they belong in a proper fenfe to bodies and fpace j and whatever other thing they are applied to, it is in a figurative and metaphorical fenfe, as here to founds ; yet the ap-. plication is very intelligible, as I fhall explain i,t. Voice or found is confidered as one invidual being, all other dif- ferences being neglected except that of acutenefs and gravity, which is not confidered as conftituting different founds, but different ftates of the fame found ; which is eafy to conceive ; and fo the feveral degrees or pitches of tune, are confidered as feveral places in which a voice may exiff. And when we . jiear a found fucceffively exiftjng in different degrees of tune» we conceive the voice to have moved from the one place to the other ; and then it is eafy to conceive a kind of difiance be- tween the two degrees of places ; for as bodies are faid to be diftant, between which other bodies may be placed, fo two (bunds are laid to be at diftance, with refpe£t of tune, be- tween which Gther degrees may be conceived, that fhall be acute with refpecl: to the one, and grave with refpect to the other. But when the voice continues in one pitch, though, there may be many interruptions and fenfible refts whereby the found doth end and begin again, yet there is no motion in that cafe, the voice being all the time in one place. Now. this motion, in a fimple and proper fenfe, is nothing elfe bu% the fucceffive exiftence of feveral founds differing in tune. When the fucceffive degrees are fo near, that like, the colours of a rainbow, they are as it were loft in one another, fo that jn any fenfible difiance there is an indefinite number of de- grees, fuch kind of fucceffion is of no ufe i« mufic j but when it is fuch that the ear is judge of every fingle difference, gt'id can compare feveral differences, and apply fome known nieafu ji to them, there the object of mufic does exift; -Q$ when © F M U- SI C. 15 when there is a fuceeffion of feveral founds diftinfr. by fen- ftble refts, though all in the fame tune, fuch a fuceeffion be- longs alfo to muiic. From this twofold motion explained, we fee a twofold continuity of found, both fubjedt to certain and determinate roeafures of duration ; the one is that arifing from the con- tinuous motion mentioned, which has nothing to do in muiic: the other is the continuity or uninterrupted exiftenceof found in one degree of tune. The differences of founds in this re- fpe£t, or the various meafures of long and fhort, or (which is the fame at leaft a confequence) fwift and flow in the fuc- ceffive degrees of found, while it moves in the fecond mannef make a principal and neceflary ingredient in mufic ; whofe effect is not inferior to any other thing concerned in the prac- tice j and is what deferves to be very particularly confidered* though indeed it is not brought under fo regular and deter- minate rules as the differences of tune. 5. Sounds are either fimple or compound; but there is a twofold fimplicity and compofition to be confidered here ; the firft is the fame with what we explained in the 1 aft article, and relates to the number of fucceffive vibrations of the parts of the fonorous body, and of the air, which comes fo faft upon the ear that we judge them all to be one continued found, though it is really a compofition of feveral founds of fhorter duration. And our judging it to be one, is very well compared to the judgment we make of that apparant circle of fire, caufed by putting the fired end of a ftick into a very quick circular motion ; for fuppofe the end of the ftick in any" point of that circle which it actually defcribes, the idea we re- ceive of it there continues till the imprelfion is renewed by the fudden return ; and this being true of every point, we muft have the idea of a circle of fire; the only difference is, that the end of the ftick has actually exifted in every point of the circle, whereas the found has had interruptions, though in- fenfible to us becaufe of their quick fuceeffion ; but the things we compare are, the fuceeffion of the founds making a fen- fible continuity with refpect to time, and the fuceeffion of the end of the fticlc in every point of the circle after a whole revo- lution ; for it is by this we judge it to be a circle, making a continuity with refpect to fpace. The author of the Elucidationes Pfayficse upon D' Cartes mufic, illuftrates it in this manner, fays he, As ftanding corns are bonded by one blaft of wind, and before they can recover themfelves- the tf A T R E ATI 3 B fhe wind has repeated the blaft, fo that the corn is ftandinS in the fame inclined pofition for a certain time, feems to b e the effect of one fmgle aclion of the wind, which is truly owing to feveral diftinct operations; in like manner the /mail branches (capilhmenta) of the auditory nerve, re* fembling fo many ftalks of corn, being moved by one vibra- tion of the air, and this repeated before the nerve can recover its Situation, gives occafion to the mind to judge the whale effect to be one found. The nature of this kind of compo- fition being fo far explained, we are next to confider what fimplicity in this fenfe is; and I think it muft be the effect of one fingle vibration, or as many vibrations as are neceffary to raife in us the idea of found; but perhaps it may be a queftion, whether we ever have, or if we can raife fuch an idea of found : there may be alfo another queftion, whether any idea of found can exifl in the mind tor an indivifible fpace of time ; the reafon of this queftion is, that if every found exifts for a finite time, it can be divided into parts of a (horter duration, and then there is no fuch thing as an ab- folute finnplicity of this kind, unlefs we take the notion of it from the action of the external caule of found, viz, the? number of vibrations neceffary to make found actually exifi,' without confidering how long it exifts ; but as it is not pro- bable that we can ever actually produce this, i, e. put a body in a founding motion, and ftop it precifely when there are as many vibrations finifhed as are abfolutely necef- fary to make found, we muft reckon the fimplicity of found,' confidered in this manner, and -with refpect to practice, a* relative thing; that being only fimple to us which is the moft fimple, either with refpect to the duration or the caufe, that we ever hear; but whether we confider it in the re- peated action of the caufe or the confequent duration, which is the fubject of the laft article, there is ftill anothef fimplicity and compofition of founds very different from 1 that, and of great importance in mufic, which I fhall next explain. A fimple found is. the product of one voice or individual body, as the found of one flute or one man's voice. A com- pound found confius of the founds of feveral diftinct voices or bodies, all united in the fame individual time and meafure of duration, i.e. all ftrikmg the ear together, whatever their other difference may be. But we muft here diftinguifh a natural and artificial compofition j to underftand this, re- member^ OF MUSIC, is member, that the air being put into motion by any body, communicates that motion to other bodies; the natural com- pofition of founds is therefore, that which proceeds from the manifold reflections of the firft found, or that of the body which firft communicates founding motion to the air, as the flute or violin in one's hand ; thefe reflections, being many, according to the circumftances of the place, or the number, nature, and fituations of the circumjacent bodies, make founds more or lefs compound. This is a thing we know by common exeprience; we can have a hundred proofs of it every day by finging, or founding any mufical inftrument in different places, either in the fields or within doors; but thefe reflections muft be fuch as returning very fuddenly do not produce what we call an echo, and have only this effect, to in- creafe the found, and make an agreeable refonance; but ftill in the fame tune with the original note ; or, if it be a composition of different degrees of tune, they are fuch as mix and unite, -To that the whole agrees with that note. But this compofi- tion is not under rules of art ; for though we learn by experi- ence how to difpofe thefe circumftances that they may pro- duce the defired effect, yet we neither know the number or different tunes of the founds that enter into this compofition ; and therefore they come not under the muficiah's direction in what is hereafter called the compofition of mufic; his care being only about the artificial compofition, or that mixture of feveral founds, which being made by art, are feparable and and diftinguifhable one from another. So thediftinct founds of feveral voices or inftruments, or feveral notes of the fame inftrument, are called fimple founds, in diftinction from the artificial compofition, in which to anfwer the end of mufic, the fimples muft have fuch an agreement in all relations, but principally and above all in acutenefs and gravity, tha€ the ear may receive the mixture with pleafure. 6. There remains another diftinction of found necefTary to be confidered, whereby they are faid to be fmooth and, even, or rough and harm ; alfo clear or blunt, hoarle and obtufe; the ideas of thefe differences muft.be fought from obfervations ; as to the caufe of thern, they depend upon the difpofttioa and ftate of the fonorous body, or the circum- fiances of the place. Smooth and rough founds depend upon the body principally ; we have a notable example of rough and harm found in ftring3 that are unevenly and not of the; fame conflitusion and duaenfion throughout j and foe thii f6 A TREATISE this reafbn that their founds are very grating, they are caTFei! falfe firings. I will let you in few words hear howMonfieur Perrault accounts for this* Reaffirms that there is no fuch thing as a fimple found, and that the found of the fame bell or chord is a compound of the founds of the feveral parts of it 5 fo that where the parts are homogeneous, and the dimenfions or figure uniform, there i9 always fuch a perfect union and mixture of all thefe founds that makes one uniform, fmooth and evenly found; and the contrary produces harfhnefs; for the likenefs of parts and figure makes art uniformity of vibrations, whereby a great number of fimilar and coincident motion* confpire to fortify and improve each other mutu- ally, and unite for the more effectual production of the fame effect. He proves his hypothefis by the phenomena of a bell, which differs in tone according to the part you ftrike, and yet ftrike it any where there is amotion overall the* parts ; he confiders therefore the bell as compofed of an in* finite number of rings, which according to their different drmenfions have different tones, as chords of different lengths have (caeteris paribus) and when it is ftruck, the vibrations of the parts immediately ftruck fpecify the tone, being fup- porfed by a fufficient number of confonant tones in other: parts : and to confirm this he relates a very remarkable thing ; he fays, He happened in a place where a bell fourided a fifth acuter than the tone it ufed to give in other places ; which in all probability, fays he, was owing to the accidental dif- pofition of the place, that was furnifhed with fuch art ad- juftment for reflecting that particular tone with force, ami fo unfit for reflecting others, that it abfolutely prevailed and! determined the concord and total found to the tone of that fifth. If we confider the found of a violin, and all ftrihged inftruments, we have a plain demortftration that every note is the effect of feveral more fimple founds ; for there is not enly the found refulting from the motion of the firing, but alfo that of the motion of the parts of the inftrument ; that this has a very confiderable effect in the total found is cer- tain b2caufe we are very fenftble of the tremulous motion of the parts of the violin, and efpecially, becaufe the fame firing' upon different violins founds very differently, which can be for no other reafon but the different conflitutions, of the part9 of thefe inftruments, which being moved by com- munication with the firing increafe- the found, and make it more or lefs agreeable, according to their different natures i 3 But O F M V S I C. if But Perrault affirms the fame of every firing in itfelf with- out confidering the inftrument ; he fays, every part of the firing has its particular vibrations different from the grofs and fenfible vibrations of the whole, and thefe are the caufes of different motions (and founds) in the particles; which being mixed and unite, as was faid of the founds, that com- pofe the total found of a bell, make an uniform and evenly compofition, wherein not only one tone prevails, but the mixture is fmooth and agreeable; but when the parts are un- evenly and irregularly conftitute, the found is harfh and the firing from that cal'ed falfe. And therefore fuch a firing, or other body having the like fault, has no certain and diftinft tone, being a compofition of feveral tones that do not unite and mix fo as to have one predominant that fpe- cifies the total tone. Again for clear or hoarfe founds they depend upon cir- cumftances tha f are accidental to the fonorous body; fo a man's voice, or the found of an inftrument, will be hollow and hoarfe, if it is raifed within an empty hogfhhead, which is clear and bright out of it; the reafon is very plainly the mixture of other and different founds raifed by reflection, that corrupt and change the fpecies of the primitive and di- rect found. Now that founds may be fit for obtaining the end of mufic thty ought to be fmooth and clear; efpecially the firfr, becaufe if they bave not one certain and jlifcernible tone, capable of being compared to others, and {landing to them in a certain relation of acutenefs, whofe differences the ear may be able to judge of and meafure, they cannot poffibly anfwer the end of mufic, and therefore are no part of the object of it. But there are alfo founds which have a certain tone, yet being exceffive, either in acutenefs or gravity, bear not that juft proportion to the capacity of the organs of hearing, as to afford agreeable fenfations. Upon the whole then we fhall call that harmonic or mufical found, which being clear and even is agreeable to the ear, and gives a certain and difcerni- ble tune (hence alfo called tunable found) which is the fub- jedl of the whole theory of harmony. Thus we have confidered the properties and affections of found that are any way neceffary to the fubjecT: in hand ; and of all the things mentioned, the relation of acutenefs and gravity, or the tune of founds, is the principai ingre- C dient iS ATREATISE dient In mufic ; the diftindtnefs and determinatenefs of which relation gives found the denomination of harmonical or mu- fical : next to which are the various meafures of duration. There is nothing in founds without thefethat can make mu- fic ; a juft theory whereof ab (traces from all other things, to confider the relations of founds in the meafures of tune and duration ; though indeed in the practice other differences are confidered (of which fomething more may be faid afterwards) but they ate fo little, compared to the other two, and under fo very general and uncertain theory, that I do not find they have ever been brought into the definition of mufic. A Definition and Division of Mus^ic. WE may from what is already faid affirm, that mufic has for its object, in general, found ; and parti- cularly, founds confidered in their relations of tune and duration, as under that formality they are capable of afford- ing agreeable fenfations. I mall therefore define mufic, a fcience that teaches how founds under certain meafures of tune and time, maybe produced; and fo ordered or dif- pofed, as in confonance (i. e. joint founding) or fucceflion, or both, they may raife agreeable fenfations. Pleafure I have faid is the immediate end of mufic; I fuppofe it therefore as a principle, that the obje61s propofed, are ca- pable, being duly applied, to affect: the mind agreeably 2 nor is it a precarious principle ; experience proves, and we know by the infallible teilimony of our fenfes, that fome fimple founds fucceed others upon the ear with a pofitive pleafure, others difagreeably ; according to the certain relations of tune and time; and fome compound founds are agreeable, others offenfive to the ear ; and that there are degrees and variety in this pleafure, according to the various meafures of thefe relations. For what pretences are made to the application of mufic to fome other purpofes than mere pleafure or re- creation, as thefe are obtained chiefly bv means of that pleafure, they cannot be called the immediate end of it. From the definition given, we have the fcience divided into thefe two general parts. Firfr, The knowledge of the Materia Mufica, or, how to produce founds, in fuch relations of tune and time asfhall be agreeable in confonance or O F M U S 7 C. 19 or fucceffion, or both. I do not mean the actual producing of the founds by an inftrument or voice, which is merely the mechanical or effect' ve part ; but the knowledge of the various relations of tune and time, which are the effential principles out of which the pleafure fought arifes, and upon which it depends. This is the pure fpeculative part of mufic. Second, How thefe principles are to be applied j or, how founds, in the relations that belong to mafic (as thefe are determined in the firfi pait) may be ordered, and varioufly put together in fuccefiion and confonance fo as to anfwer the end ; which part we rightly call, The art of compofition ; and it is properly the practical part of mufic. Some have added a third part, viz. The knowledge of inftruments ; but as this depends altogether upon the firft, and is only an application or expreffion of it, it could never be brought regularly into the definition ; and fo can be no part of the divilion of the fciencej yet may it deferve to be treated of, as a confequent or dependent of it, and neceffary to be underftood for the effectual part. As this has no fhare in my defign, I fhall detain you but while I fay, in a lew words, what I think fuch a treatife fhould contain. And imo, There fhould be a theory of inftruments, giving an account of their frame and construction, particularly, how, fuppoftng them completely provided of all their ap » paratus, each contains in it the principles of mufic, 1. e. how the feveral degrees of tune pertaining to mufic are to be found upon the inftruments. The fecond part fhould contain the practice of initruments, in fuch directions as might be helpful for the dextrous and nice handling of them, or the elegant performance of mufic : and here might be annexed rules for the right ufe of the voice. But after ail, I believe thefe things will be more fuccefsfully done by a living inftrudtor, I mean a fkilful and experienced mafter, with the ufe of his voice or inftrument : though I doubt not fuch might help us too by rules j but I have done with this. You muft next obferve with me, that as the art of common writing is altogether diitinct from the fciences to which it is fubfervient by preferving what would otherwife be loft, and communicating thoughts at diftance; fo there is an art of writing proper to mufic, which teaches how, by a fit and convenient way of reprefenting all the degrees and meafure^ of found, fuffickrit for directing in the executive part, one C 2 who 20 A TREATISE who underftands how to ufe his voice or inftrument , the artift when he has invented a compofition anfwering the principles and end of mufic, may preferve it for his own ufe, or communicate it to another prefent or abfent. To this 1 have very juftly given a place in the following work, as it is a thing of a general concern to mufic, though no part of the fcience, and merely a handmaid to the practice j and particularly as the knowledge of it is neceflary for carrying on my defign. I now return to the divifion above made, which I (hall follow in explaining this fcience. The firft general branch of this fubjedt, which is the con- templative part, divides naturally into thefe. Firft, The knowledge of the relations and meafures of tune. And, fe- condly, of time. The firft is properly what the ancients pro- perly called Harmonica* or the doctrine of harmony in founds ; becaufe it contains an explication of the grounds, with the various meafures and degrees of the agreement (harmony) of founds in refpeft of their tune. The other they called Rytbmica, becaufe it treats of the numbers of founds or notes with refpe£t to time, containing an explication of the meafures of long and fhort, or fwift and flow in the fucceffion of founds. The fecond general branch, which is the practical part, as naturally divides into two parts anfwering to the parts of the firft: that which anfwers to the Harmonica, the ancients called Melopasla ; becaufe it contains the rules of making fongs with refpect to tune and harmony of founds 5 though indeed we have no ground to belice that the anci- ents had any thing like compofition in parts. That which anfwers to the Rythmica, they called Rythmopeeia^ containing the rules concerning the application of the numbers ana time. A GENERAL ACCOUNT OF THE METHOD OF writing Music. HAT this title imports is neceffary to be well underftood, and to come to the thing itfelf let us confider. It was not enough to have difcovered fo much of the nature of found, as to make it ferviceable to our pleafure, by the various combinations of the degrees of tune, and meafure? O F M U S I C. 21 fneafures of time ; it was necefTary alfo, for enlarging the application, to find a method how to reprefent thefe fleeting and tranfient objects, by fenfible and permanent figns ; whereby they are as it were arretted : and what would otherwife be loft even to the compofer, he preferves for his own ufe, and can communicate it to others at any diftance; I mean he can direct them how to raife the like ideas to themfelves, fuppofing they know how to take founds in any relation of tune and time directed ; for the bufinefs of this art properly is, to reprefent the various degrees and mea- fures of tune and time in fuch a manner, that the con- nection and fucceflion of the notes may be eafily and readily difcovered, and the fkilful praiStifer may at fight find his notes, or, as they fpeak, read any fong. As the two principal parts of mufic are the tune and time of founds, fo the art of writing it is very naturally re- duced to two parts correfponding to thefe. The firft, or the method of reprefenting the degrees of tune, I (hall ex- plain in this chapter; which will lead me to fay fomething in general of the other, a more full and particular account whereof you fhall have in the next chapter. We have already feen how the degrees of tune or the fcale of mufic may be exprelTed by feven letters repeated as oft as we pleafe in a different character ; but thefe, without fome other figns, do not exprefs the meafures of time, unlefs we fuppofe all the notes of a fong to be of equal length. Now, fuppofing the thing to be made not much more difficult by thefe additional figns of time, yet the whole is more happily accomplifhed in the following manner. If we draw any number of parallel lines, as in plate i. fig. 7. then, from every line to the next fpace, and from every fpace to the next line up and down, reprefents a degree of the diatonick fcale ; and confequently from every line or fpace to every other at greater diftance reprefents fome other de- gree of the fcale, according as the immediate degrees from line to fpace, and from fpace to line are determined. Now to determine thefe we make ufe of the fcale expreft by fe- yen letters, as already explained, viz. c. d-, e.f: S ; a: b. C— where the tone greater is reprefented by a colon ( : ) the tone lefTer by a femicolon ( ; ) and the femitone greater by a ( . ). If the lines and fpaces are marked and named \>y thefe letters, as you fee in the figure, then according to the relations affigned to thefe letters (i, s. to the founds ex- preft 22 ATREATI.SE preft by them) the degrees and intervals of found expreft by the diftances of lines and fpaces are determined. As to the extent of the fcale of mufic, it is infinite if we confider what is fimply poffible, but for practice, it is limited ; and in the preient practice 4 octaves, or at moft 4 octaves with a 6th, comprehending 34 diatonick notes, is the greateft extent. There is fcarcely any one voice to be found that reaches near fo far, though feveral different voices may ; nor any one fingle piece of melody, that com- prehends fo great an interval betwixt its higheft and loweft note: yet we muft confider not only what melody requires, but what the extent of feveral voices and inftruments is capable of, and what the harmony of feveral of them re- quires; and in this refpeci the whole fcale is neceffary, which you have reprefented in the figure directed to j I fhall therefore call it the univerfal fyftem, becaufe it com- prehends the whole extent of modern practice. But the queftion ftill remains, how any particular order and fucctflion of founds is reprefented ? And this is done by fetting certain figns and characters one after another, up and down on the lines and fpaces, according to the intervals and relations of tune to be expreft ; that is, any one letter of the fcale, or the line or fpace to which it be- longs, being chofen to fet the firft note on, all the reft are fet up and down according to the mind of the compofer, upon fuch lines and fpaces as are at the defigned diftances, *. t. which exprefs the defigned interval according to the number and kind of the intermediate degrees ; and mind that the firft note is taken at any convenient pitch of tune; for the fcale, or the lines and fpaces, ferve only to determine the tune of the reft with relation to the firft, leaving us to take that as we pleafe : for example, if the firft note is placed on the line c, and the next defigned a tone or 2d g. above, it is fet on the next fpace above, which is d\ or if it is defigned a 3d g, it is fet on the line above which is e ; or on tne fecond line above, if it was defigned 5th, as you fee reprefented in the 2d column of the fcale in the pre- ceding figure, where I have ufed this character O for a rote. And here let me obferve in general, that thefe cha- racters ferve not only to direct how to take the notes in their true tune, by the diftance of the lines and fpaces on which they are let ; but by a fit number and variety of them (to be explained in the next chapter) they exprefs the O F M U S I C. 23 the time and meafure of duration of the notes; whereby it is plain thar thefe two things are no way confounded ; the relative msafures of tune being properly determined by the diftances of lines and fpaces, and the time by the figure of the note or character. It is eafy to obferve what an advantage there is in this method of lines and fpaces, even for fuch mufic as has all its notes of equal length, and therefore needs no other thing but the letters of the fcale to exprefs it ; the memory and imagination are here greatly affifted, for the notes (landing upward and downward from each other on the lines and fpaces, exprefs the rihng and falling of the voice more readily than different characters of letters j and the intervals are alfo more readily perceived. Obferve in the next place, that with refpedt to inftru- ments of mufic, I fuppofe their notes are all named by the letters of the fcale, having the fame diftances as already ftated in the relations of founds expreft by thefe letters j fo that knowing how to raife a feries of founds from the loweft note of any invtrument by diatonick degrees (which is al- ways firft learned) and naming them by the letters of the fcale, it is eafily conceived how we are directed to play on any inftrument, by notes fet upon lines and fpaces that are named by the fame letters. It is the bufinefs of the mafters and profeffors of feveral inftruments to teach the application more expreily. And as to the human voice, obferve, the notes thereof, being confined to no order, are called c or ; and where there is no fuch mark it is always the natural note. Thus if from a (natural} We would fet a 3d g, upward, it is cg&\ or a 3d /. above g 9 24 iA TREATISE it is b flat or fc. Thefe artificial notes are all determined on 'nftruments to certain places or pofitions, with refpeft to the parts of the inftrument and t^ie hand ; and for the voice they are taken according to the diftance from the laii note, reckoned by the number of tones and femitones that every greater interval contains. The laft general obferve I make here is, that as there are twelve different notes in the femitonic fcale, the writing might be fo ordered, that from every line a fpace to the next fpace or line fhould exprefs a femitone; but it is much better contrived, that thefe fhould exprefs the degrees of the diatonick fcale (i. e. fome tones fome femitones) for hereby we can much eafier difcover what is the true interval be- tween any two notes, becaufe they are fewer lines and fpaces interpofed, and the number of them fuch as anfwers to the denomination of the intervals; fo an o&ave compre- hends four lines and four fpaces ; a 5th comprehends three line.-, and two fpaces, or three fpaces and two lines j and fo of others. I have already (hewn, how it is better that there fhould be but feven different letters, to name the twelve degrees of the femitonic fcale ; but fuppofing there were twelve letters, it is plain we fhould need no more lines to comprehend an oclave, becaufe we might alfign two letters to one line or fpace, as well as to make it, for ex- ample, both cm and c, whereof the one belongeth to the diatonick feries, fhould mark it for ordinary, and upon oc- cafions the other be brought in the fame way we now do the figns & and b» A MORE PARTICULAR ACCOUNT OF THE METHOD J WHERE, OF THE NATURE AND UsE OF CLEFS. THOUGH the fcale extends to thirty-four diatonick notes, which require feventeen lines with their fpaces, yet becaufe no one fingle piece of melody comprehends near fo many notes, whatever feveral pieces joined in one har- mony comprehend among them; and becaufe every piece or fingle fong is directed or written diftin&ly by itfelf; therefore we never draw more than five lines, which com- prehend the greateft number of the notes of any fingle piece; and for thole cafes which require more we draw fhort lines occafionally OF MUSIC. 2 5 ©ccafionally, above or below the 5, to ferve the notes that go higher or lower. Example: 3 - — —- ■ i t: 3 - E ST Again, though every line and fpace may be marked at the beginning with its letter, as has been done in former times ; yet, fince the art has been improving, only one line is marked, by which all the reft are eafily known, if we reckon up or down in the order of the letters ; the letter marked is called the clef or key, becaufe by it we know the names of all the other lines and fpaces, and confequently the true quantity of every degree and interval. But becaufe every note in the octave is called a key, though in another fenfe this letter marked is called in a particular manner the figned clef, becaufe being written on any line, it not only figns or marks that one, but explains all the reft. And to prevent ambiguity in what follows, by the word Clef I fhall always mean that letter which, being marked on any line, explains all the reft, and by the word Key the principal note pf any fong in which the melody clofes, in the fenfe ex- plained in the laft chapter. Of thefe figned clefs there are three, viz. c, /, g ; and that we may know the improvement in having but one figned clef in one particular piece, alfo how and for what purpofe three different clefs are ufed in different pieces, confider the following definition. A Song is either fimple or compound. It is a fimple fong, where only one voice performs ; or, though there be more, if they are all unifon or oclave, or any other concord in every note, it is ftill but the fame piece of melody, per- formed by different voices in the fame or different pitches of tune, for the intervals of the notes are the fame in them all. A compound fong is where two or more voices go together, with a variety of concords and harmony ; (o that the melody each of them makes is a diftin£t and different fimple fong, and all together make the compound. The melody that each of them produces is therefore called a part of the com- pofition ; and all fuch compofitions are very properly called fymphonetic mufic, or mufic in parts ; taking the word mu- iic here for the compofition or fong itfelf. Now, becaufe in this compofition the parts muft be fome of them higher and fome lower (which are generally fo or- D defect 26 A TREATISE dered that the fame part is always higheft or loweft, though in modern compofitions they do frequently change) and all written diftin&ly by themfelves, as is very neceffary for the performance ; therefore the ftaffof five lines upon which each part is written, is to be confidered as a part of the univerfal fyftem or fcale, and is therefore called a particular fyftem 5 and becaufe there are but five lines ordinarily, we are to fuppofe as many above and below as may be required for any fingle part ; which are a&ually drawn in the particular places where they are neceffary. The higheft part is called the treble, or alt, whofe clef is £, fet on the 2d line of the particular fyftem, counting upward : the loweft is called the bafs, i. e. bafis, becaufe it is the foundation of the harmony, and formerly in their plain compofitions the bafs was firft made, though it is otherwife now j the bafs clef is /on the 4th line upward : all the other parts, whofe particular names you will learn from practice, I (hall call mean parts, whofe clef is s, fometimes on one, fometimes on another line ; and fome that are really mean parts are fet with the g clef ; and obferve that the c and/ clefs are marked with figns no-way refembling thefe letters 5 I think it were as well if we ufed the letters themfelves, but cuftom has carried it otherwife j yet that it may not feem al- together a whim, Kepler, chap, book 3. of his Harmony, has taken critical pains to prove, that thefe iigns are only corrup- tions of the letters theyreprefent; the curious mayconfult him. We are next to confider the relations of thefe clefs to one another, that we may know where each part lies in the fcale or general fyftem, and the natural relation of the parts among themfelves, which is the true defign and office of the clefs. Now they are taken 5ths to one another, that is, the clef/ is loweft, c is a 5th above it, and g a 5th above c. Example. or th- us v. E?SsF MeanC O F M U S I C. 27 Obferve, that though in the particular fyftems, the treble or g clef is ordinarily fet on the 2d line, the bafs or f clef on the 4th line, and the mean or c clef on the 3d line (ef- pecially when there are but three parts) yet they are to be found on other lines j as particularly the mean clef, which tfioft frequently changes place (becaufe there are many mean parts) is fometimes on the ift, 2d, 3d, 4th, and 5th lines - a out on their removal* have different names. Example. •£ nd ^ & ** j ft Soprano: 2d Mozzo Soprano: 3d Contra Tenor : 4th Tenor: 5th Tenor Bafs.— The perfon who fings from this laft named cliff may prove his notes either from the mean on the 5th line, or bafs on the 3d ; but on what- ever line in the feparate particular fyftem any clef is figned, it muft be underftood to belong to the fame place of the ge- neral fyftem, and to be the fame individual note or found on the inftrument which is directed by that clef; fo that to know what part of the fcale any particular fyftem is, we muft take its clef where it ftands figned in the fcale, and take as many lines above and below it, as there are in the particular fyftem ; or thus, we muft apply the particular fyf- tem to the fcale, fo as the clef lines coincide, and then we fhall fee with what lines of the fcale the other lines of the particular fyftem coincide : For example, if we find the clef on the 3d line upward in a particular fyftem ; to find the coincident five lines to which it refers in the fcale, we take with the/ clef line, two lines above and two below. Again, if we have the c clef on the 4th line, we are to take in the {bale with the clef line, one line above and three below, and fo of others ; fo that according to the different places of t'r e olefin a particular fyftem, the lines in the fcale correfpor- den* to that fyftem may be all different, except the clef line which is invariable : and that you may with eafe find in the D 2 fcale 28 A TREATISE fcale the five lines coincident with every particular fyftem, upon whatever line of the five the clef may be fet. As to the reafon of changing the relative place of the clef, i. e. its place )n the particular fyftem, it is only to make this comprehend as many notes of the fong as poflible, and by that means to have fewer lines above or below it; fo if there are many notes above the clef note and few below it, this purpofe is anfwered by placing the clef in the firft or fecond line ; but if the fong goes more below the clef, then it is beft placed higher in the fyftem : in (hort, according to the relation of the other notes to the clef note, the particular fyftem is taken differently in the fcale, the clef line making one in all the variety, which confifts only in this, viz. tak- ing any five lines immediately next other, whereof the clef line muft always be one. By this conftant and invariable relation of the clefs, we learn eafily how to compare the particular fyftems of feveral parts, and know how they communicate in the fcale, i. e, which lines are unifon, and which are different, and how far, and confequently what notes of the feveral parts are unifon, and what not : For you are not to fuppofe that each part has a certain bounds within which another muft never come ; no, fome notes of the treble, for example, may be lower than fome of the mean parts, or even of the bafs ; and that not only when we compare fuch notes as are not heard together, but even fuch as are. And if we would put together in one fyftem, all the parts of any compofition that are written feparatelv. The rule is plainly this, viz, place the notes of each part at the fame diftances above and below the proper clef, as they ftand in the feparate fyftem. And becaufe all the notes that are confonant (or heard together) ought to ftand, in this defign, perpendicu- larly over each other, therefore that the notes belonging to each parr may be diftin&ly known, they may be made with fuch differences as fhall not confufe or alter their fignifica- tions with refpecl to time, and only fignify that they belong to fuch a part ; by this means we fhali fee how all the parts change and pafs thro' one another, i. e. which of them, in every note, is higheft or lowed or unifon ; for they do fometirnes change, tho' more generally the treble is higheft: and the Bafs loweft, the change happening more ordinarily betwixt the mean parts a,rnoqg thernielves, or thefe with the treble OF MUSIC. 29 treble or bafs : The treble and bafs clefs are diftant an octave and tone, and their parts do foldom interfere, the treble moving more above the clef note, and the bafs below. We fee plainly then, that the ufe of particular figned clefs is an improvement with refpect to the parts of any compofition ; for unlefs fome one key in the particular fy- ftems were diftinguifhed from the reft, and referred invariably and conftantly to one place in the fcale, the relations of the parts could not be diftinclly marked ; and that more than one is neceffary, is plain from the diftance there muft be a- mong the parts : Or if one letter is chofen for all, there muft be fome other fign to (hew what part it belongs to, and the relation of the parts. Experience having approved the number and relations of the figned clefs which are explained, 1 (hall add no more as to that, but there are other things to be here obferved. The choofing thefe letters f. c . g for (igned clefs, is a thing altogether arbitrary ; for any other letter within the fyftem, will explain the reft as well ; yet 'tis fit there be a eonftant rule, that the feveral parts maybe right diftinguifh- ed ; and concerning this obferve again, that for the per- formance of any (ingle piece the c!ef ferves only for ex- plaining the invervals among the lines and fpaces, fo that we need not mind what part of any greater fyftem it is, and we may take the firft note as high or low as we pleafe : For as the proper ufe of the fcale is not to limit the abfo- lute degree of tone, fo the proper ufe of the figned clef is not to limit the pitch, at which the firft note of any part is to be taken, but to determine the tune of the reft with relation to the firft, and, confidering all the parte together, to determine the relations of their feveral notes, by the re- lations of their clefs in the fcale : And fo the pitch of tune being determined in a certain note of one part, the other notes of that part are determined, by the eonftant relations of the letters of the fcale ; and alio the notes of the other parts, by the relations of their clefs. To fpeak particularly of the way of tuning the inftruments that are employed in executing the feveral parts, is out of my way ; 1 fnall only fay this, that they are to be fo tuned as the clef notes, wherever they lie on the inftruments which ferve each part, be in the fore mentioned relations to one another. As 3 o ATREATISE As the harpfichord or organ (or any othar of the kind) is the moft extenfive inftrument, we may be helped by it to form a clearer idea of thefe things : For confider, a harpfichord contains in itfelf all the parts of mufic, I mean the whole fcale or fyftem of the modern practice ; the foremoft range of keys contains the diatonic feries beginning, in the largeft kind, in g, and extending to c a- bove the fourth 8ve ; which therefore we may well fuppofe teprefented by the preceeding fcale. In practice, upon that inftrument, the clef notes are taken in the places repre- fented in the fcheme j and other inftruments are fo tuned, that, confidering the parts they perform, all their notes of the fame name are unifon to thofe of the harpfichord that belong to the fame part. T have faid, the harpfichord con- tains all the parts of mufic ; and indeed any two diftincl parts may be performed upon it at the fame time and no more ; yet upon two or more harpfichords tuned unifons, whereby they are in effecV but one, any number of parts may be executed : And in this cafe we fhould fee the feveral parts taken in their proper places of the inftrument, accurding to the relations of their clefs explained : And as to the tuning the inftrument, I fliall only add, that there is a certain pitch to which it is brought, that it may be neither too high nor too low, for the accompaniment of other in- ftruments, and efpecially for the human voice, whether in unifon or taking a different part ; and this is called the Confort Pitch. To have done, you muft confider, that for performing any one fingle part, we may take the clef note in any 8ve, i. e. at any note of the fame name, providing we go not too high or too low for finding the reft of the notes of the fong : But in a confort of feveral parts, all the clefs muft be taken, not only in the relations, but alfo in the places of the fyftem already mentioned, that every part may be comprehended in it : Yet ft ill you are to mind, that the tune of the whole, or the abfolute pitch, is in it felf an arbitrary thing, quite foreign to the ufe of the fcale; tho" there is a certain pitch generally agreed upon, that dif- fers not very much in the practice of any one nation or fet of muficians from another. And therefore, When I fpeak of the place of the clefs in the fcale or general fyftem, you muft underftand it with refpeft to a fcale ot a certain determined extent j for this being undetermin- ed* OF MUSIC, 31 ed, fo muft the places of the clefs be : And for any fcale of a certain extent, the rule is, that the mean clef c be taken as near the middle of the fcale as poffible, and then the clef g a 5th above, and / a 5th below, as it is in the prefent general fyftem of four 8ves and a 6th, reprefented in, the fcheme, and actually determined upon harpfichords. In the laft place conhder, that fince the lines and fpaces of the fcale, with the degrees ftated among them by the ietters, fufficiently determine how far any note is diftant from another, therefore there is no need of different characters of letters, as would be if the fcale were only expreft by thefe letters : And when we fpeak of any note of the fcale, naming it by a or b, &c. we may explain what part of the fcale it is in, either by numbring the 8ves from the loweft note, and calling the note fpoken of (for example) c in the loweft 8ve or in the 2d 8ve, and fo on : Or, we may determine its place by a reference to the feat of any of the three figned clefs ; and fo we may fay of any note, as for g, that it is fuch a clef note, or the firft or fecond, &c. f or g above fuch a clef. Take this application, fuppofe yeu afk me what is the higheft note of my voice ? If I fay d, you are not the wifcr by this anfwer, till I determine it by faying it is d in the fourth octave, or the firft d above the treble clef. But again, neither this queftion nor the anfwer is fufRciently de- termined, unlefs it have a reference to fome fuppofed pitch of tune in a certain fixt inftrument, as the ordinary Confort Pitch of a harpfichord, becaufe, as I have frequently faid, the fcale of mufic is concerned only with the relation of notes and the order of degrees, which are ftill the fame in all differences of tune, in the whole feries. Of the Reason, Use, and variety of the Signatures of Clefs. I Have already faid, that the natural and artificial Note expreffed by the fame letter, as c and m t are both fet on the fame line or fpace. When there is no ^ or (3 marked on any line or fpace, at the beginning with the clef, then all the notes are natural ; and if in any particular place of the fong, the artificial note is required, 'tis fignifkd by the fign %t or b» fet upon the line a fuace before that nore ; but if a 3 ox 3 i ATREATISE M or b is fet at the beginning in any line or fpace with the clef, then all the notes on that line or fpace are the artificial ones, that is, are to be taken a femitone higher or lower than they would be without fuch a fign ; the fame affecls all their 8ves above or below, tho' they are not marked fo. And in the courfe of the fong, if the natural note is fometimes re- quired, it is fignified by this mark fy. And the marking the fyftem at the beginning with (harps or flats, 1 call the fig- nature of the clef. In what's faid, you have the plain rule for application ; but that we may better conceive the reafon and ufe of thefe fignatures, it will be neceflary to recoiled, and alfo make a little clearer, what has been explained of the nature of keys or modes, and of the original and ufe of the ftiarp and flat notes, I fhall explain what a key and mode in mufic is ; and diftinguifh betwixt thefe two, and fhew that there are and can be but two different modes, the greater and the lefTer, according to the two concinnous divifions of the 8ve, viz. by the 3d g. or the 3d /. and their proper accompaniments j and whatever difference you may make in the abfolute pitch of the whole notes, or of the firft note which limit all the reft, the fame individual fong muft ftill be in the fame mode ; and by the key I underftand only that pitch or degree of tune at which the fundamental or clofe note of the melody, and confequently the whole 8ve is taken ; and becaule the fundamental is the principal note of the 8ve which regulates the reft, it is peculiarly called the key. Now as to the va- riety of keys, if we take the thing in fo large a fenfe as to fignify the abfolute pitch of tune at which any fundamental note may. be taken, the number is at leaft indefinite 5 but in practice it is limited, and particularly with refpecl: to the de- nominations of keys, which are only twelve, viz. the twelve different names or letters of the femitonic fcale ; fo we fay the key of a fong is c or d, &c. which fignifies that the cadence or clofe of the melody is upon the note of that name when we fpeak of any inftrument ; and with refpecl: to the human voice, that the clofe note is unifon to fuch a note on an inftrument ; and generally, with refpecl both to inftru- ments and voice, the denomination of the key is taken from the place of the clofe note upon the written mufic, i. e. the name of the line or fpace where it ftands : Hence we fee, that tho' the difference of keys refers to the degree of tune, at which the fundamental, and confequently the whole 8ve OF MUSIC. 33 8ve is taken, in diftin&ion from the mode or conftitutlon of an octave, yet thefe denominations determine the differences only relatively, with refpec-t to one certain feries of fixed founds, as a fqale of notes upon a particular inftrument, in which all the notes of different names are different keys, ac- cording to the general definition, becaufe of their different degrees of tune j but as the tuning of the whole may be in a different pitch, and the notes taken in the fame part of the inftrument, are, without refpect to the tuning of the whole, ftill called by the fame name c or d, &c becaufe they ferve only to mark the relation of tune betwixt the notes, therefore 'tis plain, that in practice a fong will be faid to be in the fame key as to the denomination, though the abfolute tune be dif- ferent, and to be in different keys when the abfolute tune is the fame ; as if the note a is made the key in one tuning, and in another the note d unifon to a of the former. Now, this is a kind of limitation of the general definition, yet it ferves the defign beff for practice, and indeed cannot be otherwife without infinite confufion. I flull a little below make fome more particular remarks upon the denominations of founds, or notes raifed from inftrumer.ts or the human voice: but from what has been explained, you will eafily underftand what difference I put betwixt a mode and a key; of modes there are only two, and they refpccl: what I would call the internal conftitution of the 8ve ; but keys are inde- finite in the more general and abftra£f. fenfe ; and with regard to their denominations in practice they are reduced to twelve, and have refpect to a circumftance that is external and acci- dental to the mode ; and therefore a key may be changed un- der the fame mode, as when the fame fong, which is always ;n the fame mode, is taken up at different notes or degrees of tune ; and from the fame fundamental or key a feries may proceed in a different mode, as when different fongs begin in the fame note. But then becaufe common ufe applies the word key in both lenfes, i. e. both to what I call a key and a mode, to prevent ambiguity the word fharp or fiat ought to be added when we would exprefs the mode ; fo that a fharp key is the fame as the greater mode, and a fiat key a leiler mode ; and when we would exprefs both mode and key, we join the name of the key note, thus, we may fay fuch a fong is for example in the fharp or fldt key c, to fignify that the fundamental note in which the clofe is made is the note call- ed c on the inftrument, or ur ifon to it in the voices or gtnt- & rally 34 A T R E A T I S E rally, that it is fet on the line or fpace of that name in writ- ing ; and that the 3d g, or 3d /, is ufed in the melody, while the fong keeps within that key ; far I have alfo obferved. that the fame fong may be carried through different keys, or make fuccefftve cadences in different notes, which is commonly ordered by bringing in fome note that is none of the natural notes of the former key, of which more immediately : But when we hear of any key denominated c or d without the word fharp or flat, then we can underftand nothing but what I have called the key in diftin&ion from the mode, i. e. that the cadence is made in fuch a note, -^Yr. Again, Ifhall explain the ufe of the notes we call fharp and flat, or artificial notes, ard the diftinc'tion of keys in that refpect into natural and artificial, and fhew that they are necefTary for correcting the defects of infl. ruments having rixt founds, that beginning at any note we may have a true concinnous diatonick feries from that note, which in a fcale of fixt degrees in the 8ve we cannot have, all the orders of degrees proceeding from each of the feven natural notes being different, of which only two are concinnous, viz. irom c which makes a fharp key, and from a which makes a flat key ; and to apply this more particularly, ycu mull un- uerftand the ufe of thefe fharp or fiat notes to be this, that a fong, which, being fet in a natural key, or without fharps imd fiats, is either too high or too low, may be tranfpofed or let in another more convenient key, which nectiTarily brings in fome of the artificial notes, in order to make a diaton ck feries from this new kev, like that from the other ; 2nd when the fong changes the key before it comes to the final clofe, though the principal he natural, yet fome or theie into which it changes may require artificial notrs, which ate the Hien- tial and natural notes of this new key \ for though this be called an artificial key, it is only fo with rtfpedt to the names iX the notes in the fixt fyftern, wh ch are Hill natural with iefpedy is carried on to a clofe ia d, which is a third key, and with refpe£t to tint piece is in- deed the principal key, in which alfo the piece begins; but T fhall eonftder this again ; it wis enough to my purpofe here, that all the notes from the beginning to the fir ft clofe in a were natural to the octave from a with a 3d ; and tho' tbe 3d above the clofe is not u!ed, yet the 6th below it is ufed, which is rhe fame thing in determining the fpecies. I return now to explain the reafon and ufeof the fignature^' of clefs. And firft, Let us fuppofe any piece of melody con- fined flriclly to one mode or key, and let that be the natural . fharp key c, from which as the relation of the leiters are de- termined In tne fcale, there is a true mufic.;! feries and grada- tion of notes, and then- fore it requires ho -38 or b* confe- quently the fignarure of the clef mull be plain. Bat let the piece be tranfpofefJ to the key > though one fignature is *, and another b t and thefe are no 1 ib order- ed at random 3 the reafon I fhaU explain to you, in the firft place 38 A TREATISE place there is a greater harmony with refpecT: to the eye ;. but this is a fmall matter, a better reafon follows. Confider, every letter has two powers, i. e. is capable of rcprefenting two notes, according as you take it natural or plain, as c, d t &c. or tranfpofed as c * or d b ; again, every line and fpace is the feat of one particular letter. Now if we take two powers of one letter in the fame octave or key, the line or fpace to which it belongs muft have two different figns ; and then when a note is fet upon that line or fpace, how fhall it be known whether it is to be taken natural or tranfpofed ? This can only be done by fetting the proper figns at every fuch note ; which is not only troublefome, but renders the general fignature ufelefs as to that line or fpace. This is the reafon why fome fignatures are made * rather than b, and contrarily; for example, take for the fundamental c*, the reft of the notes to make a (harp key are d^,f:/^, g*, a*, c, where you fee /and c are taken both natural and tranfpof- ed, which we avoid by making all the artificial note b ; thus do, eb t f; gb, tfb, b, c, db. 'Tis true that this might be helped another way, viz. by taking all the notes % i. e. taking *3fc for/, and b%£ for c x but the inconveniency of this is vifible, for hereby we force two natural notes out of their places, wherebv the difficulty of performing by fuch di^eclion is increafed. In the other cafes where I have marked all b rather than*, the fame reafons obtain. And in fome cafes > fome ways of figningwith a * would have both thefe incon- veniencies. The fame reafons make it neceffary to have fome fignature * rather than b ; but the oclave beginning in gb is lingular in this refpedt, that it is equal which way it is figned, for in both there will be one natural note difplaced unavoidably ; b natural is figned c b, and if you make all the figns *, you muft either take in two powers of one letter, or take e^ for/. Now neither in this, nor any of the other cafes will the mixing of the figns remove the inconvenien- cies ; and fuppofe it could, another follows upon the mixture, which leads me to {hew why the fame clef is either all ^ or all b, the reafon follows. The quantity of an interval expreft by notes fet upon lines and fpaces marked fome *, fome b, will not be fo eafily dis- covered, as when they are all marked one way, becaufe the number of intermediate degrees from line to fpace, and from fpace to line, anfwers not to the denomination of the inter- val ] for example, if it is a 5th, I fhall more readily difcover , it O F M U S I C. 39 it when there are five intermediate degrees from line to fpace, than if there were but four ; thus, from g fharp to d (harp is a 5th, and will appear as fuch by the degrees, among the lines and fpaces ; but if we mark it g (harp, e b, it will have the appearance of a 4th ; alfo from / fharp to a fh3rp is a 3d, and appears fo, whereas trom^fharp to D looks like a 4th; and for that reafon Mr. Simpfon in his Compendium of Mu- fic calls it a lefier 4th, which I think he had better called it an apparent 4th ; and fo by making the figns of the cliff all of one kind, this inconveniency is faved with refpedt to al! intervals, whole both extremes have a tranfpofed letter j and a? to fuch intervals which have one extreme a natural note, or expreft by a plain letter, and the other tranfpofed, the in- conveniency is prevented by the choice of the * in fome keys, and of the b in others ; for example, from d to /"fharp is a 3d, equal to that from d to g b, but the firfr only appears like a 3d, the latter a 4th, and fo of other intervals from d. Again from f to b'b, ox f to a fharp is a 4th, but the firft is the beft way of marking it; there are no more tranfpofed notes in that oclave, nor any other oclave, whofe fundamen- tal is a natural note, that is marked with \ > . it aiufi be owned, after all, that whatever way we chufe the lignsof tranfpofed notes, the founds or notes themfelveson an intlrumer.t are individually the fame; and marking them one way rjther than another, refp p <£ls only the conveniences of reprefenting them to the eye, which ought not to be ne- glected ; especially for the direction of the human voice, be- caule that having no fixt founds (as an inftrument has, whofe notes may be found by a local memory of their feat on the inftrumenc) we have not another way of finding the true note but computing the interval by the intermediate diatonic degrees, and the more readily this can be done, it Is certain'v ihe better. Now you are to obf rve, tftat, as the fignature of the clef is defigned for, and can ierve but one key, which ought ra- ther to be the principal key or octave of the piece than any other, fhewing what trartfpof.-d notes belong to it, fo the in- conveniency laft mentioned is remedied, by having the figrts all of one kind, only for thefe intervals one of whole ex- tremes is the key-note, or letter. But a fong may modulate or change from the principal into ether keys, which may re- quire other notes than the fignature of the clef affords; fo we find fharp and b upon fome particular notes contrary to the 2 4 o ATREATISE the clef, which fhews that themelody is out of the principal .key, fuch notes being natural to fome other fubprincipal key into which it is carried j and thefe figns are, or ought always tobechofen in the moft convenient manner for exprefling the interval j for example, the principal key being c with a 3d greater, which is a natural octave (i. e. expreffed all with plain letters) fuppofe a change into its 4th/; and here let a 4th upward be required, we muft take it in b or a fharp; the firit is the beft way, but either of them contradicts the cliff which is natural ; and we no fooner find this than we judge the key Jis changed. But again, a change may be where this fign of it cannot appear, viz. when we modulate into the 6th of a fharp principal key, or into the 3d of a flat principal key, becaufe thefe have the fame fignature, as has been already (hewn, and have fuch a connection, that, unlefs by a cadence, the melody can never be faid to be out of the principal key. And with refpedt to a flat principal key, ob- ferve, that if the 6th g. and 7th g. are ufed, as in fome cir- cumftances they may, efpecially towards a cadence, then there will be neceffarily required upon that 6th and 7th, another fign than that with which its feat is marked in the general fignature of the cliff, which marks all flat keys with the leffer 6ths and 7ths; and therefore in fuch cafe (i. e. where the principal key is flat) this difference from the clef is not a fign that the melody leaves the key, becaufe each of thefe belong to it in different circumftances ; yet they can- not be both marked in the clef, therefore that which is of more general ufe is put there, and the other marked occa- fionally. From what has been explained, you learn another very re- markable thing, viz. to know what the principal key of any piece is, without feeing one note of it ; and this is done by knowing the fignature of the clef. There are but two kinds. of keys (or modes of melody) diftinguifhed into fharp and flat, as already explained ; each of which may have any of the 1 2 different notes or letters of the femitonic fcale for its fun- damental ; in the ift and 6th line of the upper part of the preceding table you have all thefe fundamentals or key-notes, and under them refpedtively ftand the fignatures proper to each, in which, as has been often faid, the flat keys have their 6th and 7th marked of the leffer kind ; and therefore as by the key, or fundamental note, we know the fignature, fo reciprocally by the fignature we can know the key ; but 'tis O F M U S I C. 41 *tis under this one limitation that, becaufe one flgna- ture ferves two keys, a iharp one, and a flat, which is the 6th above or 3d below the fharp one, therefore we only learn by this, that it is one of them, but not which ; for example, if the clef has no tr?nfpofed note but / 36, then the key is g with a 3d greater, or e with a 3d lefler. If the clef has b and e b» the key is b with a 3d greater, or g with a 3d lefler, and fo of others, as in the table : I know indeed, for I have found it fo in the writings of the beft matters, that they are not ftricl: and conftant in ob- ferving this rule concerning the fignature of the clef, ef- pecially when the principal key is a flat one ; in which cafe you'll find frequently, that when the 6th lefler or 7th leiTer to the key, or both, are tranfpofed notes, they don't fign them fo in the clef, but leave them to be marked as the courfe of the melody requires ; which is conve- nient enough when the piece is fo conducted as to ufe the lefler 6th and 7th feldomer than the greater. Of the Name, with the various Definitions and Divisions of the Science. THE word Mufic comes to us from the Latin word Muftca, if not immediately from a Greek word of the fame found, from whence the Romans probably took theirs ; for they got much of their learning from the Greeks. Our criticks teach us, that it comes from the word Mufa, and this from a Greek word which fignifies to fearch or find out, becaufe the Mufes were feigned to be inventrefles of the fciences, and particularly of poetry and thofe modulations of found that conftitute mufic. But others go higher, and tell us, the word Mufa comes from a Hebrew word, which fignifies art or difcipline ; hence Mufa and Mufica antiently fignified learning in general, or any kind of fcience ; in which fenfe you'll find it frequently in the works of the ancfent philofo- phers. But Kircher will have it from an Egyptian word ; becaufe the reftoration of it after the flood was probably there, by reafon of the many reeds to be found in their fens, and upon the banks of the Nile. Hefychius tells us, that the Athenians gave the name of mufic to every art. From this it was that the Poets and Mytholo- F gifts 4 2 A TREATISE gifts feigned the nine Mufes daughters of Jupiter, who invented the fciences, and prefided over them, to afliit and infpire thofe who apply to ftudy them, each having hzr particular province, [n this general fenfe we have it defin'd to be the orderly arangement and right difpofit'ion of things ; in {hort, the agreement and harmony of the whole with its parts, and of the parts among themfelves. Hermes Trifmegiftus fays, That mafic is nothing but the knowledge of the order of all things ; which was alfo the doctrine of the Pythagorean fchool, and of the Platonicks, who teach that every thing in the univerfe is mufic. Agreeable to this wide fenfe, fome have diftin- guifhed mufic into divine and mundane ; the firft refpecls the order and harmony that obtains among the celeftial minds ; the other refpetts the relations and order of every thing elfe in the univerfe. But Plato by the divine mu- fic understands, that which exifts in the divine mind, viz. thefe archetypal ideas of order and fymmetry, ac- cording to which God formed all things ; and as this or- der exifts in the creatures, it is called mundane mufic : Which is again fubdivided, the remarkable denominations of which are, Firft, Elementary or the harmony of the firft elements of things ; and thefe, according to the phi- lofophers, arc fire, air, water, and ear:h, which tho' feemingly contrary to one another, are, by the wifdom, of the Creator, united and compounded in all the beau- tiful and regular forms of thinp-s that fall under our fenfes. 2d. Celeftial, comprehending the order arid pro- portions in the magnitudes, diftances, and motions of the heavenly bodies, and the harmony of the founds pro- ceeding from thefe motions : For the Pythagoreans af- firmed that they produce the molt perfect: confort ; the argument, as Macrobius in his commentary on Cicero's Somnium Scipionis has it, is to this purpofe, viz Sound is the effect of motion, and fince the heavenly bodies mud be under certain regular and ftated laws of motion, they mult produce Something mufical and concordant ; for from random and fortuitous motions, governed by no certain meafure, can only proceed a grating and unplea- fant noife : And the reafon, fays he, why we are not fenfible of that found, is the vaftnefs of it, which ex- ceeds our fenfe of heating; in the fame manner as the inhabitants near the cataracts of the Nile are infenfible Of O F M U S I C. 43 of their prodigious noife. But fome of the hiftorians, if I remember right, tell us that by the exceffivenefs of the founds, thefe people are rendered quite deaf, which makes that demonstration fomewhat doubtful, finee we hear every other found that reaches to us. Others alledge that the founds of the fpheres, being the fir ft we hear when we come into the worid, and being habituated to them for a long time, when we could fcarcely think or make reflection on any thing, we become incapable of perceiv- ing them afterwards. But Pythagoras faid he perceived and underftood the celefiial harmony by a peculiar favour of that fpirit to whom he owed his life, as Iamblichus reports of him, who fays, That tho' he never fung or played on any inftrument himfeif, yet by an inconceiva- ble fort of divinity, he taught others to imitate the ce- leftial mufic of the fpheres, by inftruments and voice : For according to him, all the harmony of founds here be- low, is but an imitation, and that imperfect too, of the other. This fpecies is by fome called particu'arly the mundane mafic. 3d. Human, which confitts chiefly in the harmony of the faculties of the human foul, and its various paflions \ and is alfo considered in the proportion and temperament, mutual dependence and connection, of all the parts of this wonderful machine of our bodies. 4'.h. Is what in a more limited and peculiar fenfe of the , word was called muiic ; which has for its object motion, confidered as under certain regular meafures and propor- tions, by which it affects the fenfes in an agreeable man- ner. All motion belongs to bodies, and found is the ef- fect of motion, and cannot be without it ; but all motion does not produce found, therefore this was again fub- divided. Where the motion is without found, or as it is only the object of feeing, it was called mufica orcheftria or filtatoria, which contains the rules for the regular mo- tions of dancing ; alfo Hypocritica, which refpe&s the motions and gefiures of the Pantomimes. When moticn is perceived only by the ear, i. e. when found is the ob- ject of mufic, there are three fpecies ; Harmonica, which confulers the differences and proportion of founds, with refpect. to acute and grave ; Rythmica, which refpeits the proportion of founds as to time, or the fwiftnefs End fiownefs of their fuccefftons ; and Metrica, which be- longs properly to the poets 5 and refpe&s the verifying F 2 art : 44 ATREATISE art : But in common acceptation 'tis now more limited, and we call nothing mufic but what is heard j and even then we make a variety oi tones neceflary to the being of mufic. Arifbides Quintilianus, who writes a profeft treatife upon mufic, calls it the knowledge of fingino-, and of the things that are joined with finging {mirm^n |S*s? Demodocus is another celebrated mufician, of whom al- ready. Hermes, or Mercury Trifmigiftus, another demigod, is alfo reckoned amongft the inventors or improvers of mufic and of the lyre. Linus was a famous poet and mufician, fome fay he taught Hercules, Thamyris and Orpheus, and even Am- phion. To him fome afcrbe the invention of the lyre. Olympus the Myfian, is another benefactor to mufic ; he was the difciple of Marfyas the fon of Hyagnis the Phrygian; this Hyagnis is reckoned the inventor of the tibiae, which others afcribe to the mufe Euterpe, as Horace infinuates, " Sinaeque tibias Euterpe cohibet." Orpheus the Thracian, is alfo reckoned the author, or at leaft the introducer of various arts into Greece, among which is mufic ; he pra&ifed the lyre he got from Mercury. Some fay he was mafter to Thamyris and Linus. Phemius of Ithaca. Ovid ufes his name for any excellent mufician : Homer alfo names him honourably. 2 'Terpander O F M U S I C. 5* Terpander the Lefbian, lived in the time of Lycurgu?, and fet his laws to mufic. He was the firft who among the Spartans applied melody to poems, or taught them to be fung in regular meafures. This is the famous mufician who quelled a fedition at Sparta by his mufic. He and his fol- lowers as faid to have firft inftituted the mufical mode, ufed in finging hymns to the gods j and fome attribute the inven- tion of the lyre to him. Thales the Cretan was another great mafter, honourably entertained by the Lacedemonians for inftru&ing their youth. Of the wonders he wrought by his mufic, we mall hear again. Thamyris the Thracian was fo famous, that he is feigned to have contended with the mufes, upon conditio* he mould poflefs all their power if he overcame, fbut if' they were viclors he confented to lofe what they pleafed ; and being defeated, they put out his eyes, fpoiled his voice, and ftruck him with madnefs. He was the fiift who ufed in- ftrumental mufic without finging. Thefe are the remarkable names of muficians before Ho- mer's time, who himfelf was a mufician, as was the famous poet Pinda. You may find the characters of thefe menti- oned at more large, in the firft book of Fabritims Bibliotheca Grata, We find others of a latter date, who were famous in mufic, as Lafus Hermionenfis, Melanippides, Philoxenus, Timotheus, Phrynnis, Epigonius, Lyfander, Simmicus, Diodorous the Theban ; who were authors of a great va- riety and luxurious improvements in mufic. Lafus, who lived in the Urns of Darius Hyftafpes, is reckoned the firft who ever wrote a treatii'e upon mufic. Epigonius was the author of an inftrument called epigonium, of 40 firings, he introduced playing on the lyre with the hand without a plectrum, and was the firft who joined the Cithara and Ti- bia in one concert, altering the iimplicity of the more anci- ent mufic ; as Lyfancier did by adding a great many ftrings to the Cythara. Simicus alfo invented an inftrument called fimmicicum of 35 ftrings. Diodorus improved the tibia, which at fiifthad but four holes, by contriving more holes and notes. Timotheus, for adding a firing to his lyre was fined by the Lacedemonians, and the ftring ordered to be taken away. Of him and Phrynnis, the ccmit poet Pherecraies G 2. makes 5* ATRE.ATISE makes bitter complaints in the name of mafic, for corrupt- ing and abufyig her, as Plutarch reports ; for, among others,, they chiefly had completed the ruin of the ancient fimple mufic, which fays Plutarch, was nobly ufeful in the education and forming of youth, and the fervice of the temples, and! ufed principally to thefe purpofes, in the ancient times of greater! wifdom and virtue, but was ruined after theatrical (hews came to be fo much in fafhion, fo that fcarcely the memory of thefe ancient modes remained in his time. You fhall have fome account afterwards of the ancient writers of mufic. As : we have but uncertain acconuts of the inventors of mc- fical inftruments among the ancients, fo we have as imper- fect an account of what thefe inftruments were, fcarce know- ing them any more than by name. The general divifion of inftruments,. is into ftringed inftruments,. wind inftru- ments and the pulfatile kind ; of this laft we hear of the tym- panum or cymbalum, of the nature of our drum ; the Greeks gave it the laft name from its figure, refembling a boat. There were alfo the crepitaculum, tintinabulum, crota- lum fiftrum ; but by any accounts we have, they look "rather like childrens rattles and play things than mufical inftru- ments. Of wind-inftruments, we hear of the tibia, fo called from the {hank- bone of fome animals, as cranes, of which they were firit made. And fiftula made alfo of reeds. But thefe were afterwards made of wood and alfo of metal. How they were blown, whether as flutes or hautboys or otherwife, and which the one way, and which the other, is not fuffici- ently manifeft. It is plain fome had holes, which at firft were but few, and afterwards increafed to a greater number; fome had none ; fome were fingle pipes, and fome a combi- nation of ieverals, particularly Pan's fyringa, which con- fided of feven reeds joined together fide-ways j they had no holes, each giving but one note, in all feven diftinct notes, but at what mutual diftances is not very certain, though per- haps they were the notes of the natural or diatonic fcale, but by this means they would want an 8ve, and therefore probably otherwife conftituted. Sometimes they played on a fingle pips, fomeiimee on two together, one in each hand. And left we fhould think there could mufic be exprefTed by one hand, If. Voffiasalledges, they had a contrivance by which they made one hole exprefs feveral notes, and cites a paflage of Aicauius O F M U S I C. 53 Arcadius the grammarian to prove it ; that author fays in- deed, that there were contrivances to fhut and open the holes when they had a mind, by pieces of horn he calls Bombyces and Opholmioi (which Julius Pollux alfo menti- ons as parts of fome kind of tibiae) turning them upwards or downwards, inwards or outwards : but the ufe of this is not clearly taught us, and whether it was that the fame pipe might have more notes than holes, which might be managed by one hand : perhaps it was no more than a like contri- vance in our common bagpipes, for tuning the drones to the key of the fong. We are alfo told that Hyagnis contrived the joining of two pipes, fo that one canal conveyed wind to both, which therefore were always founded toge- ther. We hear alfo of Organs, blown at firft by a kind of air-pump, where alfo water was fome way ufed, and hence called, organum hydraulicum ; but afterwards they ufed bellows. Vitruvious, has an obfcure defcription of it, which l{. Voffius and Kircher both endeavour to clear. There were tubae, and cornua, and litui, of the trumpet kind, of which there were different fpecies invented by dif- ferent people. They talk of fome kind of tubse, that with- out any art in the modulation, had fuch a prodiguous found, that was enough to terrify one. Of ftringed inftruments, the firft is the lyre or cithara (which fome diftinguifh:) Mercury is faid to be inventor of it, in this manner ; after an inundation of the Nile he found a dead fhell-fifh, which the Greeks call chelone, and the Latins teftudo; of this {hell he made his lyre, mounting it with feven ftrings, as Lucian fays; and added a kind of jugum to it, to lengthen the ftrings, but not fuch as our vio- lins have, whereby one ftring contains feveral notes j by the common form this jugum feems no more than two diftincT: pieces of wood, fet parallel, and at fome diftance, but joined at the farther end, where there is a head to receive pins for ftretching the ftrings. Boethius reports the opinion of fome that fay, the lyre mercurii had but four ftrings in imi- tation of the mundane mufic of the four elements: but Diodorus Siculus fays, it had only three ftrings, in imita- tion of the three feafons of the year, which were all the ancient Greeks counted viz. Spring, fummer and winter. Nicomachus, Horace, Lucian and others fay, it had \zven ftrings in imitation of the feven planets. Some reconcile Dodorus, 54 A TREATISE Diodorus, with the lafl, thus, they fay the more ancient Jyre had but three or four firings, and Mercury added other three, which made up feven. Mercury gave this feven ftringed lyre to Orpheus, who being torn to pieces by the Baccannals, the lyre was hung up in Apollo's temple by the Lefbians : But others fay, Pythagorus found it in fome temple of Egypt, and added an eighth firing. Nicomachus fays, Orpheus being killed by the Thracian woman, for contemning their religion in the Bacchanalian rites, his lyre was caft into the fea, and thrown up at AntifTa a city of Lefbcs; the fifhers finding it gave it to Terpander, who carrying it to Egypt, gave it to the priefts, and called him- felf the inventor. Thofe who call it four ftringed, make the proportions thus, betwixt the ift and 2d, the interval of a 4th, 3: 4, betwixt the 2d and 3d, a tone 8 : 9, and betwixt the 3d and 4th firing another 4th : the (even firings were diatonically difpofed by tones and femitones, and Pythagoras's e ; ghth firing made up the o£tave. The occafion of afcribing the invention of this inflrument to fo many authors, is probably, that they have each in dif- ferent places invented inftruments much refembling other. However fimple it was at firft, it grew to a great number of firings; but it is to no purpofe to repeat the names of thefe who are fuppofed to have added new firings to it. From this inflrument, which all agree to be firft of the ftringed kind in Greece, arofe a multitude of others, differ- ing in their fhape and number of firings, of which we have but indiftin£t accounts. We hear of the pfalterium, trigon, fambuca, pedis, magadis, barbiton, teftudo (the two lafl ufed by Horace promfcuoufly with the lyre and cithara) epigonium, fimicium, pandura, which were all flruck with the hand or a plectrum ; but it does not appear that they ufed any thing like the bows of hair we have now for violins, which is a mod noble contrivance for making long and fhort founds, and giving them a thoufand modifications it is impofiible to produce by a pleclrum, Kircher aifo obferves, that in all the ancient monument?, where inftruments are put in the hands of Apollo and (he mufes, as there are many of them at Rome, fays he, there is none to be found with fuch a jujum as our violins have, whereby each firing has feveral notes, but every firing has only one note j and this he makes an argument of the fim- plicity O F M U S I C. 5 £ plicity'and imperfection of their inftruments. Befides feve- ral forms of the lyre kind, and fome fiftulae, he is pofitive they had no inftruments worth naming. He confiders how careful they were to tranfmit, by writing and other monu- ments, their moft trifling inventions, that they might not lofe the glory of them ; and concludes, if they had any thing more perfect, we fhould certainly have heard of it, and had it preferved, when they were at pains to give us the figure of their trifling reed-pipes, which the fhepherds commonly ufed. But indeed I find fome paffages that cannot be well underftood, without fuppofing they had inftruments in which one firing had more than one note: where Pherecrates (al- ready mentioned) makes mufic complain of her abufes from Timotheus's innovations ; fhe fays, he had deftroyed her who had twelve harmonies in five ftrings ; whether thefe har- monies fignify fingle notes or confonances, it is plain each firing muft afforded more than one note. And Plutarch afcribes to Terpander a lyre of three chords, yet he fays it had feven founds, i. e. notes. Thofe who are curious to hear more of this, and fee the figures of inftruments both ancient and modern, muft go to Merfennus and Kircher. The Excellency and various Uses of MUSIC. THOUGH the reafons alledged for the antiquity of mufic, (hew us the digni;y o? it, yet I believe it will be agreeable toenterinto a more p^rcicular hiftory of the hon- our mufic was in among the ancients, and of its various ends and ufes, and the pr-tended virtues and powers of it. The reputation this art was in wiih the jcwifh nation, is, I fuppofe, well known by 'he iaaed hiliO'V Can any thing (hew the excellency of an art more, than that it was reckoned u r eful and r.ecelTary in 'he w or (hip of Gcd ; and as iuch, diligently pradtifeo and i.u'-;iv:«eri by a people fepa- rated from the reft cf mankind, to b? wkn fil-.- lor the A ' mighty, and prefer. ■-: the true k^owfe^ge of .God »k earth? I have ■ proved and ftated ma , notd ubt that ii 56 A TREATISE of God, and Miriam the prophetefs, were the chiefs of this'fa- cred choir: and thaj from this time to that of the royal prophet David, the art was honoured and encouraged by them both pub- licly and privately, we can make no doubt; for when Saul was troubled with an evij fpirit from the Lord, he is advifed to call for a cunning player upon the harp, which fuppofes it was a well known art in that time ; and behold, David, yet an obfcure and private perfon, being famous for his fkill in mufic, was called; and upon his playing, " Saul was refrefhed and was well, and the evil fpirit departed from him." Nor when David was advanced to the kingdom thought her this exercife below him, efpecially the religious ufe of it. When the ark was brought from Kirjath-jearim, " David and all Ifrael played before God with all their might, and with finging, and with harps, and with pfalteries, and with timbrels, and with cymbals, and with trumpets," i Chron. xiii. 8. And the ark being fet up in the city of David, what a folemn fervice was inftituted for the public worftiip and praife of God ; fingers and players on all manner of in- ftruments, " to minifter before the ark of the Lord conti- nually, to record, and to thank, and praife the Lord God of Ifrael !" Thefe Jfeem to have been divided into three choirs, and over them appointed three Goragi or mafters, Afaph, Heman and Jeduthun, both to inftru,-, .. In St. John's vifion, the elders are reprefented . with' harp's in their hands ; and tho' this be only repreferiting things in heaven, in. a, way eafieft for our i conception, yet We muft fuppofe it to be a. companion to the beft manner of worihipping God among men, with, fefpecl: at leaft to the means of comppiing .and railing our minds, or keeping out other ideas, and thereby fitting us for entertaining religious thoughts, . , . Let us next confider the efteem and ufe of it among the ancient Greeks and Romans.' Tlie glory of this art among them, efpecially the Greeks, appears firft,' ac- cording to the obfefvation of Quintilian, by the names given to the poets and muiicians, which at the begin- ning were generally the fame perfon, and their charac- ters thought to be lb connected, that the names were, reciprocal ; they were called Sages or Wiferoeftj and the infpired, Salmuth on Pancirollus cites Ariftophanes' to prove, that by citharas callens, or one that was fkilled in playing on the cithara, the ancients meant a wife man, who was adorned with all the graces ; as the^, H reckoned: '$8 A T R E A T I S E reckoned one who had no ear or genius to mufic, {lupid, or whole frame was difordered, and the elements of his compofition at war among themfelves. And fo high an opinion they had of it, that they thought no in- duftry of man could attain to iuch an excellent art; and hence they believed this facu'ty to be an infpiration from the Gods ; which alfo appears particularly by their making Apollo the author of it, and then making their mofi ancient mulicians, as Orpheus, Linus, and -Amphion, of divine offspring. Homer, who was him- fe If both poet and mufician, could have fuppofed nothing more to the honour of his profeffion, than making the Gods themfelves delighted with it : after the fierce conrefl that happened among them about the Grecian and Trojan affairs, he feigns them recreating themfelves with Apollo's mufic ; and after this, 'tis no wonder he thought it not below his Hero to have been inffruded In, and a diligent praftifer of this Godlike art. And do 'not the poets' universally terrify this opinion of the ex- cellency of mufic, when they make it a part of the entertainment at the tables of kings ; where to the found of the lyre they fung the praifes of the Gods and Heroes, and other ufeful things : As Homer in the Odyffea in- troduces Demodocus at the table of Alcinous, King of Phsacea, iingmg the Trojan war and the praifes of the Heroes : And Virgil brings in Jppas at the table of Dido, ringing to the found of his golden harp, what he had learned in natural philofophy, and particularly in aftroncmy from Atlas ; upon which Quin'cilian makes this reflection, that hereby the poet intends to fhew the connection there is between mufic and heavenly thing9 5 and Horace teaches us the fame doftrine, when addref- fing his lyre, he cries out, " O decus Phcebi, & dapibus fupremi, grata teftudo, Tovis. At the beginning, mufic was perhaps fought only for the lake of innocent pleasure and recreation; in which' view Ai'JfVotle calls it the medicine of that heavinefs that pro reeds from labour; and Horace calls his lyre laborem tiix\ce lenimen : And as this is the firtfc and m )ft fimple, fo it is cerlainly no delpicable ufe of it ; Our circum fiances require iuch a help to make as under- go the neeeffary toils of life more chearfuhy. Wine' and mufic chear tire-heart, faid the wife man ; and that the OF M U S I C. 59 the fame power ftill remains, does plainly appear by univerfal experience. Men naturally feek pleafure, and the wifer fort: ftudying how to turn this defire into the greater!: advantage, and mix the utile dulci, happily contrived, by bribing the ear, to make way into the heart. The fevereft of the phi1ofopner9 approved of mufic, becaufe they found it a neceffary means of accefs to the minds of men, and of engaging their pafiions on the fide of virtue and the laws ; and fo mufic was made an handmaid to virtue and religion. Jamblichus in the life of Pythagoras tells us, That mufic was a part of the difcipline by which he formed the minds of his fcholars. To this purpofe he made, and taught them to make and fing, verfes calculated againil the pafiions and difeafes of their minds ; which were alfo fung by a chorus, Handing round one that played upon the lyre, the modu'ations whereof were perfectly adapted to the defign and fubject of the verfes. He ufed alfo to make them fing fome choice verfes out of Homer and Hefiod. Mufic was the firft exercife of his fcholars in the morning ; as neceffary to fit them for the duties of the day, by bringing their minds to a right temper ; particularly he defigned it as a kind of medicine againfr. the pains of the head, which might be contracted in fleep : And at night, before they went to reft, he taught them to compofe their minds after the perturbations of the day, by the fame exercife. Whatever virtue the Pythagoreans afcribed to mufic, they believed the reafon of it to be. That the foul itfelf confifted of harmony ; and therefore they pretended by it to revive the primitive harmony of the faculties of the foul. By this primitive harmony they meant that which, according to their doctrine, was in the foul in its pre-exiftent ftate in heaven. Macrobius, who is plainly Pythagorean in this point, affirms, That every ioul is delighted with mufical founds ; not the polite only but the moft barbarous nations pra£tiie mufic, whereby they are excited to the love of virtue, or dif- folved in foftnefs and pleafure : The realbn is, fays he 3 That the foul brings into the body with it the memory of the mufic which it was entertained with in heaven : And there are certain nations, fays he, That attend the dead to their burial with iinging ; bjcaufe they H z believe f>o A TREATISE believe the foul returns to heaven the fountain or. on* ginal'.pf rhufjc. Lib, 2, in Somnium Scipionis, And, beeaufe this fe$; believed the Gods themfelves to have celefcial bodies of a moft perfect harmonious competi- tion, therefore they thought the Gods 'were delighted \vith it • and that by our ufe of 1 it in facred things, we not only compole our minds, and fit them better for the contemplation of the Gods, but imitate their happinefs, and thereby are acceptable to them, and open for bur-* ielyes a return' into heaven. Athenaeus reports of one Clinias a Pythagorean, who, being a very choleric and wrathful man, as iboh as he* found his paffion begin to rife, took up his lyre and fung, and by this means allayed it. But this difciplind was older than Pythagoras ; for Homer tells us, That Achilles was educated in the fame manner by Chironj and feigns him,' after the hot difpute he had with Agamemnon, calming his mind with his fong and lyre ; And th.o\ Homer'fhould be the author of this ftory, it fhews however that fuch an ufe was made of mulic in his days; for 'tis reafonable to tliftik he had learned this from experience. ; The virtuous and wife Socrates was no lefs a friend to this admirable art; for even in the decline of his age he applied himfelf to the lyre, and carefully recom- mended it to others. Nor did the divine Plato differ from his great mafter in this point; he allows it in his common-wealth; 'and in many places' of his works fpeaks with the greatefV fefpeft of it, as a raoft ufeful thing in fociety. Pie fay's it has as great influence over the Vninc',' as the air has over the body ; and therefore he thought it was worthy' 'of' the law to take care of it. He underftobd the principles of the art fo well, that, as Quintilian' jufl'iy o'bferves, thete are many paifages ' in his' 'writings' not to'be underftood without a good knowledge of it. ' Ariflotle in his politics agrees with Plato in liis fentiments of ' itiufic. : ' - • - •' 1 Ariftides the plilofopher arid mufician, in the intro- duction to his 'treatife on this fubjeft', fays, 'tis not fo confined either as to the fubject matter or time as other 1 arts 'and fciencesy but adds ornament to all the parts an4 actions : bf-hurna'n life i l 'Painting,' ;; fays he, attains that good which' 'regards the eye., 'medicine and gymnaftic f ■■' i' w. v.. . .. • ■ • ■■■■ *,'--■■-■■ , . ■ ' are' O F MUSI 0. 6i are good for the body, dialectic and that kind helps to acquire prudence, if the mind be fhft purged and pre- pared by mufic. Again, it beautifies the mind with the ornaments of harmony, and forms the body with decent motions : 'tis fit for young ones, becaufe of the advan- tages got by linging ; for perfons of more age, by teaching them the ornaments of modulate diction, and of all kinds of eloquence ; to others more advanced it teaches the nature of number, with the variety of pro- portions, and the harmony that thereby exifts in all bodies, but chiefly the reaibns and nature of the foul. He fays, as wile hufband-men firft caft out weeds and noxious plants, then lo\v the good feed, fo mufic is tiled 10 cornpo'e the mind, and fit it for receiving in- fraction : for plcafure, fays he, is not the proper end of mufic, which affords recreation to the mind only by accident, the propofed end being the inftiliing of virtue. Again, he fays, if every city, and almoft every nation loves decency and humanity, mufic cannot poffibly hfj Vifelefs. It was, ufed at the feafts of princes and heroes, fays Athenaeum, not out of levity and vain mirth ; but rather as a kind of medicine, that by making their minds cheerful, it might help their digefuon : There, fays he, they lung the praifes of the Gods and heroes and other ufeiul and inilrudtive compofures, that their minds might . not be . neglected while they took care of their bodies ; and that from a reverence of the Gods, and by the example of good men, they might be kept within the bounds of fobriety and moderation. But we are not confined to the authority and opinion of phiiofophers or any particular perfons; we have the testimony of whole nations where it had public encou- ragement, and was made necefiary by the law; as irj the moft part of the Grecian common-wealths. Athenaeus allures us, That anciently all their laws divine and civil, exhortations to virtue, the knowledge of divine and human things, the lives and actions of illuftrious men, and even hiftories, and mentions Hero- dotus, were written in verfe and publicly lung by a chorus, to the found of inftruments ; they found this by experience an effectual means to imprefs morality, and a right fenfe of duty ; Men were attentive to things " that $2 A TREATISE that were propofed to them in fuch a fweet and agree, able manner, and aitra&ed by the charms of harmoni-. pus numbers, and well mod^ated founds; thev tcok. pleafure in repeating thefe examples and inftructions, and found them eaiier retained in their memories. A- riftotle alio in his problems tells us, That before the vfe of letters, their laws were fung mufically, for the better retaining them in memory. We have a very old and remarkable proof of this virtue of mufic in the ftory of Orpheus and Amphion, both of them poet* and muficians, who made a wonderful impreffion upon a rude and uncu'tivated age, by their virtuous and wife inftruftions, inforced by the charms of poetry and mu- fic : The fucceeding poets, who turned all things into inydery and fab^e, feign the one to have drawn after him, and tamed the moil favage beafts ; and the other to have animated the very trees and ftones, by the power of mufic, Horace had received the fame tra- ditions of all the things I have now narrated, and with thefe mentions other ufes of mufic. The pafTage is in his book de arte Poetica, and is worth repeating. S'dve/ires homines, facer interprefq; deorum, Gcs dibits & vifiu fado, deter ruit < hpheus : Thftui ob hoc lenire tigres, rabidyjq; hones : JOiclus tsf Jtnpbion, ThcL(r,iiio non prajlant'ior alter^ /Ere ciere viros 3 martemque accendere caniu. From Athens let us come to Lacedemon, and here we find it in equal honour. Their opinion of its na- tural influence was the fame with that of their neigh- bours : and to fhew what care was taken by the law, to prevent the abufe of it to luxury, the hiflorians tell us that Timotheus was fined for having more than feven firings on his lyre, and what were added .ordered. to be taken away. The Spartans were a warlike people, yet very fenfible of the advantage of fighting with a cool and deliberate courage ; therefore as GeHius" out of Thucydides reports, they ufed not in their armies, 1 ' inftruments of a more vehement found, that might in- flame their temper and make them more furious, as the tuba, cornu and iituus,' but the more gentle and moderate founds and modulations of the tibia,' that their minds being more compofed, they might engage, with a ratU onal courage* And Gellius tells us, the -Cretans ufed the Cithara to the fame purpole in their armies. "We have already heard how this people entertained at great expence the famous Thales to inftruft their youth ift mufic ; and after their mufic had been thrice corrupted^ thrice they reftored it. If we go to Thebes, Epaminondas will be a witneis of the efteem it was in, as Corn. Nepos informs "US. Athenaeus report,^ upon the authority of Thebpom- pus, that the Getan ambalfadors,' being lent upon an embaiTy of peace, made their entry with lyres in their hands, finging and playing to compote their minds, - and make themfelves mailers of their temper 1 ; • We need O F MUSI C. 6j need not then doubt of its public encouragement a- meng this people. But the raoft famous inftance in all Greece, is that of the Arcadians, a people, lays Poly bi us, in reputation for virtue among the Greets ; efpecially for their devo- tion to the Gods. Mufic, fays he, is efteemed every where, but to the Arcadians it is neceffary, and allowed a part in the eiiablifhment of their Hate, and an in- ciifpenfable part of the education of their children* And tho' tlrsy might be ignorant of other arts and fciences without reproach, yet none might prefume to Want knowledge in roufic, the law of the land making it neceffary ; and iniuiflciency in it was reckoned infa- mous among that people. It was not thus eftabiifhed^ fays he, fo much for luxury and delight, as from a wife confederation of their toilfonle and induftrious life, owing to the cold and melancholy air of their climate; which made them attempt every thing for foftnins; and fweetriins; thofe aufterities they were con- demned to. And the neglect of this difcipline he gives as the reafon of the barbarity of the Cyriaethians, a people of Arcadia. We fhall next confider the ftate of mufic am^ng the ancient Romans. Till luxury and pride ruin'd the Manners of this brave nation, they were famous for a fevere and exaft virtue. And tho' they were con- vinced of the native charms and force of mufic, yet we don't find they cherifhed it to the fame degree as the Greeks ; from which one would be tempted to think they were only afraid of its power, and the ill ufe it was capable of : A caution that very well became thofe who valued th.eihfelv.es fo much, and juftly, upon their piety and good manners; Corn. Nepos, in his preface, takes notice of the dif- ferences between the Greek and Roman cuftoms, par- ticularly with refpedt to mufic ; and in the life of Epaminondas, he has thefe words,, Scimus enim mufi- cum noflris moribus abeife a principis perfona 5 faltare etiam in yitiis poni, quae omnia apud Graecos & gratia & laude digna ducuntur, Cicero in the beginning of the firft book of hi? Tuf- Culart Queftions, tells us, that the old Remans did not ftudy the more foft and polite arts fo much as the S Greeks; 66 ATR£ATlSE Greeks ; being more acidised to the ftudy of morality 1 ' and government : hence mufic had a fate fomewhat different at Rome. But the fame Cicero fhews us plainly his own opinion' of it. Lib. 2. de Legibus ; AfTentior enim Platoni, nihil tarn facile in animos tenero's atque moiles infiuerc quam varies canendi fonos. Quorum dici vix poteft' quanta fit vis in utramque partem, namque & incitat languentes,- & languefacit incitatos, et turn rernittir. animos, turn contrahit. Certainly he had been a wit- nefs to this power of found, before he could fpeak fo p and I fhall not believe he had met with the experiment only at Athens. A man fo famous for his eloquence,- muft have known the force of harmonious numbers,; and well proportioned tones of the voice. Quintilian fpeaks honourably of mufic. He fays,- Lib. i. Chap. ii. Nature feems to have given us this gift for mitigatifig the pains of life, as the common practice of all labouring men teftifies. He makes it neceffary to his orator, becaufe, fays he, Lib. 8. Chap. 4. It is impoffible that a thing Ihould reach the heart which begins with choking the ear ; and becaufe we are naturally pleafed with harmony, otherwife Inft.ru-' ments of mufic that cannot exprefs words would not make fuch furprifing and various effects upon us. And in another place, where he is proving art to be only nature perfected, he fays, mufic would not otherwife be an art, for there is no nation which has not its longs and dances. Some of the firft rank at Rome practifed it. Athe- nceus fays of one Mafurius,. a lawyer, whom he calls one of the beft and wifeft of men, and inferior to none in the law, that he applied himfelf to mufic dili- gently. And Plutarch places mufic, viz. finging and playing on the lyre, among the qualifications of Me- tella, the daughter of Scipio Metellus. Macrobius in the 10 Chap. Lib.- 2. of his Saturnalia fhews us, that neither finging nor dancing Were reck- oned difhonourable exercifes even for the quality among the ancient Romans ; particularly in the times between the two Punick wars, when their virtue and manners weje at the. beft ; provided they were not ftudied with too much curiofity, and too much time fpenfc O F M U S 1 C. 67 fpent about them 5 and obferves, that it is this, and not limply the ufe of thefe, that Saluft complains of in Sempronia, when he fays fhe knew pialiere & fal- tare elegantius cjuam neceiTe erat probae. What an Opinion Macrobiijs himfelf had of mufic we have in part fhewn already ; to which let us add here this re- markable paffage in the place formerly cited. Ita denique omnis habitus animse cantibus gubernatur, ut & ad bellum progreiTui & etiam receptui canatur, cantu cc excitante & rurfus fedante virtutem; dat l'omnos adimitque necnon curas & immittit £c retrahit, iram iuggerit, clementiam fuadet, corporum quoque morbis rnedetur. Hinc eft quod aegris remedia praeftantes prsecinere dicuntur. The abufe of it, which 'tis proba- ble lay chiefly in their idle, ridiculous, and lalcivious dancing, or perhaps their fpending too much time even in the moil innocent part of it, and not applying it to the true ends, made the wiier fort cry out, and brought the character of a mufician into fome difcredit. But we find, that the true and proper mufic was full in honour and pra&ife among them: had Rome ever fuch poets, or were they ever to honoured as in Auguitus's reign ? Horace, tho' he complains of the abufe of the theatre, and the mufic of it, yet in many places he fhews us, that it was then the praftife to fing yerfes or odes to the iound of the lyre, or of pipes, or of both together; Lib. 4. Ode 9. Verba loquor fpcianda chordis. Lib. 2. Ep, 2. Hie ego verba lyrae motura fonum connedlere digner ? In the firft Ode, Lib. 1. he gives us his own character as a poet and mufician, Si neque tibias Euterpe cohibct, &c. He fhews us, that it was in his time ufed both publicly in the praife of the gods and men, and privatelv for recre- ation, and at the tables of the great, as we find clearly in thefe paffages. Lib. 4. Ode 11. Condifce modos amanda voce qups reddas, minuentur atra? carmine curae. Lib. 3. Ode 28. Nos cantabimus invicem Nep- tunum, tu curva recines lyra Latonam, &c. Lib. 4. Ode 15. Noique & profeftis lucibus & facris-Ritc Deos Erius adprecati, virtute funftos more patrum duces, ,ydis remifto carmine tibiis Trojamque, &c. canemus. Epode 9. Quando repoftum cscubum ad feftas dapes tecum, — Beate Meea?.nas bi'oam ? Sonante miitis tibiis I a carmen m A TREATISE carmen lyra. Lib, "3. Ode 11. Tuque teftudo — Nunc 6c divitum menfis & arnica templis. For alt the abufes of it, there were ftill fome, even of the bell characters, that knew how to make an in- nocent ufe of it : Sueton in Titus's life, whom he calls Amor ac deliciae generis humani, among his. other ac- complifhments adds, Sed ne Mufic.se quidem rudis, ut qui cantaret & pfalleret jucunde fcienterque. There is enough faid to fhew the real value and vife. ©f mufic among the ancients. I believe it will be neediefs to iniift much upon our own experience ; I fhall only fay, thefe powers of muiic remain to this dav, and are as univerfal as ever. We ufe it ftill in war and in facred things, with advantages that they only know who have the experience. But in common life, aimoft every body is a witnefs of its fweet infiu-» ences. What a powerful impreffion mufical founds make even upon the brute animals, efpecially the feathered kind, we are not without fome inftances. But how furpriling are the accounts we meet with among the old writers ? I have referved no place for them here, You may fee a variety of ftories in iElian's Hiftory of Animals, Strabp, Piiny, Marcianus Capella, and others. Before I leave this, I muft take notice of fome of the extraordinary effefts afcribed to mufic. Pythagoras is faid to have had an abfolute command of the human paitions, to turn them as he pleafed by mufic : they tell us, that meeting a young man who in great fury was running to burn his rival's houfe, Pythagoras allayed his temper, and diverted the defign, by the foie power of mufic. The ftory is famous how Ti- motheus, by a certain ftrain or modulation, fired Alex- ander's temper to that degree, that forgetting himfeif, in a warlike rage, he killed one of the company j and by a change of the mufic was foftned again, even to aj bitter repentance of what he had done. But Plutarch fpeaks of one Antigenidcs, a Tibicen or p?per, who by fome warlike ftrain had tranfported that hero lb farj, that he fell upon tome of the company. Terpander quelled a Sedition at Sparta by means of mufic. Tha^ les being called from Crete, by advice of the oracle, to O F M U S I C. 6$ to Sparta, cured a raging peftilence by the fame means* The cure of difeaies by mufic is talked of with enough of confidence. Aulus Gellius, Lib. 4. Chap. 13, tells us, it was a common tradition, that thofe who were troubled with the Sciatica (he calls them Itchiaci) when their pain was mod: exquifite, were eafed by certain gentle modulations of mufic performed upon the Tibiae; and fays, he had read in Theophraftus, that by certain artful modulations of the fame kind of inftrument, the bites of lerpents or vipers had been cured. Clytem- neftra had her vicious inclinations to unchaftity cor- rected by the applications of muficians. And a vir- tuous woman is laid to have diverted the wicked defign of two rakes that affaulted her, by ordering a piece of mufic to be performed in the Sponclean mode. A fhort History of the Improvements in MUSIC. FOR what reafons the Greek muficians made fuch. a difficult matter of their notes and figns we can- nut guefs, unlefs they did it defignedly to make their art myfterious, which is an odious fuppofition ; but one can fcarcely think it was otherwife, who confiders how obvious it was to find a more eafy method. This was therefore the firft thins: the Latins corrected in the Greek mufic, as we have already heard was done by Boethius, and further improved by Gregory the Great. The next ftep in this improvement is commonly afcribed to Guido Aretinus, a Benedi&in monk, of Arc- tium in Tufcany, who, about the year 1024, (tho' there are fdme differences about the year), contrived the ufe of a ftave of 5 lines, upon which, with its fpaces he marked his notes, by fetting points (.) up and down upon them, to denote the rife and fall of the voice, (but as yet there were no different marks of time ;) he marked each line and fpace at the beginning of the ftave, With Gregory's 7 letters, and when he fpake of the notes fo A TREATISE Botes, he named them by thefe inStead of the long Greek names of Prollambanomenos, &c. The Cor- refpondence of thefe letters to the names of the chords in the Greek SyStem being fettled, the degrees and in- tervals between any line or fpace, and any other were hereby understood. But this artifice of points and lines was ufed before his time, by whom invented is not known ; and this we learn from Kircher, who fays he found in the Jeiuits library at Meflina a Greek manufcript book of hymns, more than 700 years old ; in which fome hymns were written on a Stave of 8 lines, marked at the beginning with 8 Greek letters ; the notes or points were fet upon the lines, but no ufe made of the fpaces : Vincenzo Galileo confirms us alio in this. But whether Guido knew this, is a question • and tho' he did, yet it was well contrived to ufe the fpaces and lines both, by which the notes lye nearer each other, fewer lines are needful for any interval, and the diftances of notes are eafier reckoned. But there is yet more of Guido's contrivance, which deferves to be considered ; FirSt, He contrived the 6. mufical Syllables, ut, re, mi. fa, fol, la, which he tpo^ out of this latin hymn. UT aueant laxls RE fonare fibrh, Mlra geftortim FAmuli tuorum^ SQLve pollute LAbit reatum^ pater alme* In repeating this it came into his mind, by a kind of divine inStinct: lays Kircher, to apply thefe fyllables to his notes of mufic : a wonderful contrivance cer- tainly for a divine inStinct ! But let us fee where the excellency of it lies : Kircher fays, by them alone he unfolded all the nature of mufic, distinguished the tones (or modes) and the Seats of the femitones. Elfewhere he Says, That by the application of thefe fyllables he cultivated mufic, and made it fitter for finging. In order to know how he applied them, there is another piece of the hiftory we muft take along, viz. That finding the Greek Diagram of too fmall extent, he added 5 more chords or notes in this manner; having applied the letter A to the Proflambanomenos, $ n 4 O F M U S I C. 7* and the reft in order to Nete Hyperbolaeon, he added a chord, a Tonus below Proflam. and called it Hypo- proflambanomenos, and after the Latins g. but com- monly marked with the Greek F ; to fhew by this^ fome fay, that the Greeks were the inventors of mulic ; but others fay, he meant to record himielf (that letter being the firft in his name) as the improver of mufic ; hence the Scale came to be called the Gamm. Above Nete Hyperbolaeon he added other 4 chords, which, made a new disjunct Tetrachord, he called Hyper- hyperbolaeon ; fo that his whole Scale contained 20 diatonic notes, (for this was the only Genus now ufed) befides the b flat, which correlponded to the Trite; Synemmenon of the ancients, and made what was afterwards called the feries of b molle, as we fhall hear. Now the application of thefe fyllables to the Scalfi was made thus : Between mi and fa is a femitone; ut : re, re : mi, fa : fol, and fol : la are tones (without diftinguifhing greater and leffer;) then becaule there are but 6 fyllables, and 7 different notes or letters in the 8ve ; therefore, to make mi and fa fall upon the true places of the natural femitones, ut was applied to dif- ferent letters, and the reft of the 6 in order to the others above ; the letters to which ut was applied are g. c. f. according to which he diftinguifhed three feries, viz. that which began with ut in g, and he called it the feries of b durum, becaufe b was a whole tone above a; that which began with ut in c was the feries of b na- tural, the fame as the former ; and when ut was in f, it was called b molle, wherein b was only a femitone above a. See the whole fcale in the following fcheme, GUIDO'sf fi A TREATISE G U I D O's Scale. where obferve, the feries of b natural ftahds be- tween the other two, arid communicates with both; fo that to name the chords of the fcale by thefe fyl- lableSj if we would have the femitones in their na- tural places, viz. b . Cj and e . f, then we apply ut to g, and after la> we go into the feries' of b natural at fa^ and after la of this, we return tc* the former at mi, and fd on ; or we may begin at ut in c, and pais into the firft feries at mi, and then back to the other at fa : ]py which means the one tranfition is a femi- tone, viz. la . fa, and the other a tone la : mi. To' follow the order of b rnolle, we may begin with ut in c or f, and make tranfitions the fame way as formerly : hence came the barbarous names of Gam- mut, Are, Bmi, &c. with which the memories of learn- ers uled to be oppreffed. But now what a perplexed work is here, with fo many different fyllables applied to every chord, and all for no other purpofe but mark- ing the places of the femitones, which the fimple letters' a J b . c, &c. do as Well, and with infinite more eafe. Afterwards fome contrived better, by making feven fyl- lables, adding Si in the blanks you fee in the feries be- tween la and ut, fo that mi -fa and fi-ut are the two natural femitones : Thefe 7 completing the 8ve, they took away the middle feries as of no ufe, and fo ut being in g or f, made the feries of B durum (or natural,' which is all one) and B molle. But the Englifh throW out both ut and fi, and make the other 5 ferve for all. This wonderful contrivance o£ Gvudo's fbs fyllables, is f— ■ B»dur nati moUe e e la mi dd Jol re la c c bb mi ut fol t* fa a a re la mi g f e ut la fol fi. mi re ut d fit re la b f a . mi ut Jol / a re la mi G F E ut la fol > mi re ut D C B fol f a . mi re ut J re Tamm ut O P M U S I C. ji what a very ingenious man thought fit to call Crux: tenellorum ingeniorum ; but he might have faid it or any of the Methods ; for which reafon, I believe, they are laid afide with very many, and, I am lure, ought to be fo with every body* But to go on with Guido; the letters he applied to his lines and fpaces, were called keys, and at firft he marked every line and fpace at the beginning of a Have with its letter; afterwards marked only the lines, as fome old examples fhevv J and at laft marked only one, which was therefore called the figned Clef; of which he diflinguifhed three different ones, g, c, f; (the three letters he had placed his ut in) and the reafon of this leads us to another article of the liiftory, viz. That Guido was the inventor of Symphonetic compofition, (for if the ancients had it, it was loft; but this fhall be confidered again) the firft who joined in one har- mony feveral diitinct melodies, and brought it even the length of 4 parts, viz. Bafs, Tenor, Counter, and Tre- ble ; and therefore to determine the places of the feve- ral Parts in the general lyflem, and their relations to one another, it was neceffary to have 3 different figned Clefs. He is alfo faid to be the contriver of thofe inftru- ments they call Polypleftra.j as ipinets and harpfichords i however they may now differ in fhape, he contrived what is called the Abacus and the Palmulae, that is, the Machinery by which the firing is ftruck with a Plect- rum made of quills Thus far go the improvements of Guido Aretinus, and what is called the Guidoniari Syftem ; to explain which he wrote a book he calls his Micrologum. The next confiderable improvement was about 306 years after Guido, relating to the P.ythmus, and the marks by which the duration of every note was known ; for hitherto they had but imitated the fimpiicity of the ancients, and barely followed the quantity of the fyllables, or perhaps not fo accurate in that, made all their notes of equal duration, as ibine of the old Ec» elefiaftic mafic is an inftancq of. To produce all the effects mufic is capable of, the neceiftty of 1 notes of different quantity was very obvious ; for the Rythmus is the foul of mufic ; and becaufe the natural quantity 74 A TPvEATtSE of the fyllables was not thought fumcient for all th& variety of movements, which we know to be fo agree* able in mufic, therefore about the year 1330 or 1333* fays Kircher, the famous Joannes de Muris, Doctor at Paris, invented the different figures of notes, which exprefs the time, or length of every note, at leaft their true relative proportions to one another. Anciently they were called, Maxima, Longa, Brevis, Semibrevis, Minima, Semiminima, Chroma, (or Fufa) Semichroma. What we call the Demifemiquaver is of modern addi- tion. But whether all thefe were invented at once is not certain, nor is it probable they were $ at firft 'tis like they ufed only the Longa and Brevis, and the reft were added by degrees. Now alfo was invented the divifion of every iortg in feparate and diftinfl bars of meafures. Then for the proportion of thefe notes one to another it was not always the fame % fo a Long was in fome cafes equal to two Breves, fometimes to? three, and lb of others ; and this difference was marked generally at the beginning ; and fometimes by the pofition or way of joining them together in the middle of the fong ; but this variety happened only to the firft four. Again, refp.ecting the mutual proportions of the notes, they had what they called Modes, Prolati- ons and Times : The two laft were diftinguiihed into Perfect and Imperfect ; and the firft into greater and leffer, and each of thefe into perfect and imperfect : but afterwards they reduced all into 4 modes including the Prolations and Times. I could not think it worth pains to make a tedious defcription of all thefe, with their marks or figns, which you may fee in the already mentioned Dictionaire de Mufique : I mall only ob- ferve here, That as we now make little ufe of any note above the Seinibreve, becaufe indeed the remain- ing 6 are iufficient for all purpoles, fo we have call off that difficulty of various and changeable proportions* between the fame notes : the proportions of 3 to 1 and a to 1 was all they wanted, and. how much more eafy and fimple is it to have one proportion iixt, viz. 2 : 1 (i. e. a Large equal-to two Longs, and fo on in order) and if the proportion of 3 : 1 between two fucceffive notes is required, this is, without any manner of con-, fufion or difficulty, expreffed by annexing a point (.) on O F M U S I C. 75 on the right hand of the greateft of the two notes, as * has been above explained ; fo that 'tis almoft a wonder how the elements of mufic were fo long involved in thefe perplexities, when a far eafier way of coming to the lame end was not very hard to find. We fhall obferve here too, That till thefe notes of various Time were invented, inftrumental performances without fong muft have been very imperfect if they had any ; and what a wonderful variety of entertainments we have by this kind of compofirion, I need not tell you. There remain two other very considerable fteps, be- fore we come to the prefent ftate of the fcale of mufic. Guido firft contrived the joining different parts in one concert, as has been faid, yet he carried his fyftem no further than 20 diatonic notes : now for the more fim- ple and plain compofitions of the Ecclefiaftic flile, which is probable was the moft confiderable application he made of mufic, this extent would afford no little variety ; but experience has fince found it neceflary to enlarge the fyftem even to 36 diatonic notes, which are repreiented in the foremoft range of keys on the breaft of a harpfichovd ; for fo many are required to produce all that admirable variety of harmony, which the parts in modern compofitions confift of, according to the manv different ftiles pradVifed : but a more confiderable defeft of his fyftem is. That except the tone between a and b, which is divided into two femitones by L (flat) there was not another tone in all the fcale di- vided ; and without this the fyftem is very imperfedt with refpe£t to fixed founds, becauie without thefe there can be no right modulation or change from key to key. Therefore the modern fyftem has in every 8ve 5 artifi- cial chords or notes, which we mark by the letters of the natural chords, with the diftinction of ^< or (,. Obferve, That by thefe additional chords, we have the diatonic and chromatic Genera oi- the ancients mixed ; fo that compofitions may be made in either kind, tho' we reckon the diatonic the true natural fpecies ; and if at any time ? two femitones are placed immediately in fucceflion : for example, if we fing c . c>& . d, which is done for variety, tho' feldom, fo far this is a mixture of the chromatic • but then to make it pure chromatic, no K 2 fmaller 76 A TREATISE {mailer interval can be fung after two femitones afcend- ing than a Triemitone, nor descending lefs than a Tone ; becaufe in t;he pure chromatic fcale the Spiffum has al- ways above it a Triemitone, and below it either a. Triemitone or a Tone. The lafl thing I fhall confider here is, how tn§ modes were defined in thefe days of improvement ; and I find they were generally charafterifed by the fpecies of 8ve after Ptolomy's manner, and therefore reckoned in all 7. But afterwards they confidered the harmonica! and arithmetical divisions of the 8ve, whereby it re- folves into a 4th above a 5th, or a 5th above a 4th, And from this they conftituted 12 modes, making of each 8ve two different modes according to this different divifion ; but becaufe there are two of them that can- not be divided both ways, therefore there are but 12 modes. To be more particular, confider, in the natural fyftem there are 7 different oftaves proceeding from thefe 7 letters, a, b, c, d, e, f, g ; each of which has two middle chords, which divide it harmonically and arithmetically, except f, which has not a true '4th, (becaufe b is three tones above it, and a 4th is but two tones and a femitone) and b, which confequently wants the true 5th (becaufe f is only two tones and two femitones above it, and a true 5th contains three tones and a femitone) therefore we have only 5 oclaves that are divided both ways, viz. a, c, d, e, g, which makes 10 modes according to thefe different divifions, and the other two f and b make up the 12. Thefe that are divided harmonically, i. e. with the ^ths loweff. were called authentic, and the other plagal modes. See the following fcheme. To thefe modes they gave the names of the ancient Greek tones, as Dorian, Phrygian : but feveral authors differ in the application of thefe names, as they do about the order, as, which they fhall call the firft and fecond, &c. which being arbitrary things, as far as I can underitand, it were as idle to pretend to reconcile g — c g — c a ___ d — a — d b — e — b — e c ... /"- c — f d — g — d — g e --- a — e — a O F M U S I C. 77 MODE S. them, as it was in them to Pineal. Authentic, differ about it. The material Zve. $ve. point is, if we can find it, to > A > know what they meant by r- *- » thefe distinctions, and what 4tb. 5^A. 4tb. was tl ie rea i u f e f them in mufic ; but even here where they ought to have agreed, we find they differed. The beft account to be given of it is this : They confidered that an 8ve which wants a 4th or 5th, is imperfect ; thefe being the concords next to 8ve, the fon£ ought to touch thefe chords molt frequently and re- markably ; and becaufe their concord is different, which makes the melody different, they eflablifhed by this two modes in every natural octave, that had a true 4th and 5th : then if the fong was carried as far as the oftave above, it was called a perfect mode; if lefs, as to the 4th or 5th, it was imperfeft ; if it moved both above and below, it was called a mixt mode : thus fome au- thors fpeak about thefe modes. Others confidering how indifpenfable a chord the 5th is in every mode, they took for the final or key-note in the arithmetically di- vided octaves, not the loweft chord of that octave, but that very 4th ; for example, the octave g is arithme- tically divided thus, g - c - g, c is a 4th above the lower g, and a 5th below the upper g, this c therefore tiiey made the final chord of the mode, which therefore properly fpeaking is c and not g ; the only difference then in this method, between the authentic and plagal modes is, that the authentic goes above its final to the oftave, the other afcends a 5th, and delcends a 4th, which will indeed be attended with different effects, but the mode is effcntially the fame, having the fame final to which all the notes refer. We muft next con- lider wherein the modes of one fpecies, as authentic or plagal, differ among themfelves : This is either by their ftanding higher or lower in the fcale, i. e. the different tenfion of the whole octave ; or rather the different Subdivifion of the octave into its concinnous degrees ; there is noi; another. Let us confider then whether 5 8 A TREATISE whether thefe differences are fufficient to produce fa very different effects, as have been afcribed to them for example, one is faid to be proper for mirth, another for fadneis, a third proper to religion, another for ten- der and amorous fubje&s, and fo on : whether we are to afcribe fuch effects merely to the conftitution of the octave, without regard to other differences and ingre- dients in the compofition of melody, I doubt any body now a days will be abfurd enough to affirm ; thefe have their proper differences, 'tis true, but which have fo little influence, that by the various combinations of other caufes, one of thefe modes may be ufed to dif- ferent purpofes. The greateft and moft influencing dif- ference is that of thefe octaves, which have the 3d 1. or 3d g. making what is above called the fharp, and flat key : but we are to notice, that of all the 8ves, except c and a, none of thern have all their eifential chords in juft proportion, unlefs we neglect the differ- ence of tone greater and leffer, and alfo allow the femi- tone to ftand next the fundamental in fome flat keys (which may be ufeful, and is fometimes ufed ;) and when that is done, the octaves that have a flat 3d will Want the 6th g. and 7th g, which are very neceffary on fome occafions ; and therefore the artificial notes 3gC and f are of abfolute ufe to perfect the fyftem. Again, if the modes depend upon the fpecies of 8ves, how can they be more than 7 ? And as to this dif- tinction of authentic and plagal, I have fhewn that it, is imaginary, with refpect to any eifential difference conftituted hereby in the kind of the melody j for tho* the carrying the fong above or below the final, may have a different effect, yet this is to be numbered a- mong the other caufes, and not afcribed to the conftitu^ tion of the octaves. But 'tis particularly to be re-; marked, that thefe authors who give us examples in actual compofition of their 12 modes, frequently take in the artificial notes ^ and j, to perfect the melody of their key ; and by this means depart from the confti- tution of the 8ve, as it Hands in the iixt natural fyftem. So we can find little certain and confiftent in their way of fpeaking about thefe things ; and their modes., are all reducible to two, viz. the fharp and flat ; other deferences j;efpecting only the place of the fcale where O F M U S I C. ft t^ie fundamental is taken.: I conclude therefore that the true theory of modes, is where they are diftinguifhed into two fpecies, fharp and flat, whofe effects muft be allowed are different ; but other caufes muft concur to any remarkable effect ; and therefore 'tis unreafonable to talk as if all were owing to any one thing. What they called the feries of b molle, was no more than this, That becaufe the 8ve f had a 4th above at b, ex- ceffive by a femitone, and confequently the 8ve b had a 5th above as much deficient) therefore this artificial note b fiat or h , ferved them to tranfpofe their modes to the diftance of a 4th or 5th, above or below ; for taking k a femitone above a, the reft keeping their ratios already fixt, the feries proceeding from c with b natural (i. e. a tone above a) is in the fame order of degrees, as that from f with b flat (i. e, \, a femi- tone above a ;) but f is a 4th above c, or a 5th below ; therefore to tranfpofe from the feries of b natural to b molle we afcend a 4th or defcend a 5th; and contra- rily from b molle to the other : This is the whole myftery; but they never fpeak of the other tranfpofi- tions that may be made by other artificial notes. You may alfo obierve, that what they called the ecclefiaftic tones, are no other than certain notes in the organ which are made the final or fundamental of the hymns ; and as modes they differ, fome by their place in the fcale, others by the fharp and flat 3d ; but even here every author fpeaks not the fame way : 'tis enough we know they can differ no other way, or at leaft all their differences can be reduced to thefe, Ac firft they were four in number, whofe finals were d, e> f, g, conftituted authentically : this choice, we are told, was firft made by St. Ambrofe, bifhop of Milan ; and for being thus chofen and approved, they pretend the name authentic \vas added : afterwards Gregory the Great added four plagals, a, b, c, d, whole finals are the very fame with the firft four, and in effect, are only a continuation of thefe to the 4th below ; and for this connection with them were called plagal 3 tho' the de- rivation of the word is not fo plain. The fo A TREATISE The Ancient and Modern Mufic compared. TH E laft age was famous for the war that was raifed, and eagerly maintained by two different parties, concerning the ancient and modern genius and learning. Among the difputed points mufic was one* I know of nothing new to be advanced on either fide. The queftion in general is, Whether the ancients of the moderns beft underftood and pradtifed mufic ? Some affirm, that the ancient art of mufic is quite loft, among other valuable things of antiquity, vid. Pancirollus, de Mufica. Others pretend, That the true fcience of har- mony is arrived to much greater perfection than what was known or pra&ifed among the ancients. The fault with many of the contenders on this point is, that they fight at long weapons ; I mean they keep the ar- gument in generals, by which they make little more of it than fome innocent harangues and flourifhes of ihetorick, or at moft make bold affertions upon the authority of fome mifapplied expreflions and incredible ftories of ancient writers, for I am now fpeaking chiefly of the patrons of the ancient mufic. If Sir William Temple Was indeed fefious, and had any thing elfe in his view, but to fhew how he could declaim, he is a notable inftance of this. Says he, " What are become of the charms of mufic, by which *' men and beads were fo frequently inchanted, and plainly becaufe we know all theirs; and that we have improved upon their foundation, will be as plain j from the accounts I have given of both, and the com- panion I have drawn all along in explaining the ancient , theory j therefore I need infill no more upon this part. The great difpute is about the practice. To understand the ancient practice of m'ufk, we are firft to confider what the name lignifiecl with them. Mufic included thefe three things, harmony, rythriius, and verfe : if there needs any thing to be added, take L theie 82 A T R E A T 1 S E thefe few authorities. In Plato's firft Alcibiades, So- crates afks what he calls that art which teaches to firig, play on the harp, and dance ? and makes him anfwcr, Mufic : But finging among them was never without^ verfe. This is again confirmed by Plutarch, who fays, " That in judging of the parts of mufic, reaibn and " fenfe muft be employed : for thefe three muft al- 4< ways meet in our hearing, viz. Sound, whereby we A T Pv E A T I S E lor curing the bites of ferpents, we cannot fo muck doubt it, fince that of the Tarantula has been cured in Italy. But then they have no advantage in this in- stance : and we mnft mind too, that this cure is not performed by exquifite art and {kill in mufic ; it does not require a Correili or Valentini, but is performed by drains discovered by random trials without any rule : and this will ferve for an anfvver to all that's alledged of the cure of difeafes by the ancient miific. Tis time to bring this comparifon to an end ; and after what's explained, it mull be owned, that the #ate of mufic is much more perfect now than it was among the ancient Greeks and Romans. The art of mufic, and the true fcience of harmony in founds is greatly improved. Their mufic has been allowed (in- cluding poetry and the theatrical action) to have been very moving ; but at the fame time it ranft be faid, Their melody has been a very fimple thing, as their fyitcm or fcale plainly fhews. And the confining all their rythmus to the poetical n nmbcrs, is another proof of it, and ihews that there) "has been little air in their mufic ; which by this apr pears to have been only of the recitative kind, that is, ■only a more muiical fpeaking, or modulated elocution ; ihb character of which is to come near nature, and be only an improvement of the natural accents of words by | more pathetic or emphatical tones ; the fubjecl: whereof may be either verie or profe. And as to their instruments of mufic, for any thing that appears cer- tain and plain to us, they have been very fimple. In- deed the public laws in Greece gave check to the im- provement of the art of harmony, becaufe they forbade all innovations in the primitive fimple mufic ; of which there are abundance of teftimonies. Plato fays, in his Treatifc of the Laws, viz. That they entertained not in the city the makers of fuch inftruments as havo many fixings, as the Trigonus and Pectis ; but the Lyra and Cithara they ufed, and allowed alfo fome iimple Fiftulae in the country. Bat 'tis certain, that primitive iimplicity was altered ; fo that from a very tew firings they ufed a great number : but there i« maeh unc^rurnty about the ufs of thcm ? as whether it was O F M U SIC, $ was for mixing their modes, and the genera, or for linking two chords together as in tire magaqis. Since instruments have been mentioned, two things muft be obferved, firft, That they pretend to have had tibial of different kinds, whofe Specific founds were excellently chofen for exprcSSing different Subjects. Then, there is a defcription of the Organum hydraulicum in Tertul- lian, which fome adduce to prove how perfect their in- struments were. — Spedta portentoiam Archimedis muni- ficentiam; organum hydraulicum dico, tot membra, tot partes, tot compagines, tot itinera vocum, tot com- pendia fonortim, tot commercia modorum, tot acies tibiarum, & una moles erunt omnia. But it will not be pretended to have been more perfect than our mo- dern organs : And what have they to compare of the ilringed kind, with our harpfichords ; and all the in- struments that are Struck with a bow ? After all, if our melody or fongs are only equal tcr the ancients, it is to be hoped, the art of mufic is not loft as fome pretend. But then, what an improvement in the knowledge of pure harmony has Ixren made, Since the introduction of the modern fymphonies ?' Here it is, that the mind is ravifhed with the agree- ment of things feemingly contrary to one another. We have here a kind of imitation of the works of na-r ture, where different things are wonderfully joined in one harmonious unity : And as fome things appear -at firft view the fartheft removed from Symmetry and order, which from the courfe of things we learn to be abfolutely neceSTary for the perfection and beauty of the who e ; fo difcords being artfully mixed with con- cords, make a more perfect compolltion, which fur- prifes us vviih delight. If the mind is naturally pleafed with perceiving of order and proportion, with compar- ing Several ih5 i -; ( i7 ■ (m. v ^ j \ tA \^- .. s9 \ : jSV I £to ■b y