'm\\v'. CORNELL UNIVERSITY LIBRARY MUSIC Cornell University Library MT 55.B85D7 3 1924 021 750 934 Cornell University Library The original of tliis book is in tlie Cornell University Library. There are no known copyright restrictions in the United States on the use of the text. http://www.archive.org/details/cu31924021750934 SIXTH THOUSAND. NOVELLO, EWER AND CO.'S MUSIC PRIMERS. Edited by Sir JOHN STAINER. Double Counterpoint AND CANON BY J. FREDERICK BRIDGE HUS. DOC, OXOM,; ORGANIST AND MASTER OF THE CHORISTERS OF WESTMINSTER ABBEY; PROFESSOR OF HARMONY AND THE ORGAN AT THE NATIONAL TRAINING SCHOOL FOR MUSIC, KENSINGTON, AND AT THE CRYSTAL PALACE SCHOOL OF ART; LATE ORGANIST OF THE CATHEDRAL, AND LECTURER ON HARMONY AND MUSICAL COMPOSITION AT THE OWENS COLLEGE, MANCHESTER; EXAMINER IN MUSIC TO THE UNIVERSITIES OF OXFORD AND CAMBRIDGE (x888). PRICE TWO SHILLINGS. In Paper Boards, Two Shillings and Sixpence. loo LONDON &■ NEW YORK NOVELLO, EWER AND CO. LONDON : KOVELLO, EWER AND CO., -PRINTERS. INTRODUCTION. Those who propose to study Double Counterpoint and Canon should already have acquired the art of writing the various species of Simple Counterpoint in four or five parts, together with a good knowledge of harmony. There seems no reason why the student who has been through this preliminary work, should be debarred the use of the resources of modern harmony when writing his examples. If he has diligently worked at Simple Counterpoint, with its restricted progressions of melody and har- mony, he will not fail to feel its good influence, and to apply, as far as is consistent with the greater ireedom he now enjoys, its many valuable precepts. The application of Double Counterpoint and Canon to fugal writing will, in all probability, be the direction in which the student will make the first use of his knowledge of this branch of the art. With this in view the Author has thought it well to choose many of his examples from works of a fugal character. Although it is in this style of composition that Double Counter- point is most used and most necessary, yet it has often been employed in music not of a fugal character, examples of and references to which are g^ven in the course of this work, and many opportunities for its happy introduction will be found by those who take the pains to master a subject so necessary and so useful to the true musician. iv INTRODUCTION. An effort has been made to avoid all useless and pedantic rules; but at the same time, for the student, rules are absolutely necessary, until he -has acquired the knowledge which will justify him in departing from the strict letter while he is observing the spirit. The Author's best thanks are due to Miss Smart, for kindly allowing him to insert the interesting canon by Mendelssohn, hitherto unpublished (No. ip of Appendix) ; to F. Locker, Esq., for bringing to his notice and permitting him to copy from the ori- ginal MS., the canon by J. S. Bach (No. 9 of Appendix) ; to Dr. Gladstone for Example 128, together with many valuable suggestions ; and to James Higgs, Esq., Mus. Bac, for kind assistance and most useful advice which his well-known acquire- ments and special studies in this branch of the musical art hav; rendered invaluable. The Cuoistees, Westmifstbf Aensr. Septemoer, ibSi. CONTENTS. CHAPTER I. PAOB Definition of Double Counterpoint — General rules — Double Counter- point in the octave — Examples — Double Counterpoint in the fifteenth — Examples — Subjects to which Double Counterpoints may be added — Examples of models derived from simple phrase . i — 15 CHAPTER II. Double Counterpoint in the tenth — Examples , - . • • . l6~a4 CHAPTER III. Double Counterpoint in the twelfth — Examples 25 — ^33 CHAPTER IV. Added thirds — Examples 34 — 3S CHAPTF" " Counterpoints invertible in various intervals — Examples . . 39 — ^45 CHAPTER VI. Triple and quadruple counterpoints — Examples — Quintuple counter- point — Example 46 — 5a CHAPTER VII. Imitation — Strict and free — Examples 53 — 57 CHAPTER VIII. Imitation by contrary movement — Free — Examples — Strict — Examples — Imitation by augmentation — By diminution — By augmentation and contrary motion — By diminution and con- trary motion — With reversed accents — Examples . . . 58 — 63 CHAPTER IX. Partial imitation — Examples — Chorales on vifhich are constructed imitations 64 — 75 CHAPTER X. Canonicalimitation— Origin of term— Examples .... 76—79 VI CONTENTS. CHAPTER XI. PAOE Canons : Finite — Infinite — Finite by augmentation — Infinite by aug- mentation — By diminution— Retrograde — Circular — Examples . 80 — gi CHAPTER XII. Polymorphous canon — Examples — Sequential canon — Example . 92 — 96 CHAPTER XIII. Methods of exhibiting canons — Open — Close — Canon four in two — Round 97 — 100 CHAPTER XIV. Hints to the Student — To compose a canon — Modulation in canon . loi — 102 APPENDIX. Examplef) of Double Counterpoint io'> — 12a INDEX. Paraoraph. EXAMPLB. Added free parts to model for Double Coun- ) terpoint in tenth . . . . | Added thirds to models for Double Counter- \ point . . . . ■ . j Addition of accidentals in inversion of model Addition of accidentals in inversion in the] - tvirelfth J Antecedent Canon 35- 59, a, b, c; 60, 61, 62, 63, 64 29. 30 43 • 80 . „ circular (per tonos) , . „ close „ by diminution . . . • „ enigmatical .... ,, finite „ finite by augmentation . . „ infinite by augmentation . . „ infinite or perpetual . „ ' „ „ with coda . „ open „ polymorphous .... „ ' retrograde .... „ sequential . . . ■ Canoni Chromatic notes „ progressions . . . Clefs prefixed to a close canon . Contracted parts ..... ,, subjects .... Contrary and oblique motion generally 1 employed f Contrary in Double Counterpoint at the) tenth .... J ,, motion Counterpoints invertible. in various intervals Consequent Crossing of parts Double Counterpoint . . . • Double Counterpoints most used . 91 (g6 (note 108 117 to 102 109 96, 97 124 100 lOI 13 99. 117 no to I 103 to 105 "5 93- 29. ,106, 118, 124 3 (notes to ! 3 (Sec. 3) 3 (Sec. 3) 34 • 3 (Sec. 3) 65 to 71 81 3 (Sec. 2) 1 . 2 . 107, Sec. i) 42; 51,6 68 to 74 •■ 39. c; 40, e 136, 14a 137 '33 124, 125 129 130. 131 126, 127 128 137 to 143, 133 to 135.. H3 75 to 81 VI 11 INDEX. Paragraph. Example. Double Counterpoint in the octave „ „ „ iifteenth . „ „ „ octave displayed 1 at the doubleSve J „ „ „ octave inverted I at the fifteenth J II 11 1, tenth .1 I. II twelfth- . „ „ „ tenth combined with thatintheSve „ „ „ tenth,modeland' inversion at the same time. ,, „ I, eleventh, thir- teenth, and fourteenth ... Example of simple model elaborated . Expansion of parts Fourth, augmented Fifth, dimmished or minor .... Figures denoting the interval in which a) canon is made .... J Fugue in epidiapason . . . . ■ Fuga ligata General rules Hints to attain clearness in canonic writing How to avoid modulation in a canon . Imitation „ by augmentation .... „ „ and diminution,! combined with contrary motion J „ by diminution .... „ canonical . . > . . „ on a chorale .... ,. by contrary motion . . „ free or irregular .... „ in two parts, with independent) accompaniment . . J „ partial or periodical . „ retrograde {per rede ei retro} or cancrissans ... J „ reversed accents (per arsin ei tkesin) ,, reverse retrograde ,, strict or regular .... „ on a theme or canto fermo . Methods of exhibiting canons when written Model Modifications of terminations in Double) Copnterpoint in tenth and twelfth J Octave on gccented beat .... Qniission of accidentals in inversion ofmodel ) for Pe»ble ConjiteFpoipt in tenth . / 7 (note), 21 19. 3 (notes to Sec. i),] 25 3 (notes to Sec.i),] ( 41 . 59- 40. 58. 3 (note to Sec 8, 10, 34 (Sec. 8, 10, 34 (Sec. 119 93>94 i2g (Sec 126 (Sec, 76. 83- 85, 84. 88,91 90. 81 . 79 • 88, 8g, g 87. 86. 87. 77.78 89. 117 3 (Sec. i) 29 (note) 14. 29. I, 2 4), 3.4) 127 15 to 24 25 to 30 461050; 76,4 62 to 69, 78, 79 37, u, b, c, d, t 41 144, u, b 122, b III "3. "4 112 iig to 121 105 to no 96 to 99 100 to 104 "5 90 to 95 116 to iiS 39. 6 INDEX. !x Origin of the term " canon " . . Partial or periodic imitation. Preparation and resolution of seventh in Double Counterpoint at the twelfth Progressions by similar motion in Double Counterpoint at the tenth PiOposition ..... Quadruple Counterpoint Quintuple Counterpoint Reversed clef and time signature Riddle Canon .... Round Rule for discovering the inversion of any| interval (Sir J. Goss) . Seventh diminished Simple model from which others are derived Sixth augmented Sixths in Double Counterpoint at the tenth » I. >, ,> twelfth Solution Stretto Subjects to which counterpoints may be added Suspension of the second . ,, „ fourth „ „ seventh . ,, ,, ninth Table of inversions in the octave „ „ tenth . ,, „ twelfth Third, diminished Thirds in Double Counterpoint at the tenth Triple Counterpoint . To compose a canon . Two ways of inverting in the tenth Unessential note ..... Unprepared discords .... Use of three staves in inverting exercises Usual method of describing canons . Paragraph. 93 51,52 . 34 (Sec. I, 2, 3) 80 . 72 to 74 75 ■ 103 log 126 16 . i2> 13.34 (Sec, 24. 11,34 (Sec. 2, 31 to 33 47. 48, 51 log 116 1.3 3). 50 36. 36. 37. 37 ■ 53.54 38,54 16. 27 . 43.44 31 to 33 72 to 74 126 28,30 7 • 4 22 . 9a. Example. 58,59 41 88 8g 133 41 37, a, b, c, d, » 41. 57 32 to 36 43 44, 60, 61 44. 47. 49 45,61 81 to 87 (38, a,b,c; \ 40, a. 6, c DOUBLE COUNTERPOINT & CANON. i^se;^-! CHAPTER I. I. A TWO-PART phrase is said to be in double counterpoint when both subject's admit of double employment, i.e., when either may act as upper or lower part ; in other words, when they will invert : — Ex. I. F*^=r= s- — 1 — 1 — 1 m — & — m ^1 The same inverted : — i Ex. 2. a ^r.jrw BE ^^^w :^ ^^^- !-- '^J I JjJJN^^ij.jjL a For a corrected form of the above example see page i8. Ex. 6, a, is a model for double counterpoint in the twelfth (see page 25) witK similar faults. At b it is inverted with the same results. Ex.6. M a Model for d.c. in twelfth. J=¥=f * ' Q • y --. ^. ^. 13 14 ^m^=^^ :$=&: :t=E 6 Inversion. i pr^r :$: It ^P -»-f^ Lower part of model a twelfth higher. &c. ^ - .° <-J - ^ ' o (2.) The parts should not cross in the model. It will be seen- in Ex. 7, a, b, that the effect of the -intervals marked * * • is rpractically the same. In this case the intervals marked * * ' in the model a are expanded, not inverted, at b. Ex. 7. gS n rs* — »!- m g^=^ a^ T^"jyr ^^B * I I ^Si 4 DOUBLE COUNTERPOINT AND CANON. (3.) The two subjects forming the model should be well con- trasted both as to length of notes and melodic progression, contrary motion being always preferable to similar motion ; the two parts will thus possess individuality and be easily dis- tinguished from one another. It is well that they should not begin together, but that one should enter after a short rest (see preceding examples). 4. It will, of course, be understood from the Introduction to this work that the student is not confined to the progressions and chords used in simple counterpoint in the strict style. While, however, chromatic progressions and unprepared dis- cords are available, it must be remembered that the model will probably be heard alone {i.e., without accompanying parts), and therefore a somewhat strict rather than free use of such discords is advisable. DOUBLE COUNTERPOINT IN THE OCTAVE. 5. The intervals of the fifth and fourth are those which will most require the student's care when constructing the model. 6. The perfect (or major) fifth, although consonant in the model, becomes by inversion a discord, viz., a fourth. This condition must therefore be provided for, and as a fourth will seldom appear upon the accented beat without preparation, the fifth must conform to this usage (Ex. 8, a, b). Upon the unac- cented beat fifths and fourths are of course often taken without preparation, especially when they occur as passing notes (Ex. 8, c), or by conjunct movement in at least one of the parts (Ex. 8, d). i Ex.8. a ■3±L uaz =g= ^C2= =pzz =r T=^ The bar marked d is not very good in two-part writing. 7. Even upon the accented beat cases may occur where these intervals maybe used without preparation, particularly when one of the notes forming the interval is an unessential note. At Ex. 9. a, is an unprepared fourth upon the accented beat, the E in the upper of the two parts being clearly an unessential- note,— an appoggiatura. INVERSION IN THE OCTAVE. ^^^1 ^ Ex. g. The above is double counterpoint in the fifteenth or double octave (see par. 2i). 8. The augmented fourth (Ex. lo, a, b,c) and its inversion, the diminished (or minor) fifth (Ex. lo, d, e, /), may be freely used on either accented or unaccented beats. Inversion. g. The avoidance of consecutive major fifths is of course necessary, and the student will understand that consecutive major fourths are equally objectionable. lo. Some authors allow a major fourth, followed by an aug- mented fourth (Ex. II, a), resulting, when inverted, in a major fifth, followed by a minor (or diminished) fifth (Ex. ii, b); but these fourths should be avoided unless the model is accompanied by another part, which renders such harmony unobjectionable (Ex. II, c). Ex. II. g f F^; ll f_tf-H=^ ^-l jl l ;'-<^; l l If the first note of the lower part at Ex. ii,b, were dotted, all objection would be removed, as the G would then be a passing note (Ex. ii, d). II. The augmented sixth (Ex. 12, a) cannot be used because its inversion, a diminished third (Ex. 12, 6), must be avoided in two-part writing. • a h Ex. 12. "^ -P" jlBSl 6 DOUBI-E COUNTEJlPOmX AND C^NON. 12. The diminished seventh may be used if care be taken in its resolution, as, for example, if one of the notes forming the interval be resolved before the other (Ex. 13, a b), or if, resolving on a fifth, such resolution falls on the unaccented beat ; but this is not recommended (Ex. 13, c). Ex. 13. i A=[^A H iri- 'I r^rW^fZ I i "p^^^~p" 13. The diminished seventh should not be resolved upon a fifth on the accent (Ex. 14, a), because in its inversion a fourth results (Ex. 14, b). •'■$ -W=^ Ex. 14. The octave becomes by inversion an unison, and in this species of double counterpoint should be .used sparingly, except at the beginning and end of the model, or perhaps occasionally as an unaccented note. It should not be taken by a skip on the accented beat, especially by similar motion. 15. With the exception of the fourth and fifth, to which special attention has been called, those intervals which are discords in the model (the seconds and sevenths) are discords in the inver- sion (becoming sevenths and seconds respectively), and the concords in the model (the thirds, sixths, and octaves) are con- cords in the inversion, becoming sixths, thirds, and unisons respectively. 16. The following table ..shows the result of inversion in the octave -. — Model ... Inversion It may perhaps be useful to mention the rule given by Sir J. Goss in his " Rudiments of Harmony," for discovering the inver- sion of any interval [in the octave] by referring to the number g, " since each interval when added to its inversion will make up that number." This rjile may, of course, be expanded to apply to inversion in other intervals, the principle being to add one to the number of the interval in which the inversion is to be made. Thus, for inversion in the tenth (see par. 27)- each interj^al added to its inversion will make 11, and for inversion in the twelfth INVERSION IN THE OCTAVE. (see pars. 43 and 44) each interval added to its inversion will make 13 ; the addition of one is necessary, because the central note on which the inversion turns is counted twice, thus : — i f ■3 + 6 = g. 17. Examples of double counterpoint in the octave are give»' below. Some of the inversions do not appear in the compositions from which they are extracted, in the keys here given. The inversions of the first few examples which follow are, however, given in the same keys as their respective models, in order that each counterpoint and its inversion may be more readily seen by the student. It is not thought necessary to adhere to this plan ' throughout the work. i Ex. 15. a Model. Handel, r=^ Oboe Concerto, ^ '--L^r i ^m s^ • d * $ b Inversion. ^ I^E ■#-»- tr ^ ^ E^ t=^ p=s= Ex. 16. a Model. $m Handel. Te Deum in B|?. ^ atl^i^p^z^izhzi T3- i PH * i P e^ ?3= 6 Inversion. T^Tm gjj ? -2_g = s ^i ^ izi: ^ Ex. 17. a Model. lit: DOUBLE COUNTERPOINT AND CANON. GusTAV Merkel. Organ Fugue. 3^ ■• 1:!?::?^: =PP :e 3z^ i M ^ &^ p g Ex. 18. a Model. Leo. Kyrie. fe^ ^ m fTf ^ -^ •r , -r- =^^ P i f frn* f - > • # .WIl ~7rr n r ^. * ? t^* & ^ r? o i ^± Ex ig. a Model. Haydn. Creation, i ^^kmxTjVj =^ 6 Inversion. -\i : — ^,-r-n- JNVERSIDN IN THE OCTAVE •jg s m ^^ m^ f=w^ 35ES ^^^ SI i8. The inversions of the models which follow are given as they stand in the compositions from which they are extracted. Ex. 20. a Model. KiRNBERGER. h Inversion. :t- i» The skip of a third at * * is necessary for " tonal " reasons. See Primer on " Fugue," par. 34. The C at is replaced by B in the movement from which this is taken, for contextual reasons. ig. The following model is also double counterpoint in the octave, although it is, so to speak, accidentally displayed at the double octave, but that it is not truly in the .fifteenth: is evident from the fact that the upper part maybe brought down an octave; or vice versd, without involving any crossing of the parts. In practical composition it frequently happens that double counter^ point, essentially in the octave, is exhibited both in the model and its invfersion at the distance of two or even -three octaves. The difference between this and double counterpoint in the fifteenth will be seen further on. 10 DOUBLE COUNTERPOINT AND CANON. Ex. 21. a Model. From PoRPORA. pig rjcsz r \ \ u ^ • \ f ^i±^ #r-=^^^rcr^ nr'' M " H '1 6 Inversion ^^ r? iR ^ fe S aii f7t:frrir-G^f-|f ii 20. Still more often, when the model is within the octave, the inversion is exhibited at the double octave (fifteenth), the upper part being transposed two octaves lower, or the lower part two octaves higher, or both parts an octave in opposite directions. The following (Ex. 22 to 24) are inverted on the latter plan. Ex. 22. , a Model, From an Organ Fugue by Albrechtsberger. |iS ^ :t -P — P — ^-F ^ ^ r f i f j^r, ^ i m % b Inversion. M^ ;C_i: f I r r-^^F " INVERSION IN THE FIFTEENTH. II I Ex. 23. a Model. Bach. Art of Fugue. ^^ ^^M ^ Ti 6» i ^rrmrr-n^ m :ii>^ ^E 6 Inversion. ^^m ^^Jf¥=^ ^ a W^^Si^ ^ Ex. Z4. a Model. GusTAv Merkel. Organ Fugue in A minor. b Inversion. ^m i ^ • I* . f S^^ -<' - -ti I i- ^g^ =B: F t yi r DOUBLE COUNTERPOINT IN THE FIFTEENTH. 21. Double counterpoint in the fifteenth (double octave) is essentially the same as double counterpoint in the octave, except that the wider interval (two octaves instead of one) allows greater scope for the two parts forming the model. Although, as was said in par. 20, double counterpoint in the octave is often inverted at the double octave (fifteenth), the upper part of the model being transposed two Octaves lower, or the lower part two octaves higher, or both parts an octave in opposite directions, it fz DOUBLE COUNTERPOINT. ANt> CANiON. should be observed that a model for double countei point in the fifteenth cannot be contracted so as to invert in the octave^ Some examples of double counterpoint in the fifteenth are given below : — i Ex 25. a Model. Beethoven. Et vitam, Mass in D. 000 ^ o \i r} -rj- te^ :Phe: \' Arv f f SE ^ m b Inversion. 3E^ M r f f f f ■m-^W^ r I r 1^^ F4=4=± i fi fi f-i ^# ^^ I Ex. 26. a Model. JOMELLi. Requiem. J ; ^i> -J-h f=r=mi M ¥=F^ ^ ^ i J Inversion. :k ^F=F=*: =t=F ^^ ^^ ^ °v_^ * ' g> - ss fefc^ 32= =pz; Ex. 27. a Model. Marthji. INVERSION IN THE FIFTEENTH I3k i 6 Inversion. I J . i pn^^t--^ m 1 • ! * -•i. :ft Pi^^ 'r T i * -ftr ^ t=i=t ^ &c. ^rrrl^"-^ s =t=t= =F+=F t=& ^a The rest at • takes the place of the note D in the model, Martini evidently regarding the figure given in the inversion as the real counter-subject. The D appears in another part when the model is inverted.^ • Ex. 28. , a Model. Handel. $ ^^r^rif-H g^ &c. b y> - r - * 42- i m pc s :^ ^ 6 Inversion. i =k :?2Z :^E ^ :?2- &ci r r- r 'h^Um ^^ fe^ Ex. 2g. i o Model. -f3- n^^rf Haydn. ^ ^^"X^ fr^^^j:^ r-rr( J Inversion. ^b''(M,rjj-^feff^^^ Hrufc ^ :^ 3 ^^ ^^ ^£^ H DOUBLE COUNTERPOINT AND CANON. Ex. 30. a Model. ^ , n -^- ^^ . . .rjj Martini. a i I i B^a ^fe 1^ b Inversion. ^^^^ffil r""£r^-'^' ^e ^ l^g At * a slight alteration of the counter-subject leads to a contraction of the paits, the lower being brought an octave nearer the upper than its proper position by inversion in the fifteenth. The possibility of this arises from the fact that the model was at this point within the limit of an octave. 22. The Student should now construct models of double counterpoint in the octave and fifteenth by the aid of the precepts and examples already given. It will be found advisable to use three staves in the way indicated in Ex. 31, as we are thus enabled to see readily what the intervals in the model become when inverted. The two uppier staves of Ex. 31 contain the model ; the two lower its inversion in the octave : — Model. Inversion. i EE ^^ Intervals ] in the Model. 3 4 i =F7=P ^ Intervals inverted. ^S 7 Subjects to which Double Counterpoints may be added. 23. For those who at first find it difficult to construct , 6o• The varied model at b is formed chiefly by the aid of passing and auxiliary notes ; at <: by adopting a sequential form in the upper part, and introducing a chromatic note in the lower part; at d and e by exceeding the limits of the original model, and in the latter case also by modulating to the sub- ^bminant at bar 2. The models at b and c axe for inversion in the octave, those at d and e for inversion in the fifteenth. CHAPTER II, DOUBLE COUNTERPOINT IN THE TENTH. 25. Although taken next in order, this counterpoint by itself is by no means next in value, inversion in the twefth being used far more frequently. There is, however, an incidental variety of double counterpoint in the tenth, combined with that in the octave, of considerable value and interest, which will be fully, treated of further on. (See par. 59.) 26. The general ruleson pages2,3,and4 must be borne in mind. 27. When the subjects are inverted in the tenth above or below, the consonances in the model change into other con- sonances, thus : — Model 10 8 6 5 3 I Inversion i 3 5 6 8 10 and the dissonances into other dissonances, thus : — Model g 7 4 2 Inversion 2 4 7 g 28. By the use of three staves as suggested in par. 22, the student will easily discover the inversions which the intervals in the model involve (see also par. 16). This method, however, will show only one inversion, whereas there are two ways of inverting a model for double counterpoint in the tenth, the two inversions differing considerably in their effect. This will be best seen from an example. Ex. 38, a, is a model ; b shows the inversion of the upper part a tenth below, c the inversion of the lower part a tenth above, both inversions being rendered in accordance with the signature of the model. Ex. 38. M a Model. Albrechtsberger. t sr dLi^ ) I* ^ 3 t ^ i; b Inversion. i i E Upp^ paTt a*ten^ bllow^ i1 INVERSION IN THE TENTH. J7 i 14;=^ ^ Lower part a tenth above. i =e=q^- =p=i= ^ E ii;;^ 29. Such inversions will often be satisfactory enough, but if the model contains chromatic notes, or notes inducing modu- lation, the result in the inversions will generally be that some modification of one or other of the parts will be necessary. In some cases this may be by the omission of an accidental employed ' in the model, in others by the addition of an accidental. Ex. 39, a, is a model commencing in C major and modulating to, G by the F sharp marked * ; 6 is one of the inversions, the acci- dental being omitted at * ; c is another inversion containing an additional accidental at *. Ex. 39. a Model. ^^ -+- f- =t=F: -f*t] H- =n L-i — —et- =1^ 1 ~ UM± r -M—» — +- 1 \ — i — $ b Inversion. -• — ^ — t Lower part a tenth above. i eS c Inversion r> r J Upper part a tenth below. ^ mt WT^ Some modification of the terminations of models for double counterpoint in the tenth and twelfth when inverted will also frequently be found necessary, though,' as has been well observed,* " In actual composition double counterpoint is generally employed for a limited period only, and under circumstances which' render unnecessary the introduction of a full close or authentic cadence, or even forbid it." * Richtec. i8 DOUBLE COUNTERPOINT AND CANON. 30. At par. 28 it was said there were two ways of inverting a model for double counterpoint in the tenth, the higher part being .put down a tenth lower, or the lower part a tenth higher. But these inversions may be arrived at by other processes, some subjects inverting more agreeably in one way than in another. Ex. 40, a, is a model for inversion in the tenth : — Ex. 40. P«-r i 3=P ' ^Jlj^ » s » -*-»- ^g ^ -i-r-r At h the model (a) is inverted by taking the lower part an octave higher and the upper part a third lower : — h fs s » » Lower part an octave higker. Upper part a third lower. t-^-^ ^^ £= d * ^^ At t the same model is inverted by taking the lower part a third higher and the upper part an octave lower : — K ^^ ^ Lower part a third higher. Upper part an octave lower, fe ¥ s F=^ W^ m ^ Notice the numerous accidentals necessary to render the inversion satis- factory. The usefulness of this method of inversion for the purposes of modulation in fiigal writing is obvious. 31. As thirds become octaves when inverted, they must not be used consecutively. Sixths become fifths and follow the same rule, but in some cases (see par. 34 (3), and Ex. 41, A, t, f) consecutive sixths are possible. INVERSION IN THE TENTH. '9 32. Even single thirds and sixths must be used with judgment, remembering that in the inversion they become octaves and fifths respectively, and, however taken, they of necessity render the harmony somewhat bare. A reference to Ex. 40 will show this. 33. We should not approach these intervals by similar motion in two parts, if by inversion objectionable hidden octaves and fifths are produced. 34. It is apparent from par. 31 that contrary and oblique motion must be generally employed. A few progressions, however, where the parts niave by similar motion may be used, viz. — (i) A w wyB i fourth, followed by an augmented fourth (Ex. 41, a), becoming in the inversion, by the aid of accidentals (see par. 29), a minor seventh, followed by a diminished seventh (Ex. 41, b, c). (2) A perfect «)Mttfi^r fifth, followed by a diminished owiminor fifth (Ex. 41, d), becoming in the inversion a major sixth, fol- lowed by an augmented sixth (Ex. 41, e), or a minor sixth, followed by a major sixth (Ex. 41,/) : — Ex. 41. Lower part a tenth above. Model. Upper part a tenth below. ^- U '^ ^ ^m ^-l^lMs^jp l r T f- Observe the different effect produced by the two inversions (see par. 28). (3) It is obvious that a minor seventh, followed by a diminished seventh (Ex. 41, b and c), producing the fourths at a, and the sixths at e and/, producing the fifths at d, are equally allowable. 35. In a two-part phrase these progressions, particularly the fourths, should be avoided. If, however, other parts are pro- ceeding at the same moment with the counterpoint, they may niore readily be admitted, their imperfections being at least hidden if not made good. The questionable progressions in Ex. 41 are given in Ex. 42 with an added free part. 20 DOUBLE COUNTERPOINT AND CANON. Ex. 42 Fourths with lower free part. Fifths with lower free part. Sevenths with inner free part 36. The suspensions of the second and fourth occur only in the lower part, i.e., the note causing either discord must be prepared and resolved in the lowest part. The second must not be prepared by a third as at Ex. 43, a, or hidden octaves \yill be produced when the passage is inverted (b). The second may be prepared by the unison (c), fifth (rf), or sixth {e). The hidden octaves produced by the inversion of d and e could be softened in effect by suitable accompanying harmonies. (See small notes.) Ex. 43. Inversion. ■ Model. m m^m i ^ <^ 1 i 3E ^ ^ 37. As has been seen in Ex. 41 certain fourths and sevenths are admissible without preparation, particularly the dominant and diminished sevenths, with their inversions the major and augmented fourths. But a suspension of the fourth takes place only in the lower part (as was said in par. 36), and is generally resolved into a fifth or sixth (Ex. 44, a, b, c). The suspension of the seventh will occur in the upper part, and will resolve into a sixth or fifth (Ex. 44, d, e,f): — ,6, . ... -^Q-ljT^ujm^j ^ 1 f^rn^rj^r r 4 5 76 73 75 4 & 4 & 38. The progressions contained in the two upper staves of Ex. 43, c, d, e, show the preparation and resolution of the suspended ninth. It should be added that when the ninth falls to its note of resolution, the lower part may rise a third {i.e., to INVERSION IN THE TENTH. 21 the first inversion of the chord on which the ninth would resolve, Ex. 45, a), or a fourth {i.e., to another chord — a triad on the fourth above — Ex. 45, b): — Ex. 45. ± T r r 9 zpz^-b 39. The following are examples of double counterpoint in the tenth : — Ex. 46. Model. Schneider. ■ W'T'~=rf^~w~i \ T T \ ^ T ^ r~r — ■ f^ ^^ ^ 1 1 ■ r 1 1 — ^^-f-r — ^ — ^^ '■■' ^-^ i f — 1 c — Inversion. EE Lower part a tenth higher. ^^ r r r i Ex. 47. a Model. Schneider. ^ EEE =!=ii= ^ =^ Lower part a tenth higher. ^ ^m -< — F— ^ =£?= , In Ex. 47, a, the suspended seventh at * is resolved ornamentally into the sixth (see par. 37). 1 22 DOUBLE COUNTERPOINT AND CANON. Ex. 48. a Model. A. F. C. KoLLMAtW. ^i I [ O -e- &c. ^^ :^^^ ^^ S TT5T1 ai^TK; ^ * i 6 Inversion. H b- — s I I =1= -i ■-*- ^ Lower part a tenth higher. ^ ::^czK c:Sja^,St ^L > :^^=F ^^ T<* • P - =t=t: i 6 Inversion. ^ -TT i =FFF= BS m ' » Lower part a tenth higher. L In Ex. 49, a, the suspended seventh at • is resolved (ornamentally) into a fifth (see par. 37). \ ii INVERSION IN THE TENTH. 83 Ex. 50. a Model, Albrechtsberoer. ^ ^ =P2= » I -0—0-4- -m—J — I ^- m^ iF=F :4=r: ±3z ^ • b Inversion. i q?=«: b' (', r ^F=r rf-P ^-d: =1=1= =tii zs:t: -m—0- m^ ^ ± S.2?- =!=iiB ; The parts move in thirds here (Ex. 50, a, * *) which necessitates a slight alteration when the parts are inverted, to avoid consecutive octaves (see par. 31). I 40. In double counterpoint at the tenth it is often possible to use an inversion of one of the subjects at the same time with the model, thus giving a three-part phrase. Here follow some examples : — Ex. 51. Schneider. ' MODEI.. Inversion. t=t= &% ■wrrH-\m =r^:pa =1=1= Ex. 52. Model. Inversion. a ^ :f^-0- ^ I i I Reicha. ^m J * p" ZC2Z 24 DOUBLE COUNTERPOINT AND CANON. g^g^ =P=P ^ I 1 I $ n=t: II I ^ =P=I?: =l=t The following inversion is obtained by taking the lower part a third higher^ and the upper part an octave lower. An added part, such as is suggested in small notes at * would remove all objection to the inversion : — b Inversion. ^ ^ 1^1; (: - r^H^^ 4=t T3~ =P- » I ^m -p- % ^ r ip=t: I Another important example of this counterpoint will be found in Ex. 76, c. CHAPTER III. DOUBLE CpUNTERPOINT IN THE TWELFTH. 41. Double counterpoint in the twelfth is, in point of useful- ness, next to double counterpoint in the octave. 42. The rules on pages 2, 3, and 4 must be remembered.' 43. When the subjects are inverted in the twelfth above or below, all the dissonances change into other dissonances except the seventh, which becomes a sixth. Model Inversion 4 9 Concord 6 9 4 44. All the consonances change into other consonances except the sixth which becomes a seventh. Model I 12 3 ID 5 8 6 8 Inversion •■• Discord 7 5 45. As in double counterpoint in the tenth so in this species fccidentals will sometimes be necessary when the model is in- verted. A phrase, however, transposed to the twelfth above or below so nearly resembles the original as regards the position of the semitones, &c., that the student will at once see acci- dentals are not required in this species to the same extent as in that of the tenth (Ex. 53). Ex. 53. Model. - Inversion. - i Lobe (slightly altered). fe -l-^-t- •-•-d- ^ ^ 4= tF^ :rt7- ?3= i?2= ?sS a Upper part a twelfth lower. SfcEE ^ f: ^ q= ^ d ^ 4. ^M 26 DOUBLE COUNTERPOINT AND CANON. 46. As the third becomes a tenth, and vice versa, these in- tervals can be readily used, and may be taken by similar motion. For the other intervals contrary and oblique motion will be found generally necessary. 47. The sixth when inverted becomes a seventh, and will often require preparation. The preparation and resolution must be in the lower part, as this becomes the dissonance when inverted (Ex. 54, a,b). Ex. 54, ' a b Model, - Inversion. znt: m ^ 32 ~r?~ IZSZ ^ ^ 7 6 4: , When, however, the sixth inverts into a dominant or diminished seventh, preparation is not necessary. It may also be used as a yassing note. 48. Two sixths (Ex. 55, a) which by inversion produce a minor -seventh followed by a diminished seventh (Ex. 55, b) may be used. From Marpurq, ed. by Choron. b Ex. 5S. ^^=i= r^ ■ ; — [— "1 U\ ((1) * ^ 1" 6 6 '0 1 i.'i — 1 — ^ — 1 4 1 — ^ — 1 7 7 1 — ^ — n 49. If the passage at Ex. 55, a, be inverted as at Ex. 56, it produces two minor sevenths. These are allowed by some authors, but such a progression is best avoided. Ex. 56. i '^ -S- ^g^ J I J i .\ INVERSION IN THE TWELFTH. 27 - 50. The augmented sixth producing by inversion; a dimit)ished seventh needs no preparation (Ex. 57). Ex. 57. „ ^ Inversion. Model. e $ S ^ mz =t= 51. The sixth does- not usually (see, however, next paragraph) prepare a seventh in the upper pari, as it is itself a discord when inverted. The seventh maybe prepared by any concord except the sixth {i.e., by the third, fifth, octave, or tenth), and the note to which the seventh falls generally rises a second (Ex. 58, a) or fourth (Ex. 58, 6), i.e., it takes the usual progression of the bass of chord of the seventh, which it becomes when inverted. Ex. 58. Inversion.. - . ( Model. I t -rr- S m zz i 7 zz: 7 32: 7 6 -e» — 2z: 52. The following example (from Kirnberger) shows that a sixth may occasionally prepare a seventh. In this case, the latter being resolved ornamentally, does not follow the progression suggested in par. 51, Ex. 59. Model. Inversion. Kirnberger. ^m ^ i -^ ^ ' J 1.J- w ^ p as DOUBLE COUNTERPOINT AND CAKON. S3. The suspended fourth (in the upper part), when inverted, ; becomes a suspended second. Ex. 60. Model. Inversion. - $ m- ^ .g - -^ ^i -cr- 54. The suspended ninth (also in the upper part) becomes by inversion a suspended fourth, falling to a iifth (Ex. 61, a). This harmony is so bare that the suspension is best avoided in the model unless there are accompanying parts. If this be the case, the ninth may sometimes be taken without preparation. (Ex. 61, b.c.) Ex. 61. INVERSION. Model. ,^1 -«t- J J RiCHTER. H s ^ 9 8 55. Some examples of double counterpoint in the twelfth are given below. Ex. 62. a Model. KiRNBERGER. ^ m qtqt =S=p: ^S I I I I N»J- ! ^^ INVERSION IN THE TWELFTH. 29 b Inversion. ^ m^ ^ =PC5: f , pr^^=p \ \ \ Ex. 63. Inversion. Model. Reicha. i^^^ f^ ^ Lower part a twelfth higher. ^f :* — I- ^a 5.V ^'tvSJ-^ J 2- i y 1=t± rt i: SI T=p: There is also this inversion, which Reicha has omitted to give :— c Inversion. _ ■ — m fJTr. r F n :p=f= ^S *=t: '^ V, r r r rrr =*^ rH^lf :rir r ip^ ^^ Ex. 64. it ^a a Model. No. 47 of Bach's 48 Preludes and Fugues. f^T aap ?=e: P h •M. ^m b Inversion. ^ 3Z Upper part a fifth lower. '^ Lower part an octave higher. ^fttt 30 DOUBLE COUNTERPOINT AND CANON. Ex. 63. a Model. liA m-0 HS '■ — Handel. =^* ^^£B P=e=p^ The sequential sevenths at* * become sixths in the inversion (see par. 49). b Inversion. t\U'. .^"^"Ti^^ -^=w^ ! ' I Ex. 66. a Model. • i i J r- 1 Handel. 'is m ^ £-^ Ui'iLBt-TV? @f 3^ b Inversion. i^ i=i: The two sixths in the model (Ex. 66, a, * *) would produce consecutive', sevenths in the inversion. Handel, however, departs from the strict inversion of the model at this point (Ex. 66, 6, * *). 56. Ex. 67 is an interesting specimen of the use of this "counterpoint. The model and its inversion are shown in lai^e type. INVERSION IN THE TWELFTH. 5.1 Ex.67. From " The White Delightsome Swan," Madrigal by Orazio Vecchi (1589). ' S ^ - W • m- and har mo-ny di vine, I ISE 3: \ ^ ' \ \ X » j - and har - mo-ny di-vine, and har - mo-ny di te ;t e£ W^ vme. and har • mo - ny di-vine, ^^ =t: har - mo-ny di-vine, blest vine, i m d d vine, and har -mo-ny di-vine blest thoughts in - spi I 1= ^^ r ^3 vine, and har -mo-ny di-vine blest thoughts in - spi life i -rr- -J31 thoughts ppi mf and. 32 i DOUBLE COUNTERPOINT AND CANON. ring, blest i Mf w ^ =^=^ - ring. i ^ and har - mo -ny di - vine, di ^ and har - mo - ny di-vine, di - vine, and har - mo ^ ;fe¥^ nng. and har - mo-ny di - vine and ^ ^ -p-^r -i<=^ har - mo-ny di - vine. and har - mo - ny di i -rr thoughts spi I =^ ^=X i and har - mo - ny di - vine Efe ^ :t ny di-vine and har - mony di - vine i =p=^ ^= har - mo-ny di-vine - and har - mo - ny di ^ ^ ^ vine and har - mo-ny divine blest thoughtg INVERSION IN THE TWELFTH. 33 P ring spi nng. m ^ ^■ gi I «- blest thoughts in - spi ring. g blest thoughts in spi ring. i ^^ blest thoughts in spi nng. spi - ring 57. Ex. 78 (from Mozart's " Requiem") also shows an ad- mirable use of this counterpoint. See also Ex. 79 (Albrechts- ■berger). 58. Double counterpoint in the remaining intervals, viz., ninth, eleventh, thirteenth, and fourteenth, being of little or no use, is not treated of here ; but the student can of course work out such exercises if he so desires. If the plan of using three staves (par. 22) be followed, he will readily perceive what is possible in a model designed for inversion. CHAPTER IV. ADDED THIRDS. eq Before proceeding to triple and quadruple counterpoint, consisting respectively of three or four different subjects capable of inversion, a method of supplementing the parts of a model for double coUntetpoirit must be coifsidered. This consists of a duplication of one or both subjects in the third above, or m some cases below. In order that the model shall allow of the addition of thirds, the following precautions will be necessary in its original construction, in addition to the rules already given :— . (fl.) Use only oblique or contrary motion. (6.) Dissonances can only occur as passing notes, not as essential notes. (c.^ The same kind of interval must not occur upon successive ac- cented notes ; thirds, sixths (also fifths for inversion in the tenth and twelfth), and octaves being taken, as far as possible, alternately. 60. In double counterpoint in the octave, thirds above or sixths below, either subject may. be used. According to. Albrechts- berger, thirds helow are also available ; but the effect is not very good, qn account of the uncertain tonality induced. Ex. 68, a, b, c, d, e, f, is, a model for inversion in the octave, thus treated. Of course sixths below, instead of thirds above, might be written, and the student may so arrange it. ^^- ^8- Albrbchtsbergeh. Model. i =P2= T^ S -•^•4= ^S: ^:^ W 3=C ^f FF S i 6 Inversion. ^ :P= T!=P- S * s V * =p= i ; o =Ui: Thirds added to the upper part : — c i ^ 1 Bz «=g- 4-"pl-i-^ W — I — i — 1 — :g= EE ^ IS S=P: £^ t :^i?E V, r f f ^ ADDED THIRDS. 35 '■ Thirds added to the lower part. (For an explanation of the altered position of the lower part, see par. 64.) d i ^cgz s rj I 3=±: The following shows tlie previous example in another and perhaps more effective position : — i ^^e^ It =p=i= i=t m » \ f m ^ ^T^ E ^EE ^ ^ i Thirds added to both parts '.—^ f ' =Pi= i^ tfe=e EEE w ¥=^ -m^ U^^M ^^—^ t n^^rn p , -p- ^ ? £: ^ -I — r 61. In double counterpoint in the tenth and twelfth, thirds below the upper part or above the lower may be freely used. 62. In double counterpoint in the tenth, thirds added according to par. 61 are simply the^ inversion of the original parts in the tenth put back an octave. ■ 63. We have seen that in double counterpoint in the tenth and tSveifth both the fifth' and sixth may be used as essential notes ; but if thirds are to be added below the upper part or above the lower, to he subsequently inverted with the model, the fifth should 36 DOUBLE COUNTERPOINT AND CANON. be used in preference to the sixth. Ex. 69, shows a sixth (with its added third) inverted in the tenth, which produces a seventh.* Ex. 69. Model. Inversion in the tenth. P ^ Inversion in the tenth. i 1 Model. -A ^ a I 7 ^^1 r 6 Ex. 70, shows a sixth (with its added third) inverted in the twelfth producing a ninth. Ex. 70. Model Inversion in the twelfth, i rJz 4 Inversion in the twelfth. f^^ f^ Model. ^ I '9 7 |^P=B ^ 1T G The crotchets in the above examples show the added thirds. 64. It will be gathered from what has been already said, that the addition of thirds to the subjects combined in double counter- point may be effected in a variety of ways. The precepts given by different authors are exceedingly diverse and perplexing, although possibly applicable under various conditions. If to the three important rules for the addition of thirds already given (see par. 59, a, h, c) we add a fourth, viz., " the general use of conjunct ■ movement in the model," we shall find ourselves free to make the addition in question in almost any position, since every discord will be approached and quitted by step of a second. The positions of the various subjects and their duplications will depend upon the particular voices or instruments employed, some positions being more effective than others. All possible superpositions of the parts will scarcely be required in the actual composition for- which the model is intended, and therefore those inversions; which are least effective, or which entail objectionable points, may be avoided. The author does not think it necessary to go, * It is obvious that the addition of a third above the upper or below the lower part of any model containing a fifth also at once produces a sevenths ADDED THIRDS. 37 into this matter at greater length, since after all only incidental use is made of this method of adding parts. It is also somewhat opposed to the spirit of good counterpoint, which delights in contrast. Nevertheless, as will be seen from a few examples appended, occasions may offer for the effective use of the subjects (or portions of the subjects) in thirds, particularly when the thirds are added to parts inverting in the octave. Ex. 71. Model, No. zo of Bach's 48 Preludes and Fugues. Inversion of the above in the fifteenth with thirds added below the (original) upper part and above the (original) lower part. In the following example the lower part is the imitation of the upper by contrary movement. The upper part has added sixths below it (the inversion of thirds above) for the first two bars, then thirds below. The lower part has added thirds abpve : — i Ex. 72. l^a -^ r = r — -J u -^ ^ J. S. Bach. m O — ' =1 J- ^ 38' DOUBLE COUNTERPOINT AND CANON'. Ex. 73, a, is a model for inversion in the octave ; at 6 it is expanded in the fifteenth, and thirds added to the lower part. Ex. 73. . From an Anthem by Dr. Greene. fe =f2= hF — W o —A-^ ^^$ -<. ^4 M m — * ^ J I Ii?3 t=t ^ 1, 1 m-teB J — L- ^v *^-A-. — J -?-rnr < p ^ * ^S ^=?«= ~T frfe ^ — I **** pTi Ll Tl| III' k S ^^^ : g- -^ -1* ^^ CHAPTER V. COUNTERPOINTS INVERTIBLE IN VARIOUS INTERVALS. 65. Bv the addition of thirds to a model for double counter point in the octave (see par. 60) such model becomes available for inversion, either in the octave or the tenth. It is possible also to construct models which will invert in the octave and twelfth, and even in the octave, tenth, and twelfth. 66. If a model is to invert in both octave (or fifteenth) and tenth, the rules in par. 59 (for the addition of thirds) will apply. We may, however, depart slightly from the strict rule against using similar motion. For instance, a third may be followed by a sixth, entailing a hidden fifth when the subjects are inverted in the tenth. (Ex. 75, a, b, * *,) Ex. 75. a Model. . Inversion in the octave. ^^ Inversion in the tenth. izzfc i^ "pc 40 DOUBLE COUNTERPOINT AND CANON. 67. But anything objectionable in this point can be easily mitigated by the accompanying parts, and one of the two subjects may be placed in an inner part, where hidden fifths are of little or no consequence. (Ex. 75, c.) Free Part. Inversion in the tenth. w PT^-r i* Sfc ^fc m =p= B8. See also tlie following example, which inverts in the fifteenth and tenth. The sixth at the beginning of bar 2 is practically approached by-similar motion from a third, the E in the lower part in the previous bar being a passing note, (Ex. 76, «. * * •) Ex. 76. a Model. i £^ i^ ■J . rrr}rj^l^^ Bach. 4 BB =t: 5ts* a fp — i w^" — r 6 Inversion in the fifteenth. F H i B g =0 •