arW 8891 CORNELL UNIVERSITY LIBRARY l^ffilinililii.Ml!!ly^''S'TY LIBRARY 3 1924 101 873 804 Cornell University Library The original of tiiis book is in the Cornell University Library. There are no known copyright restrictions in the United States on the use of the text. http://www.archive.org/details/cu31924101873804 RUDIMENTS OF MUSICAL GRAMMAR. BY JOHN HULLAH, LL.D., PEOrESSOB IN queen's COILEGE, LONDON. J? ^ NEW EDITION. L N D N t LONGMANS, GREEN, READER, AND DYER AND LAMBOKN COCK, 23, HOLLES SIEEET. *^3 m/ K ^^/2-^ SALLANTVNE, HANSON AND CO., EDINBUHGf' CHANDOS STREET, LONDOK PREFACE. The title of the followiug work will, it may be hoped, render any expla- nation of its aims unnecessary. The mode of treatment of the subject, and the order in which the different branches of it are brought before the student, differing essentially from those adopted in most other works of the same kind, require, however, a few prefatory remarks. We often find the earlier chapters of rudimentary treatises, whether on music or any other subject, occupied, not with attempts to convey ideas of the things to be first studied, but with explanations of the symbols which represent them, — many of these latter, perhaps, not being called into requisition till an advanced period in the study, when they have to be learned a second time. Thus the beginner in music is made to exhaust the subject of the stave before he is in the least informed as to the naturj of the scale ; or is called upon to consider the peculiarities of five-crotchet time, while as yet he has no practical acquaintance with the first principles of rhythm. In the following work no attempt is made to introduce the student to the alphabet of music till he has learned something about music, or, more properly, the musical system itself; nor is he instructed in the difierent kinds of measure, nor even made aware of the existence of bars, until he has acquired some idea of the limits of a musical phrase, and the nature of a musical foot, — things altogether mdependent of any forms by which they may be represented, a,nd which, as they certainly existed ages before the invention of the present musical alphabet, will as IV PREFACE. certainly exist ages after that ingenious contrivance has become matter of history, or even of speculation. The history of an art or science may often be brought to bear prac- tically on the process of teachuag it ; and the order in which discoveries or improvements have been made wiU often suggest that in which a knowledge of them may best be communicated. So that the considera- tion even of exploded theories and obsolete forms may not be without its use, as keys to those which have superseded them. The musical student, for instance, will never appreciate the special merits of modem, unless he have learnt something of ancient, tonahty ; nor would it be easy t© devise any shorter or more simple method of explaining the nature of a mode, than through acquaintance vnth the fact that, though but two modes are used by modern musicians, the number of modes possible is only hmited by that .of >the Eounds of the natural scale. This latter fact is briefly alluded to in an early chapter, and more fuUy treated in a later one the object of which has been rather to excite than to satisfy cmiosity on a very interesting branch of musical science. The chapters on the Alto and Tenor Staves—^aii of a subject treated elsewhere* by the writer more fuUy — wiU, it is hoped, be found suffi- cient to meet the practical wants of the student. The practice of orriting alto and tenor parts an octave higher than they are to be sung has no doubt largely superseded the older and more simple one of writing them at their proper pitch. Whether this practice prove per- manent or not, the student may rest assured that, unless he make him- self fejniliar with at least two of the four different staves headed by the C clef, a very large proportion of the works of the greatest writers must remain unintelligible to him. It can liardly be necessary to say, that the foUowing work, though * A Short Tiealise on the Stave. LoiigmaDS & Co.; London, PREFACE. V dealing for the most part with first principles, is not adapted to the use of beginners, save in connexion with mnsical practice of some kind, undei the direction of a teacher. Music is an art as well as a science ; and no art can be learned wholly from books. Nor is it likely that even first principles should ever be so simply stated, or so clearly expounded, as to be intelhgible to those who make no attempt to turn them to ac- count. To two classes of persons such a book as this may be of use (1) To those who, having attained some skill in the practice, and acquired some knowledge of the theory of music, may desire to have a connected view of those parts of the latter which are indispensable to the former : — and (2) to those — a very large and increasing class — , Avho, familiar with other subjects, and accomplished in other ways, with little hope of becoming skilled musicians, may still desire to make some acquaintance, if not with the syntax, at least with the ortho- graphy, etymology, and prosody of the only grammar which can fairly be called universal "Were I to begin life again," said the late Sydney Smith, " I would devote much time to music :" and " not six: months before the death" of Samuel Johnson, he said to Dr. Bumey, " Teach me at least the alphabet of your language." The following pages, it may be hoped, may in some degree enable those who have not had the advantage of early training to devote, with pleasiore and profit, some time to music, mthout "begimiing life again," and to acquire something more than the alphabet of the language of musicians. J. H. December, 1858. C O N T E N T S^ CHAPTEK ViOg I. Musical Sound .e.«ti...... i II. Tuue. The Scale 2 III. Time. Rhythm = . < . 4 IV. Notation ? t . . , . . . . 6 V. Forms of Notes 8 YI. Intervals 11 Vlt. The Modern Modes 11 VIII. The Natural Scale 16 IX. Altered Notes , , 18 X. Altered Intervals 20 XI. Altered Scales 21 XII. Scales in Actual Use 23 XIII. The Chain, or Circle, of Scales 26 XrV. The Minor Mode 29 XV, The Signatures of Minor Scales t 31 XVI. Bars and Measures 33 XVII. Time — Simple and Compound 36 XVIII. Time Signatures 38 XIX. Accidentals 41 XX. Chromatic Intervals ,, 43 Vm CONTENTS. CHAPTEB 1>A0S XXI. Modulation 46 XXII. Transposition 48 XXIII. Ehythmical Licences 51 XXIV. Graces " 52 XXV. Signs of Eepetition, Contractions, &c , . 55 XXVI. Marks of Expression 57 XXVII. Words relating to Pace, Intensity, and Style 69 XXVIII. The Tenor and Alto Staves 62 XXIX. The Syren and the Metronome 65 XXX. The Ancient Modes 68 Appendix »...71 RUDIMENTS OF MUSICAL GRAMMAR. CHAPTER I. Musical Sound. 1. Sound is the result, or effect on the ear, of motion communicated to the air by some disturbing force. Such motion is called vibration, or undulation. 2. When the vibration of air is regular {isochronous, or equal-timed) the result is musical sound ; when it is irregular the result is z<«musical sound, or noise. 3. In the regulated production, by voice or instrument, of musical sounds con- sists the art of music; in a knowledge of the laws which govern the succession and combination of musical sounds consists the science of music. 4. The art and science of music involve the consideration oi/our properties o* miisical sounds, their />«Vc/i, duration, intensity, and timbre. 5. 'Y\^% pitch (acuteness or gravity, height or depth) of a musical sound depends on the number of vibrations communicated to the air in a given time. As this number increases or diminishes so does the sound become more acute (higher), or vaoxQ grave (lower). 6. The duration of a musical sound depends on the time during which the air continues to vibrate at the same pace. 7. The intensiti/ (loudness or softness) of a musical sound depends on the extent of the vibrations by which it is caused. 8. The timbre of (quality by which we are enabled to recognise) a musical sound is supposed to depend on the forms of the vibrations from which it results. Timbre (French) literally, stanif. No English word has jet been adopted to express the same property of sound. 9. These properties are, for the most part, relative. Every sound is assuredly jf a definite and appreciable pitch and duration ; but the musical student is chiefly concerned with the pitch or duration of sounds as compared with one another— technically, tu7ie and time. The ultimate source of the pleasure afforded by musical sounds is time; since tune entirely depends on the order, or regular succession of the vibrations which affect us as sound. As a matter of prao- tivjo, however, time and tune must be considered separately, — the latter first. K. M. G. * CHAPTER 11. Tune. The Scale. 10. Different sounds (sounds of different pitch) prodaced at the same instant, form harmony. Melody results from a succession of different, or even a repetition of the same, sounds. 11. Harmony or melody can be produced from the combination or succession of such sounds only as are found in the same musical system. 12. The basis of the modern musical system is the connexion of a given sound with another, standing in the relation to it of 3 : 1, by means of intermediate sounds also related, though less simply, to that (given) sound and to each other. 13. Such sounds presented in regular succession, form a scale, of which the topmast step is the 8"", or octave, from the 1". {Fig. 1.) 14. The sounds of that scale which begins on the central sound of the modern musical system, are named by letters of the alphabet, or by syllables, as follows ; — 1 2 3 4 5 6 7 8 c D E P G A B C Do Be Mi Fa Sol La Si Do The alphabetical names will be used exclusively in this work. The student should sing, or play {on a piano-forte or other instrument) the scale of C, until Jie is thoroughly familiar with the sound of it. 15, With a little attention, even from an uncultivated ear, it will be perceived that the successive steps of this " natural" scale are not all equal, and that some adjacent sounds are less unlike one another than others; also, that the smaller steps lead to, or immediately precede, places in the scale at which the voice easily pauses, and on which the ear is willing to dicell. These are the 4'" sound, P, and the 8'", C, the sounds immediately leading to which, E and B, are severally less unlike P or C than any two other adjacent sounds are to each other. 16. Moreover, further observation will prove that, notwithstanding the differ- ence of pitch, the musical effect of C, D, E, F, heard in succession, is strik- Chap. U.] TUNK THE SCiLE. ingly like that of G, A, B, C ; in fact, that the melody or tune of both series is the same. 17ie student should satisfy himself of the truth of this hy sinking or playing the two series, or any portions of either in immediate succession. 17. The cause of this similarity is to be found in the fact that melody, or tune, does not depend on the absolute, but on the relative, pitch of sounds- -oq their distances apart. F the 4?'' sound of the natural scale, stands in the same rela- tion to C the 1*', as C the 8'" sound, does to G the 5'" ; while E, the S'", is to P the 4^ as B the 7'\ is to C the 8'\ 18. The relation of (difference or distance between) two musical sounds is called an interval. The intervals found in passing up or down the natural scale are tones and semitones ; the (two) semitones falling between the S'^ and 4"' sounds (B and F), and the 7* and S-"" (B and C) ; the (live) tones falling between every other two adj,acent sounds. Each half oi the scale, therefore, consists of four sounds separated by tieo tones and one semitone; 19. A succession of four sounds separated by two tones and a semitone is called a tetrachord. The natural scale, therefore, is divisible into two tetrachords, the 1" sound of the upper of which (two tetrachords) is separated by a tone from the 4"' sound of the lower. In fig. 1, the several intervals between the different sounds are expressed hy the greater or lesser distances between the lines which represent them. The division into two tetrachords is also shown, and the tone which separates them specially indicated. 20. The modern musical system consists in a suc- cession of scales of like construction, the highest or lowest sound of each of which is identical with the lowest or highest of the one immediately above or below it.. (See fig. 2.) The 8"^ sound of one scale is therefore the 1" likewise of another, and the 1'* of one scale the 8* likewise of another. This similarity in the conditions of the 1" and S"" sounds of a scale is the cause of their bearing the same names, and, ulti- mately, of all sounds bearing the same names as their octaves. For as the upper C of fig. 2 is the octave to .the lower C, so the D immediately above the former is the octave to the D immediately above the latter. And so of all the other sounds. Thus by a repeated application of the seven letters, C, D, E, F, G, A, B, to the seven corresponding sounds 1, iJ, 3, 4, 5, 6, 7, in each successive scale, names are found for all the sounds of the entire musical system, and would still be found could that system be extended ad infinitum. Pig.% 4 CHAPTER III. Time. Rhythm. 21. Time and tune, ultimately so closely connected (Chap. I.), may exist, and are often found, independently. Neither, however, can alone give perfect satisfac- tion to the musical sense, which is incapable of appreciating any prolonged succes- sion of musical sounds the proportionate durations of which are not regulated by some law. The result of this kind of law is rhytlim. 2-2. Every rhythmical passage or strain of music is divisible into phrases — successions of sounds dependent for their meaning on each other, and presenting a certain completeness. The first strain of the National Anthem cousistxi of three phrases, each ending in the word "queen." {See fig. 3.) 23. Every phrase is further divisible into feet, and every foot into times or heats Each phrase of the first strain of the National Anthem consists of two feet, ending severally in the words "our," "queen," "the," &c. {(See fig. 3.) Fiy. 3. N- 3 ^ -^ Phrase, Foot. j Foot. l\/2V^3\i/lV2V3Ni/l V 2V 3NJ/1 V2 N/3 V1V2V3V 1 V2V3> God save our | gra - cious Queen, Long live our no - ble Queen, God save the Quee - - - - n. The student, though as yet unacquainted teith musical notation, may he supposed to Icnow, hy ear, " The National Anthem." Otherwise, he must take some means of learning it. 24. The times, or beats, of a musical foot are accented or w?(accent-ed. A foot consists either of two beats, one accented the other unaccented, or of three beats, one accented and two unaccented. By the old masters the latter form of foot was held in the highest estimation ; a foot of three beats being said by them to be in " perfect" time, and a foot of two beats in " imperfect" time. The National Anthem is in " perfect" time. 25. In the division of musical passages into phrases, of phrases into feet, and of feet into beats, musical rhythm resembles poetical rhythm. Here, however, the resemblance ceases ; since while the number of syllables into which the poetical foot may be divided is very limited, the number of sounds into which the musical foot may be divided is very great. And not only may any one foot be divided into a vast variety of sounds, but any one sound may be prolonged through an en- tire foot, or through any number of feet. E.g. The sound sung to tlie word " queen," in fig. 3, is to be prolonged during an entire foot. CHAPTER IV. ISoUitioi). 26. The musical alphabet is chiefly composed of characters ca.\\ed'no/&s, the relative positions of which on a stave, or staff', indicate the relative pitch of the sounds they represent, and the different forms of which indicate their relative length. Pig. 4 is a stave, on which are placed four notes, of which the ^^' ^' second is higher in pitch (and in position) than the first, the third is of the same pitch as the second, and the fourth is lower in pitch than the third. Moreover, the first is a longer note than any of tlie others. -^ <^ 33[ the second a shorter note than any of the others, and the third and fourth are of the same length. 27. But neither the ahsolute pitch of sounds, nor even their exact relation to each other in that particular, can be indicated iy notes alone. A clef, or key (to their meaning) is wanted at the beginning of the stave on which they stand. 28. A clef is the only character by which a musical sound can be absolutely represented. 29. There are three clefs, and therefore three sounds only which can be abso- lutely represented — C, G, and F. 30. The G clef represents the C which occupies the middle place in the system of musical sounds, — it having about an equal number of sounds above and below it. It is the C nearest the middle of a piano-forte, called therefore middle C. The G clef represents the B"' sound of that scale of which middle C is the 1" ; and the P clef the 4* sound of that scale of which middle C is the 8'^ Fig. 5. H '§ O: C G F Tliese three clefs are corruptions of old forms of the letters C, G, F, 31 . Notes may stand in the spaces between the lines of a stave as well as upon them. [See fig. 4.) The notes of the natural scale occupy following lines and spaces of a stave alternately, without exception. 32. The lines and spaces of a stave are called indifferently degrees, or posi- tionsj and adjacent lines and spaces, following degrees. NOTATION. rCu*p. IV, Kg. 6 consists of tvvo successive scales of C. The 1" note of the upper scale is identical with the S" of the lower. (Compare par. 20.) Fig. ^^ ^•^^ -xy -^ 33. The note on the 2°* line (from the lowest) of fig. 6 is known as F, because the F clef stands upon it. The note on the 4"' line is known as C, and that on the G"" line as G, for a similar reason. Moreover^ the notes above and belo^v those designated by the clefs are recognised by their positions in relation to the latter ; the note in the space immediately below P being E, that in the space immediately above it, G ; and so on. 34. When higher or lower notes than those in fig. 6 are to be expressed, more lines must be added to the stave. All the notes (twenty -three) required for average vocal music can be placed on a stave of eleven lines, on the middle line of which would stand " middle" C — having the same number of notes (eleven) above as below it ; and on the 4''' and 8*" lines F and G. F!g. 7. r^ '"^ / r~. < > *-* / -—, C > <^ oth It ^ n <^"> ^-^ y- ^ <-i '^ > TWirlrlla it ■. . • ^^ < ) ^-» J '- ^ <. > ,—, 4th ry " <^ ^ t )' *— ' t ) — . ^-^ < * r-^ t J. ^ 35. No individual voice can utter all the sounds represented in fig. 7. Con- sequently, in writing music for individual voices, a smaller number of lines suffices. Practically, whether for vocal or instrumental music, a stave oi Jive lines is generally adopted ; the particular sets, or staves, most used being the five highest and the five lowest of the Great Stave above. {Seefig. 8.) 36. The lower one of these sets or staves of five lines is used for voices and in- struments oi\o\\ pitch. It is distinguished as the hass stave. The iipj^er stave is used for voices and instruments of higher pitch. It is distinguished as the treble stave. is also called the treble clef, and Ql the hass clef. 37. The two staves are joined by a brace, when used together for piano-forte or harp music ; the upper stave being chiefly devoted to the notes to be played by the right hand, the lower to those played by the left. (Seefig. 8.) 38. When the middle line of the Great Stave is required, it is introduced as a leger line. (Compare figs. 7 and 8.) Liyer (French) means light. Fig. 8. Chai'. rv.] KOTATION. 7 3.9. Music for the lower voices of women, and the higher voices of men, de- mands other staves vchich are, equally with the treble and bass staves, extracts from, or parts of, the Great Stave. Of these we shall speak fully, later. For the present, the treble and hass staves will be used exclusively, such leger lines being added to them as may be required. When more than one leger line has to be added to the top of the bass stave, it must be considered as an extract from the treble stave: vice versa, v^\\e,n more than one leger line has to be added to the bottom of the treble stave it must be considered as an extract from the bass stave. (See Jig. 9.) Fig.^. =:::::]^ ^ 40. The ascending natural scale which begins on middle C, will appear on the trehle stave as in fig. 10. The 1" or loivest sound stands on the leger line identical with the middle line of the Great Stave. (Par. 38.) Fig. 10. "c^- -€>^ Xi -^ ZS -^ X3: 41. The descending natural scale which begins on middle C, will appear on the bass stave as in fig. 11. The S"* or highest sound stands on the leger line identical with the middle line of the Great Stave. {Par. 38.) Fig. 11. S <. > O- rx ^- rz ^9- TT" 43. By joining together (with a brace) the staves on which these two scales are placed, the relation between them will be made plainer. The lowest note of the one scale is identical with the highest of the other, and the leger line on which it stands is common to both staves. Fig. 12. ^^ Bt X7 X2l 22 -^ 23 -^ rz ^- rx ^- Ci It will have teen seen already that the variety of intervals in the natural scale (Par. 18) is not made manifest by the ordinary musical alphabet. To the eye, the relation between E and P is the same as that between G and A. (See fig. 12.) There is nothing in the arrangement of the lines of a stave analogous to that of the lines of the ladder in Chap. I. — reminding us always, by the different distances between them, that E and E, and B and C are severally a semitone apart, and that the other sounds which follow one another scalewise, are separated by tones. On this fact, however, depends the modern musical system; and of all things the student has to learn and to keep in mind, it is incomparably the most important. It will receive further illustration as we proceed. CHAPTER V. Forms of Notes. 43. The relative duration of sounds is known by the different forms of the notes which represent them. The number of these forms, at present in common use, is six. Semibreve. — e> — Minim. "1- Crotchet. Fig. 13. Quaver. • — Semiquaver. Demiaemiquaver. 8 — 44. These names neither describe the forms, nor even for the most part ex- press the relations, of the notes under them. The two first have been retained from a period when, with three others, they were the only notes in use. Maxim. ^ Long. ig. 14. Breve. Semibreve. M Minim. 45. To these the cj'ofc/ie/, originally a //oo^erf minim ,— J was afterwards added. When the crotchet took its present form the hook was transferred to the quaver. The maxim and long are obsolete, and even the hreve (short note) is now rarely used ; while the minim {least note) is often with us, practically, the maxim [greatest note) . 46. The modern forms are well described by the French names, and their re- lations one to another by the German. Konde. Kound. —G> Ganze note- Whole note. Blanche. White. — ©1 Noir. Black. — •— Fig. 15 Croche. Hook. « Halbe note. Half note. Viertel, Fourth. Achtel. Eighth. Doublecroche. Doublehook. — s — Sechzehntel. Sixteenth. Triplecroche. Triplehook. Zwei-und-dreiszigatel. Thirty-second. 47. The stems of notes may be turned up or down indifferently, notes are frequently grouped and contracted. (&c fig. 16.) The hooked CHAr. v.] FORMS OF NOTES. 48. These notes, as respects their length, stand in the most simple relations to each other, each note being ha// the length of the one before it. Fig. 16. Setnibreve C> equal to 2 or 4 1 i r Minim equal to 2 t-t-trttuf- or 16 tfO^ or 32 8 f -P — *- -r- tKftf .8-^- L»U or 16 Crnlrlil't • eiitial to 2 -« ^ or 4 or 8 tna Quaver 1/ etjual to 2 b .equal or 4 to 2 bad E JJ Exceptions to the rule whereby these notes are proportioned to each other are presented in the occasional compression of more than its proper complement of notes into a single time, or beat. Of these the only instance which need be mentioned here is the triplet. 49. A triplet is a group of three notes, which (by licence) is performed in the time of two notes of ihe mmeform. A triplet is generally specially marked 3. Fig. 17 (ot). • • • • u Fig. 17 (6). 50. The hrere, {csj . often found in old music, and occasionally in modem, is equal to two semibreves,/o2/r minims, and so on. 51. Shorter notes even than the demisemi- qiiaver — the «e;w«demisemiquaver and the demi- .s'SOTedemisemiquaver— have been used in mo- dern instrumental music. In clioral music even the demisemiquaver is of rare occurrence. B. M. G. M Fig. 18. 0| C"> | d Fig. 19. .^ = .^ I I I i • • iO FORMS OF NOTKS. [CHiP. V 52. As musical sounds are represented by notes, so are the interruptions, ov cessations, of- musical sound represented by rests, the different forms of which indi- cate tlie relative duration of such interruptions, or cessations. Fig. 20. Seinibreve Reat. Minim Rest. Crotctet Rest. Quaver Rest. Semiquaver Rest. DemisemiquaverRest. ^ ^ "t 53. The stems of rests are invariably turned down. Rests are never grouped. Another form of crotchet rest J* is gradually superseding that in fig. 20. It has the advan- tage of being more readily distinguishable from the quaver rest. 54. These rests indicate, severally, silence as long as would be the sound of the notes whose names they bear. 55. The variety afforded by those forms is greatly increased by the use of the dot which, being added to a note, or rest, increases its length one-half. Fig. 21. Fig. 22, O. = O Q _^ O- = 0. I T r V ^ 9 1 r 1 The dotted rest is little used ; the last form in fig. 22 is the more common one. The dot was called by the old masters " the point of perfection," because 'it brought the note to which it was added '-oAo perfeet {i.e., triple) time — making it divisible by tliree. Fig. 23. 56. The double dot increases the length of a note by three-fourths ; the second dot standing in the same re- lation to the first as the first to the note it follows. Thus, a crotcliet followed by a dovMe dot is equal to seven semi- quavers—the note itself being equal to four, the first dot to two, and the .second to one. (Fie/. 23.) O-- Oi- Q = Q r p r 11 GTIAPTER Vr. Intervals. 57. The relation of two sounds in respect to pilch is called an interval. In passing up or down the natural scale without missing a step (by degrees), we meet with no interval greater than a ifo«e; but in skij/jji/tff i'vom one sound to another not next above or below it, we traverse, or measure, a larger interval. Intervals are named— P', according to the relative positions of the notes which compose them ; 2"% according to the number of tones and semitones into which they can be divided. 58. For example, D and C are said to be a second apart, or D is said to be the second above C because, taking those notes as they appear in the natural scale, D is the 2"* pound from C. And as D is the Z"^ above C, so is E the 3'^ F the 4'^ G the 5*, A the 6'^ B the 7'^ C the 8'" or octave, D the 9'"; and those pairs of notes, severally, are said to form a second, a third, &c. {Pig. 24.) Second. Third. Fourth. Fig. 24. Fifth. Sixth. Seventh, Octave. Ninth. <^- :o: ^^- :c3ii -^- JZ e5 By the same rule, E is the 2'"' to D, F the 3"", &c. ; and so with all the other notes. €3 ^ Fig. 25. Second. Third. "CT -^ XT" ~r~? 59. But intervals admit of, and require, another and more exact kind of measure- ment. {Par. 67.) E is the 2""* to D, aud F the 'Z''^ to E. But it has been shown {Par. 18) that E is a tone above D, and F only a se^nitone above E. Therefore the second between D and E, must be a second of different quality from that between E and F. The two qualities of second are distinguished as major (greater) and minor (lesser). 60. 1'he natural scale includes Jive major, and two minor, seconds ; major second being but another name for tone, and minor second but another name for that hind of nemitone which is found in the natural scale. (Compare par. 18.) There is another kind of semitone, which will be explained hereafter. Seconds. Fig. 26. X5" ajor. Major. -^- 22: xz -^- ^^ 221 ss -^ -e^- 23: finor. M.'tjnr. Major. 12 INTER \^-\LS, [CuAP. YI. 61. As there are major and minor seconds, so there aie major and minor thirds. Tlie major third is composed of (or divisible into) two terns ; the minor third, of one tone and a semitone. C2. From C to E there are two tones; from D to P, only one tone and a semitone. Consequently, C — E form a wajor third, D — F a minor third. The natural scale presents examples oi three major a.x\A four minor thirds. Thirds. Piy. 27. CT ZX -^- -^ 22 XZ -^ -^- X2: X3I €5 -^- Major. Minor. Minor. Major. Major. Minor. Minor. 63. The intervals produced by the inceraion. of seconds and thirds are called also major and minor. 64. By the inversion, of an interval is meant the placing the lower note an octave higher^ or the hiyher note an octave lower ; thus producing a different interval Ly notes of the sunie name. 65. Two notes a second apart form, on inversion, a seventh ; two notes a third apart form, on inversion, a sixth. Second. Seventh. Third. Sixth. Fig. 28. irx T^" Fig. 29. 66. Un inversion, two notes form an interval which is not only different in kind but in qualitij. Major seconds become minor sevenths, and vice versa ; major thirds become -minor sixths, and rice versa. (Five) Major Seconds. (Two) Minor Seconds. Fig. 30. ?=J-^-CT -^- S2: ^^ ^^- Z3: - <-5-o- -€> cy ^^ ZZ (Five) Minor Sevenths. Fig. 31. Pig. 32. irx "t:5 -^ ^^ -e> o- _Ci^ (Two) Major Sevenths. Xll -e>- -EX X3I -e>- (Three) Major Thirds. (Four) Minor Thirds. 22 X3: -^ -€> "CT 23: -o -^ 22 221 -e>- -e3- i?(>. 33. (Thre^ Minor Sixths. -^- _C2_ ~CT~ 221 -€>- -€3- (Four) Major Sixths. -^- 32: 221 -©- -&- O' Chap. VI.] TNTf.UVALS. 13 G7. The fourth and its inversion tlie Ji/lh, together with the octave which is the inversion of the imisoti — not properly an interval — are called, for the most part, perfect ; the only exceptions found in the natural scale being o)ie plu-^exiact fourth and one //wperfect fifth. The octace is, in every case, perfect. 68. The perfect fourth is composed of two tones and a semitone, the perfect fifth of three tones and a >iemiione. The (one) p^wperfect fourth is composi^d of three tones, wherefore it is called also trilotie ; the (one) w«perfect fifth, of two tones and two semitones. (One) (Six) Perfect Fourths. Plup. Fourth. Fig. 34. <> €3- TIT" _o: o- rcx -e^- -69- zz 321 -<-^- -e^- X2; (Six) Perfect Fifths. Fig. 35, ■s^ T~r -^ f^- 33: 231 -O 2X "CT" -e^- -^- (One) Imp. Fifth. ^ -<=5- i 69. On inversion perfect intervals remain perfect, but p/tfperfect intervals be- come JOTperfect, and vice versa. 70. Intervals fjreater than an octave are generally to be regarded as mere re duplications of those formed by notes of the same name within, the octave. Thus fig. 36, practically a tenth, is still considered as a third ; fig. -37, practically an eleventh, as a fourth ; fig. 38, practically a twelfth, as a fifth, and so on. Fig. 36. Fig. 37. ^ Fig. 38. I C3_ Intervals of this extent are of rare occurrence in melody. €=i 71. An exception, however, is presented in the case of the ninth, which is not ahraijs to be regarded as an octave, or compound, second, but often as a distinct in- terval. The ninths (like the seconds and sevenths) are called major and minor. Ninths. C2 ^ Fig. 39. -f^- cx €3 Major. "C5 Major. -€^ -^ Minor. 231 €3- ZX -^- Major. Major. Minor. 72. Intervals greater than an octave do not admit of inversion. The ninth, therefore has no inversion. The pluperfect fourth and imperfect fifth are less often found in melody than the perfect intervals of the same kind; whereas the major and minor intervals are used with equal frequency and freedom; presenting no difficulty in execution nor, in ordinary cases, any striking diUeA^nce in effect. 14 CHAPTER YII. The Modern Modes. 73. The 1" sound of a scale is called its tonic, key note, ox final. The tonic of the natural scale is C. 74. Any note of the natural scale may be used as a tonic ; i.e., we may pass, by steps not greater than tones, or smaller than semitones, from any note to its octave. But in the scales up which we shall pass, in so doing, the tones and semi- tones will fall always in different 'places ; so that we shall find as many different' ki)uU of scale, in respect to the succession of tones and semitones, as tonics, viz., seven. (Fig. 40.) Fig. 40. 1" Mode. ^ m ^^ u cy e3- 22 -^ 22 e^ ^ 2°'' Mode. 3'" Mode. i -.^'•^ 50 tj -^ X5: -^ 22 -^ £31^ zx 4"' Mode. S"" Mode. Chap. VII.] THE MODERN MODES. 15 75. In these seven scales the semitones fall as follows :^ In the 1", between the S"'^ and 4* and the 7"' and 8"' sounds. — the 2"^ 2"" and 3'"' 0* and 7'" — the 3'\ P' and 2"" 5'" and 6'" — the 4'", — 4'" and 5'" 7* and 8'" — the 5'^ 3'" and 4"' (>'" and 7"'. — the 6"', ■ e"" and 3"' 5'" and 0'" ■ — the 7'% ■ P' and 2"" — 4'" and 5"' 76. The order of tones and semitones in a scale is called a mode. Seven modes, or forms of scale, are therefore possible ; and at least that number was once in use. Among modern musicians only two modes are used, the P' and 6'" (of fig. 40), and the latter not without occasional modifications which tend to assimilate it to the former. 77. The former of these (modern) modes is called the major mode, the latter, the minor mode ; because the 3''* sound of the one is distant from the 1" two tones, or a major third; and because the 3'''' sound of the other is distant from the 1" only one tone and a semix.ow%, or du minor third. {Compare Pars, 61 and 62.) Major Third. Minor Third. Fig. 41. \\) / ~^ ^' Fig- 42. „ Tone. Seniitonp. Tone. Tune. From C to D is a tone, and from D to E another ; therefore from C to E is a major thii-d. From A to B is a tone, and from B to C a semitone ; therefore from A to C is a minor third. 78. As recpects the relation between their 1'' and 3"''' sounds, all the modes are either major or minor ; the P', 4"', and o*"" being major, and the 2"'', '6'^, 6"", and 7"" being minor. The positions of the tones and semitones are however, in some way, difibrent in all the modes ; and without some contrivance by which they could be assimilated, only two sounds, C and A, could be used as tonics at all, and the latter only under certain conditions. 79. For, the modern musical system demands that the 7* of a scale be followed by the 8"^ at the smallest recognised distance ; in other words, that the T"" and 8"' sounds of an ascending scale be separated by a semitone, the 7"" in this case being called the leading note ; also, that the 4"" and 5* sounds form, respectively, a perfect fourth and a perfect fifth with the tonic. 80. On the first of these conditions, the 2"^ 3'■^ 5^ 6* and 7* modes (of fig. 40) are inadmissible ; and on the second, the 4"" and 7*. The five former are deficient in leading notes, and of the two latter^ one (the 4'") has a jjfepei feet fourth, the other (the 7"*) an imperfect fifth. The reasons for this rejection of all but the 1" and " nnder certain conditions," 6"" modes, will appear as the student becomes better acquainted with the science of music; the fact of their rejection is indisputable. Use is second nature. The modern musician is used to the modern system ; itistho idiom in which composers have, for at least a century past, expressed their thoughts ; and every mode but that of C or A, with the modifications alluded to, is, to the modern ear, if not disagreeable, certainly quaint and unsatisfactory. The modern composer can no move express himself with freedom in the obsolete 2°'', S"", 4"", and 5"" (the 7"" has never been used) modes, than the modern poet in the language of Chaucer. Indeed, it is a question how far music, professedly in these modes, was ever practically performed, even in the ages when their existence was recognised, without such modifica- tions as must have assimilated them, in most essential particulars, to those with which we are familiar. IG CHAPTER VIII. The Natural Scale. 81. " The 1" sound of a scale," as also the 8'", "is called its tovic, key note, or final." {Par. 73.) The 7"" sound of the natural scale, and of every scale con- structed like it, is called the leading note. (Par. 79.) The fitness of these names needs no demonstration. The 1" and 8"" sounds are those on wiiich alone a musical passage can be brought to an end with perfect satisfaction to the ear; the 7"' sound is that which suggests, or causes expectation, that the 8"' will follow it. 82. Everv other sound of the natural scale has a like name, i.e., a name due to its position in, and relation to the other sounds of, the scale. 83. The 5"' sound of a scale is called the dominant, and the 4* the swidominant. " Dominant " is one of many old musical terms which have altogether lost their Fig. 43. original r.'.eaning. The dominant is properly the reciting note, and therefore the principal, or governing , note of the ecclesiastical chant. It is applied bj' modern musicians to the 5"" of a scale, because that sound will bear a combination which, '\ij) as it can only exist in one scale, governs, or decides, it beyond the possibility of doubt. For further explanation of the properties of the dominant, the student is referred to the Author's " Grammar of 3£usical Harmony," Chap. XVU. 84. The 3'''' sound of a scale is called the mediant, and the 6"" the sMiniediant. The 2"'' is called the xnpertomc. 85. " Mediant" and " submediant" are used in reference to the positions of the 3'" and 6'" of a scale, as the inner, or intermediate, sounds of the triads of the tonic and of the subdominant. 86. The triad to any given note is formed by the addition to it of its 3'* and 5*. 87. E, the 3"''' of the scale of C, is the inner or intermediate sound of the triad of C, the tonic [Fig. 44) ; A of the triad of F, the subdominant. (Fig. 45.) Fiy. 44. Fig. 45. -€=i- Chap. VIJI.] THE NATURAL SCALE. 17 Fig. 46. —i— Tonic -7 — Leading Note- -6 — Submediant — — 5 — Dominant- -4 — -Sui dorii inant- — 3 — Mediant — -2 — Supertonic — — 1 — Tonic rig. 46 .shows the name which each sound of the scale derives from its position in, and relation to the other sounds of, it. " A succession of four .is on the dominant, and the lower ends on the subdominant. The mediant holds the same place in relation to the subdominant, as the leading note does to the tonic: and the supertonic holds the same place in relation to the tonic as the submediant does to the dominant. On this account the submediant is sometimes called the super- dominant. 89. As the leading note has a tendency to rise to the tonic (par. 79), so the supertonic, the subdominant, and the submediant have each a tendency to rise, or fall, to that note of the triad of the tonic which is nearest to them : e. g. that of the supertonic is to fall to the tonic (fig. 47), or to rise to the mediant (fig. 48); that of the subdominant to fall to the mediant (fig. 49); that of the submediant to fall to the dominant (fig. 50). Fiij. 47. Fig. 48. Fig. 49. Fig. .vO. -o-e^ Z^21 ^- II sx ^?- 90. Thus the triad of the tonic (the I"', ?>'^, and 5"' of the scale) has an ah- sorbii:>g or attractive force, fully justifying the importance attached to it in the modern system. 91. The progressions treated in par. 89 are all parts of one or other of those closes or cadences so familiar to the modern musician. They are distinguished as the perfect cadence (fig. 51 a and b) and the iplagal cadenoe (fig. 62). The former is the more modern and familiar form. Fig. 49 appeairs in both. See also the AutJwr's " G-ranunar of Musical Sarmomj," Chap. 30'. XXVII. Fig. 51 (a). Fig. 51 (h). Fig. 62. <":> e^ -t:>0^ a? 2X ~r-r V The student .should take pains to familiarize his ear to these p^-eyressions, playing them on the piano-forte, or hearing them played, and, at the same time,, smgm^ first one, then anothei , of tha iiidimdval parts. R. M. O- 18 CHAPTER IX. Altered Notes. 92. Between every two sounds separated by a tone another sound may be placed, whereby the tone is divided into two semiiones. 93. On a piano-forte, the . natural Bcale is produced by striking a suc- cession of white keys exclusively. Most of these white keys are separated by black keys — the intermediate sounds spoken of above ; the exceptions being the keys representing E and F and B and C in each octave, which have no black key between them, — those sounds being severally a semitone apart, and a semitone being the smallest recognised musical interval. (.See fig. 63.) Fig. 53. 94. These intermediate sounds take their names either from the upper or the lower sounds adjacent to them ; or, more properly, they are regarded as elevations or depressions of the latter, aud are called such and such notes sliarp or fiat, accordingly. In fig. 54, the ruled lines represent the sounds of the natural scale (as in fig. 1), and the dotted lines the sounds which divide each tone into two semitones. Each of the latter, it will be seen, has two names, e.g., C sharp and Hflat. Strictly speaking, C sharp and D flat are not identical, i.e., it is not mathematically true that they are the same sounds — produced by the same number of vibrations in a second. {Par. 5.) For all practical purposes, however, they may be considered as liuch ; as, indeed they are ou the piano-forte. (See fig. 55.) Fig. 64. Fig. 65. -C- p --i J> Bb-- ..a| -G- .,\ ..FJI- -F- Gb-- -E- -D- -G- -Eb-. -Db-. Fb E# Cv BJt Chap. IX.] ALTERKD NOTES. 19 95. The depression or elevation of one of the sounds of the natural scale a semi- tone, or, in other words, the substitution of a flat or sharp sound for a natural sound, of the same name, is indicated by placing jt, called a sharp, or \>, called s,flat, before the note which represents it. The substitution of P sharp for F natural, or of B flat for B natural, would be expressed aa in figs. 56 and 57. Fig. 56. ^^^ ^^.«7. : gC=r ^ ^^ 96. A natutal note is specially indicated by placing jj, called a natural, before the note which represents it. The substitution of P patural for P sharp, or of B natural for B flat, would be expressed as in figs 58 and 59. A natural is only palled into requisition when it is necessary to contradict a foregoing sharp or flat. 97. Sharps, flats, and naturals are placed before the notes they alter. "We say " F sharp, B flat," &c., but wHte, " Sharp F, flat B," &c. 20 CHAPTER X. Altered J ntervals. 98. By the alteration of one of the two notes composing it, the quality of an interval may be changed from major to minor, or from perfect to pluperfect or im- perfect ; and vice versa. 99. A major second is made minor by flattening its upper or sharpening its lower note ; and a minor second is made major by sharpening its upper, or flattening its lower, note. (Fig. 60.) Fig. 60. Seconds. -^ X3: -e>- ZCE ■i:r-. < > \:^ 3ZE Major. Minor, Minor. Minor. -^ # in. Major. Major. 100. A major third is made minor by flattening its upper, or sharpening its lower, note ; and a minor third is made major by sharpening its upper, or flattening its lower, note. (Fig. 61.) Fig. 61. Thirds. -^ -G>- -^ % ■^ ]|^ O '.^ -^ -^ -^ ■i;^- ■^ ^ -^- ^^ Major. Minor. Minor. Minor. Major. Major. 101. A Tpei-fect fourth is made pluperfect by sharpening its upper, or flattening its lower, nftte ; and vice versa. (Fig. 62.) Fig. 62. Fourths. (Tir -^>- -^- ^ =^ 33: €3- -^ "TT- :^ ^> "r^~ ^ -^ ^-^ Perfect. /"faperfect. Pfoperfect. PZaperfect. Perfect. Perfect. 102. So also the inversions of these several intervals (the seventh, the sixth, and the fifth) admit of alteration ; the two first from major to minor, and the last from perfect to imperfect, and vice versa. 21 CHAPTER XI. Altered Scales. 103. By the alteration of one note in eachj the scales of F and of G may be arranged in the same (major) mode as that of C. (Compare Jig. 40.) From A, the 3"" of the scale of F, to B M would be a major second (or tone) ; in flattening B (the 4"') the interval between it and A is reduced to a minor second. {Pig- 63.) From G (the 8"" of the scale of G) to F jjj would be a major second ; in sharpening F (the T") the interral between it and G (the S"") is reduced to a minor second. (Pig- 64.) Fig. 65. 104. By a similar alteration, the scales "vT/ ,.(—)<> ^ ^&o -^- of D and E can be arranged in the same (minor) mode as that of A. (Compare fig- 40.) Fig. 66. -^. #?: as^ IZT -^ r~?" -^ From A (the 5"" of the scale of D minor) to B |Jj would be a major second ; in flattening B (the 6"") the interval between it and A (the 5"") is reduced to a minor second. (Fig. 65.) From G (the S"" of B minor) to F fj would be a major second ; in sharpening F (the 3°'') the interval between it and G (the 3"*) is reduced to a minor second. (Fig. 66.) Fig. 67. 105. The scales of D and of B require, -UV) ,~. itr^ "~^ each, two alterations to assimilate them, ^EEr^^ © sererally, to those of C and of A. (Compare fig 40.) %. 68. C5. 1^ ^^^1^^ r3 -^- C5 3 22 ALTERED SCALES. [ClfAP. XI 106. Moreover^ by still further alteration, the three major scales in fig. 40 (those of D, P, and G) can be made minor, and the four minor scales (those of D, E, A^ and B) major. {F^- 69.) Fiff. 69. Major Scales. Minor Scales. ^ =^ $&=^ ^> a G)^ XX T3i 2 3 5 6 XT -^ S O- 2 3 V^ (^^=^ . >bo < > Q 5 6 2 3 5 6 f J ^ — ' '' Q A T y^ €3- 3 i 7 8 MN^ 5g>75H^ 3 4 -r-r-^4^ -^ 7 8 ^^J-S •a^ 'i ^:^: ^-^"' ^ r^ 3 4 7 8 107. In fact, by the alteration of a sufficient number of notes, both a major and a minor scale may" be constructed, not only on every one of the natural notes, but on every one of the altered notes. So that any note, natural, sharp, or flat, may be used as a tonic. %R CHAPTER XII. Scales in Actual Use. "Any note, natural, sharp, or flat, may be used as a tonic." {Par. 107.) 108. There are seven natural notes, and each of these is alterable both by a sharp and by a flat. It follows, therefore, that no fewer than twenty-one major, and twentij-one minor, scales could be expressed in musical characters, — seven beginning on natural notes, seven onjlat notes, and seven on sJtarp notes. 109. It has been shown, however {Chap. IX.), that every sound raised by a sharp is, practically, identical with the sound a tone above it lowered by a flat j e.g., that C sharp is produced by the same piano-forte key as D flat, G sharp by the same key as A.fl,at, &c. {Pig. 55.) 110. The number of major and minor scales, therefore, in actual use is much smaller than the number possible : it rarely exceeds tivelve, and never, except transiently, fifteen. In only one instance, C, is the same note, made sharp as ivell as flat, used as a tonic ; the remaining six notes being used as tonics when made sharp or flat, — not both. 111. The sharp tonics are C ;|jl F ;{J!. — natural tonics are C, D, E, P, G, A, B. — flat tonics are C b, D b, E b, G b, A b, B b. In fig. 70, the series of tonics in actual use is given in musical notation. The notes connected by r"^ are identical. """' *=^^iiiiSEi^.^°«°^-^5^'^ -O] .^^,. 112. Each of these scales requires for its completion a different number of sharps or flats ; e.g., the scale of D requires two sharps, that of E b three flats, &c. Were the number and order of these sharps or flats irregular, or without system, they could only be retained by a very laborious act of memory. Such, however, is not the case. The scales grow out of one another, and add to their number of sharps and flats, according to a simple rule which admits of no exception. 24 SCALES ES ACTUAL USK. rCirip. XIL 113. "The natural scale is divisible into two tetvachords, the 1" sound of the upper of which is separated, by a tone, from the 4*" sound of the lower." (Par. 19.) F"j. n. 1st Tetrachord, 7~r -^ 311 -^ xx c 2nd Tetrachord. 114. AVhat is true of the natural scale is true oi every scale constructed like it, t.f., oi eoery major scale. 115. If the second (or upper) tetrachord of any one scale be taken as the first (or lower) tetrachord of another, the new upper letrachord added to complete the latter scale will demand a new sharp, — i.e., a sharp not found in the scale to which its lower tetrachord is common. [Fig. 72.) Fig. 72. -O ror -t^ 211 -e> 2ZI -^ 22 -€^- J^ -O- The upper tetrachord of C [fig. 72) consists of G, A, B, C. Let these four notes be taken as the lower tetrachord of a scale of (i.e., beginning and ending on) G. A new upper tetrachord is required to complete this (new) scale of G, in which the F must be made sharp; — otherwise, the semitone will not fall between the 3'^ and 4"" sounds, but between the 2°'' and 3'''' ; since F natural and G are separated by a tone, and E and F natural by a .semitone. In fact, without the F sharp, the scale of G will be imperfect for want of a leading note. (Compare par. 79.) This experiment repeated in any other part of the musical system will be attended with a similar result, — the upper tetrachord of the neio scale will, in every case, require the introduction of a new sharp. 116. A similar process applied in an opposite direction, will be attended by a similar result, — in the production of a series of scales Withjlats. 117. If the Jirst (or lower) tetrachord of any one scale be taken as the second (or upper) tetrachord of another, the new lower tetrachord added to complete the latter scale will deinand a neto flat, — i.e., a flat not found in the scale to which its lower tetrachord is common. (Fig. 73.) Fig. 1Z. C~> ^> cx &- tj: ^- rs ^^ nr ^ o Fig. U. The lower tetrachord of C (fig. 73) consists of F, E, D, C. Let these four notes be taken as the upper tetrachord of a (descending) scale of F. A new lower tetra- chord is required to complete this (new) scale of F, in which the B must bo made^a<; otherwise, the hur notes vriW not include a semi- tone (fig. 74), and will, therefore, not form a tetrachord ; for a tetrachord is a " succession of four sounds separated by two tones and a semitone." {Par. 19.) tJ This experiment, again, repeated in any other part of the musical system will be attended with a similar result, — the lower tetrachord of the new scale will, m every case, require the introduction of « new flat. -t> nn XX Chap. XIL] SCALES IN ACTUAL USE. 25 118. The second tetvachovd of every scale begins a fifth above the first ; vice versa, the firiit tetrachord of every scale begins a fifth below the second. Sharps, therefore, are ge- nerated in an order oi ascending, &nA fiats in an order of descending, fifths. {Seefiga. 76 and 76.) From fig. 75 it will be seen that— ll!). In a series of scales, the tonics of which are perfect fifths above one another, each scale requires a sharp more than the one before it. This additional sharp is always the leading note, and consequently always a perfect fifth above the sharp last added to form the preceding scale. 120. The tonics, perfect fifths above each other, are, — C, G, D, A, E, B, F |, C |. P natural is an imperfect fifth above B. 121. Of these scales the leading notes (also perfect fifths above each other) are, — B,F|,C#,G|,D#,Afl:,E|,B#. Pi-om fig. 76 it will be seen that — ■ 122. In a series of scales the tonics of which are perfect fifths helow each other, each scale requires a fiat more than the one before it. This additional flat is always the subdominant (4"' sound) of the scale, and consequently always a perfect fifth below the flat last added to form the preceding scale. 123. The tonics, perfect^fifths heloio each other, are, — c, F, B b, E b, /^ b, D b, G b, c b. B natural is an imperfeot fifth below ¥. 124. Of these scales the subdominants (a'so perfect fifths below one another) are, — - p, B b; E b, A b, D b, G b, c b, F b. ^W^ L$ R. M. 0. {) ^- % c fc Ch Is 6 rO i- 4\v= ^s? ^ J^ ^ iX^^z ^F 1 t -^^ ly **= F 3 r 26 CHAPTER XIII. The Chain, or Cu'cle, of Scales. 125. •" Every sound raised by a sharp is practically identical with the sound a tone above it lowered by a flat." {Par. 109.) 126. By availing ourselves of this circumstance once we may form a chai9i, o, circle, of scales, co?mected on the system explained in the last chapter. 127. The perfect fifth above C is Gj above G, D; above D, A; above A, E; above E, B ; above B, F if. F it is identical with G b- {Figs. 6i md 55.) The perfect fifth above G b is D b ; above D b, A b ; above A b, E b ; above E b, B b ; above B b, F ; above F, C — the note from which we started, and in returning to which we complete the chain, or circle, of scales. {Fig. 77.) 128. A transition like that from F |; to Gb is called an en/ia7-?Homc change. The enharmonic change in the above series could be made from B to C bj or from C I to D b ; indeed, it could be made, though not so conveniently, in any part of the series. Enharmonic (from the Greelt) is a word having reference to a musical system in which intervals smaller than semitones formed part. To keep within the limits of the treble stave every alternate note in Tigs. 77 and 78 is placed a fourth below instead of a fifth above. Tho fourth is the inversion of the fifth. {See par. 64.) Fis- ft==z==i==S5--^zbcxr=«: 129. The same process reversed will be attended by the same result. 130. The perfect fifth below C is F ; below F, B b ; below B b, E b ; below T&'i, Ab; below Ab, Db; below D b, G b- Gt? is, identical with F^. The perfect fifth below F tt is B ; below B, E ; below E, A ; below A, D ; below D, G and below G, C — the note from which we started. {Fig. 78.) *- ^ bn Fig. 78. Cu.u'. XUL] THE CIIATX, Oil CIRCLi:, OF SCAI.KS. 27 131. The sharps or flats essential to the scale in which a musical composition is said " to be," are not placed before every individual note which may require alleriition, but together, at the beginning of each stave. In this collected form they are called the (scale) signature. The signature of every major scale is exhibited in fig. 7&, which will further illustrate the contents of the preceding paragraphs. A u is placed afourth below D Tl, instead of a fil'th above, to keep within the limits of the ti-ebb stave. 132. In the signatures, the order, whether of the sharps or flats, is never changed. If there is one sharp in a signa- ture, it is Fifj if there are more sharps than one, F tt is always the Jirst, Ctl the second, and so on. The same rule holds in respect to the flats. The note after each signature (in fig. T9) is the toni© indicated by it. Observe that — 133. The last added sharp is always the leading note, or 7"* of the scale — a minor second below the tonic ; and that the last added flat is always the subdominant, or 4"' of the scale — a perfect fifth below the tonic. Therefore — 134. The tonic of the major scale is always to be found a minor second above the last added sharp of a signature, or a perfect /owri/i below the last added flat. E.g. If the last sharp is D li, the tonic is E. If the last flat is A b' the tonic is E b- 135. The signatures over and under each other {inpj. 79) are those of tonics practically identical : viz., B and C b, Pjj: and 6 b, C;^ and D b- Without the enharmonic change, the next tonic of the ascending series would be G tt — of which the leading note would be P double sharp; and the next of the descending series, F [7 — of which the subdominant would be B double flat. 136. A double sharp, formerly written M, is now com- monly abbreviated thus X . There is no contraction of the double flat, which is expressed thus, bb. 137. A double sharp raises a note, and a double flat lowers a note, two semitones. F X is therefore identical with G jj[, and B bb with A U[, — practically, but not theoreti- Callv. (Compare Chap. IX.) 138. It it most important, in respect to the theory of scales and intervals, that the distinction in name between notes having the same sound be always observed T' tt: 4* Fffl © ipf ^'i^F. 4X n **= :28 THE CIIAIX, OR CIRCLE, OF SCALES. [0. AP. xin. 139. By substituting G jj for F X in the scale of G tt, or A fl for G \h in the scale of F \), we should interrupt the succession essential to a scale, by omitting one note, and repeating another. {Compare fig. 80 with fig. 81, and fig. 82 with fig. S3.) Fig. so. =>35tt^^^ Fig. 82. w^^^ Fig. 81. te.1i^5L^== Fii/. 83. ^1^^^ .a>_ f5E5^= ii^Ell^ liO. So again, the interval formed by C Ji and F X is the one pluperfect fourth of the scale of G jt ifia- 8*) ; that formed by C u and G 0, the one imperfect fifth of D (fig. 85) ; while the interval formed by E b and B bb is the one imperfect fifth of the scale of F b {fig. 80} ; that formed by E bb and A g, the one pluperfect fourth of B b. (-Pis'- 87.) Fig. 8S. J'iS'. 87. :^. srr ^^- 141. No alteration, by whatever number of sharps or flats, of either of the two notes forming an interval, can change its name and kind — which depend on the number of positions of the stave, not on the number of tones or semitones, it in- cludes. From C to F is a. fourth, whether the C or the F be natural, sharp, double sharp, or double flat. The intervals in Fig, 88 are all fourths, though of different qualities — some as yet nnexplained. Fig. 88. -^- IC3: -^- :;a: _C3. ■o- bci -^- :l: :c3: I 142. Neither the double sharp nor the double flat ever appear in a signature; they are invariably accidentals. 143. "When the signature is changed, in the course of a piece of music, for another of a lesser number of sharps or flats, the places of the latter are sometimes taken by naturals, in order that special attention may be directed to the chano'e. (Fige. 89 and 90.) The naturals should never appear but once in each part. Fig. 89. Fig. 90. Fig. 89 exhibits a change' of signature from B to E ; fig fE^rz -^ M^- Fig. 98. XT -^. IQ_ ttQ- ^^- ■C3 15.3. The third of these forms (fig. 98) has the advantage that while, equally with the second, it presents a leadiiifi note— so satisfactory to the modern ear — its 6* (to the tonic) remains minor {fig. 99). 154. The quality of the 6"" of a scale is hardly less characteristic of its mode than til at of the 3"''^. Fig. 99. 69- Minor Sixth. 155. The chromatic form has also the advantage over both the others, that it is equally practicable (though somewhat difficult) to the voice, and satisfactory to the ear, ascending or descending. 156. Whatever form be adopted for the upper tetrachord of the minor scale, the lower tetrachord is invariable, so far as the place of the semitone is concerned, — the 3''' is always minor. Hence the term minor mode. Fig. 100. 33 -^ XS ©^ X3I "T"?' Minor Thiv* SI CHAPTER XV. The Signatures of Minor Scales. 157. Scales which result from different modes of arranging the same sounds are feaid to be relative. The natural scales of C and A are therefore relative ; and as the one is major and the other minor, the scale of A is said to be the relative minor of C, and the scale of C the relative major of A. 158. Every major scale has a relative minor, the tonic of which (as in the case of the natural scale) is the 6"' sound of its relative major scale. The 6"' sound of the scale of C is A; A, therefore, is the relative minor to C. 159. "The sharps or flats, essential to the scale in which a musical composition is said to be," placed " together at the beginning of each stave," " are called the (scale) signature." (Par. 131.) 160. Every minor scale bears the same signature as its relative major j the 6'" and T"" sounds being altered, if necessary, by accidentals. In fig. 101 the signature of every major ocale, and of its relative minor, is exhibited. It will be seen that — 161. The minor, like the major, tonics follow one another in an order of ascending and descending perfect _/i/it/is. Fig. 101 is a transcript of fig. 79, with the 6* to each major tonic added (in small black notes) above it. The 6"" of a major scale is the tonic of its relative minor. The black notes, therefore, in fig. 101 are the relative minors of the white notes beneath them, and the signatures belong equally to both. {Compare par. 160.) The table may be read thus.— The relative minor of C is A; signature, neither sharp nor flat. J'he relative minor of G is E ; signature, f j^. And so on. 162. The signatures of minor scales being identical in every case with those o( their relative majors, it is of course impossible to decide, fro7?t the -signature alone, in what scale a piece of music may be. A slight inspection and a moment's con- sideration will, however, generally remove all uncertainty on the matter. With rare exceptions, every piece of music ends with a combination formed of the tonic, its 3'" and 5'"— the triad of the tonic— to which the 8"" is as often added j the !?hole combination forming the common chord of the tonic. {Fir/. 102.) 32 THE SIGNATUKFS OF MINOR SCALES. [Chap. XV, Fig. 102. ft e <~> ~cr -e^ m zx zz 22: -€> -O- 2X XX -^ 22; The relative positions of the notes of a common chord admit of great variety ; e.g., sometimes the 8" is uppermost, sometimes the 3"" and sometimes the 5"' (see fig. 102, u, h, c.);but the notes form always the same intervals with the tonic, viz., the 3" lid 8'\ 16:3. Tlius if a piece of modern music has for signature two sharps, it will certainly be either in the scale of D, or in that of its relative minor, B. If it is in D, the last combination will be that of D with its 3'", 5'" and (per- haps) 8'^ viz., D, P |, A, and D : if it is in the scale of B minor, the last combination will be that of B, viz., B, D, F it, and B. Moreover, in the majority of modern movements the last chord of the tonic is immediately preceded by that of the dominant. The dominant (.5"') of D is A; the triad of A "is A, C ^, E. The dominant of B is F |; the chord of F ^ is F, A | and C ^— which A it, not being in the signature, will be specially marked. The dominant chord is always major. Fig. 103 is the ordinary ending of a piece in D major ; fig. 104 that of a piece in B minor. The signatures of both are the same. Fig. 103. Fig. 104. Both figui-es diTe. perfect cadences. [Compare par. 91.) 164. A certain index of the minor mode is the frequent recurrence of the sharpened 7"* and, with it, that of the sharpened 6*. The sharpened 7* of B minor is A it^ the sharpened e"", G tt. In a piece of music bearing tioo aharps for its signature, the presence of A jt, especially near the beginning or the end, would indicate the scale of B mmor. 16.5. The sharpened 6'" is of itself (as will be shown hereafter) by no means so certain an index of the minor mode as the sharpened 7"'. This, however, is attended with little inconvenience, since the former is generally followed immediately by the latter. ^WA^ Wt ^ •: **: aj*^ =1* T <) % 1* +r i**= 9tt .:s *;= ^*= W" =*ff *^f 33 CHAPTER XVI. Bars and Measures. 166. "Every rhythmical passage or strain of music is divisible into phrases. 'Par. 22.) "Every phrase is further divisible into feet, and every foot into times, or beats." {Par. 23.) 167. The times or beats of a musical foot are accented or awaocented. A foot consists either of two beats, one accented and one unaccented, or of tlwee beats, one accented and two unaccented." {Par. 24.) 168. A musical passage composed of the former kind of feet is said to be in duple time ; of the latter kind, in triple time. No kind of time essentially different from these two is used or, perhaps, possible. 169. The places of the accented beats in musical feet are indicated by lines dra^n at right angles with the slave on which the notes composing them are placed. Such lines are called bars. 170. The group of notes enclosed by two bars is called a measure. The term bar is sometimes improperly applied to the measure itself. 171. The measures in the same musical passage are all of the same value ; i.e. each measure takes the same time to perform. If one measure consists of a minim, each of tlie other measures will also consist of a minim, or of something equal to it; — e.g. two crotchets, four quavers, one crotchet and two quavers, eight semi- quavers, &c. &c. Fig. 105 is in duple time ; fig. 106, in triple time. Pig. 105. HaxeeI. t ^# :l± &c. tj pig. 106. PUKOELL. —9 1 1 B . ^— r #='P^- =t=H #ft N^ -^j-J-- 5"! 1 ' &c. K. M. Ci. 34 BARS AND MEASURES. [Chap. XVI. 172. The end of a movement, or section of a movement, is usually marked by a double bar. When the last measure of the movement, or section, is complete the double bar takes the place of the single bar. When it is iucomplete, the double bar serves simply as a sign that the movement or section is ended— having no effect on the time whatever. (Fig. 107.) Pig 107 consists of the end of one section and the beginning of another. The measure in which the double bar falls is to be performed at the same pace as those measures which precede and follow it. Fig. 107 MOZAKT. 173. The last double bar of apiece of music is generally in- Fig. 108. creased by the addition of two or three bars diminishing towards the end 1±E 174. In practical music time is conveniently marked, or measured, by heats made with the hand, or a stick — in duple time, down and up (fig. 109), in tnple time, down, right and up (Fig. 110.) Fig. 109. Fig. 110. « C3 5 I t V 1:3 In figs. 109 and 110 the lines indicate the spaces traversed by the hand (or stick) in beating time, and the arrows, the directions in which it moves. 175 It matters not by what form of note each beat of a musical passage is represented, provided that the other notes are properly proportioned to it, and to one another, and that the beats are made throughout at the same pace. Fig. 105 might, with equal propriety, be written like fig. Ill, each beat being a minim ; and fig. lOS like fig. 112, each beat being a quaver : provided only that each minim in fig. Ill, and each quaver in fig. 112 was performed at the same pace. as each crotchet in figs. 105 and 106. Fig. 111. -G^- -e^ -e^ m Handel. X3; &c. Fig. 112. ^ UXS^ P0KOELL. &C. 176. The monotony arising from a too frequent recurrence of accented notes, together with other practical inconveniences, has given rise to another formj in which two measures are thrown into one. Chap. XVI.] BARS AND 'MEASURES. Ftg. 113. 35 MOZAET. m m - &c. 177. This form is called common time; and, as its name would imply, it is the kind of time most frequently usod. Fig. 114. 178. In common time the beats are made, — down, left, right, up ; the note performed when the down beat is made receiving a strong accent, and that on the right beat another accent, somewhat less strong. 179. The down beat in ei^er^/ form of measure is naturally the accented beat. Accentuations at variance with the natural (and ordinary) form are, however, oc- casionally made. 180. For example ; notes lasting longer than one beat are sometimes begun on an wizaccented part of a measure {Fig. 115), or are prolonged from the e^td of one measure to the beginning of another. {Fig. 116.) In either case the natural and ordinary accent is disturbed. Fig. 115. Mendelbsohn. Fig. 116. Geeen. -^ &c. ^m i^^fe &c. The form in fig. 116 is generally expressed by modem musicians in another way. {See Par. 277.) CHAPTER XYIL Time — Simple and Compound. J 81. Music of which the times ov beats can be divided, ((fZ infinitum, by two, is said to be in simple time, All the examples iu the last chapter are in simple time; for the value of each beat is in every case an entire note — a crotchet, a minim, or a quaver — divisible by two, ad infinitiim. 182. Compound time arises from a mixture of the two species, duple and triple ; each beat, in a measure of compound time, being a dotted note — divisible by tliree. (Pigs. 117 and 118.) Fie/. 117. F!{/. 118. js_e_jB__e •_ \-tT LU f-Tr-\-tn-t-tT-\\ 183. A measure is said to be in duple, or in (ripZe, time according to the number of heats into which it is divisible ; it is said to be in simple or in compound time, according to the sitftdivision (duple or triple) of which each beat is capable. Pigs. 119 and 120 are both in duple time, because each measure consists of two beats; but %. 119 is in simple duple time, because each beat is a whole note (divisible ad infinitum by two) ; and fig. 120 is in compound duple time, because each beat is a dotted note (divisible by three). Fig. 119. H^-^^f Fig. 120. rn N -^-^ Pigs, 121 and 122 are both in triple time, because each measure consists of three beats ; but fig. 121 is in simple triple time, because each beat is a whole note ; and fig. 122 is in compound triple time, because each beat is a dotted note. 4^: Fig. 121, Fig. 122. i4^|^7^4^^^ 184. In a measure of simple time there is but one principal accent — that on the first heat; in a measure of comp)ound time there is often (and always may be) a subordinate accent — on the first note of each heat. In fig. 133 the accent falls on but one note and syllable (the *irst) in each measure — when, lit, heigh, &c. Fig. 123, Old English Air. ^i=^:t^^^ ^ ^ ^^^f^^ ^Vhen that I »J5 i»< - tie ti - ■ uy l.ny, Witii a keif/li Lo I tie &C. Chap. XVII.] TIAIE — SIMPLE A\D COilPOUND. 37 In fig. 124, besliles the principal accenU (on soiu/s and rus), there are suhoi-dinate accents [onsTiep and round), necessitated by the triple division of the heais to whicli those notes behing. Fig. 124. Old English Air. Songs of shep - herds and ^^^ &C. ru» ti - cal round lays 185. When a beat, in a measure of compound time, consists of a single note the subordinate accent is not felt ; the time being compound to the eye only. In the^?'*^ measure of fig. 125 the subordinate accent is not expressed, seeing that the second beat is entirely filled by the one note over the syllable way. In the second measure, the subordinate accent is indispensable, because the second heat consists of three notes. The tJdrd measure is practicalh) in simple time, since hoth the beats consists of single notes. Fig. 125. =E ^ -• S5P &c. Come a - way come a way to the wild - woods come. 186. The beats, as well in compound as in simple time, are sometimes (more especially when the j)ace is very slow) subdivided. Thus four heats might be made to each measure of fig. 123, or six to each measure of fig. 124, were they to he sung at a slow pace. This, however, is a matter simply of practical convenience, in n(. way luterfenng with the real divisions of the measure. Fig. 124 could, by no possibility, he regu- lated hyfou^ equal beats, nor fig. 123 by three. 38 CHAPTER XVIII. Time Signatures. 187. The number, accent, and kind, of the notes container! in each measure of a musical movement are indicated by the time signature, placed at the beginning, immediately after the scale signature. 188. Time signatures consist, for the most part, oi fractions — having reference to the modern ivhole note, the semibreve ; the fraction showing how much of, or how much more than, a semibreve each measure contains. Thus I indicates a time of two crotchets, i.e., irao/oMr^A* of a semibreve, in a measure; |, a time of six quavers, i.e., six eighths of a semibreve, in a measure. 189. Quadruple, or common, time of four crotchets in a measure is specially indicated by a character, (^ (_^ is not, as might be supposed, the initial of the word " common," but properly a half circle (^^ the symbol of what the old masters held to be impe^-fect time, — in contradistinction to verfeH. or triple time, indicated by an entire circle (~). (Oompa/re ^ar. 24.) 190. Units are occasionally, though not commonly, used as time-signatures. 1 indicates a time of 07ie semibreve in a measure (common time) ; and 2 the older form of two semibreves. 191. Thus at the opening of a movement we find commonly three characters, or groups of characters — the clef, the essential sharps or flats, and the time signa- ture. The first two are usually repeated at the beginning of every stave of each part ; the last is never expressed but once in each part — at the beginning. Fig. 126. ±z Fig. 126 is the commencement of a (piano-forte) movement (compare par. 37) in the scale of E b {see fig. 79), and in "three four" time; i.e., triple time of three crotchets in a measure. In iig. 127 all the time signatures in common use are exhibited and explained. The number of the notes following each signature shows the number of beats in each measure- the form of each note shows the value of each beat. The forms marked * are only found in ancient music ; those marked f are modern, but rarely used. Musical practice is not consistent in regard to the character marked % ; some composers designating I time by and others by (^ , or even Q, (the sign of | time), restricting (t^ to f time. It is greatly to be wished that all three characters were banished from the time table, and that the signa- tures were couflned to numbers. Chap. XVIII.] TIME SIGNATURES. 39 192. The numerator in triple time signatures is always an odd number — in simple triple time, three, in compound triple, nine. The numerator in duple and quadruple time signatures is always an even number — in simple time, two or four, in compound time, six or twelve. Fig. 127. Table of Time Signatures. Simple. * ^ -CJ Xli. f 0' 2 2 "t-^ r-^ • * -C2 CJ CL Eh s S SO Ji. 2 ^ -Q_ip_Q. I 4 111 -§— f — • — ^■ ^C^ 4 2 it i=^ ^ ^ c-ttm Compound. £_ ^ -Ca • o n -Q- ^ « I I ^ 2 <->.<->.(-> Q-n-n - « I I 1 :a i%rt^r 1 2 rtTT o± JL2- ^ »•» -y f 193. The fractions in time signatures are not always expressed in their simplest or lowest forms, i.e., reduced to their lowest terms. Nor could this reduction be made in every instance with safety ; seeing, for example, that f and § are the signatures of two kinds of time differing in every essential particular. 194 3_6 A measure with the former signature may, and often does, contain the same number of the same kind of notes as a measure with the latter signature, viz., six quavers. Yet | being the signature of simple triple, and 6 of compound duple time the accentuation of those six quavers will be altogether different. 40 TIME SIGNATURES. [Chap. XVIII. 195. The natural divisions (times or beats) of a measure of | time are crotchets, of which it will contain three, or their value. The natural divisions o a measure of § time are dotted crotchets, of which it will contain two, or their value. These divisions are generally e.xpressed by the grouping. {Seejigs, 128 and 129.) Fig. 128. Mg. 129. ^P^ -^K^- ?£ ^^ -F^^ The system of time signatures is certainly far from perfect ; it is, however, universally accepted and (among musicians) understood. As any change in the alphabet of a universal language lilta music irt likely to be made very slowly, and as no change would affect eccisting music, the student must be content, for the present, to remember that though in arithmetic | = g in musio, those frac- tions represent things essentially different. Seo Appendix — " Time Signatures.'' 41 CHAPTER XIX. Accidentals. 196. Sljarpa or flats which, being over and above those in the signature of a piece of music, are placed before individual notes, are called accidentals. Under this term are included also those naturals which contradict foregoing sharps or flats, whether essential or accidental. 197. The effect of an accidental lasts throucjJiout the measure in which it is once used; i.e., it alters every following note in it, of the same name as the one wiiioh it immediately precedes, — unless it be contradicted by another accidental. In fig. 130, the second F is sharp as well as tlie first. In fig. 131, the second B is Jlat as we'l as the firet. Fig. 130. Fig, 131. M 198. When the Jirst note of one measure is %misonous with the last note of th« measure immediately preceding it, an accidental placed before the latter note affects also the former, and any number of like notes in immediate succession. When the two notes axe tied (see Chap. XX7 1.), the accidental is usually repeated before the second of the " like notes in immediate succession." The Fs in th-e second measure of fig. 132 are sharp ; so also is ^ejtrst F in the second measure of fig. 133. Fig. 132. ^■ rrtr^ Fig. 133. 199. When the repetition of a note altered in the foregoing measure is inter- rupted, the accidental must be repeated. {Fig. 134.) Fig. 134. ^' r Cr ^ ji^ «-"i The student must be prepared tO' meet with many inconsisteneies in musical practice as respects accidentals — more especially douMe sharps and flats. 200. "A double sharp raises, and a double flat lowers, a note two semitones,''' — not a tone. (Compare par. 137.) Rvery tone may be divided into two semitones, but every two semitones do not rnalce a tone. R. M. G. <* 42 ACCIDENTALS. [Chap. XIX 201. When a note essentially sharp or flat is „ ^^9- 135. required to be raised another semitone, a single sharp or flat, in addition to that already in the signature, makes it, assuredly, doubly sharp or flat. (Fig. 135.) 202. This rule is observed bj^ some composers. Others, however, desirous of avoiding ambiguity, inva- riably precede double sharp or flat notes by X or bb, without reference to the single sharp already markod in the signature. {Fig. 136.) Theoretically, the Ps in fig. 136 are certainly trehle sharp. 20.3. Again. When a double sharp or flat note is followed, in the same mea- sure, by a single sharp or flat note of the same name, some writers precede the latter by a single sharp or flat, and others by a natural, as well as a sharp or flat. Fig. 137. Fig. 138. The form of fig. 138 is the more common. The natural is of more recent invention than the sharp or flat; and in music printed as late as the beginning of the last century the sharp is often uscij, aa the natural is now, to restore a flat note to its original pitch. The following is from Purcell's Orpliens Brittamcus. Third Edition, 1721. Fig. 139. 1 fcd2=ts ±^ ^ Teach me in soft me In modem notation tlie passage would stand thus : — lo - dious songs to move JT \— IS- Pig. 140. 31=*: ^ Teach me in soft me lo - dious songH to move ro CHAPTER XX. Chromatic Intervals. 204. The epithet diatonic (fro-m ike Greeli) is applied' to the natural scale (and to all scales of lifee construction) because, in singing it, we pass princi- pally through tones. A scale purely diatonic would be inconsistent with the modern, or perhaps with a»y, mnsic-dl system; it would certainly be intolerable to the modern ear. 205. By a diatome scale is now understood a series of eight different sounds, the extremes of which are octaves to each, other, separated by Jive tones and two semitones. The scales in fig. 40 are all diatonic. 206. The two semitones essential to the (modern) diatonic scale are called diatonic semitones. Two notes separated by a diatonic semitone are invariably of different names. 207. A chromatic semitone is the interval between two proximate notes of the same name, one &f which is altered by a sharp or flat. 208. " Between every two sounds separated by a tone, an intermediate sound may be placed, whereby the tone is divided into two semitones." {Par. 92.) One of these two semitones will, of necessity, be chromatic. Diat. Diat. Sem. _ Sem. Fi§. in. Chrom. Chrom. Sem. Sem. In fig. 141, the first semitone (G-G it) is eliromatic, the second (G It -A is diatonic. In fig. 142, the first semitone (G-A |?) is diatenie, the second (A P-A H) is chromatic. 309. Intervals resulting from any arrangement or juxtaposition of notes found in the same diatonic scale are called diatonic intervals. 210. Diatonic intervals {compare Chap. F7.)are major and minor seconds and thirds, and their inversions minor and major sevenths and sixths ; perfect fourths, and their inversions perfect fifths ; pluperfect fourths, and their inversions imperfect fifths (of each of which the same diatonic scale never includes but one) ; and the octave, of which the inversion is the unison — not properly an interval. 44 CHROMATIC IXTEBYALS. [CuAP. XX. 211. Certain intervals of which the upper notes are raised, or the lower de- pressed, a chromatic semitone, are said to be augmented. Certain intervals of which the upper notes are lowered, or the lower notes raised, a chromatic semi- tone, are said to be diminished. 2] -2. The unison, major second, perfaet fifth, and major sixth admit oi augmen- tation only ; and their several inversions, the octave, minor seventh, perfect fourth, and minor third, of diminution only. The unison, though " not properly an interval," is, ior the sake of sjsteja, often classed as such. The augmented unison, i. e., chromatic seniitone — the agent of all augmentation and diminution — is one of the most important of intervals. 213. The augmented unison, second, fifth, and sixth, and their inversions, the diminished octave, seventh, fourth, and third, are classet] under die general name of chromatic intervals. Fig, 143 contains an example of *ach of the chromatic intervals. Fig. 143. Augmented. m 3iii:;cz fj zz: ^ -€^ i&- -^ -bcT^ Unison. Second. Fifth. ■Sixth. 22: 1^ Diminislied. — ^ i;:^- cx ;;^- -^ ?Q- Octave. Seventh. Fourth. Third. The word chromatic (from ithe -Greek, xP'^f"'> colour), originally had reference to the ink (of difierent colour) used to express altered notes; it has heen retained possibly on account of the peculiar effect (figuratively, colour) which such notes gave to passages in which th«y were introduced. 214. A scale which contains one or more chiomatic intervals is called a c]iro- matic scale. 215. The third form of the minor mode {Fiff. 98) is chromatic, because its 6* and 7'" sounds are separated by an augmented second. 216. A scale is more or less chromatic, according to the number of eliromatic intervals it contains. The third form of the minor scale is only chromatic in so far as one interval, the augmented second, is concerned. Fig. 144 the most chro- matic form of scale possible, is generally called the chromatic scale. It consists exclusively of semitones— in all, ticelie; seven diatonic, and five chromatic. Fig. 144. As every sound is practically identical with another (C ji with D b, &c.), there are many different ways of expressing the chromatic scale, the choice among which will be governed by circum- stances. Fig. 144 is the commonest form. Chap. XX.] CHROMATIC INTERVALS. 45 217. Of the chromatic intervals {Fig. 143) the augmented second and diminished foiirth are more frequently used, especially in melody, than any others, — because they can be produced by the ju.Ktaposition of notes whieh form j)art of the same (minor) scale. }\u. U5 Scale of A minor. ^ :.x^#?^ ^ F and G tt form an augmented second; G JI and C a diminished r fourth. The latter interval includes the two most characteristic Vf notes of the scale in which it is found — the leading note and 43 the S"". , *^ 218. The inversion of the first of these intervals, __, the diminished seventh, is more sparingly, and that ^ of the latter, the augmented fifth, hardly ever used M in melody. t7 Fig. 146. IQ- {■;©- .CL '::e^- Fig. 147. s ^^ -^ fe 219. The diminished third and the augmented sixth are of still less frequent occurrence ; the former being, by some theorists, considered altogether inadmis- sible in harmony, the latter in melody. 46 CHAPTER XXI. Modulation. 220. Accidental sharps, flats, or naturals may arise, as we have seen, from either of two causes, — the introduction of the altered 6"" or 7"" of the minor mode Chap. 14), or a change of genus, from diatonic to chromatic. The sharpened 6"" and 7"" of the minor scale, never being marked in the signature, are of necessity expressed by accidentals (Pa;-. 160) ; and no chromatic interval can be formed without at least one altered note. 221. To these two causes of accidentals is to be added a third which, though partially connected with the first two, must be considered separately — modulation. 222. Every musical movement is said to be in some particular scale. This expression, though true in the main, must be understood with some qualification. Since, though in every well constructed movement " some par- ticular scale" prevails, or furnishes the majority of the notes of which it is made up, few movements, however short or simple, remain throughout in one scale ; on the contrary, most movements present points of deviation into other scales, and even contain passages the scales of which are equivocal. 223. This deviation, when made into scales connected with the original scale and with one another, is called modulation ; when made, at once, into scales not so connected, it is called transition. 224. Modulation is much more frequently used than transition ; and the most common modulations are between scales which contain the greatest number of common notes, and which are therefore most intimately " connected." 22.5. Thus the scale of C differs from that of G only m one note, F, which is natural in the former scale, and sharp in the latter, — from that of F only in one note, B, which is natural in the former scale and flat in the latter. While the connexion between the scale of C and that of A minor is still closer — the latter, in its original unaltered form, consisting of the very same notes as the former. (Pa/r. 157.) 226. The commonest modulations, therefore, are from any given scale to that of the perfect 5'" above it — requiring but one additional sharp {Par. ii9); to that of the perfect 5* below it — requiring but one additional flat (Par. 122) ; to that of its relative minor ; and to that of the relative minors of the 5'" above and of the 5'" below. The recognition and oonsciousness of the tonic, under whatever variations of tonality (changes of scale), is indispensable to the intelligent and certain performance especially of vocal music • and it*- frequent modulation constitutes one of the principal difficulties of modern music Thin difficulty la Chap. XXI.] MODULA-IION. 47 especially felt in performance from single parts, wherein the modulations are often but imperfectly ex- pressed. Indeed, without examining a score, it is often difficult, and sometimes even impossible, to tell hy the eye, into what scale a composition has wandered. Two or three rules will however serve to meet cases of ordinary difficulty, and enable the vocal performer to ascertain the tonic for the time being. 227. The tonic of the new scale {i.e., the scale into -which the last modulation has been made) is generally found a minor second above the last added sharp, or a (perfect) /oMrt/t below the last added flat. Fig. 149. Fig. 148. ¥ <3) sg r± The F ft in fig. 148 indicates a modulation into G: the B [?, in fig. 159) a modulation into F. 228. The new scale is unmistakeably indicated by the presence of a pluper- fect fourth, or an imperfect fifth ; since there is but one of either in every scale. These intervals may appear either between two notes following in immediate suc- cession or produced simultaneously; i.e., either in melody (^^. 150) or in harmony {fig. 151). Fig. 150. =^=p=r: 'M :^ Fiy. 151. Fig. 150, an eitract from a movement in F, ends with a modulation into C. Either of the two notes (P or B H) which mark the modulation might belong to many difierent scales, but both together can only be found in C. So G W and C tt (jfy. 151) can only be Combined in D. 229. The mode (major or minor) of a Mew scale can only be determined by the presence of the 3"''' from the tonic. (Par. 145.) In fig. 152, there is a modulation from C into D ; whether it is into D minor or D major is uncertain, seeing that F (the 3"' to D) is tiot expressed. The addition of the (major) 3"*, F tt, to the last chord of fig. 153 decides the mode. Fig. 152. Fig.US. i f^ l^-^dU 1 I r^f^ p^ =te IS CHAPTER XXII. Transposition. 230. In the natural scale of C are fonnd five major and tico minor seconds, and (their inversions) _/ire minor and two major sevenths; three major and /owr minor thirds, and (their inversions) three minor and four major sixths ; one plu- perfect and six perfect fourths, and (their inversions) one imperfect and six perfect fifths. {Compare Chap. VI.) 231. The 3'''' and 7'" sounds (mediant and leading note) bear minor seconds — all the other sounds bear major seconds ; the 1" and 4"' sounds bear major sevenths, and all the others, minor sevenths. (See fig. 154.) 232. The V\ 4'% and 5'" sounds (tonic, dominant, and subdominant) bear major thirds — all the other sounds bear minor thirds; the 3'''', 6*, and 7* sounds bear minor sixths, and all the others, major sixths. 23.3. The 4"' soimd (subdominant) bears a pitqDerfect fourth — all the' other sounds bear perfect fourths. The 7"" sound (leading note) bears an imperfect fifth — all the others, perfect fifths. Seconds. Sevenths. (Fig. 154.) Intervals found in the Natukal Scale, O -^ ^ r^-l-TT^ ^^-^ 3131 IE2 -^ -e^- -^v y ICX X3" -^- -^ ICX 33" ^ -^ ^^- -Ct- 331 ^- Thinls. i^ CT 3zi: €5- -e> 2S 32e: ^ o- 33 XX -^ -€> Siji-.hs. ICE -^ -€^ XT" irx ^ "^ -€3- 331 "33 -^ ^^ Fourths. Fifth* ^^ -<=J- CZ> 3^ €?- €3- JZH XX -€>- -^- 331 XX -^ fc=^ 33: XT" -^- o- :ai -^- x~s 1-Q- 3311 _i_j_ -e?- ^^ Chap. XXII.] TRANSPOSITFOI^. 49 The two minor seconds and the two major sevenths, the three major thirds and the three minor sixths, and the one pluperfect fourth and the one imperfect fifth, heing severally inversions of each o^her, are found hetween notes of the same name. The two minor seconds are E-F and B-C, the two major sevenths are P-E and C-B; the thren major thirds are C-E, F-A, and G-B, the three minor sixths are E-C, A-F, and B-G; the one plu- perfect fourth is F-B, the one imperfect fifth is B-F. {Seepj. 154.) 234. The natural scale of C is the type, or model, of all major scales, in the modern system. In all major scales, therefore, the several sounds (1", S"", &c.) bear the same intervaJs as in the scale of C ; for the sharps or flats by whose agency the order of tones and semitones is adjusted in the scale itself, operate equally on every individual, intei-val which may be drawn from it. 235. £.£f." The ^'^ sound" of the scale of C" bears a pluperfect fourth— all the other sounds bear ver/ect fourths." (Par. 233.) So does the.4"' sound of the scale of D, viz., G, the 4'" to which is C ft; the C in the scale of D being essentially sharp. All the other sounds bear perfect fourths. (Compare fig. 154.) Fig. 155. 236. Again, "the 1", 4"", and 5'" sounds of the scale of G heAr major thirds — all the other sounds bear minor thirds." (Par. 232.) So do the 1", 4?^ and B"" sounds of the scale of E b, viz.. E b, A b, and B b (all flat in the scale of E b), the 3'^" to which are G, Cj.and D. All the other sounds bear minor thirds.- (Compare fig. 154.) Mg. 15S. ± ^A ^ ^ A- -o- :a: O-r Id X2_ -^- ^^» 311 3I2E &h- -^- znji T~r _o_ 1 4 5 Pars-. 231i2-and 3 are, therefore true, nfjl only of the scale of Cv but of every other major scale. 237. " Melody, or tunCj does-aot depend on the absolute, but on the relative, pitch of sounds— on their distances apart." (Par. 11.) When the notes of a musical passage are separated- by the same intervals, the melody they form will be the siime, Any- musical idea may, therefore, be expressed at any pitch, i.e., in any scale. 238. The expression of a musical idea in a scale other than that in which it was first conceived or expressed, is called transposition. 239*. In' transposing a passage from one scale to another, we represent each note in the one scale by the corresponding note (the note occupying the same place) in the other, and adjust the intervals of which it is composed, by substituting the sigvfiture of the new scale for that of the old one. K. M. G. H 50 TRANSPOSITION. [Chap. XXII. Thus, tig. 157 is in the scale of C, which requires neither sharp nor flat. To transpose it into D we must place two sharps at the head of the stave; to transpose it into B v, three flats ; into E, four sharps ; into F, one flat ; into G, one sharp, and so on. Fig. 157. Haydn. InC E fj ^ ^?fS^'^P ^ InB 1^ ty -•-# &C. &c. •^^ ^"^^ - iy^^^-i-^ ^^i - |— |— - - &c. InE In F 4* v^ — =t_*-» — si i^ S - ^i ^ 33^ S 5 &c. &c. &c. The Btudent is recommended to try the effect of the above transpositions teithowt sharps or naw. 51 CHAPTER XXIII. Ilh3/thmical Licences. 240. The rhythmieal licences admissible in musical performance consist in the compression of more than its proper complement of notes into a single beat, and in the slackening, or accelerating, the pace of particular beats. Of the former, the most common example, the triplet or triolet, has been already noticed. 241. "A triplet is a gi-oup of three notes, which (by licence) is performed in the time of two of the same kind." (Par. i9.) 242. The triplet is but another mode of indicating a change of time, from simple to compound, in the particular passages where it is introduced. Figs. 158 and 159 ate identical. Fig. 15S. Jt' Jt' Jl> ^ ^^ 3 3 Handel. « rig. 159. 1 B fe ^^m 243. With the triplet may be classed all groups whatever of irregular rhyth- mical formation. In modern instrumental music these are found in great numbers and variety, — -five or more notes being sometimes compressed into the time oifour of the same kind,/oitr or more, into that of three, &c. &c. Such groups are best studied in connexion with musical practice. Departtre from the average pace of a movement in the case of " particular beats," is indicated by tba It-alian words, Rallentando, Accelerando, &c., to be explained in Chapter XXVIL b-^ CHAPTER XXIV. Graces. 244. Passages not forming an integral part of a movement — which without essential loss to it might be, and often aie, omitted — are called graces, or embel- lishments. The principal graces used in melody are the appoggiatura, the beat, the shake, the turn, the acciaccatura, and the portamento. The principal graces used in harmony are the tremolando and the arpeggio. Graces are, for the most part, expressed in smaller notes than tliose used for the integral parts of a movement. 245. The appoggiatura (from appoggiare, Ital., to lean) is a small note, which, being prefixed to another, robs it of its accent and a portion of its time. 24(>. In general, the appoggiatura is a note of half the length of the note which it displaces ; but its full time should be given to the appoggiatura, whatever be its length — the following note being shortened accordingly. Figs. 160 and 161 are severally identical with figs. 162 and 163. Fig. 160. Handel. f^f^T^ Fiff. 161. E * Fig. 162. 3=^f^ i T-r $ Fig. 163. S 3 fzt -.^=V p-f-f- Latterly, the appoggiatura has been falling into desuetude ; modern composers preferring the less equivocal forms of ordinary notation. Tig. 164 would certainly have been expressed by an earlier master as fig. 165. Fig. 164. „ Fig. 165. Mozart. n ] ^ ^"■^^^ 247 The beat is a short appoggiatura, made on the semitone below a principal note. Its effect is to give force and especial emphasis to that note. Pig. 166. =r m Chap. XXIV,] GRACES. 53 248. The acciaccatura (irom acciaccare,lta.\., to pound) is a group of two notes, introduced with the utmost rapidity, before another note. The interval formed ov the two notes should never exceed a minor third. FW- 167. A 249. The appoggiatura, beat, and acciaccatura should severally be uttered on the beat due to the note which they precede — not before it 2-50. The shake consists in a rapid alternation of two adjacent notes. It is indicated by tr., a contraction of the Italian word tiillo, placed over a note which is generally preceded by an appoggiatura. Pig. 168 is to be performed like fig. 169. Fig. 168. Fig. 169. rrrrfTTr mrmf ffffff ri 251. The shake, unless it be a very short one, is always coacluded by a turn. (Seefig. 169.) 252. The turn is a group composed of a principal note, and two subsidiary notes, one above and one below it. It is indicated by '■^, or ^ placed over the principal note. '■^ is the sign of the direct, and ^ of the inverted, turn. Fig. 170, which contains an example of the direct, as well as of the inverted, turn, should be performed like fig. 171. } Fig. 170. ~r]! r3 Fig. 171. 253. The turn, like the appoggiatura, beat, and acciaccatura, should be begun on the beat due to the note over which it is placed. When it is placed bettveen two notes, it should follow the first cf uit^m. Fig. 172 is to be performed like fig. 17^. Fig. 172. -^*-^ Fig. 173. 54 GRACES. [Chap. XXIV. 254. The portamento (from portare, Ital., to carry) consists in the smooth utterance of two following notes, part of the time due to the first of which is given to the anticipation of the second. When (in vocal performance) each note has its own syllable, the anticipated portion of the second note is sung to the first syllable. Fig. 174 is to be performed like Fig. 175. Fig. 174. ^ 3=? n < r3 / 4 i ; i < ' Fiy. 1,5. /, \ . _ • V- r • • U 255. The tremolando (from tremolare, Ital., to tremble) is produced either by the rapid iteration of the same sound or the alternation of different sounds in the same combination. Figs. 176 and 177 are performed like figs. 178 and 179. Fig. ] 76. Fig. 177. -:e: m o" cr ^^.178.^ Fig. 179. 256. The arpeggio (from arpeggiare, Ital., to play upon the harp) consists in striking the sounds of a chord in rapid succession, instead of simultaneously. It is indi- cated as in fig. 180. CHAPTER XXV. Signs of Kepetition, Contractions, &.c. 257. The alphabet of music includes, besides notes, many characters, and even words, indicative of the style or manner of performance of the movements, particular passages, or individual notes, to which they refer. 258. Repetition is indicated by dots enclosing the passage to be repeated. These dots are generally, though not always, placed at the beginning and end of a measure. Fig. 181. ; ^ ? O^ 259. Sometimes one or both of the bars enclosing a passage to be repeated are doubled ; but the double bar is most often, though not always, introduced when the last measure of the passage to be repeated is incomplete. Fig. 182. ■ i -& -& &c. 260. The beginning of the passage to be repeated is frequently indicated by a sign :^:, referred to at the end of it bj the (Italian) words Dal Segno, i. e.,from the sign. Thus, fig. 182 might be expressed like fig. 183. Fig. 183. : ^ -& i Dal Segno. -& &C. 261. When the repetition is to be made from the beginning of a movement tha dots are often omitted, and the words Da Capo (from the beginning), or Da Capo al Segno (from the beginning, at the sign), if there be a sign, are used. Thus, fig. 181 might be expressed like fig. 184 T~rT Fig. 184. ^ * Da Capo. -©I- 56 SIGNS OF REPETITION, CONTRACTIONS, ETC. [Chap. XXV. 262. When, on repetition, any measure or measures are to be omitted, the words " 1" Time" are placed over tliem, and the words " 2"" Time" over those to be sub- stituted for them. lat time. 2nd time. Fig. 185. ^^m^^^ S &C. 26-3. The repetition of a single measure is sometimes marked hy the «ord bis (twice) placed over it in addition to, or instead of, the dots. Bis. Bis. Fig. 186. • P r • ^ I ^ ? 264. Silence lasting an entire measiu-e ("properly represented only by rests equal to the contents of that measure) is often expressed by a semibrere rest, ■whatever be the kind of time employed. Fig. 187. Fig. 188. Fig. 189. Fig. 190, m^l = 11^ V r r r S :& ^ r 1 r 1 :9- ±t r ir ir 1 rigs. 187, 188, 189, and 190, are all occasionally represented by fig. 191_ the form properly applicable to common time only. ■"£'• ^^^' 266. Silence lasting longer than one measure is, in single parts, generally in- dicated by a number, or numbers, placed over a semibreve rest, representing the number of measures of silence. 266. In ancient music the necessity for these figures was obviated by the em- ployment of the breve, and the long {double breve) rest. Fig. 192, equally with fig. 193, indicates a rest of eleven measures. The two fonns are sometimes combined, as in fig. 194. Fig. 192. Fig. 193. Fig. 194. 11 11 • BEBE^ E SEE 2u7. In counting rests of more than one measure the numbers (of the mea- sures) should be told off on the first beat of each. Thus fig. 192 should be counted. One, two, three, four ; Ttvo, two, three, four ; Three, two, three, four ; and so on to Eleven, two, three, four. 268. A jMuse placed over or under a note indicates generally that the sound due to it may be sustained as long as the ]>erformer pleases. (Fig. 195.) A pause is sometimes used to mark the end of a movement. ^O Fig. 195. ^m ^ ~W' 269. The direct {w) is used to indicate a following note which it is not con- venient or necessary to express. It is especially used at the end of a line or the bottom of a page, as a preparation for the next. 57 CHAPTER XXVI. Marks of Expression. 270. A dash f)laced over or under a note indicates that it is not to be sus- tained throughout the beat, or portion of a beat, due to it, but interrupted, as though it were a much shorter note followed by rests. A dot placed over or under a note Indicates a modified form of the effect due to the dash. Fig. 196 should be performed like fig. W, and fig. 198 like fig, 199. Fig. 196. I I I Kg. 197. ^=^^-y 1 1 g 1 . 3=5^=3 Fig. 198. • m [/ A 9 p ih m V-y • Fig. 199. N-s- :± ^ 271. Dashes are sometimes placed over minims, where they are understood to imply the effect represented by the word sforzato (forced). {See fig. 211.) 272. Notes with dashes over them are said to be performed staccato, i. e., cut off, separated; notes with dots over them, mezzo-staccato, i. e., half-staccaXo. 273. A slur placed over or under two or more notes indicates that they are to be performed legato, i. e., smoothly (literally, bound together). In vocal music, the slur indicates that the notes under or over it are to be vocalized, i. e., sung to one syllable. Handel. r\ Fig. 200. ^ i^ i e ^ Tune your harps to songs to songs of praise. 274. When ttvo notes only are slurred, a sti'ess should be laid on the first, and the second should be made staccato. rig. 201 should be performed like fig. 202. Fig. 201. Fig. 202. ±* -\=^ ^-=dt-» TTf^f^f]^ 275. The last of a group of slurred notes is always short, by virtue of its position. R. M.G. 1 58 MARKS OF EXPRESSION. [CHAr. XXVI. 276. When the slur is placed over two or more notes of the same name and pitch, it is called a tie or bind, and has the effect of turning them into one note — equal in length to the two added together. {Compare Par. 198.) rigs. 203 and 204 are identical. Fig. 203. Fig. 204. 277. The tie is generally used to connect tico notes, the first of which is un- accented, and, more especially, the last note of one measure with the first of another. Sounds beginning on accented beats are generally expressed by entire notes, or by dotted notes. The form in fig. 205 {Compare par. 180) is now obsolete, that in fig. 206 having superseded it. Fig. 207, however, is not incorrect, though more often written as fig. 208. Fig. 205. Fig. 206. Fig. 207. Fig. 208. S i-\ ^ 278. In prolonging a note begun on an Mwaccented beat to an accented beat, "the natural and ordinary accent" of the measure in which it appears "is dis- turbed." {Par. 180.) The result of this disturbance is called syncopation. Syncopation is rendered more apparent by the employment of the sign :r—~, or the letters Sz. {&« Fig. 211.) 59 CHAPTER XXVII. Words relating to Pace, Intensity, and Style. 279. The vocabulary of music has been enriched, or corrupted, by the contribu- tions of every people among whom musical composers, performers, or even tran- scribers, have been found. Lively, Doucement, Feierlich, &c. &c., are used severally to indicate the pace, intensity, or style, of music printed in England, in France, or in Germany. 280. These words carry with them the disadvantage of being intelligible only to the people of those countries, or to those who have studied their language, — a disadvantage the more to be deprecated from the fact that musicians possess a sort of common language in Italian, the musical terminology of which is more or less accepted by every musical people. A complete list of Italian words relating to pace, intensity, and style, would furnish material for a Musical Dictionary.. The following lists contain some of the most important, classed under their several heads. The English words immediately following the Italian are such literal translations .as would be found in a dictionary. They represent very imperfectly the meanings of the latter as applied to m\isic, which indeed are only to be ascertained from a close study of ItaUan, or considerable expe- rience in musical performance. Thus, Grave, Lento, and Largo, may be regarded as equivalents, so far as, pace only is concerned; but each indicates a different style of performance, — Grave implying more solemnity than Lento, and Largo more dignity or breadth than either. 281. Words relating to pace, intensity, and style, admit in every instance of contraction, and generally of modification, by the augmentation or diminution for which the Italian language presents such facility. Sometimes two or more are joined together in a way that appears somewhat contradictory, until it is under- stood that they refer not only to pace, but to style also. Thus, Allegro Andante means lively in manner, but somewhat deliberate in face. Each of the words in fig. 209, excepting the three first, may be considered to express a quicker movement than the one before it. Fig. 209. Words relating to Pace. ( GRAVE, grave. \ LENTO, slow. { LARGO, broad. Laeghbtto, rather hroad, not so slow as Laego. Adaoissimo, very leisurely, flower than Adagio. ADAGIO, leisurely. Andantino, going gently, slower than Andante. ANDANTE, going at a moderate pace. Allbgeetto, rather merry, not so fast as Allegbo. ALLEGRO, merry, lively. PRESTO, quiclc. Peestissimo, very quiejc. GO WORDS RELATING TO Connected with the above ar« the following : — Fig. 210. [Chap. XXVII. AccELEEANDO,* ACCEL"., accelerating {the pace). Railentando,* eall"., slackening ( ). Steingendo, stein"., pressing onwards. Pw Mosso, more moved, quicker. ElTAEDANDO, EITAE"., retarding. EiTENTTTO, EITEN"., holding hack. A Tempo, in time, {after an Accel", or Ball".). In Istesso Tempo, in the same time ; i. c, the times, or beats, the same, whatever be the forms of the notes. Alla Beeve, by the breve ; i. c, the breve being regarded as the whole note — each beat being a minim. Tempo Oedinaeio, {in) ordinary time \ CoMODO — convenient > neithefrfast nor sloio. * * These words are correlatives. Miidern composers frequently add to the words above, an exact indication of the pa<:e of their music, by a reference to the Metronome. (-Sse Chap. XXIX.) Fig. 211. Words relating to Intensity. Piano,* pia., p, soft. Mezzo Piano, mez. pia., mp, rather soft. Pianissimo, PiAN'"°.,^jti, very soft. FoETE,* FOE.,/, loud. Mezzo Foete, mez. foe., mf rather loud. FoETissiMo, EOB""., ff, very loud. Cbescesdo,! GEES., or -=:r:, increasing {in loudness). Deceescendo,! decees., or ^=^, decreasing {in loudness). To the above may be added : Foete Piano, ^, loud and {immediately after) soft. Sfoezato, sz, forced {applicable to single notes only). EiNFOEZANDO, nmvoiLZ., forcing {applicable to passages). Calendo, deseendina '^ Peedendosi, losing itself Diminuendo, diminishing Smoezando, extinguishing Dolce, soft. decreasing in speed and {generally) in intensity. * t These and their dependent words are correlatives. All these words are liable to modification by the addition of one or more others, expressive partly of pace, but more especiaUy of style. The foUowing are some of the most important of them :- WHAP. XXVII.] PACE, INTENSITY, AND STYLE. 61 Fig. 212. Words relating (chiefly) to Style. Agitato, agitated. Mabstoso, majestic. Animato, animated. Maecato, marked. A poco A poco, by degrees. MoLTO, much, very. AssAi, suiEciently. Mbno, less ; e. ff., Meno Allegro. Ben, well ; e.g., Ben Maroato. Mezzo, half. Bbillante, brilliant. Modbeato, modei'ate. Con, with. Non, not ; e.g., Non troppo Lento. (Con) Bbio, mirth. Piu, more; e.y., Piu Animate. ESPEESSIONB, expression. Poco, little. Fttoco, fire. Quasi, almost, as though. MoTO, motion. Sempeb, always ; e. g., Sempre pp. Tbnbebzza, tenderness. SosTENUTO, sustained. EsPEBSsivo, expressive. Staccato, cut off. GitrsTO, exact. Tenuto, held, sustained. Geazioso, graceful. Vivace, lively. Lbgato, bound. VoiTi, turn. Ma, but ; e. ff., Ma non Eall°. Segue, it follows. 282. The words in fig. 209 are all used occasionally as noun-substantives. We speak of an Adagio, an Andante, an Allegro — as of movements to be per- formed in the styles indicated by those words. 62 CHAPTER XXVITI. The Tenor and Alto Staves. "All the notes (twenty-three) required for average vocal music can be placed on a s'.ave of eleven lines." {Pa/r. 34.) But "no individual voice can utter" twenty-three sounds; consequently, in writing music for individual voices, a smaller number of lines suffices. " Practically, whether for vocal or instrumental music, a stave oi five lines is generally adopted; the particular sets, or staves, most used being the five highest and the five lowest of the Great Stave" of eleven. {Par. 35.) " The lower one of these sets, or staves, of five lines is used for voices and instruments of low pitch , the upper, for voices or instruments of higher pitch." (Par. 86.) " Music for the ^wer voices of womeii and the higher voices of men demands other staves, which are, equally with the treble and bass staves, extracts from, or parts of, the Great Stave of eleven lines." [Par. 39.) 283. The voices of men (beginning from the lowest) are Bass, Barytone, Tenor, and Counter-tenor; those of women are Contralto, Mezzo-soprano, Soprano, and Treble. The highest of the former, the Counter-tenor, is almost identical in compass with, though very different in timbre from, the lowest of the latter, the Contralto. The Treble may be regarded rather as a -puerile than a female voice. The relative places, in the musical system, of these voices is exhibited in fig. 213, and the relations of the different staves they occupj' to the Great Stave is shown in fig. 214. Fiff. 213. Contralto. Mezzo Soprano. Soprano. -f r^ / * > ii X4 < ) V ) ( ) ■ < ) < •> < > C ) /\. r c > t )' < ) < ) C ) Counter i'enor. Fig. -Hi. 11 10 9 8 7 6 6 2 1 1- Barytone, i tt Tenor. b- i- ■S- n- 1- n Alto. li n Mezzo Soprimo. Soprano. Treble. Chap. XXVIII.] THE TENOR AND ALTO STAVES. 63 284. Of the seven staves (in fig. 314) two are headed by the F clef, forir by the C clef, and one only by the G clef. 285. The 4* line of the Great Stave (indicated by the P clef), is also the 4'" line jf the hass stave ; but it is the S"" line of the barytone slave, the 2"^ of the tenor, md the 1" of the contralto. 286. The 6'^ or middle, line of the Great Stave (indicated by the C clef), which, forms no part of the bas^ or of the treble stave, is the 5"" line of the barytone, the 4"* of the tenor, the 3"" of the contralto, the Z"" of the mezzo soprano, and the 1" of the soprano. 287. The 8"' line of the Great Stave (indicated by the G clef), which forms no part of the bass, barytone, or tenor stave, is the 5'" line of the contralto stave, the 4'" of the mezzo-soprano, the 3'''' of the soprano, and the a'"" of the treble. 288. Two of these staves, the barytone and the mezzo-soprano, have become obsolete. Music for the barytone voice is now commonly writteu on the bass stave ; music for the mezzo-soprano voice, on the contralto, the soprano, and even the treble stave, which latter, in England, is generally substituted for the soprano. The treble stave was once used exclusively for instrumental music, and lias not even yet been universally adopted for vocal. The soprano stave is still much used on the Continent. 289. Thus the staves in actual use are but five, and, in England, only four, — the bass and tenor for the voices of men, the contralto (or alto) and treble for the voices of women and children. The bass and treble staves, the lowest and the highest of the Great Stave of eleven lines {see Chap. 77.), can need no further explanation. 290. On the 4'* line of the tenor stave is found the C clef. (See fig. 214.) The C clef, it will be remembered, is the distinguishing mark of the 6'", or middle, line of the Great Stave of eleven lines. Consequently, the 4'" line of the tenor stave is identical with the 6'" of the Great Stave ; and.-turther, the 1"', 2""', 2,'^, and B*"" lines of the former are identical with tlxe 5~, *'", o"'-, and 7'" of the latter. 291. On the S'* line of the contralto stave {See fig. 214) is found the C clef— the distinguishing mark of the Q^^ or middle line of the Great Stave. Consequently, the 3'''' line of the contralto stave is identical with the 6"" of the Great Stave ; and further, the 1", 2''^ 4*, and 5"" lines of the former with the 4*, 5* 7'", and 8'" lines of the latter. Familiarity with the tenor and contralto staves is only to be attained by practice ; but it is certain that the difficulty sometimes attendant on this arises entirely from the fact that their relation to the Great Stave, and therefore to the more familiar treble and hass staves, is not at all, or but imperfectly, understood. One stave is of course, of itself, as easily mastered as another ; and any difficulty found !» readino- from the tenor and alto staves must arise from a hitherto exclusive use of the treble and tiiss. Let the following facts be borne in mind : — 64 THE TENOR AND ALTO STAVES. [Chap. XXVIIl. 292. The 1", 2"^, 3'Mines of the tenor stave are identical with the 3'^ 4*", and 5'" of the bass ; the top line of the tenor stave is identical with the bottom line of the t7-eble ; and the 4*" (or clef) line of the tenor stave is that leger line which connects the bass with the treble. [Pig. 215.) 293 The 1" and S"* lines of the contralto stave are identical with the 4'" and 5"" of the bass ; the 4'" and 5'" lines of the contralto stave with the 1" and 2°'* of the treble; and the S"" (or clef) line of the contralto stave is identical with the leger line connecting the bass with the treble. [Fig. 216.) Fig. 215. Fig. 216. The student must be warned that, notwithstanding the recent multiplication of editions of popular musical works, in which parts for the alto and tenor voices are printed on the treble stave (the former sometimes, and the latter always, an octave higher than their proper pitch), anything like an extensive acquaintance with cla.ssical music is quite impossible without familiarity with the alto, tenor, aiid soprano staves. 65 CHAPTER XXIX. The Syren and The Metronome. 29J. "The pitch of a musical sound depends on the number of vibrations communicated to the air in a given time" {Par. 5),— its duration, " on the time during which the air continued to vibrate at the same pace" (Par. 6.) 295. Although " the musical student is chiefly concerned with the pitch and duration of sounds as compared with one another," yet, " every sound is assuredly of a definite and appreciable pitch and duration." {Par. 9.) 296. C, the centre of the musical system {Par. 30), is the result of 256 vibrations per second; its octave above, of 512; and its octave below, of 128. The highest C on an ordinary Piano-forte is the result of 2048 vibrations per second ; the lowest C, of S2, The octave below the latter, the result of 16 vibrations per second, has till lately been thought to be the lowest sound appreciable by the human ear, 297. It is difficult to believe that even the lowest of these numbers is to be counted ; yet methods whereby their correctness could be ascertained indirectly have been known for a great length of time ; and niechanieal science has recently made even a direct estimation of it possible. The most perfect of these con- trivances is an instrument called the Syren, invented by a French mathematician, Cagniard de la Tour. 298. The Syren {see fiff. 218) consists of cylinder A, generally about 2 inches long and 3 inches in diameter, the table, or top, of which is pierced with 25 holes placed in a circle at equal distances apart. In immediate contact with this table is placed a disk B, about \^ inch in diameter, pierced with the same number of holes as, and exactly coinciding with, those in the table of the cylinder. By means of a short pipe C, communicating with a bdllows-,a blast of air, slightly compressed, is forced into the cylinder, from which its only means of escape is through ibe holes in the top of it, ivlien those of the disk are brought itnmediately over them. The holes of the disk and of the cylinder being cut obliquely and in opposite directions, the air, in its effort to escape from the latter, sets the former spinning, and brings each of the holes of tlie one successively over each of those of the other. Every time this happens, the compressed air, in its escape from the cylinder, gives a pulsation to the external air, which pulsation, if repeated at regular intervals and with sufficient rapidity, produces necessarily a musical sound. 299. " As the number of vibrations (or pulsations) communicated to the air in a ;;iven time increases or diminishes, so does the sound become more acute or more grave." {Par. 5.) In the case of the Syren, the number of vibrations will depend on the pace at which the disk revolves, — which pace, again, depends on the force with which the air is driven into the cylinder, K. M. G. '^ 66 THE SYKEN AND THE METRONOME. [Chap. XXIX. •300. The number of revoliitious, and portions of revolutions, made by the disk, are recorded by two hands, somewhat similar to those of a watch, each being centred on a separate dial, and acted upon by a mechanical contrivance which connects them with the axis of the disk D ; the time in which these revolutions are made being ascertained- by a stop-watch, or a pendulum beating seconds. Thus, supposing 5 revolutions of the disk to he made in a second while a note of a given pitch was maintained, it would prove that that note (e. g-, jig. 217) was the result of 125 vibrations per second ; seeing tiat, the disk being pierced with 25 holes, each revolution of it was the cause of 35 vibrations. Fig. 217. ^ 231 Fig. 218. THE SYREN. The application of the Syren to practical nrnslc is at present too remote to justify a more minute account of it here. The exact measurement of the time of sounds is at once more simple, and prac. tiually more important to tke student, than that of their tune. This is effected by means of Maelzel's ^letroumme. 301. Maekel's Metronome {fig. 219) consists of a pendulum A B, having an index B C, which is furnished with a weight M, easily moveable along its whole length. On the position of M depends th« -pace at which t!*e pendulum A B will oscdlate to and fro, or, more properly, the numbar of oscillations it will make in a given time. The figures on tbe index B C indicate this number per minute, sup- posing the moveable weicht M to be ulaoed immediately wilder any tme of them. Cbap. XXIX.] THE SYREN AND THE METRONOME. 67 Thus, if the top of M be placed against the line marked 160, the pendulum A B, and the index B C, will make 160 vibrations per minute : if it be placed against the line 50, it will make 50 vibrations per minute; the former being the largest, the latter the smallest, number possible. 302. A composer or editor, who desires to indicate the exact time at which a given movement is to be performed, has only to mark against the form of note which represents each beat the figure under which the weight M is to be placed on the index B C, and the pendulum will oscillate at the pace at which each beat is to be made. Thus ^ ■= 100, means that eaeh crotchet is to be performed, and each beat (equal to a crotchet I made, in the time of cue oscillation of the pendulum, when M is placed aghast the line. marked IOC . Fig. 21 9i THE METRONOMF. Although, for the purpose o? cheeping time in musical performance, the Metronome never ha» been nor perhaps ever can be used, for the purpose of indicating it, it is most valuable. When at hand it is, of course, an indisputable evidence of the intention of the composer ; and even \ hen no at hand it is hardly less useful, since a moderate degree of practice will enable a conductor, or per- former, to rem&mher the pace at which the pendulum vibrates when the weight is in this or that position, and thus to carry out the design of the composer, if not perfectly, at least with far more certainty than when aided only by such words as Andante, Allegro, &c. &e. 68 CHAPTER XXX. The Ancient Modes. " Tlie order of tones and semitones in a scale is called a mode. arc therefore possible; and at least that number was once in use." Seven modes, or forms, of scale {Pai-. 76.) 303. It has been shown {in aiap. YII.) that of the seven modes " possible" only two are available, or have hitherto been made available, in the modern system — the 1'' and the &^ {of fig. id) ; that the 2'"', 3'■^ and S''' have been rejected be- cause they are wanting in leading notes, and the 4"' because of its pliqiei'fect fourth ; and that the T"" " has never been used," on account of its imjierfect fifth. 304. The importance of the leading not€, though not altogether unappreciated, would seem to have been less sensibly felt by the Old Masters than by us ; for they certainly recognised and executed music written in the 2"'', 8'''*, and 5"' modes {of fig. 40), and, by a different disposition of the notes of each, formed as many others — in all twelve. Fig. 220. — The Ancient Modes. Authentic. Ist. 3rd. Sth. 7th. 9th. nth. -€^- X5" msL -^- -^- X3: _cx -o- 33: 2nd. 4th. Plagal. 6th. 8th. 10th. t2th. -^- "C5" -€?- Tir -es- XX 305. The first six of these modes (those in the upper line of fig. 220) they eg,lled Mithentic, the others (those in the loivei- line) they called plagal; giving the odd numbers to the former and the even numbers to the latter. By the " Old Masters" are generally understood the composers who flourished before the end of the sixteenth century ; though the ancient sfi/le was maintained in many instances much later. The large notes in fig. 220 are the tonics, or rather Jinals, of each mode. 306. The final of each authentic mode is identical with that of its plagal ; e.g., D, not A, is the final of the 4* mode as well as of the 3''''. A passage in an authentic mode, therefore, would range between the final and its octave ; whereas a pas^^age in a plagal mode would range between the 5"' of the final and its octave; the final being, in an authentic mode^ a boundary, and in a plagal mode, a centre. Ch--.? XXX.] THE ANCIENT MODES. C9 307. Of these twelve " possible" modes only a certain number have been in common use at any time. Most of the old Theorists limited the number of modes to eight, four authentic and four plagal, counting the authentic mode whose final is D as the 1", and the plagal mode whose final is G as the 8*, and last ; thus rejecting the only two used in the modern system — those beginning on C and A. The arrangement of fig. 220 is that given by Zarlino in his " Instituzioni Armoniclie ;" but the one most commonly adopted was the following. (.See fg. 221.) Fiff. 221. — The Ancient Modes. A uthentio. let. 3rd. 5th. 7th. C2_ -65- "CT- irx -65- -65- HT -65- 2nd. Plagal. 4th. 6th. 8th. ^E TCJ' -65- HZE -^- i Fig. 222. 308. Of the above, llie modes most com- monly used were the 1" and 3"''', whose finals are D and E. (Figa. 222 and 224.) They are both minor modes, but differing from the modern type (fig- 223), the former in its major 6"", the latter in its minor 2"". (Compare figs. 222 and 224 will, fig. 223.) 1 X3: -^ X3: -^ Fig. 223. znj -e5 X3: 6> 33 -^- Fig. 224. - <-> -CI f- "t^-F -^ — n- TIT ii-x-2- c-t • . r7> . <~> 2 <-* -^-3- 4 3 .. _o. n -T Di • r:^ -x-- f 16 ^-^ « a I < ©■fc t-rrn .Jt ^00 \ 1 4 ^ 1 1 i I INDEX. 2'Se numbers refer to the Paragraphs, which form an vminterrupted series from the beginning to the end of the work. Accent, 184. Acciaccatura, 248. Accidentals, 196 ; effect of, in the same measure, 197, — in the next measure, 198, 199. Appoggiatitra, 245 ; length of, 246. Arpeggio, 256. Bars, 169 ; double, 172, 173. Beat, 247. Beats, accented or unaccented, 24 ; made by the hand, 174 ; down beats usually accented, 179 ; subdivision of, 186. Bis, 263. Brace, 37. Breve, 50. Cadence, perfect and plagal, 91. aefs, 28, 29, 80. Bash, 270. Degrees, 32. Bemisemiguaver, shorter notes than, 51. Bired, 269. Bominant, 83. Bot, after a note or rest, 55 ; double, 56 ; over a note, 270. Enliarmonic Change, 128. mfth (Imperfect), its place in the natural scale, 233. R. M. G. Mfths, perfect and imperfect, 67, 68 j augmented, 212, 213. Finals, of the ancient modes, 306. ' Mats, 95 ; how generated, 117, 122, 123 ; double, 136, 137, — always accidentals, 142,— how contradicted, 201, 202, 203. Feet, divisible into times, or beats, 23. Fourth (Pluperfect) its place in the natural scale, 233. Fourths, perfect and pluperfect, 67, 68 ; diminished, 212, 213. Graces, the principal, 244; expressed in smaller notes than other passages, 244. Sarmomf, 10. Idea (Musical), to be expressed at any pitch, 237. Intensity ( Words relating to) ,281, Jig. 161 . Intervals, 18 ; in the natural scale, 18 ; how named, 57 ; inversion of, 64 ; greater than an octave, 70-72 ; alte- ration of, 98, — does not aifect their names, 141 ; diatonic, 209, 210 ; aug- mented and diminished, 211-213 ; chromatic, — the most common, 217. Inversion, 64 ; quality of an interval altered by, 66. Italian, the common language of musicians, 280. L 74 INDEX. Leading Note, 79, 81, 89; last added sharp always the, 119'; how regarded by the Old Masters, 306. Legato, 273. Lines (Leger), 38, 39. Long, fig. 14. Maxim, fig. 14. Measure, 170, 171. Mediant, 84, 85. Melody, 10 ; dependent on the relative pitch of sounds, 17. Metronome, 301 ; application of, 302. Mode, 76 ; not determinable without the 3'''' sound, 229. Modes, the modem, 77, the ancient, figs. 220, 221,— aU, major or minor, 78,-t- authentic and plagal, 305, — ^liable to modification, 309. Modulation, 222, 223 ; the most common form of, 226. Musical Sounds, their pitch, 5 ; duration, 6 ; intensity, 7; timbre, 8. Naturals, 96 ; in signatures, 143. Ninths, 71; not invertible, 72. Note, position and form of a, 26 ; un- meaning without a clef, 27. Notes (Forms of) in common use, 43; their names unmeaning, 44 ; stems of, 47 ; only indicate the relative lengths of sounds, 175. Pace (Words relating to), 281 ; figs. 159, 160. Passages, divisible into phrases, 22. Pause, 268. Phrases, divisible into feet, 23. Portamento, 254. Bepetition, indicated by dots, 258, — ^by a sign, 260, — by words, 261 ; measures omitted in, 262. Ttests, 52-54 ; of a whole measure in any kind of time, 264 ; of more tlian one measure, 265, — ^how expressed in an- cient music, 266, — mode of counting, 267. fihythm (Musical), how far resembling poetical, 25. IScale (The Natural), formed of unequal steps, 15 ; divisible into two tetra chords, 19 ; how expressed on a stave, 31 ; the type or model of all major scales, 234. Scales, of P and G, 103 ; of D and E (minor), 104; of D (major) and B (minor), 105; of 0, F, and G (minor), and D, E, A, and B (major), 106 major and minor, why so called, 145 relative, 157, 158 ; diatonic, 204 chromatic, 214-216. Scales, different kinds of, 74, 75 ; of C and of A, types, 144 ; not decided by signatures alone, 162 ; how de- cided, 163, 164 ; the new scale, how recognised in modulation, 227, 228. Seconds, major and minor, 69, 60; alte- ration of, 99 ; augmented, 213. Seconds (Minor)., their place in the natural scale, 231. Semitone, the diatonic, 206; chromatic, 207. Sevenths, major and minor, 63 ; alteration of, 102 ; diminished, 213. Sevenths (Major), their place in the uatm-al scale, 231. Shahe, 250, 251. Sha/rps, 95 ; how generated, 115, 118, 119 ; double, 136, 137,— a.lways acci- dentals, 142,— how contradicted, 201- 203. Signatures (Time), 187, 188 ; sometimes units, 190; imperfection of, 193, 194. Signatures (Scale), 131 ; of minor scales, 160. Sixths, major and minor, 63, 60 ; alteration of, 102 ; augmented, 213. mDEX. 75 Sixths (Minor), their place in the natural scale, 232. Slur, 273 ; over two notes, 274 ; over two identical notes, 276. Sound, cause of, 1 ; musical, 2. Spaces, 32. Stave, 26 ; of eleven lines, 34 ; of five lines, 35 ; the bass and treble, 36 ; the barytone and mezzo-soprano ob- solete, 288 ; the tenor, 290, 292 ; the alto, 291, 293. Staves, seven different, Jlffs. 163, 164. Staccato, 272 ; mezzo, 272. Style (Words relating to), 281, Jiff. 162. Suhdominant, 83 ; its tendency towards the mediant, 89 ; last added fiat always the, 122. Submediant, 84, 85 ; .its tendency towards the dominant, 89. Supertdnic, 84 ; its tendency towards the tonic, or mediant, 89. Syncopation, 278. Syren, 298. System (The modern musical), basis of, 12 ; a succession of scales, 20. TetracJiord, 19 ; the upper, variable in minor mode, 146, 152. Thirds, major and minor, 61 ; alteration of, 100 ; diminished, 212, 213. ■ Thirds (Major), their place in the natural scale, 232. Tie, or Bind, 276. Time, perfect and imperfect, 24 ; duple and triple, 168 ; quadruple or com- mon, 176-178 ; simple and compound, 181, 182. Time Table, Jig. 16; suggestions for a new. Appendix. Tone, division of into two semitones, 92. Tonic, 73, 81 ; triad of the, 90 ; any note may be made a, 107 • the tonics in actual use, 110, 111 ; how ascertained from the signature, 134 ; how ascer- tained in ancient music, 211. Transposition, 238 ; how effected, 239 ; examples of. Jiff. 165 ; practised by the Old Masters, 210. Tremolando, 255. Triad, 86 ; of the tonic, 90. Triplet, 49 ; marks a change of time, 242. Turn, 252. Voices, of men, 283 ; of women, 2S3. THE KMI>. PEINTED BY EALLAHTTJIE, HANSON AND CO. LONDON AND EDINBUBQH ' ■> ,ir'J iisig'ijf