m it'*'^ "Z~,, II 3' x. CORNELL UNIVERSITY LIBRARY MUSIC The original of this 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/cu31924022370682 GRAMMAR OF MUSICAL HARMONY ©Se S>ub8tance of Hectureis DELIVERED IN ST. M A R T I N'S HALL THE TEAINING INSTITUTIONS OF THE NATIONAL SOCIETY, BY JOHN HULL AH, PR0FSS80R OF VOOAI, MUSIO IN KINO'S OOLLEOE, AND IN QUEEN'S COLLBOE, LONDON, AND ORGANIST OF OHARTEEHOUSE. NEW EDITION. LONDON: LONGMANS, GREEN, READER, AND DYER. 1871. lOBDOH ; SAVILl, 1DWARD3 ASD CO.. PEIMTKES, OaAHDOS BTBEEt, COVENT QAKDBN. PREFACE. There are some terms belonging to every art or science whiclij thougli convenient or indispensable to adepts^ are a source of embarrassment to beginners. In music, melody, harmony, and counterpoint, are among these. A succession of individual sounds, and a succession of combinations of sounds, are obviously different things, and as such they require different designations, — the very existence of which makes it difficult to appreciate the fact that the things designated, though different, must never be considered separately. For, a succession of sounds can hardly be recognised as melody, unless it be capable of proof, by the addition of that harmony of which it is only one part/ while a succession of combinations of sounds will be unworthy of the name of harmony, unless the various parts of which it is composed be individually melodious. Certain it is that a musician never conceives melody without associating it with harmony, as he never hears harmony without being able to trace out more or less of the melody which it must of necessity contain. The line of demarcation between harmony and counterpoint being less strongly marked than that between melody and harmony, their distinction by different names is attended with much greater inconvenience. For that distinction would seem to imply that the arrangement of individual parts was something over and above, or even different from, making the chords in which they are contained succeed one another properly. Now, no one could be considered as a harmonist who could not connect one consonant combination with another, prepare and resolve discords, and reconcile the frequently conflicting interests of combination and progression. And yet by the term counterpoint is understood little more ; for the treatment of mere passing notes can hardly be brought altogether under those strict rules to which a science is generally supposed to be amenable. The musician who may have the curiosity to look into the following " Geammar iV PREFACE. OF Hakmony" must therefore be prepared to find that it contains much that relates to those parts of musical science which are commonly treated under the separate heads of Melody and of Counterpoint; and that many things usually reserved for subsequent explanation axe introduced, as it may seem, prematurely. Should he find, also, that some points on which musical theorists are not agreed, are put in a dogmatic form, it may be hoped he will attribute this, not to ignorance of, or indifference to, the opinions of others, but to a conviction that beginners should not be distracted by the consideration of opposite theories, and that, as a consequence, all discussions on disputed points should be kept out of elementary books.* The student who is desirous of mastering the contents of the following pages should come prepared for the task, not only by the possession of some theoretical knowledge, but also of some practical skill. He must be familiar at least with the treble and bass staves; with the construction of major and minor scales, and the relations of one scale to another ; with the nature and names of the various musical intervals; and, in short, with whatever may be classed under the name of the " accidence" of music. Moreover, he must have some idea of, or some means of ascertaining, "the sound of what he sees;" and — inversely — some power of expressing the effect of what he imagines. It is difiicult to conceive any means by which this sympathy of eye and ear can be attained excepting singing or playino- in concert with others, or the practice of an instrument like the pianoforte from which many different sounds can be produced at the same instant. Considerable proficiency in the art of music has been often attained by persons who have had little or no knowledge of the science ,- or, more properly speaking to whom the neglect of study has been partially supplied by favourable organization or that indirect culture which, bemg unconsciously received and therefore never taken into account, is often mistaken for it. But to pursue the science of music without reference to the art would seem, if not altogether a profitless occupation certainly a very laborious and uninteresting one. The musical student must begin —as he should go on— with thp consideration of what is practical; he must collect his facts before he can theorize upon them. Of what avail can it be to inquire why this combination or that progression is pleasing to the ear, unless he have • In one case has this ]ule been violated. See Chap. XXII. (Third Edition.) PREFACE. V ascertained, or can ascertain, for himself that it is, or that it is not so ? — It is from the neglect of this preliminary training of the ear (hardly possible without training of the voice or the hand) that so many, especially of those who begin its study late in life, fail in acquiring any real acquaintance with, or living interest in, music. Dealing with symbols of whose powers he knows nothing, the mere theorist in music is in a position akin to that of an artist painting on porcelain — ^ignorant of the fact that his colours will come out of the furnace other than they went in. Music has a body as well as a soul ; and we shall form but an imperfect acquain- tance with her whole being, if we study the one without reference to the other, J. H. March, 1852. The reprint of this work has afforded an opportunity for revising the text, and for making several alterations in the examples. A copious Index has also been substituted for that appended to the First Edition. A series of " Exercises to accompany" the foUowiag Grammar is published in a separate volume. J. H. August, 1853. The demand for a Third Edition has presented a second opportunity for making such emendations as the experience of another five years has shown to be needed. In the body of the work these have not proved many ; but the last three Chapters ■ — embracing a very difficult and important part of the subject of the work — have been entirely remodelled. J. H. N'ovemher, 1858. CONTENTS. OHlfTBB PAGH I. The Harmonio Chord 1 II. Intervals — Consonant and Dissonant 3 III. The Triad and Common Chord 4 IV. Arrangement of the Triad . . . ^ 6 Y. Figured Basses 8 VI. Motion of Parts 10 VII. Connexion of Chords 14 VIII. Sequences 17 IX. Resolution of Dissonances 18 X. Discords by Suspension 20 XI. Inversions of the Triad 23 XII. Suspensions on Inversions of the Triad 27 XIII. Fimdamental Discord of the Seventh 30 XIV. Eesolution of the Fundamental Discord of the Seventh 33 XV. Suspended Eesolution 37 XVI. Discords by Suspension on Fundamental Discords 40 XVII. Inversions of the Discord of the Seventh 41 XVIII. Licences in the Eesolution of the Seventh 47 XIX. Interrupted Resolutions of the Seventh 51 XTC Changes of Root on a Single Bass Note 53 VUl CONTENTS. CHAPTER rk»M XXI. Fundamental Discord of the Ninth 55 XXII. Chromatic Intervals 57 XXIII. Discord of the Diminished Ninth 59 XXIV. Inversions of the Discord of the Ninth and Seventh 60 XXV. Chromatic Intervals 66- XXVI. Chromatic Harmony .68 "XXVII. Pedal Points 71 XXVIII.* Cadences or Closes 72 XXIX. Progression of Fundamental Basses 75 XXX. Modulation 77 XXXI. Rhythm ....,- 78 XXXII. Harmonizing 80 * The attention of the Teacher is especially directed to the note in p. 47, referring to the study of these last Chapters. GRAMMAR OF MUSICAL HARMONY. CHAPTER I. The Harmonic Chord. 1. All sound results from vibrations communicated to the air by some disturbing force. Sound is musical or otherwise according to the regularity with which such disturbing force is exercised. 2. The modes by which musical sounds are produced and controlled^ though susceptible of infinite modification, may be classed under two heads : — 1st, wind instruments — pipes through which air is forced^ and which produce grave or acute sounds as the pipes are large or small; 3ndly, instruments oi percussion, the gravity or acuteness of whose sounds depends on the size, weight, or tension of the material of which they are composed. The single law of sound which for our present purpose it is necessary to understand, is best explained by reference to a,. string fastened at both ends. 3. A simple, unmixed sound can never be maintained for more than an instant. Every principal sound generates others which, though often inaudible, and never heard with the same force as their generator, no less certainly exist, and that in infinite number. Fig. 1. 4. Suppose a string of a certain length and thickness gives a sound called Do. For an instant after it has been set in vibration, it sounds that Do only; then, in addition, though more faintly, the 8™ above; then the (perfect) 5^'^ to that 8™; then the double 8™; then the (major) 3'^, the S**", and the (minor) 7"" to that double 8™; then the triple 8™; then the 9*^ to the double 8™; then the 3"> and 4'" to the triple 8™; and so on, ad infinitum. ^ So that when a violoncello player draws his bow across the lowest sti-ing of his instrument, he produces not only the sound literally due to that string, but all the sounds in fig. 1. 5. Subordinate sounds thus unconsciously produced, are called harmonics to the prime, or lowest sound. The combination of a prime and its harmonics is called an harmonic chord. 6. Now it is found that sounds identical with those in an harmonic chord may be produced artificially, by dividing the string which gives the same prime into aliquot parts. For if a string thirty inches long gives the lowest Do in fig. 1, G. M. H. B -^- m 2 THE HAEMONIC CHORD. [Chap. I. i of it (fifteen inches) will give Do, the 8™; f of it, Sol, the (octave) b*^; 4- Do, the double 8^«; J- Me, the 3^"; ^ /So^, another S""; f Si\>, the minor 7**; i Do, the treble 8^«; ^ i?e, the 9*''j -^V Afi, the 3rd ; -jV -Fo, the 4* ; and so on. {Compare figs. 1 anrf 2.) /■tff. 2. The notes and fractions marked * are not mathematically in strict accordance ; i. e., the sounds recognised by uniyersal consent as the minor 7"" and perfect 4"" to Do, are not produced by precisely ^, and precisely -jlj- of the string. 7. This artificial arrangement partially accoimts for the phenomenon of har- monics. It is evident that while a string produces one sound (the prime), it vibrates during its whole length, and that as soon as the octave is heard, each half of the string vibrates separately ; in fact, that divisions like those indicated above are made by Nature, ad infinitum. Fig. 3. + The ruled line in fig. 3 represents a string at rest ; the dotted lines indicate the directions which the string would take when sounding the prime, its 8'°, and octave 5*. The points of intersection (marked in fig. 3) are called nodes. 8. Harmonics, up to a certain point, are imitated in the construction of the organ, the peculiar fulness in the quality of which instrument results chiefly from this imitation ; the term " full organ" being apphed to the combination of various harmonic " stops" with those producing primary sounds. The further consideration of this subject belongs rather to natural philosophy than to music; but the necessity for the foregoing explanations will be found in their practical application to what immediately follows. CHAPTER 11. Intervals — Consonant and Dissonant. 9. Sounds are consonant (fit to be sounded together) with one another, according to the order in. which they are generated in an harmonic chord. As harmonics become more remote from their prime, they become less perfectly consonant with it or with one another ; then, dissonant ; and, finally, their relation ceases to be appreciable in any musical system. 10. The relation of two different sounds one to another is called an interval. As musical sounds are consonant or dissonant with one another, so are the intervals which they form said to be consonant or dissonant. 11. The consonant intervals are the octave, the fifth, and the third; with the inversions of the two last, the fourth and the sixth. The dissonant iatervals are the seventh and the ninth ; with the inversion of the former, the second. 13. The ninth does not admit of inversion. 13. The imperfect fifth and its inversion the pluperfect fourth are anomalous, being, though essentially dissonant, sometimes treated like consonant intervals. 14. Consonant intervals are further divided into perfect and imperfect. 15. The perfect consonances are those found between the sounis first generated in the harmonic chord — viz., the octave, the fifth, and its inversion, the fourth. The imperfect consonances are the third, and its inversion the sixth. 16. Examples of all these intervals are contaiued in the harmonic chord, either between the prime and the harmonics or between one harmonic and another. Fig. 4. Consonant. Dissonant. Anomalous. 33! feo: -^- :§: ?^ ?^ o o -^- -^ XX T~T xz TT xx O Maj.&Min. Maj. &Mm. Octave. Kfth. Tourth. Thirds. Sixths. Perfect, Imperfect. Seventh. Second. Imperfect Pluperfect Ninth. Kfth. Fonrth. 17. In an harmonic chord consonances are generated before dissonances, and perfect consonances before imperfect. {Compare figs, i and 4.) CHAPTEE III. The Triad and Common Chord. 18. From the three notes of different names first generated in a harmonic chord is formed the simplest of musical combinations, the triad — a bass note with its 3"^* and 5*''. When the 8™ is added, the combination is called a common chord. By the term hasa is here meant the lowest part, whatever be its pitch, or on whateyer stave it may be written. Fig. 5. Fig. 6. TT" S -^- 19. A common chord contains none but consonant intervals. Fig.T. 331 -^ "TT" -^- -^ :^ \S J <■ > «.' -e- o -- '"»• < > y — V /— \ <: > » )' <■ ■) < > < ) • L MMI^IWWXP CHAPTER iV. Arrangement of the Triad. 27. The sounds of a triad — still more of a common chord — admit of much variety in their arrangement. Since, so long as a combination consists exclusively of S^ S*"^ or 8^^ to a bass note, it is still a common chord, let those notes stand in what relation they may to the bass or to each other, or be their number ever so great. -^ HE -^ HE JZi. Fig. 13. 3ZZ -^ O ■ O H -^ xx TT -^ SIE HE X3IIO: HE HE -nr-c^ HE -^ s TX HE S HE HX HE © HZ Of the chords in fig. 13 some consist of four notes, some of more, and some of less ; moreover, some are well arranged, some badly, some indifferently ; but they are all equally common chords, or triads, of Do. The principles which guide us in our judgment of these chords must be deduced from the harmonic chord. =P m 28. As the eye passes up fig. 14, (the harmonic chord,) it , „ ^y- 14. will be perceived that the notes lie nearer together; that the largest intervals are at the bottom of the chord and the smallest at the top ; moreover, that this diminution of the intervals is gradual, and that there is nowhere any disproportionate hiatus. We have first an octave, then a fifth, then a fourth, then a major third, then two minor thirds in succession, then three major seconds, and then a minor second. " ^ 29. In writing chords, of whatever kind, the arrangement of the harmonic chord should be imitated as far as possible. The lower notes should be separated by the largest intervals, and the diminution of the intervals should be gradual. In fig. 15 this rule is more or less strictly observed; in fig. 16 it is altogether disregarded. Fig. 15 91 -^ JOT H3: <~> T-r -^- ~Ci Hz: -^ jCC - ~cr- -^>- iB: 23: S -^ "ry -^r Fig. 19. BE 122: "C7- ~ <■ > < > < > O Compare severally a, and 6, and c, in figs. 18 and 19. 33. Lastly, in arranging chords for fewer than four voices (and occasionally from other causes) we must of necessity omit some of the notes due to a complete common chord. In the choice of these notes Nature wiU not assist us ; but ex- perience gives the following rule, which, though apparently contradictory to the " last, will be seen eventually to be perfectly consistent with it, and founded on the same principle. 33. Omit the 8™ (to the root) rather than the 5*^, and the B*'' rather than the 3"> In fig. 20 this rule is observed ; in fig. 21 it is violated. abed abed Fig. 20. -^ 221 -^ -^ -^>- ^ ~g2- 321 rcj ~<3~ 221 ■~ c_> < > ig. 21, <> <> < > < > Compare severally a, b, e, and d, in figs. 20 and 21. 8 CHi PTER V. Figure d Basses. 34 Musicians use a kind of "short-hand," wherein the intervals which the notes of a chord form with its bass, are expressed by figures. A bass so accom- panied is called a figured hass, or thorough bass; i.e., a bass written throughout a composition, in such a way as to indicate (partially) the general effect. 35. Thus a bass note which is to be accompanied by a common chord (its 8™ 5^ and 3'*) is figured e or ^ or even 3 ; the highest number usually at the top. The common chord however (as its name would imply) is so much more often used than any other single chord, that, save to contradict other figures before them, the above are seldom written ; it being understood, in thorough bass, that a bass note without figures is to bear a common chord — of any number of notes in any position. Thus fig. 22, or any other form of the chord of Do, is implied by flg. 23, fig. 24, or fig. 25, and still more often by fig. 26. F'S- 22. Fig. 23. T7' "TT" Fig. 24. 331 5 3 Fig. 25. "g:r- Fig. 26. "TT^ The figures may be placed over or under the bass notes, indiflferently. 36. When accidentals are to be introduced into the chords, the figures must be preceded by accidentals (or otherwise modified) accordingly. In the case of a common chord, the interval to be altered is often the only one marked at alL More- over, the 3^'^ requires so much more frequent alteration than any other note of a chord, that the accidental is usually put without the figure to which it refers. 37. Thus I, or b, or ^, under or over a bass note, means jf3, or b3, or 113; that the 3^ (from the bass note) is to be made sharp, or flat, or natural. iFig. 27.) No interval but the 3"* is ever thus implied by an isolated accidental Fig. 27. ^^ ^fe=@ ^ ~CS — C5" QE -O — ^ ■ O O I' n Chap. V.] PIGUKED BASSES. Fig. 28, 38. A short line drawn obliquely across the right extremity of a figure indicates that the note corresponding with it is to be raised a semitone. Thus g; is a contraction of 1 5, ify. 28), or, contra- dicting a flat, of tl 5 ifig. 29.) Fig. 29. -^- C5~ :^ ^ fcitt ( > 321 -^ & \> In old figured basses, the elevation of a note a semitone is often indicated by a sharp, although the particular note referred to is really to be made natural — in contradistinction to a preceding _/?a«. Fig. 30. Fig. 31. 39. It is not usual to express alterations in the 8™, which must be made perfect {fig. so), unless expressly marked otherwise Cfig. 3i.) "t I fr J -;^ S ZQ_ #« rrif ( fi f f iiiiii fwiri mnn iw ftu. *m .»\ a.if.i CHAPTER VI. Motion of Parts. 40. Continuous harmony may be produced either by the combination of several instruments capable of sounding but one note at a time, (such as the human voice, the oboe, and others,) or from one instrument capable of sounding many notes at a time, (such as the organ and the pianoforte.) In a series of chords arranged for voices, the particular notes sung successively by each individual voice are said to form a part ; and although with equal propriety we might speak of the individual parts in continuous harmony performed on the organ or pianoforte, such parts are less easily discriminated by the ear or the eye. The science of harmony is most con- veniently studied, by supposing, at first, all successions of chords to be intended for performance by voices. The examples which immediately follow are in four parts, which parts, for the present, will severally be spoken of as the Soprano, the Alto, the Tenor, and the Bass. 41. When two or more voices sing the same notes in two or more following chords, they are said to sing in unison. The unison of two or more different voices is forbidden in music of any definite number of parts ; since if two out of fotir voices sing the same notes in following chords, not only are the (supposed) four parts reduced to three, but an undue prominence is given to the one part thus doubled. Thus fig. 32 begins and ends in four parts, but at * * there are only three; because the Bass and Tenor sing the same notes in two following chorda. Fig. 32. m Fd=- J |.l o ll .f^ 'r - T^° \ ' i^T^ J 2zr ? 3D -^ J- n 33 23 :ni -o- :x3i »>. Chap. VI.] MOTION OP PARTS. 13 55. Moreover, two parts moving for any length of time in consecutive intervals of exactly the same kind, be they what they may except octaves, give an impression of, and often are in two different scales. Fig. 44. O < > -^ 123; -^ 33lfe <~> "C5" -O- <> Q TT" o <„>^_S_o - 33 XT' ■ o Q - Fig. 46. The upper part of fig. 44 is the scale of Sol; that of fig. 45, of Fa; that of fig. 46, of Mi; while the lower part of all three is the scale of Do. More convincing than argument will be any attempt to sing or play these passages, the effect of which (of the last especially) is abominable CHAPTEE VII. Connexion of Chords. It will be remarked that the two chords in fig. 37 hare no notes in common; not one note in the first chord is repeated in the second. Mi, Sol, and Do are the 3"" 5"" and 8'"" to Do ; Fa, La, and Be, to Be. 56. The chords which follow one another with the best efifect are generally those which contain one or more notes in common; such common notes being said to connect together the combinations of which they form part. Thus, ia fig. 47 the 8* of the first chord serves as the 5* of the second ; the 8* and 3"^ of the second chord as the 3"^ and S*"" of the next, &c. The common notes are tied. Fig. 47. p^ e l^ TT P -^ 57. Successions of unconnected chords (as of the chord of Do by that of Re in fig. 37) are exceptional ; being peculiarly susceptible of consecutive fifths or octaves, always somewhat harsh, even when free from positive error, and generally difficult to sing in some one or more progressions. 58. When two notes of the same name and pitch occur in two following chords, it is desirable that they be in the same part, (i. e., be sung by the same voice,) in both chords. In fig. 57 nearly every one of the chords is connected with that next to it by a common note. The connexion in each case is indicated by a tye. 59. Wben two notes of the same name but of different pitch occur in two following chords, it is necessary that they be in the same part — i.e., be sung by the same voice ia both chords. m Fig.iS. znsi -oi — ^- 35: "f:^ not Fig. 49. ^ 23: 60. In fig. 49 the Mi l> of the Soprano part of the second chord is said to stand in " false relation" to the Mi ^ of the Alto part in the first. False relations of this kind were allowed by the old masters; possibly from the difficulty found in singing the chromatic semitone. {See fig. 48.) Chap. Vn.] CONNEXION OF CHORDS. 15 61. Harmony of wMch any individual part contains many large intervals has always an effect more or less disjointed; large intervals, too, in rapid succession are more difficult to sing than small ones. As a rule, therefore, — 62. In continuous harmony, the parts should move mostly by small intervals ; large intervals being introduced sparingly, and generally in not more than one part at a time. 63. Kgs. 50 and 51 consist of the same two chords. The effect of the former, though consecutive octaves and fifths are avoided, is disjointed, and the parts (especially the Alto) are difficult to sing. On the contrary, the effect of the lattei is good, and the progressions are easy ; because each part moves to the note of the second chord which is nearest to the note it has just quitted in the first. Fig. 50. Fig. 51. ^^ "T Fig. 52. ^- xx -^ i ■i < • — 1 T- i > — ©1 _ 64. In a mere change from one position to another of the same chord {fig. 52), Httle difficulty will be foimd in singing large intervals. They shoidd, however, be used sparingly, even in this case. Large intervals are found more often, and are generally used with better effect, in the Bags than any other part ; indeed, in successions of common chords they are unaToidahle. 65. The pluperfect fourth or tritone, though not a very large interval, should be avoided in the progression of parts, on account both of the difficulty of singing it, and of its somewhat harsh effect. Its inversion, also, the imperfect fifth, should be used sparingly. Fig. 54 is to be preferred to fig. 53 ; and the progression of the Tenor part in fig. 55 is objectionable. S Fig. 53. P 52: TT Fig. 54. -^ <> ^ ^ -^- 2ZE -i&- -^ T~r Fig.i >5. < > n ^— ^ :\<. <^'^ <~. 1 i t 16 CONNEXION OF CHORDS. [Chap. VIL 66. Parts are allowed to cross one another ; i. e., the Tenor may rise above the Alto, or the Alto above the Soprano. {See fig. 56.-) No part, however, must faL below the Bass ; unless, indeed, the part so falling is qualified to take the place of the Bass — the lowest part. Fig. 56. -©f ^i^^ 2± -& -^ > / ^ Q | xi 3ZI -^- 33 -Or -0| XX X3I 3Ii: "TT- In fig. 57, the rariouB rules and recommendations giren in the foregoing chapter are generally observed. u Fig. 57. d -tTTT- ^ Z2: -^ ^^ -^ ^ TV l °l ' tt' ° l ^^ ' iin S3: b5 67. The laws which regulate the influence of accidentals on the stave, apply equally to figuring. In bar 5 of fig. 57 the minor S^ to the second bass note {Do) is not expressed in the figuring, because it has been already lowered a semitone as the 8* to the first note o/^Ae same bar {Mi b). " It is not usual to express alterations in the 8" " (Par. 39.) 17 CHAPTER VIII. Sequences 68. By the repetition of the same succession of intervals on different notes, a sequence is produced. In each part of fig. 58 eyery alternate note rises or falls by the same interval; the Bass hj fourths and fifths, the Tenor by seconds, the Alto by seconds and thirds, and the Soprano by thirds, sxidi. secpnds. Fig. 58. ^ -& ^ 321 -& ^ ^ 7^ ^B^ :^^ -^- 69. A sequence may be tonal or real. n 70. In a ^ona2 sequence the intervals are perfect or imperfect, major or minor, as they present themselves in the scale. Fig. 58 is a tonal sequence; the progression of the Bass in the first complete bar is by an imperfect fifth; in the next bar by a perfect fifth. The first interval in the Soprano part is a minor third; the next but one, a major third, &c. 71. In a real sequence the respective intervals are exactly alike, involving generally very rapid modulation. ^ By making fig. 58 a real sequence (fig. 59), we shall modulate in four bars from Do into Do b. Fig. 59. m f^ I J b J' ^^ m zzc?: J2c^: ^P=t^^^ Tonal sequences are much more frequently used than real. 72. When a bass part, or any portion of a bass part, moves in sequence, every other part should move in sequence also. G. M. H. S 18 CHAPTER IX. Resolution of Dissonances. " The dissonant intervals are the seventh and the ninth; with the inrersion of the former, the second," {Par. 11.) " The ninth does not admit of inversion." (_Par. 12.) " The imperfect fifth and its inversion the pluperfect fourth" are also " essentially dissonant" intervals. {Par. 13.) 73. By a dissonant interval is not meant anything of necessity harsh, or dis- agreeable to the ear ; but, technically, a combination on which the ear cannot rest, and which therefore suggests another combination, to foUow it. 74. The progression of two parts separated by a consonant interval is, to a certain extent, a matter of taste or choice ; in general they may make contrary motion, oblique motion, or similar motion. But a dissonant interval must be resolved; the parts between which it is found must make certain definite pro- gressions in relation one to another, in order that the ear may be relieved from the feeling of suspense to which it uniformly gives rise. 75. Dissonant intervals are mostly resolved by contrary or oblique motion, one of the notes invariably moving one degree. 76. Of two parts separated by a seventh, the upper should fall one degree, while the lower may keep its place {fig- 60), rise a fourth {fig- 6i), at fall a fifth {fig- 62> Fig. 60. Fig. 61. Fig. 62. -^ — ^ — — ^ — ©- As a fifth is the inversion of a fourth, figs. 61 and 62 are theoretically identical. 77. Of two parts separated by a second, the lower should /oW one degree, while the upper may keep its place {fig- 63), rise a fourth {fig- 64), or fall a fifth {fig. 65 -Q q 8 —^ 0—5— Q q ^er Fig. 66. < •> c? -^ The last rule is but a repetition of the one before it, since a second is the inversion of a seventh. In fig. 65 the parts cross one another {Par. 66) ; Fa falls to Mi, and Sol to Do. Chap. IX.] RESOLUTION Or DISSONANCES. 19 78. Of two parts separated by a ninth, the uj^er should /a// one degree, while the lower note may keep its place (,Jig. 67), rise a fourth ifig. 68), ovfall a fifth (Jig. 69). Fig. 67. Fig. 68. Fig. 69. 221 O ^^ ^ — — ^— — ^ 79. The mm^A must he carefully disthiguished from the second; since though found between notes of the same name, those intervals are not inversions of each other. " The ninth has no inversion." (Pan 12.) This caution is the more necessary, because the second, like every other interval, is sometimes made compound, (i. e., increased to an octave second,) (/?. 66,) while a ninth can never with propriety be reduced to a second, since two dissonant notes cannot be resolved by melting into one. Fig. 70. Compare the resolution of the compound (or octave) second (fig. 66) with that of the ninth {figs. 68 and 69.) Also the resolution of the /[ ninth (Jig. 67) with fig. 70, the first interval in which is not a ninth, vj) '■■^Qcp^- but a second improperly resolved. ^ 80. A second can always be made compound, {i.e., increased to an octave second j) but a ninth must never be reduced to a second- 81. A dissonance should always be resolved; it must sometimes, also, be pre- pared; i.e., the note which causes it must appear in the combination immc diately preceding. 82. A dissonant interval is therefore liable to three processes — preparation percussion, and resolution. In the following examples, the dissonances are prepared, as well as sounded and resolved Fa, the dissonant note, appears in the Jirst as well as the second combination of each. Fig. 71. Fig. 72. Fig. 73. cT^ .. .Ci_ my o ^e_ ^j <>o ^— t > o Q - Fig. 75. Fig. 76. £3_ ^^^ -^> 20 CHAPTER X. Discords by Suspension. 83. A combination in which is contained a dissonant interval is called a discord; as one composed only of consonant intervals is called a concord. 84. By prolonging a note not common to two following chords from the first into the second, we produce a discord by suspension. A discord by suspension (as its name might imply) must be prepared (.par. 81), as well as sounded and resolved. 85. In fig. 77, the chord of Fa is followed by the chord of Sol ; but in the Tenor part the note Do (not common to the two chords) is maintained during, half of the time due to the chord of £10/. Thus a dissonant interval (a second) is produced between Do and Re ; whereby the bass note Sol is made to bear a discord by suspension ; the dissonant note (Do) being prepared in the chord of Fa, sounded in the first half of the chord of Sol, and resolved in the second half. 86. Again, in fig. 78, the chord of Fa is followed by the chord of Sol; but in the Soprano part the note La is maintained during half of the time due to the chord of Sol. Thus a dissonant interval (a ninth) is produced between this La and the Bass note (Sol), which, there- fore, bears a discord by suspension; the dissonant note (La) being prepared in the chord Fa, sounded in the first haK of the chord of Sol, and resolved in the second half. 87. A double discord by suspension is produced by yvolonging two notes not common to two following chords, from the first into the second. Thus, in fig. 79, the two suspensions in figs. 77 and 78 are combined. Fig. 77. ^ -^>- T-y FS=S | J-^-^A "<-> Fig. 78. J- X2 -^ m -^ <_> ±± Fig. 79. r^ -ri- -^ ~C5" S3I -ci 4 3 88. A discord by suspension is distinguished from any other species of discord by its place in a bar ; being sounded on an accented beat, and resolved on an unaccented beat. 89. The resolution of a discord by suspension is usually made by the dissonant note taking the same progression it would have taken had there been no suspension. Thus, in fig. 77 the progression of Do is only delayed, not altered. This rule, however, explains nothing : for the Do does not fall to Si, because it would probably have done so had there been no suspension, but because the ear requires relief from the dissonance formed bv Do and Re. Chap. X.] DISCORDS BY SUSPENSION, 21 90. The agreeable eflfiect of a discord by suspension results from the delay of the dissonant note in making the progression expected of it. A dissonant note, having been prepared, must be sounded and then resolved. Suspense and certainty cannot be simidtaneous : it is manifestly absurd that percussion and resolution should take place at the same instant. 91. A dissonant note and the note by which it is to be resolved must never be sounded together. 92. Prom a discord by suspension, omit the note by which the dissonance is ta he resolved ; and, except in the case of the ninth, even the 8™ to that note. In fig. 80, the combination at * is intolerably harsh from the percussion of Do, the dissonant note, with Si, the 8" of the note on which Do is afterwards resolved j while the combination at f contains two Si's — major 3^ to the bass. In fig. 8 l,the dissonance at * is not a ninth, but a second improperly resolred. (_Seepar. 79.) Fig. 80. Fig. 81. -^>- gL=iJ 4 3 9 8 Compare figs. 77 and 78 with the abore. 93. A dissonance should be prepared, sounded and resolved in the same part, — the dissonant note and the notes which prepare and foUow it should be sung by the same voice. In fig. 82, the dissonant note. Do, is prepared in the Temor part and sovmded in the Soprano. In fig. 83, the dissonant note, La, is prepared in the Alto part, and sounded in the Soprano. Fig. 82. ^ Fig. 83. "C5~ *• T d J- ^s "nrr- -^ -a 4 3 Compare figs. 77 and 78 with the abore. 94. In order to prepare a discord by suspension (as well as from other causes) it becomes necessary sometimes to alter the position of the chord immediately preceding it. This may be done by writing two chords to a single bass note, instead of one (.see Jig. 84), but more elegantly by writing two notes instead of one in a single part (.see fig. 85), which is made to cross the other. (Par. 66.) 22 DISCORDS BY SUSPENSION [Chap. X. Fig. 84. Fig. 85. ^m ^ fi: The relations of the upper parts of a musical comhination to their bass are expressed by figures placed under or over that bass. (Chap. F.) 95. A straight line after a figure indicates that the note due to that figure is to be continued, whatever changes may be made in the other parts or even in the bass of the combination in which it first appeared. The passages in figs. 77, 78, and 79 a.re fully and exactly expressed as follows. Fig. 86. Fig. 87. Fig. 88. 3 8 3 9 8 3 9 8 8 5 8 5 — 8 5 5 4 3 5 3 5 4 3 96. Of these figures, all that refer only to the notes of the triad are superfluous (par. 35) ; those only which express the suspended notes being essential : viz., 4 3 to the second bass note in fig. 77; 9 8 to that of fig. 78 j and | § to that of fig. 79. Fig. 89 contains examples of the suspensions treated of in the foregoing pages: the rules laid down are strictly obseryed. ,i J, j , I , , Ijo Lj- ^ I , I J ^-4 TT ' ^ *°i I ^^j ^f^ ^^ffrW^ M- JH ^ ^ tin £98 98 98 98 ^ 4 3 4 3 rs OnX3 2X3 HE 9 8 4 3 ■■■**■■!*■■ ■***■* m^^^m^^m^m^^^g^^- g.^ — inH mmnrin.rtAAjT-nj i j i 23 CHAPTER XI. Inversions of the Triad. 97. The different arrangements of wliicli the upper notes of a chord are susceptible are generally described as changes of position. These changes, as we have seen, are numerous, and afford much variety of effect to the combinations in which they are made. This variety is greatly increased by inversion ; wherein one or other of the upper notes of a chord being substituted for the root, becomes the bass. Thus, of a combination containing no sounds but those found in the triad of Do, Mi or Sol may be the lowest. (^Compare Jigs. 90, 91, and 92.) Via. 90. Mg. 91. Pin. 92. ^^ -^>- -<^- m TT- T~y "TT" -^ 98. The prime or root of a chord is therefore not, of necessity, the bass. The bass of fig. 91 is Mi, of fig. 92, Sol; the root of both chords is Do. Of fig. 90, Do is both bass and root. 99. When the 3'^'^ from the root of a chord becomes the bass (as in fig. 91), the first inversion is said to be used. 100. It is " understood that a bass note without figures '-^'^' ®^' ^^- ^^• is to bear a common chord." (.Par. 35.) Were the bass of fig. 93 presented alone, the common chord of Mi would be due to it. Some indication, therefore, is wanted to show that the chord in fig. 93 is to be written or played, and not the chord of Mi. On comparing fig. 93 with fig. 94 (the triad of Mi), it will be found that the differ- ence between them lies in one note ; that in fig. 93 there is Do, a sixth to the bass, and in fig. 94, Si, a fifth. 101 . This difference is expressed under fig. 93 ; § implying that instead of the 5*^ and 3^^ to Do, the 6*'' and 3'"* are to be written. 103. As the chord of the Sixth differs from the triad only in one interval, it is generally sufficient to express that interval only, in the figuring. The 3"^ to the bass, being common to both chords, is seldom marked. 103. Thus when we find a 6 under a bass note, we know at once that the bass is not the root ; and, in the present instance, that it is the third to the root. "cr c^ 24 INVERSIONS OF THE TKIA.D. [Chap. XT. 104. For the arrangement of chords with the root in the bass, two rules have been given: — "Double the 8" rather than the 5* and the S* rather than the 3'S especially when the 3"* ip major." {Par. 31.) « Omit the 8" rather than the 5% and the 5"^ rather than the 3'"." {Par. 33.) 105. These rules, " apparently contradictory," {par. 32,) are based on the same principle :— that the notes of a chord may be multiplied or omitted in pro- portion to their importance or effectiveness. 106. The 8™ is the least effective note in a chord, and therefore when doubled is less obtrusive, and when omitted more easily spared than any other note. Whereas the 3"^ (especially when major) is the most effective note in a chord, and therefore when doubled is more obtrusive, and when omitted is less easily spared than any other note. 107. Of the chord of the Sixth, the bass is itself the S^ from the root ; and the S'* and 6** from the former are 5*'' and S"- to the latter. I^. 95. See fig. 95, where Mi, the bass, is the 3'^ from the root Do (indicated by a dot). While Sol, the 3'S and Do, the 6"" from the bass, are the 5"" and S'" from the root. The rules in par 31 and 33, therefore, slightly modified, may be applied to the first inversion of the triad, thus : — S T7~ 108. In writing the chord of the Sixth, omit the 8™ to the bass, (especially if the bass be a major 3^ from the root,) and double the G"* rather than the 3^. Of the three following, fig. 98 is preferable to fig. 97, and fig. 97 to fig. 96. Fig. 96. Pig.J7. Fig- 98. -TT Fig. 97. ~r-T- -^ -©- -^ m ~r-r XX nzn 6 6 6 In fig. 102, several chords of the Sixth are introduced ; the 8" to the bass is omitted from all of them, and the 6"" is generally doubled rather than the 3'*. J , I rJ Fig 99. 3ii: jz^a^ CT^ -^ IZL -^1^ 3Zf ^W ^fA -^ T^T^ -^ m -Or zx ^ "T HE t i Chap. XI.] INVERSIONS OF THE TRIAD. 25 109. When the 5* from the root of a triad is the hass, the second inversion is said to be used. Fig. 100 is an example of the second inversion of the chord of Do. Fig. 100. m jCSI Fig. 101. ^e^ "TT- 110. Were the bass of fig. 100 presented without figuring, the chord of Sol woidd be due to it. On com- paring fig. 100 with the triad of Sol {fg. loi), a difference of two notes will be found. In the latter there are Re, a Z^, and Si, a 3"* to the bass ; in the former, Mi, a 6"", and Do a 4"' to the bass. 111. This difference is expressed under fig. 100; 4 implyiag that instead of the 5*^" and 3"^, the &^ and 4«' to Uie bass are to be written. * 112. Thus when we see % under a bass note, we know that the baas is not the root, but the 5"* to the root. Fig. 102. 113. Of the chord of the Sixth and Fourth, the bass is itself the 5** from the root ; and the 4"* and &^ from the former are the S"* and 3"* to the former. See fig. 102, where Sol, the hats, is the S* from the root Do (indicated by a dot). While Do, the 4'\ and Mi, the 6'" from the hass, are the 8* and 3"" from the root ^ 331 The rules repeated from pars. 31 and 33 may therefore be applied to the second in- version of the triad thus:— 114. In writing the chord of the Sixth and Fourth, omit the 8™ to the bass rather than any other note, and double the 4* rather than the 6*''. Of the three following chords, fig. 105 is preferable to fig. 104, and fig. 104 to fig. 103. Fig. 103. Fig. 104. X3I Fig. 105. "n- -et- -^ m TT- -e>- zm 115. The omission of the 8™ to the bass iu the chord of the Sixth and Fourth is recommended, not, as in the case of the chord of the Sixth, enjoined. Fig. 106. 116. I is often followed on the same bass by |. When two sets of figures are placed under the same bass note, half the time of that note would be given to one chord, half to the other. More- over, it is generally understood that the 5*'' is to follow the 6*'', and the 3'''' to follow the 4"^, in the same parts. In this progression, too, the 8™ to the bass, being the only note common to the two chords, is generally added. {See fig-. 106.) G. M. H. J=^ -e>- J ffi X2 CL 26 INVERSIONS OP THE TRIAD. [Chap. XI. In fig. 107, several chords of the iSixth and Fourth are introduced ; the 8" to the bass is omitted from moat of them. "ig. 107. A ^-U-^^ hh^ -^ ^ 3Zi: Or 3 <:±.:^ m zx: -©r 33 xn -©r 2=? "T~r HE 4 4 117. In passing to or from inversions of the triad, or of any other combination, the "fundamental progression," i.e., the progression which the root wovld take were it in the bass, is often made in one of the upper parts. See fig. 99, bars 1 — 2, where the Fa in the Soprano part falls to Do, which Do again rises to Sol; all three notes being octaves to the roots. See also fig. 107, bars 1 — ^2, where the Sd in the Tenor rises to Do; both notes being octaves to the roots. 27 CHAPTER XII. Suspensions on Inversions of the Triad. 118. " By prolonging a note not common to two following chords from the first into the second, we produce a discord by suspension." (^ ow. 84.) A note may be thus prolonged or suspended not only when the root is the bass, but when any of the inversions of a chord are used ; the suspension itself occasionally appearing in the bass'. 119. Fig. 108 is the suspension (4 3) on a root {Sol), explained in Chap. X. Fig. 109 is the same suspension on, or rather of, the first inversion of Sol; the suspended note and that by which it is resolved appearing in the bass. Fig. 110 contains the same suspension on the second inversion of the same chord. Fig. 108. rTn— 5 J. Fig. 109. <•> -^ J. Fig. 110. <'> 1^=^ -r-> I < > =ni — r ^ -^>- ^ «P. Q -&- -&- (~i -©r -^- 7 6 4 — 120. Inverted suspensions are subject to the same rules as suspensions in a direct form ; the dissonant intervals they produce being equally liable to prepara- tion, percussion, and resolution. (,Par. 82.) Observe, that in fig. 109 there is but one chord to two bass notes, each of which is figured, since the notes which are the 5"" and 2°^ to Do are likewise the 6"" and S"" to Si. Fig. Ill contains examples of the suspensions explained above. The suspension on the second inversion of the triad (fig. 110) is not much used. Fig. 111. 28 SUSPENSIONS ON INVERSIONS OP THE TRIAD. [Chat. XH. 121. Fig. 112 is the suspension (98) on a root {Sol), explained also in Chap. X. Fig. 113 is the same suspension on the first iMWmore (of /So?); fig. 114, on the second inversion. Fig. 115 is the same suspension of the root {Sol), the suspension appearing in the bass. Fig. 112. E ^ J Ei ^ ^^ "TCT" t > 9 8 Fig. 113. 3 <=* <_> -€3- 7 6 ii-i^Sr. 114. 1 1 < i < > <— 1 1 , 1 n ^ B 1 1 1 1 6 4 Fig. 115. 3Zt 3q: -^>- Tzr -• — The resolution of the second chord in fig. 115 shows that the interval between La and Si is a compound second, not a ninth. (Compare par. 79.) 122. " lu writing discords by suspension, omit the note by which the dissonance is to be resolved, and, except in the case of the ninth, even the octave to that note." (Par. 92.) 123. From aU inverted discords by suspension, it is desirable to omit the 8™ to the note by which the dissonance is to be resolved. In figs. 113, 114, and 115, the places of these notes are indicated by black dots, to show where they should be introduced, if at all. The inversions of 9 8 are, perhaps, more elegantly used in harmonj of three parts than of four. The following example is treated in both ways. Fig. 116 (o.) ^ gg k^ i 3ZZ -Gi- © 6 6 7 6 -er Ck *3:^ -^ S -ej- us -^ nr 2=o=^ 7 6 6 4 6; 4 5 6 4 2 3 7 6 6 7 6 Fig. 116 (5.) ^:= - «^ iizrir- 1^-=^ =X3= ^ HE W^m -^- ^ — ©- -©r-^ ^^^m <~> k-^ -^ S Gr-r^ X3 -€>- ZX^I ^ rx 766 76^4 5 6 76 6 76 4 ' 4 2 8 6 — 5 4 CHAP.Xn.] SUSPENSIONS ON INVERSIONS OF THE TRIAD. 29 134. Fig. 117 is the double suspension (2 §) ou a root (Sol), explained also iii Ghap, X. All its inversions are shown in figs. 118, 119, and 120. Pig. 117. ^ n u wr^ y ; V]) < i ^ '^^' r-k t ) *)• o V. I 1 Fig. 118. ^ v^ ^ -C3- 61 el €3r 6 1 6 16 4 2 3 Fig. 119 Fig. 120. sx:^ 33 ^^^ -€>- "o^ r"6 I B i I ^^ <•> < 4 6 3 I 3 The inversions of | | may be elegantly used in three parts. (Compare fig. 121, o anrf 6.) Pig. 121 (o.) y: ^^ > < > -&^ ^ C7" eE -T-rl-e^^^qFTP < ^ I f • Q l-^T^ -^ 7~ -e^r 13=0^=221 7 6 6 5 4 6 4 5 6 4 5 3 3 6 4 5 6 3 3 6 6 2 3 ^^kd A Pig. 121 (5.) . k^H X3. ? -^ Vfu i zx ? < > I < > Q I Q 7 6 6 5 4 6 45 645 6556 3 3 3 3 3 3 6 6 2 S '60 CHAPTER Xm. Fundamental Discord of the Seventh. 125. In the harmonic chord of Do (Jig. i), immediately above the second 5* (Sol), is found the minor 7* (Si\,). 136. The seventh is a dissonant interval. (.Par. ii.) "A comhination in which is contained a dissonant interval is called a discord." (Par. 83.) A discord com- posed only of sounds found in the harmonic chord is called a Jundamental discord ; that under consideration is called the discord of the Seventh. Fig. 122. ^ 137. In fig. 133 are combined ,Siib and Mi^. The former of these notes indicates a scale of at least one flat; the latter proves a scale of not more than one flat ; i. e., the scale of Fa. 138. The root of the harmonic chord (of which the fundamental discord of the Seventh is but an extract) is therefore n^t the tonic of the scale to which the notes composing it belong. A major common chord, iudeed, may be formed on the domiaant or on the subdomiuant of a major scale,, as weU as on the tonic j but the minor seventh can only be combiaed with the common chord on one of these notes — ^the dominant. 139. In treating each note of the natural scale (or any scale of like construction) as the bass of a discord of the Seventh composed only of such sounds as are found in the scale itself, we shall produce but one chord exactly like fig. 133, i. e., combining a major S^ with a minor 7*^. This one chord will be formed on the dominant. i^. 123 Perfect Chords. 3 4 :S: Imperfect. 7 # Major 3'* Minor S"" Minor 3"^ Major S'* Major 3** Minor 3"i „ 7"^ „ 7"^ „ 7«^ „ 7"" Minor 71^ „ 7»^ Minor 3"" „ 7tt 130. In fig. 133 are exhibited no less thau/oMr different kinds of discord: — On the 1°' and 4"' a perfect majoi shord with a major 7"" 2"^ 3"^ and 6'" „ minor „ „ minor 7* 7"' an iwperfect „ „ „ „ 7* » 5"" (only) a perfect mqjor chord with a minor 7*" Chap. XIII.] FUNDAMENTAL DISCORD OP THE SEVENTH. 31 131. This last combinatioii governs, or decides th6 scale ; which none of the others are competent to do. Since of fig. 123 — Chord 1 may be formed on the 4"' of the scale of Sol, 2 « » gth Fa, 3 y> » 6th Sol, 4 » }) 1* Fa, 6 i> J3 3rd >J >f » 7 1) » 2nd ff ii La minor Whereas Chord 5 can only be formed in the scale of Do, and that on the 5"" sound; which in all scales is called the dominant, because the discord peculiar to it contains two sounds (its 2t^ and 7"') which, being combined, decide, beyond the possibility of doubt, what the scale is. 132. The variable 7** of the minor mode arises from the need of a true dominant, which the minor scale in its original form would not furnish. La minor consists of the same sounds as Do major; i.e., of natural sounds exclusively; the wder alone of those sounds is different in either scale; that which was the 1*' in the latter becomes the 3"^ in the former. 133. Of such a scale unaltered, the dominant would bear a minor 3"*. Fig. 124. ^8=^* 33: ^ s ~o~ 134. By raising Sol to Soli, on the 5* of the scale, a true dominant is pro- duced, inasmuch as it has a major 3"*, and perfect 5*, and will bear a minor 7^. Pig. 126. i ^±^ # or --f 135., Remark, that the 2°'^ of the minor scale (f) bears an imperfect chord, as does likewise the 7^ (*), when made a leading note. The following are all tuajor chords with minor 7"", and conseouently their roots are all dominanta. The first of Fa, the next of Sol, &c. P of Fa. -TT -^ 7<-> b7 of Sol. &- Fig. 126. Dominant Sevenths. .of La. of Do. J ~o~ -*-- -^ -^ "cr -^- -TT- -f^ -^5- ofRe. :* d: -^- < rr T-r of Mi. ::^- 4 £31 -^>- -^>- 32 iTTNDAMENTAL DISCORD OF THE SEVENTH. [Chap. Xllii 136. The epithet " fundamental" is not confined to discords of the dominant Seventh, but is applied also to those quasi-harmomc chords which consist of a bass note with its 3"* 5* and 7^, even though the 3"* be minor, the 7* major, or the 5* imperfect. The discords in fig. 123 are all " fundamental." 137. A bass note bearing a 7* in addition to a common chord, is Jiillff 8 . g figured l- But it has been shown that the figures s are seldom used save to 3 . * contradict others. A single figure 7, therefore, is in general suflScent indication of the discord of the Seventh 138. In writing common chords, the student has been recommended (where the progressions admit) to double and omit certain notes rather than others. (Chap. /F.) The same rules, drawn from Nature, are generally applicable to the discord of the Seventh ; save that in the latter the 3"* to the root is not of such vital importance as in the former ; since if the 3"* to the root be omitted from the common chord, it then contains no imperfect consonance, whereas if the 3"" be omitted from the discord of the Seventh, there still remains an imperfect consonance between the 5* and 7^ sounds, whatever be their relative positions. ^ "TT- Fig. 128. Fig. 129. -€^ -Gf- ^ TT" 33: 7ig. 130. r-» ^-* < > 1 i ■> 1 1 1 1 Neither in fig. 127 nor in fig. 128 is there any imperfect consonance (third or sixth) ; in fig. 129 there is a third between Re and Fa, and in fig. 130, a sveth between Fa and Re. 139. In no case can the 7* be omitted from the discord of the Seventh ; but any other note may. Other considerations are, however, mixed up with the doubling or omission of notes in dissonant combinations which can only be treated in connexion with their resolution. 33 CHAPTER XIV. Resolution of the Fundamental Discord of the Seventh. " A dissonant interval must be resolved; the parts between which it is found must mate certain definite progressions in relation one to another, in order that the ear may be relieved from the feeling of suspense to which it uniformly gives rise. {Par. 74.) 140. The fandamental discord of the Seventh in its complete form includes at least two dissonant intervals — the seventh or its inversion the second (sometimes both), and the wwperfect fifth or its inversion the /^^wperfect fourth (seldom both.) {See fig. 131.) , Fig. 131. -^- -Qcy- ei :S- " Of two parts separated by a seventh, the upper should faU one degree, while the lower may keep its place, rise a fourth, or fall a fifth." {Par. 76.) " Of two parts separated by a second, the lower should fall one degree, while the upper may keep its place, rise a fourth, or fall a fifth." {Par. 77.) 141. Of two parts separated by an imperfect fifth, the upper should fall and the lower rise, each one degree. {Fig. 132.) While of two parts separated by a pluperfect fourth, the lower should ya^/ and the upper rise, each one degree. {Fig. 133.) Fig. 132. — ^ Fig. 133. -e>- S -^>- "i-T ~r~r -e>- 143. When a bass note bearing a discord of the Seventh rises a fourth ox falls a. fifth, all the dissonant intervals contained in it can be properly resolved on the following chord. Fig. 134. -^ 3Ze: -e^ -f^- xx Fig. 135. ( > ' r< JZL .o- < ■> < > Fig. 136. 3IE ■CT" -^- i > i > C ) — ^ — 1 _ In fig. 134 there are three dissonant intervals — a seventh between the Alto and the Soprano, another between the Bass and the Soprano, and an imperfect fifth between the Tenor and the Soprano. In fig. 135, there are a ^feperfeet fourth between the Tenor and the Soprano, a second between the Alto and the Tenor, and a seventh between the Bass and the Tenor. In fig. 136, there are an imperfect fifth between the Alto and the Soprano, a seventh between the Tenor and the Soprano, and another seventh between tho Bass and the Soprano. Sach of these intervals is properly resolved on the following chord. G. M. H. F 34 RESOLUTION OP THE [CHip. xrv. . 143. With one exception, the progression (or more properly, resolution) of every note in tlie fundamental discord of the Seventh is subject to rule. Fig. 137. The Bass usually rises a fourth (or falls a fifth); the its place ; the 3'''' rises, and the 7"" falls; each one 144. 8™ keept degree. The 5* alone, not forming a dissonant interval with any note in the combination, may rise or fall. It generally falls; because, by rising, it produces two 3"*^ in the next chord. (See fig. 137.) 145. The resolution of the upper parts of a discord of the Seventh entirely depends on the progression of the bass ; since if the latter were to move to any note but the 4"" above or the 5* below, the former could not make the progressions due to them. 146. Thus were Sol (the Bass of fig. 137) to move to Re {see fig. 138), the 7^ {Fa) could not fall one degree (to Mi), because Mi is not a note of the chord of Re. Neither for the same reason could Si {the Z'^) rise to Do, nor Sol, the 8™, keep its place. On the contrary,- progressions would have to be made intolerable to the ear. (See fig. 139.) Fig. 138. ^ -w Fig. 139. -^ — . — Gh- ~w- -^>- 33: ^ :S: Ji4!L ifil -e>- -^>- -^>- 147. To only one note besides that a 4* above or a B**" below it, can a bass note bearing a 7"* move with any propriety, viz., to the next note (or 2°*) above it. (See^j. 140.) This progression generally involves the omission of the 8™ from the chord of the 7*'' and the doubhng of the 3"* in the chord which follows it. It is termed (not very correctly) the " interrupted cadence.'' (See Chap. XXYIII.) Fig. 140. -^ XT -^ &M It has been shown (in Chap. XIII.) that a scale contains only one note (the dominant) which rill bear a true fundamental discord, but that that combination may be imitated, more or less imperfectly, on euei-y note of the scale. (See fig. 123.) The term "fundamental discord" is extended to those g^asi-harmonic chords ; which are, for the most part, treated in the same manner as the combination distinguished as the fundamental discord of the dominant Seventh. 148. Besides resolution, a dissonant interval admits of preparation — ^that the dissonant note be first heard in the preceding chord, and in the same part. (Par. 93.) " A discord by suspension (as its name might imply) must be prepared, as well as sounded and resolved." (Par. 84.) A fundamental discord may be prepared, but its preparation is not indispensable. 149. A discord by suspension is invariably sounded on an accented beat and resolved on an wwaccented beat — the resolution being almost always made on the Chap. XIV.] FUNDAMENTAL DISCORD OF THE SEVENTH. 35 satne root as the suspension. A fundamental discord is generally resolved on an accented beat ; the resolution being always made on a different root from the per- cussion. (Compare figs. 141 and 142.) Fig. 141. Discords by Suspension. -^ J ^m E2 ^ JZi m -TT ^ -^^ iS: J- r:^ 9 8 Fig. 142. Fundamental Discords. _ci ^ -^5- XT" lOI -©- -^- <>^ ~rq , - X3: -^ J ^^- rx ^^ ^ iSi -^ iS: iz X2I -€> <:_> c:> ifi: -^ Z3: Great variety may be aflfbrded, especially in harmony of only duction of such progressions as the above. 8 7 parts, by the intro- 153. In the doubling or omission of notes, regard must be had, in the case of a discord, not only to the effect of those notes in themselves (as in a concord), but to the possibility of resolving them, and to their influence on the following chord. It is obvious that certain notes of a discord if doubled could not be regularly resolved without consecutive octaves, while the omission of others would "mpoverish 36 RESOLUTION OF THE DISCORD OF THE SEVENTH. [Chap. XTV. the next chord. And although various licences (to be explained hereafter) are admitted in the resolution of discords, they are to be regarded rather as last resources than legitimate means. For the present, therefore — 153. In writing discords of the Seventh (and their inversions) double only the 8™ to the root, which " keeps its place" (par. 144) ; for though the 5*^ may rise as well as fall, by doubling it we produce two 3"^ in the next chord. (Fig. 148.) Fig. 148. ^ ?3r s w. iB^ -^- 331 331 154. Omit the 5* rather than the 3"^, and the S'^ rather than the 8™j for the omission of the 8™ deprives the next chord of its 5th. Fig. 149, Fig 150. Fig. 151. -^ S2: -G>- m -e>- 3zz: — — 1 f ~> -ex ..Q. r-> — © — i ^ 1 <-> — c^ -o -o. < > — ^ — 1 I_ In fig. 149, the 5'" is omitted from the discord of the Seventh ; in fig. 150, the 3"" ; and in fig. 151, the 8™. The last chord of flg. 151 has three Bos and no Sol. " In no case can the 7* be omitted from the discord of the Seventh." {Par. 139.) Fig. 152 (a.) t «. f a ^ TT ' :^ ^ ^ 3Z^ J ^ -J-U m » 231 -e^ -€^- ~r^ ^- b: Fig. 152 (ft.) gs rt -o- Ei -^- <3L-i^ -^ ?:^ *Tc> ^ ZI ^ J^ ^#^ j:3. J 1-Q— M- "r^- ex' b? 7 I 7 I -^ "T^ rrrv: 37 CHAPTER XV. Suspended Resolution. 155. The resolution of a fundamental discord is often delayed by the suspension of any of the notes composing it on the Bass of the following chord. In fig. 153, Fa, the 7"" to Sol, instead of falling at once to Mi, forms a discord by suspen- Bion (4 3) on Do. In fig. 154, Be, the 5"" to Sol, forms a discord by suspension (9 8) on Da In flg. 155, Si, the 3"" to Sol, forms a discord by suspension (7 8) on Do. ^ Fig. 163. ^ xx l^f^ r^-^ Oi xx Fig. 154. -d, — l -d-fj^ ^ d -^- XT" Fig. 155. I^ ^ Ho^-^ ~r> From the last example, we deduce a rule ; that — 156. In a discord ty suspension, of two parts separated by a Fig. 156. xuu. J« u, uisuuiu uy suspenswn, ui uwu parts isepaiaieu uy a /[ ^_ j major seventh, the upper rises one degree, and the lower keeps its ((j) place. cT ^ " In writing discords by suspension, omit the note by which the dissonance is to he resolved; and, except in the case of the ninth, even the 8" to that note." {Par. 92.) From fig. 155, the black notes are better omitted. 157. The last suspension (7 8) is most commonly used in combination with one or both of the two first (4 3 and 9 8.) :.^ Fig. 157. Fig. 158. :^r^. lo: 5f^ -en Q— ^ Fig. 159. -^ ^ :&—ct -iO- ^^^ -e*- < ) <:^_ -o- .d -J ~n~ _<:± ■^ il 33: The suspension in fig. 159 is sometimes improperly figured '*. 38 SUSPENDED KESOLUTION. [Chap. XV. Fig. 160. 158. Occasionally, an entire fundamental discord {lass as well as upper parts) is treated as a discord by suspension ; i.e., sounded on an accented and resolved on an wwaccented beat. (Par. 149.) 159. As a general proposition it may be asserted, that in passing from one combination to another, a7iy note of the former may be suspended, provided the conditions of the latter admit of that note being properly resolved. 160. Thus, the 8™ to one bass note can never prepare or be suspended as the 9* to the next, since the resolution of that 9* would involve hidden consecutive octaves. Though the bass Be in fig. 161 does not move to Do at the tame instant as the Soprano, the progressions follow one another BO quickly, that the effect is that of consecutive octaves. Fig. 161. dSM -et- 321 161. By suspension, combinations are sometimes pro- duced not in themselves dissonant, which it is still con- venient to class with " discords by suspension ;" applying to them the rule in par. 89, — that, " the resolution of a discord by suspension is usually made by the dissonant (in this case, the suspended) note taking the same pro- gression it would have taken had there been no suspen- sion.^^ Fig. 162. 162. Even the suspension 4 3 ceases to be dissonant when the 5** to the root is omitted (fig. 164) ; or when the 6"' is substituted for the 5* (fig. 165) ; since the disso- nance is not between the suspended note and the root, but between the suspended note (the 4*) and the 5*. The treatment is in no way altered by the omission of the 5*. (Compare figs. 163 and 164.) Fig. 163. ^ -^- "C5~ J¥^i Fig. 164. 311 -^>- 3 4 3 Fig. 165. ^^ -Gh -€^ 3X: 6 5 4 3 Fig. 166 contains examples of most of those suspensions; a in four, and 6 in three parts. Chap. XV.] SUSPENDED RESOLUTION. F%g. 166 (a.) 39 r^ "^1 "1^^|-^ \^ m : j <~> i>7 43 tie .7 6 4| Tsl 7 987986 98 4 3 4 3 7 7 8 4 3 Fig. 166 (5.) 1^-^- e? 3:^ E? €> 1^^ R= l^r-r^l 0> < ^ ^ Tty—Q" -^ -^ "CX -©I ~rT E3 <)^ r2 \)7 4 3 {[( 7ti4# 787 98 7 98 6' 987 4— If 4 3 4 3 7 8 4 3 40 CHAPTER XVI. Discords by Suspension on Fundamental Discords. 163. The discords by suspension of the Fourth or the Ninth (Chap. X.) may be made on Hhe fundamental discord of the Seventh as well as on the common chord : the presence of the 7"" in no way interfering with their resolution, nor their resolu- tion with that of the 7^K Fig. 167. Fig. 168. Fig. 169. gK yl o.7Tg=F ^ 22 ^ M J. 32_ ==^ -^ ±k -J- -J-^ A -^ 9 8 7 — ^ -©r- 3=? 9 8 7 — ^ 3 164. These examples demand no explanation ; they speak for themselves. So long as the distinguishing characteristics of the two kinds of discord are kept in mind {par. 149) no difl&culty about their treatment need occur, however they may be intermixed in composition. Fig 170. MVWMOWX W WWWIW 41 CHAPTER XV 11. Inversions of the Discord of the Seventh. 165. The discord of the Seventh contains four notes of different names; it admits therefore of three inversions. When the 3'"' from the root is the bass, the first inversion is said to be used ; when the h'^ is the bass, the second inversion ; when the 7* is the bass, the third inversion. Fig. 172 is an example of the first inversion of the discord of the seventh on Sol, with its resolution on Bos fig. 173 of the second inversion; fig. 174 of the third. Fig. 171 is the discord in its direct form. Fig. 171. -©I TT ^ n Fig. 172. ilE ^^ I^^C ^ I ^ Fig. 173. ^ -^^- ^ Fig. 174. M "CS -e^ -e^i xi -Oi ^ 166. On examining fig. 172, it will be found that the upper parts form with the Bass, the intervals of a 6**", a 5*, and a 3"^, — not a 6* instead of a 5*, as in the first inversion of the triad, but a 6"» in addition to a 5*. As in the first inver- sion of the triad, the figure 3 is superfluous ; so that when we see | imder a bass note, we know that the bass is not the root, but the 3"* to the root, and that the roo* bears a discord of the Seventh. 167. The resolution of the discord of the Seventh in the fundamental position, i.e., with the root in the bass, was fully explained iu Chap. XIV. The resolution of a discord in an inverted form is in general similar to that of the same discord in its fundamental position : i. e., the several parts make the same progressions, what- ever may be their place in the chord in relation one to another. 168. Thus, in fig. 172 one 8™ to the root (and 6"^ to the bass) rises a 4*^ while the other keeps its place ; the 3"^ to the root (the bass), Si, rises one degree j the 5* to the root (the 8"^ to the hass), Re, falls one degree ; and the 7*"* to the roc* (the 5"" to the lass\ Fa, falls one degree. {Compare figs. 171 and 172.) 169. In writing chords of the Sixth and Fifth, double the 6* to the bass (the 8™ to the root), rather than the 3"* (the 5*'' to the root) ; and omit the 3"^ to the bass rather than the 6"*. The S'*" to the bass (7"" to the root) is indispensable. G. M. H. G 42 INVERSIONS OP THE DISCORD OF THE SEVENTH. [Chap. XVTI, Fig. 176. Pig. 177. =glT?J= H= -^jA -^ -^ -&■ ^^ Fig. 178. ^ 1 — -f |- -<_> Aj. Fig. 175 is preferable to fig. 176, and fig- 177 to fig. 178. The omisBion of the e* from the first chord of fig. 178 deprives the next of its 5"". 170. Although the 7"" can be added to 'any of the triads to be formed on the notes of a major or minor scale (see Chap. XIII.), it is, for obvious reasons, more often added to the dominant triad than to any other. The inversions of the " dominant seventh" are, therefore, more often used than those of any other fundamental discord of the Seventh. This has naturally led to the use of contractions in the figuring of some of these inversions. 171. A single figure 5 on any of the Jirst six notes of a scale would indicate a common chord — that the bass was also the root. But the 7*^ of a scale is rarely used as a root ; first, because it bears an imperfect fifth ; secondly, because its natural progression is to rise directly to the S*"*, with which it has no note in common. " The triads of two bass notes occupying following degrees of the scale, in no case contain a common note." {Par. 150.) 172. Only in a tonal sequence (.par. 70), where the quality of particular in- tervals is not felt, can the 7*^ of a scale be used as a root. (See t. Jig. i79.) When- ever the 7*'' rises directly to the 8**, or in any way manifests itself as a leading note, it is treated as the first inversion of the dominant, — ^never as a fundamental Compare fig. 180, a and 6. Fig. 179. Fig. 180 (o.) n Fig. 180 (5.) ^ ^±^ ArA_ Jr^ JoJ 3L^^ 1^ A^ q^--tx|n^^ ^^ ^ 1731 In fig. 180 a, the leading note falls to avoid consecutive octaves with the bass (also a leading note), which takes " its natural progression ;" and the im- perfect fifth betweer- the Alto and the Soprano is (from the same cause) left unresolved. Moreover, the efiect of the first chord, from its imperfect fifth, is of itself most unsatisfactory j while it is in no way connected with that which imme- diately follows it. Chap. XVII.] INVERSIONS OF THE DISCOKD OF THE SEVENTH. 43 174. Wterefore 5 on the y*** of a scale means not g, but %, — not tliat the basa IS also the root (as of any other note so figured), but the S'"^ from the root ; in fact, that the^rs^ inversion of the dominant Seventh is to be written, and that the root is a 3"^ below the bass, bearing a 7*. Pig. 181. ^^©! s -Q -^ 3 Fig. 182, XH ;:^ 'J. Fig. 183. J-^ 3^ bs" 3 Fig. 184. ^ * " ' 175. No difficulty can occur in recognising the bass notes figured 5 in the above examples as leading notes, since their fifths are aU imperfect. Fig. 181 is in Do; fig. 182 in Sol; fig, 183 in Fa; fig. 184 in La minor. 176. The progressions described in par. 151 may be made with equally good effect in the first inversion as in the discord of the Seventh in its direct form. Fig. 185. Fig. 186. Fi^. 187. rf ^ o' i Ji, =d=J -e>- xi ^ -^ -^ T~r -^- -^s- -^>- 3IE -e> i?iS'. 188, ^^ szi -^ -^ -^ -^ £ -^ TT < ) ©- -^ 6 — 3 5 ?F TT -e>- lu: 4 3 2 6 — 6 5 Fig. 185 is marked 6 5 ; the 5 being a contraction of |. The /mH figuring would be Is 177. The discords by suspension of the Fourth and of the Ninth may be made (together or separately) on the first inversion of the fundamental discord of the Seventh, as well as in the direct position. Fig. 189. ^ i^LX ^ ^ -of- -©I £X 2^ -O- ^ Fig. 190. 23 ^ ^ ^ -^ i?iff. 191. ^ 212 22^ ^ 3 tSi «- 6 5 6 6 7 6 6 6 6 4 4 5 4 5 — 4 4 ."5 » 3 2 3 44 INVERSIONS OF THE DISCORD OF THE SEVENTH. [Chap. XTIL Fig. 192. T~r ^T ^T-r7.|.l i o l ^l|.^ r^ -fc>- s 5 56 elbslesl es 666 221 ■U C )| ^ 4 5 2 3 4 5 ii-ii^. 193. 178. "When the S**" from the root is the bass of a chordj the second inversion is said to be used. Fig. 193 is an example of the second inversion of the discord of the Seventh on Sol, with its resolution on Do. 179. On examining fig. 193 it will be found that the upper parts, in relation to the bass, form the intervals of a G***, a 4"* and a 3"*; not a 4*'' instead of a 3"*, but in addition to it. So that on seeing * under a bass note, we know that the bass is the 5** to the root, and that the root bears a discord of the Seventh. 180. " The resolution of discord in an inverted form is in general similar to that of the same discord in its fundamental position." (JPar. 167.) Thus in fig. 193, one 8™ to the root (and 4*'* to the bass) rises a fourth ; the S*** to the root (the bass). Re, falls one degree ; the 7** to the root (the 3^^ to the bass). Fa, falls one degree ; the 3"* to the root (the B"" to the bass). Si, rises one degree. 181. As of the figuring of the first inversion of the dominant Seventh (^par. 174), certain contractions are used, so of the second ; and for the same reason. 182. A single figure 6 on the 1=' 3"^ 4*'' 5** 6* or 7*^ note of the scale would indicate the first inversion of the common chord — that the root was a 3"^ below. But 6 on the Z"" of a major scale means not the first inversion of the leading note, which " is very rarely used as a root," but the second inversion of the dominaat Seventh; in fact, that the root is a. fifth below the bass, bearing a 7'"- Fig. 194. Fiq. 195. Fig. 196. Pig. 197. -e^- x£ ^ ^pE^ lyF^- ^ ?i ei r^ _ -^- A. A. J- -el ^ ^ ^^ -^- ^ — fc^ < '. — T— 33 -©r -£i -^ Chap. XVII.] mVERSIONS OF THE DISCORD OF THE SEVENTH 45 183. The sharpened 6 in fig. 195 proves that the note above it {La) is the 2"" of a scale j since Fa # can only be combined with Do IH in the scale of Sol. The root is, therefore. Be, with a major 3"^ (^«4), and a minor 7"" {Do). The elevation of a note a semitone is sometimes indicated by "a Bhort line drawn obliquely across the right extremity of the figure corresponding with it." {Par. 38.) 184. By similar investigation, we ascertain the root of fig. 196 to be ?iot Mi, to which Si flat is an imperfect fifth, but Do, with the minor 7"*. Neither can the root in fig. 197 be Sol^, the third below the bass, but Mi, the fifth below it. 185. Therefore 6 on the 2°^ of the scale means 1. 3 186. The progressions described in par. 151 may be made with good efiect in the second inversion, as in the discord of the Seventh in its direct form. Fig. 198. Fig. 199. ©1- -^ TT €9- -^ -^ XZ -^ -o^ Fig. 200. -€>- SZE Fig. 201 &€^~ rx -e> ei < > -^ -^ xz c~> -^ -^ -© TT c^ -^>- -^ -^ TT^ 6 — 4 3 6 4 4 2 6 3 4 — 6 — 4 3 187. The discords by suspension of the Fourth and the Ninth may be made on the second inversion as well as on the discord of the Seventh in its direct form. Fig. 202. Fig. 203. Fig. 204. :£5: €5; £21 -J-- ^- A -J ^^ -e>- ^^^E^ ^M-.^-1-^JJz -^ -^ TT -^ -^ 7 6 4 — 3 — 6 — 5 4 3 — Fig. 205. d£^ 1^ r± ^ iJ-J. 7 6 5 4 3 — o. i:±3ti=o: ^±^£ ^ — ^ — o_ii l ^n -< \ < ^ i S V\ I _ 8^ ;:^;=^^= ^ 1 ' 4 zx: c^^ 4 3 6 b 4 3 6 4 3 7 6 4- 46 mVEKSIONS OF THE DISCORD OF THE SEVENTH. [Chap. XVII. 188. When the T*"* from the root is the bass of a chord, the third iaversion is said to be used. Fig. 206 is an example of the third inversion of the discord of the Seventh on Sol, with its resolution on Do. 189. On examining fig. 206, it will be found that the upper parts in relation to the bass, form the intervals of a 6*"^, a 4*"^, and a 3°*. So that seeing I under a bass note, we know that the bass is the 7"" to the root. Pig. 206. M ^ A -^ ^W^ 190. "'The resolution of a discord in an inverted form is in general similar to that of the same discord in its fundamental position.'" Thus, in fig. 206, one 8™ to the root (and 2°* to the bass) rises a 4*, while the other keeps its place j the T*"" to the root (the bass). Fa, falls one degree ; the 3"* to the root (the 4*"^ to the bass), St, rises one degree ; the S*** to the root (the 6*'* to the bass). Be, falls one degree. 191. The progressions described in par. 151 may be made with good efifect on the third inversion of the discord of the Seventh, as in the fundamental position. Fig. 207. Fig. 208. Fig. 209. Fig. 210. -^>- -^ Xi -^ -^ X3; -^ -^>- -^ -^ :^ ST -^ m -Ci. -^ Xi. -^ -^ -^ -^ CT -©l- -^ ^-^ 5 — 3 — TT -^ 6 I 2 3 I — xz 193. The full figuring of the second note in the first bar of each example above is I ; this may be contracted to f (.fig. 208), and even 2 (.fig. 209) ; the lowest figure never being omitted, unless the sign — be substituted for all the figures, which it generally is when the preceding bass note is a degree higher (or a seventh lower) than that which bears f . (See figs. 207 a7Ki2io.) 193. The discords by suspension of the Fourth and Ninth may be made on the third inversion of the fandamental discord of the Seventh, as well as on the discord in its direct form. Fig. 211. -J Fig. 212. d -J Fig. 21s. ^^"[# ^^^ d ^^ 6 — b 4 2 2 g Chap. XVn.] INVERSIONS OF THE DISCORD OP THE SEVENTH. Fig. 214. 47 X3I -^>- m s 3 ±TE 121 4 61 ri! #4 6 J— 6 T^ #4 6 ft— 6 5 4 5 6 6 5 "2 ** 2-23 3 The Student is recommended to begin the study of the lastfowr Chapters at this point; and to eatrry it on dmultcmeously vnth that of the Chapters wMoh irnmediately foUow this. 48 CHAPTER XVIII. Licences in the Resolution of the Seventh. 194. The regular resolution of the discord of the Seventh treated in the fore- going pages, includes the hest progressions of the notes composing it, i.e., the progressions most easy to sing and most satisfactory to the ear when sung. The desire to sound or hear sounded, the 8'" of the scale after the 7'", the 3'* after the 4"", the 1" after the 2°'', or (ia the bass) the tonic after the dominant, is, if not a natv/ral feeling, certainly one which use has made part of our " second nature.'' 195. By licence, however, certain other progressions are admitted, not only in addition to those heretofore treated, but even instead of them. Of these pro- gressions some are peculiar to certain inversions, and some can be used in all. 196. From the discord of the Seventh "omit the 5'" rather than the 3"*, and the 3''^ rather than the 8'"; for the omission of the 8" deprives the next chord of its fifth." (Par. 154.) Fig. 215. Fig. 216. Fig. 217. Fig. 218. __ . _ — H Qi — "- c ■ - -& 3zi: ^ "T ^ "T -r^ ^ =^=F^ <: < ; 197. The last chords both of figs. 215 and 216 have no 5"": so also the ^rst chords both of figs. 217 and 218. To remedy these inconveniences (inseparable, in four parts, from a strict adherence to rule) some exceptional progressions are occasionally used. 198. In a discord of the Seventh of which the root is the bass, one of two 3"** maj/all two degrees (_fig. 219) j or a single 3"^ may make this progression for the sake of enriching the next chord with a 5^ {fig. 220). Fig. 219. Fig. 220 Fig. 221. 1 —^ H _?LJ__J_||_ _Jkp Chap. XVin.J LICENCES m THE KESOLUTION" OF THE SEVENTH. 49 199. In the ^rsr inversion of a discord of the Seventh, an 8™ to the bass (3"* to the root) may fall two degrees. (Fig. 222.) Fig. 222. Fig. 223. e^ _Q! i^: -A -^ — ri — _LJ_zLe^_lE Jj|,]|, "^ — M — 5 It is very undesirable, ho-wever, that more than one S"" to the root should ever appear in a discord of the dominant Seventh. 200. The dissonant note in a discord of the Seventh, vrhether in its direct form or in any inversion, may he deprived of its regular resolution by the motion of some other part to the note, or the S'" of the note, to which the seventh ought to fall. In this case, the latter rises one degree. Fig. 224. ^^^ Et^ Fig. 226, ?ig. 226. Fig. 227. ^ ipi J m: 3 3E T-t <~v J. -^r A J. -^ 3=5 S 3 In figs. 224, 225, and 226, the Bass falls or rises to Mi, the 8" of the note to which Fa (the T" to the root of each) ought, by rule, to fall. While in fig. 227, the Alto falls to Mi, the 8" of the note to which the Bass should fall. Of these progressions, fig. 226 is that in most common use. 201. The upward progression of a single 7'" to the root is always made to avoid some effect stiU more objectionable; e.g., doubling the 8'° in the chord of the Sixth {figs. 229 and 230), or hidden consecutive octaves {figs. 228 and 231). -^- ^3 Fig. 229. :c^ 3:± Fig. 230. ^ H A AA liE 1 Fig. 231. XX n -^- O. M. H. 50 LICENCES IN THE RESOLUTION OP THE SEVENTH. 202. In the second inversion of a discord of the Seventh, two 3'" to the bass (7'" to the root) may he written, one of which must rise one degree. {Fig. 232.) From this combination, the 4'" to the bass (8" to the root) is usuaUy omitted. This licence is frequently resorted to by the best composers. 203. In the third inversion of a discord of the Seventh^ an 8" to the bass (7"" to the root) may rise one degree. (Pig- 233.) From this combination, the 2°* to the bass (8" to the root) is usually omitted. This licence is rarely used. 204. A discord of the Seventh may be formed on any bass note which rises a fourth or descends a fifth, since its resolution is provided for in the next chord. When a bass part moves thus by a sequence of fourths and fifths, a 7'" may be added to every triad; one discord being resolved by another. In such case, each S'" (from its root) pre- pares the 7'" of the next chord 8 7 7 8 l7 ^ 8 7 205. By making the sequence real {par. 71), the discords all become dominant Sevenths. In this case, each 3'* (from its root) must fall a chromatic semitone (Hg. 236); unless the 7'" be preceded by the 8"' {fig. 287. Fig. 236. f ^i=j^ fVj. 237. |l^-L F| ^ 1 ^ ^^^ m J- &c. ^ T: t >< •> 3 7 8 7 8 Ib7 8 b7 Figs. 235 and 237 explain figs. 234 and 236 ; the two former containing in every pro- gression an ellipsis of the two latter. Chap. XVIIT.] LICENCES IN THE RESOLUTION OP THE SEVENTH. 51 206. The above sequence of sevenths may be treated on any inversions of the discord of the Seventh. Fig. 238. 32: X3: :e= 5 ^W=^ l&r 3ZI X3 6 4 6 4 S 2 5 2 Mg. 239. ^ "TT" -^ 4 7 4 7 3 3 Fig. 240. s T 3 J.Ocl..J.oJ- J^Jj-OeL -efd 4 6 4 6 2 5 2 5 ii'j^'. 241i ^^^ i'iS'. 242. Fig. 243. Hj- jJW safe jQia ^ Jr^j[.j ^;:k ,^ ^ 31? 6 4 6 4 S 2 bs 2 #6 ^7 6 b7 It 6 4 |:j5 2 bs Several of the licences explained above are resorted to in the following example. Fig. 244. i J -o- 3zi: -^ s HL m^^ m: 6 6 d! 6 Jt6#*6 46 7 — 5 2 5 2 4 3 62 CHAPTER XIX. Interrupted Resolutions of the Seventh. 207. The resolution of a discord of the Seventh, both in its direct and iu its inverted forms, may be not only delayed by the suspension of the dissonant note [see Chap. XF.), but interrupted, by the interpolation of one or more notes or chords between the dissonant note and the note or chord by which it is eventually to be resolved. Fig. 246. Fig. 246. 3q= -^■ :r± :^ -J o J J J, Of these examples, fig. 247 is that in most common use. In all, the 7"' from the root of the first chord is sustained until it is resolved on the 3"" of the next chord but one. 208. " The dissonant note in a discord of the Seventh may be deprived of its regular resolution by the motion of some other part to the note, or the 8™ of the note, to which the 7^ ought to fall." {Par. 202.) Fig. 249. 4=^3^ The dissonant note in the first chord of flg. 249 (Do) is in the Tenor ; it is resolTed wentiMtlly (in the last bar but one) by the Soprano, which falls from Do to 1^1, Chap. XIX.] INTERRUPTED RESOLUTIONS OF THE SEVENTH. 53 309. The 8™ to the root is often introduced between a 7"" and -the note by which it is afterwards resolved. Pig. 250. -^- 3ZE -^ m XTT -^ Fig. 261 -e>- 3ZX -^- JCi. -^ -^- xx Fig. 252, -Gf- XT" -^- C-> -^ -^- XX i?»fl'. 2S3. -^ -^- xx -^ c~>. -^ ^-M- XX 4 — 2 — 210. The discord of the Seventh, containing in its complete form four sounds of different nameSj cannot \>g fully expressed in less than four parts. By judicious omission of the least important notes, it may be indicated, especially in its inverted forms, beyond the possibility of mistake, in three, and even in two parts, especially with the hel^ of the licences just explaiaed. In fig. 254 , a, 6, the discords (suspended and fundamental) are all regularly prepared sounded, and resolved. U a ^AJ+J ==^ Fig. 254 (a.) sq^ :# XX ^^u^ m Q w "^^n "cr -^ ei^ ^ m ^^ M • ^ 1 ( ) ^ ] l- Q . *| Or -^- "TT 6 S ;jf4 6 6543— 6 4 \> S 6 9 8 G 2 3 /■~\ Fig. 254 (5.) ^^ P=»= XX wr^jLiu^i ©^ <3) •I* W < ^ ^S^ * ^^-^ ^^h> ^ ^ 0| . a -Or -^ I^ 6 5 6 6 5 4 3 6 4 b 5 6 9 8 6 2 3 54 CHAPTER XX. Changes of Root on a Single Bass Note. 211. Two or more sets of figures are often found on the same^ or a repetition ol the same, bass note. In some cases, they merely indicate changes in, or additions to, the up'per parts ; the root, as well as the bass, remaining the same ; as in 8 7 and its inversions, and in all discords by suspension. More often, however, they imply a change of root ; since every note forms part of more than one chord — a fact recognised in all good average progressions. (Par. 56.) 213. The possible number of changes of root on the same note (whether in the bass or not) depends on the number of combinations of which that note may form part. This number is great : e. g., Do is not only the 8™ in the common chord of Do, but the 5*'' in that of Fa, the minor 3"''^ in that of La, the major 3"^ in that of La b. Over and above these, it may form part of various discords fundamental and suspended, several of which have already been explained. (See fig. 255.) Fig. 255. ^ ^^ icn T-r S or xx 331 ^m ?oi '&C. TT 213. In the treatment of different chords on the same bass, the Student may, for the most part, be safely left to the guidance of the general principles of musical progression laid down in the foregoing pages. Some few cases, however, require special consideration. Pig. 256. 312 -^ cT" A ^ A -^- 3ZE -^ 3ZE ~r-r Fig. 257. —\ l— < > < : '-' ' i > 1 (— ^ 1 . :§: 3IE <> 5 6 214. " 6 on the 2°^ of the scale means |" (par. 186.) In the first bar of fig. 256, the root changes from Re to Sol with the. 7* ; two chords with but one common note being due to the bass. But " in the second inversion of a discord of the Seventh, two 21^ to the bass (7"" to the root) may be introduced, one of which must rise one degree" (.par. 202.) This licence affords another note common to the two chords {see fig. 257.) Chap. XX.] CHANGES OF ROOT ON A SINGLE BASS NOTE. 55 215. When a bass note figured 5 6 rises one degree, its 8™ usually forms part of the chord, and its 3"* (the 7"' to the second root) rises also, to avoid the 8™ to the bass ia the next chord of the Sixth. (Compare Jigs. 258 and 259.) Fig. 258. znl -& 7?r=" XX m -e^ xx =^ xx Fig. 259. 3 -^ TT JZL -^- TT- 3_2_ In fig. 260 the progression 5 6 is treated in various positions, and resolved in various ways. In bars 6 and 7 the resolution is interrupted in one of the modes shown in Chap. XIX. (Compare fig. 247.) Fig. 260. a J J | < ' cJ 1 ^ ^ ^ -^ in -^ -^ \cx ^ ^fOE r> -^ zi TIT 5 6 6 5 6 \ 1 43 A— 6 5— 3 4 4 3 — e 7 56 CHAPTEE XXI. Fundamental Discord of the Ninth. 216, In the harmonic chord, "immediately aboye the triple 8™ to the prime, is found the 9*," which, being added to the discord of the Seventh, produces a com- bination of six sounds of different names, fuUy figured 7 (i'7j.26i.) 3 217. From the fundamental discord of the Ninth and Seventh, the 8™ to the root is usually excluded ifig. 262) ; of the other sounds, the 5* should be omitted ifig. 263) rather than the 3"* ifig. 264.) The ninth and seventh are, of course, indispensable. Fig. 261. Fig. 262. — e:- -Gf- -^ X3l ^ X3I Fig. 263. O — o — Fig. 264. O < ) -Gt- -^ -^- 218. " Of two parts separated by a ninth, the upper should fall one degree ; while the lower may keep its place, rise a fourth, or fall a fifth." {Par. 78.) 219. ^n the resolution of the discord of the Ninth and Seventh, the sounds which form dissonant intervals one with another take the same progressions as in the discord of the Seventh ; i.e., the bass rises a fourth or falls a fifth, the 3"^ rises one degree, the 7"" falls one degree, and the 8™ if retained, keeps its place. The 5"" alone, not forming^a dissonance with any sound in the combination, may rise or fall, and when doubled takes both progressions. In certain positions, however, it must rise, or form consecutive fifths with the 9**. {Compare figs. 265 and 266) Fig. 265. Fig. 266. ^- ZSD.- Tjr -<=>- BE :§: -^ -&, HJC TTT- 3ZE S -^ m • ( ■> ^ 1 _ The ascent of the 5"' (Be) in fig. 265 produces two S""' in the following chord — a lesser evil, however, than the consecutive fifths produced by its descent in fig. 266. Chap. XXI.] FUNDAMENTAL DISCORD OP THE NINTH. From fig. 265 we gather that, — 57 Fig. 267. 230. Of two parts separated by a seventh, the lower may /a ' \ 4 3 G. M. n 58 CHAPTER XXII. Chromatic Intervals. 235. The semitone between two notes of the same name but of different pitch, is called chro- matic. Fig. 274. ^^ &-<>&^ 226. From the augmentation or diminution of diatonic intervals by the chromatic semitone chromatic intervals are produced. 337. Thus, the imperfect fifth and the perfect fifth, being both found in the diatonic scale, are diatonic intervals (^fig. 275), but the augmented fifth, which is a chromatic semitone larger than the perfect fifth, is a chromatic interval. (.Fig. 276.) Imperfect Fifth. —9- €5 Perfect Fifths. Fig. 275. -^- -^ ?Q- 4 -^ W: Fig. 276. Augmented Fifth, -Jr- * ^ Diatonic. Chromatic. 338. Every diatonic interval can be either augmented or diminished by a chromatic semitone j being called augmented or diminished accordingly. Pig. ■ill. -^ W. "W -^w- 339. Thus, by flattening the upper of two notes a miwf A apart, the interval of a diminished ninth is produced between them. In figs. 278 and 279 are contained all the chromatic intervals within the octave ; those in the latter being inversions of those in the former. For the sake of classification, the chromatic semitone is sometimes called the augmented unison; although the unison is not an interval. Unison. Fig. 278. Second. Fifth. -^-;i*=> ifa^ -ff ;©- Sixth. ic -€5- Augmcntcd, Fig. 279. Octave. Seventh. Fourth. . ^:^- ±n H*^. EE i;^- Diminished. Third. m i Chap. XXII.j CHKOMATIC INTEUVALS, 230. The second, fifth, and sixth cannot be diminished, nor can the seventh, fourth, or third be augmented. The unison, of course, cannot be diminished ; but the octave can be augmented, — or rather the chromatic semitone (augmented unison) can be made compound. -^- 231 . A chromatic interval is essentially dissonant ; it is " a combination on which the ear cannot rest, and which therefore suggests another combination to follow it." (Far. 73.) 232. "A dissonance should always be resotoerf';" it must " sometimes also be prepared." {Par. si.) 233. Two parts separated by a diminished ninth are resolved i in the same manner as when separated by a perfect ninth ; the Q "^' <~> upper part falls one degree, while the lower may keep its place, / I .» rise a fourth, or fall a fifth. (Fig. 28i.) ((j) Q Q- "The ninth does not admit of inversion" (par. 12); neither must it be confounded with ttio octave (or compound) second, an interval requiring altogether dilforeiit trpatraent. (See par. 79.) 234. Of two parts separated by an augmented second, the upper should rise one degree ; while the lower may fall (also one degree) or keep its place. (Figs. 282 and 283.) f235. Of two parts separated by a diminished seventh, the lower should rise one degree ; while the upper may fall (also one degree) or keep its place. (Figs. 284 and 285.) Fig.2&2. Fig.2SS. 7fi <>c> X bP^.o H -^ Fiff. 284. Fig. 285. -^^-^ -&^-o- The last rule is but a repetition of the one before it ; since the diminished seventh is the inversion of the augmented second. The remaining chromatic intervals will be treated hereafter The two kinds of ninth are sometimes called major and minor, on the ground that two examples of the latter interval are to be formed from notes in the same diatonic scale ; e.g., in the scale of Bo, from Mi-Fa, and from Si-Bo. The 7"" of the scale, however, as has been repeatedly stated, is never used as a root, except in a sequence ; and it would be difficult, perhaps impossible, to furnish any instance from a good composer of the use of the S"" of the scale as the root of a fundamental discord of the ninth and seventh. The ninth is scarcely, if ever, lowered a chromatic semitone in a combination of which the 3"" is minor, and never in one of which the 7"" is major. The proper seat, therefore, of th< interval in question is the dominant, in relation to which it is essentially a chromatic, and, therefore, in this case, a diminished, interval. 60 CHAPTER XXIII. Discord of the Diminished Ninth. 336. "Every diatonic interval can be either augmented or diminished by a chromatic semitone ; being called augmented, or diminished, accordingly." {Par. 228.) 237. The ninth in the fundamental discord of the Ninth and Seventh is especially liable to this treatment; the chromatic form being as often used in modem music as the diatonic. Fig. 286. 238. The resolution is in no way affected by the change j whether the 9** be perfect or diminished, it falls one degree, and the other parts take the progressions assigned to them in Chap. XXI. (See fig. 286.) I ^^^ £ Try ^ 289. These progressions are even more imperatively demanded in the discord of the diminished, than in that of the perfect Ninth ; since the former contains always either a diminished seventh or an augmented second — chromatic intervals which must be resolved according to the rules given iu the last chapter. (Par*. 234 ond 235.) Fig. 287 is but a transcript of flg. 273— with every 9"" diminislied. The progressions of rknrfa nvfl lHfint.ififl.l. the parts are identical. Fig. 287. ^ferf^S 61 CHAPTER XXIV. Inversions of the Discord of the Ninth and Seventh. 240. The discord of the Ninth and Seventh contains five sounds of different names ; it admits, therefore, of four inversions. Fig. 289 is an example of the first inversion of the discord of the Ninth and Seventh on Sol, with its resolution on Do; fig. 290, of the second inversion; fig. 291 of the third; fig. 292, of the fourth. The second chord of each example shows the resolution of each. Fig. 288 is the discord in its direct form. Fig. 288. Fig. 289. ^ A ±: -©r-M- - 7 ' Fig. 290. 3:? -^- AA 3 6 6 5 Fig. 291. -^--H-- -^-ry;: Fig. 292. AeA ^^' •©t—' I ■^ 6 6 4 4 2 241. The upper parts of fig. 289 form, in relation to the bass, a 7"" B*"" and 2i^; figured I or merely 7. 242. Now, this is the figuring of the discord of the Seventh in its direct form ; and in the case of a single hass note figured 7, there would he no means of knowing which chord was intended. The following hass note in all cases removes the doubt, since the root of a discord of the Seventh rises a fourth or descends a fifth; whe eas the 3'''* from the root of a discord of the Ninth rises one degree. (Compare figs. 293 and 294.) ^ Fig. 293. Fig. 294. -^ 33 A. 23 ^ g! 1 }j II- — ' 1 c^ : -fr^^r^ 62 INVERSIONS OF THE DISCORD OP [Chap. XXIV 243. The distinction between the 7"" on a root and the 7"" on the 3"^ from a root, is not only of great importance theoretically^ but practically ; since when the bass is also the root, its 8™ may form part of the chord {see fi^. 293) ; but when the bass is the S"^ from the root, neither the 8™ to the bass nor the 8™ to the root can with propriety appear in the chord ; the former, because it could not be resolved without consecutive octaves, apparent or hidden {fig, 295) ; the latter, on account of its very harsh effect. {Fig. 296.) Fig. 295. Fig. 296. J- zm "T5~ x±: ^ BE J.^ ¥^ -J-pn=F -rt-T"- 1 344. From the first inversion of the discord of the Ninth, omit the 8™ to the root and the 8™ to the bass. 245. The first inversion of the discord of the diminished Ninth is called the discord of the diminished Seventh. The treatment is the same as in the diatonic combination. {See fi^. 297.) Fig. 297. -J- ^ -s^ :^ n Ed=FEE^ A ^ A ^ A ffi b7 ^ 246. "The resolution of a fundamental discord is often delayed by the suspension of any, or all of the notes composing it, on the bass of the following chord." {Far. 155.) 247. In resolving discords of the Ninth, direct or inverted, suspensions are often introduced not only for the sake of effect, but to avoid error. In bars 6 and 7 of fig. 298, consecutive fifths between the Tenor and Alto are avoided by deferring the resolution of the latter, half a bar. Fig. 298. m :Iii TT rT tT 4ti— s — ^ — 1=: — ?— s ~rx -O- ^^ ^;tx: 1)7 i^S: ^ -e5- Chap. XXIV.] THE NINTH AND SEVENTH. 63 248. When the 5** from the root is the bass of a chord, the second inversion is said to be used. Mg. 399 is an example of the second inversion of the discord of the Ninth and Seventh on Sol. 349. The upper parts of fig. 399 form, in relation to the bass, a 6* 5* and 3"^, figured | or merely %. 350. Here, as in the case of \he first inversion, we have figuring belonging to another chord; since % expresses also the first inversion of the discord of the Seventh. The following bass note, however, again removes all doubt ; since the 3"^ of a discord of the Seventh rises one degree, the following bass note bearing a common chord; whereas the 5"" of a discord of the Ninth rises one degree, the following bass note bearing a chord of the Sixth. (Compare figs. 300 and 299.) 351. From the second inversion of the discord of the Ninth, omit the 8™ to the root, and, in general, the 8™ to the bass ; the former, on account of its harsh eifect ; the latter, because it adds little to the harmony, and is liable to cause both consecutive octaves and fifths. 253. The treatment of the second inversion of the diminished Ninth is the same as that of the diatonic com- bination. {See fi^. 301.) ^ Pig. 302. Jq^d^RdfeJ -^- I xx -^- --^>-Jb- X3: 6 6 5 I 64 INVERSIONS OP THE DISCORD OP [Chap. XXIY. Fia. 303. 253. When the 7"" from the root is the bass of a chordj the third inversion is said to be used. Fig. 303 is an example of the third inversion of the discord of the Ninth and Seventh on Sol. 254. The upper parts of fig. 303 form, in relation to the bass, a 6'^ 4* and Z^, figured S. Fig. 304 255. Here again we have figuring belonging to another chord; but, as before, the following bass note removes aU doubt ; since the 5* of a discord of the Seventh falls one degree, the following bass note bearing a common chord; whereas the T**" of a discord of the Ninth falls one degree, the following bass note bearing a chord of the Sixth. {Compare figs. 304 and 303.) 256. From the third inversion of the discord of the Ninth omit the 8™ to the root and the 8™ to the bass. ig. SOS. 257. The treatment of the third inversion of the diminished Ninth is the same as that of the diatonic com- bination. {See fig. 305.) Fig. 806. ^ pl^cl . J J . J | „i . J J . J I, I q^^4^iq,4±jjj^ ^4^l-i^^ i^j^^^ X3: -^ ^ -J- ^ -J J J- I J J r^ |4 .^ ^ ^ I/— ^ «.' 6 — 1 3 Chap. XXIV.] THE NINTH AND SEVENTH. 258. When the 9^ from the root is the bass of a chord, the fQurth inversion is said to be used. Fig. 307 is an example of the fourth inversion of the discord of the Ninth and Seventh on Sol. 259. The upper parts of fig. 307 form, in relation to the bass, a 6** 4*" and 2°*, figured 1. 65 Fig. 307. ^ 3± 260. Once again we have figm-ing belonging to another chord ; but distinguished, as before, by the following bass note. Since the 7^ of a discord of the Seventh falls one degree, the following bass note bearing a chord of the Sixth ; whereas the Q"* of a discord of the Ninth falls one degree, the following bass note bearing a chord of the Sixth and Fourth. ^Compare figs. 308 and 307.) ^ Fig. 308. 261. From the fourth inversion of the discord of the Ninth and Seventh, omit the 8™ to the root and the 8™ to the bass. Fig. 309. 262. The treatment of the fourth inversion of the diminished Ninth is the same as that of the diatonic com- bination . (See fi^. 309 .) ^ 3Zt f^ qtH^f^ M. Fig. 310. n=* ^ xx -^ n -^ dm =a -^- Oi-t?^ &r ^ n^^^ln l '1-l^a T2u S T~r r^Sr TX -©r # 6 8 ~r-r -Or 3ZC ~rx f T-r 67 CHAPTER XXV. Chromatic Intervals. 265. The chromatic intervals were all exhibited in Chap. XXII. [figs. 278 and 279) and the treatment was explained of those in most common use ; viz., the diminished ninth, the diminished seventh, and its inversion the augmented second — the last two intervals forming part of the discord of the diminished ninth. The remaining chromatic intervals are, the augmented unison, fifth, and sixth, with their inver- sions the diminished octave, fourth, and third. 266. Of two parts separated by an augmented unison, the upper should rise one degree; while the lower may keep its place {fig. 312), or fall one degree (fig. sis). 267. Of two parts separated by a diminished octave, the lower should rise one degree ; while the upper may keep its place (fig. 3u), or fall one degree {fi^. 3X5). Fig. 312. Fig. 313 s± TTfr =^' Fig. 314. Fig. 815. rJ J - i^'^=F^ ^^ ^^ The last rule Is but a repetition of the one before it ; since the diminished ootare is the inversion of the augmented unison. 268. Of two parts separated by an augmented ^A, the upper should rise one degree, while the lower may keep its place, rise a fourth, or fall a fifth. {Fig. 316.) 269. Of two parts separated by a diminished fourth, the lower should rise ne degree, while the upper may keep its place, rise a fourth, or fall a fifth. Fig. 317.) Fig. 816. Fig. 317. 5^- x± g^tff 1^ I ns ^^ The last rule is hut a repetition of the one before it. 68 CHROMATIC INTERVALS. Xhap. XXV. 270. Of two parts separated by an augmented sixth, the upper should rise and the lower fall — each one degree. {Fig. 3i8.) 271. Of two parts separated by a diminished third, the lower should rise and the upper fall — each one degree. {Fig. 3i9.) Fig. 818. Fig. 319. -^ The last rule is but a repetition of the one before it. 273. In the resolution of two parts separated by an augmented interval, the upper part always rises, and the lower, when it moves, falls ; while in the resolution of two parts separated by a diminished interval the lower part always rises, and the upper, when it moves, falls. 273. In an augmented interval, the tendency of the two parts is to separate ; in a diminished interval, to approach one another. G9 CHAPTER XXYl. Chromatic Harmony. 274. The augmented unison, fifth, and sixth, with, their inversions, chiefly arise iSrom the introduction of passing notes iato harmony otherwise diatonic ; such passing notes being considered to give variety or smoothness to the progressions from one chord to another. 275. A chromatic interval may he thus introduced into any chord, provided the conditions of the next chord admit of its heing regularly resolved. 276. Neither the augmented unison nor its inversion the diminished octave, are much used in their original forms. (JFigs. 320 and 321.) m Fig. 320. ~nr T-r^- ^ Tl 3ZX -©r 6 — 77 6 ^ 331 -^ ffi Fig. 821. ^ A. 3ni --d ^ -^ 5 — 76 3 — 277. But the compound augmented unison (or augmented octave) is more common, es- pecially in inversions. (See Jig. 322.) m Fig. 322. -^ "TT- -^ jC3Z ^AJ m — 7 70 CHROMATIC HARMONY. [Chap. XXVI. 278. The augmented fifth or its inversion the diminished fourth, may be intro- duced with good eflfect into any chord the root of which rises a fourth («ee figs- 323, 4, and 5), or falls a third. {See figs. 326, 7, and 8.) Fig. 323. 331 ^F^ ^ 3zr t= jCH -€5- J%. 324. S CT ^ -^- Fiff. 325. < > <■ > ^ 1 < > <^ # <^ J^iy. 326. "r> "T^^ %. 327. TZI ^F^ s 1 — ^ — < > < > "~^— --'' 6 — ftgr. 328. < > <■ ■) ^ 1 ^ ^^ -^ 279. The augmented sixth may be introduced on the^r*^ inversion of the chord of the subdominant imimr {see fig. 329), or on the second inversion of the discord of the dominant seventh. {See fig. 330.) Fig. 329. -J-^d- m -b:e-- <~> -^>- 331 Fig. 330. "T-y- <~> -^>- Q OO i X3. TT- 6 - 280. In fig. 329, the chromatic interval is produced by the augmentation of the 8™ to the root Fa ; in fig. 330, by the diminiution of the 5'^' to the root Re. The second chord in fig. 329 admits also of another interpretation — that the root changes from Fa to Be with an imperfect fifth. 281. The augmented sixth may also be introduced on either of the foregoing chords {figs. 329 and 330) when they are accompanied by a 5"* (from the bass.) Chap. XXVI.] CHROMATIC HARMONY. 71 383. In. this case, the immediate resohition of the S*'', which forms an augmented second with the (augmented) 6*, cannot he made without consecutive fifths. By deferring the resolution the fifths are avoided, and a sLagle or douhle discord by suspension is introduced at the beginning of the next chord. {See figs. 331 and 332.) Fig. 831. Fig. 332. y^ * -^ J ?ig. 333. ^Jdi J U ?©- ^ ^ O i p er "T-j- -^ ^©r "T^r ^^5 be 3 6 b5 be 4 -^ ?Or X2: b^5 H6 4 383. The 5* is also allowed to rise a chromatic semitone before being resolved. The progression in fig. 333, though of late somewhat vulgarized, is certainly one of the most beautiful in music. 384. The roots of the chords iu the first bar (of each fig.) may be considered to be either Re with y, the 5"" being lowered a chromatic semitone in the latter part of the bar ; or Fa, with b 7, and then Re, with . , &c. 285. By inverting the progressions in figs. 331 and 333 the diminished third is introduced. Fig. 334. Fig. 335. Fig. 336. 3 te '^- §^ ^^ -^- -^ -a IQ- b7 3ZZ "^ L± b 386. These inversions are rarely used. It is even laid down as a rule in some treatises that " the diminished third must never be used in harmony, nor its inversion the augmented sixth in Tnelody." There appears to be more ground for the latter than the former rule. 72 CHAPTEE XXVII. Pedal Points. 287. Appended to every complete organ is a set of keys for the feet, called pedals — as the keys for the hands are called manuals. From a very obvious and effective mode of using these (foot) keys has arisen the term pedal point, by which is understood a note maintained during several successive changes of chords, or passages of melody. In the course of these changes, not only is it allowable to introduce all the combinations of which the sustained note might possibly form part (Cojnparepar. 212), but various other combinations with which it could never other- wise accord; — provided always that they be properly adjusted in relation to one another. 288. A pedal note is not of necessity confined to the bass, though the bass is, more often than any other part, the seat of it. 289. The S"" of the scale in which a pedal point begins and ends is the note in most common use as a pedal note, especially when it is in the bass. The termina- tion of a passage is often protracted by a pedal point on the last tonic. Fig. 337. — © n ^ _CL 4=A -&^ ffi m -^- -^ -^ -Gh- -G>- -^>- 73 CHAPTER XXVIIl. Cadences or Closes. &90. A cadence, or close, is a musical figure composed of two chords, the first of which is usually sounded on an wwaccentedj and the second on an accented, beat. 291. A cadence may he perfect, imperfect, ot plagal. "£9a. A perfect cadence is formed by the progression of the chord of the domi- nant (with or without the 7'") to that of the tonic. {See Jigs. 338 md 339.) 293. An imperfect cadence is formed by the progression of the chord of the tonic to that of the dominant. {See fig. 340.) 294. A plagal cadence is formed by the progression of the chord of the suh- dominant to that of the tonic. {See fig. 341.) The plagal differs from the imperfect cadence only by its place in the scale. (Compare figs. 340 and 341.) Fig. 338. Fig. 339. Fig. 340. -fe> :r± -& ^ Bi ' 1 "^ " ^f^ 3Zt "T ^ — "CT Fig. 341. E^E^ ^ ^ - CJ 1 r < J 1 — <: r ^A ^ 295. The term cadence (from cado, to fall) refers to the root of the first of the two chords of which it is composed, which {see the above examples) falls a fourth or fifth. A cadence is said to be interrupted when the ear is disappointed of the progression or resolution suggested by the first chord. {See figs. 342 and 343.) Fig. 342. tf— -&- T-y- -^ <-> ~crr- 331 -^ <~i -e>- - ~r~r ~ry- -^ -^ e>- ifii xx -^- "C3- "TT- -^- <^- ■*>--' <~> 9 303. The progression of a root to another one degree above or below it is objec- tionable {paa: 56), chiefly from the want of connexion between their triads. (Figs. 349 and 350.) 304-. Two chords, however, standing in the relation of those in fig. 349, may be connected by the addition of a 7* to the latter; provided, of course, it can be resolved afterwards. {Seefig. 351.) And the harsh effect of the progression (%. 349) may be lessened by the introduction of a 7* on the first chord. (Fig. 352.) Fig. 349. Fig. 350. Fig. 351. Fig. 352. ^ f O -^ I_E -TT -^ TZ 33: &- -^ -Q^Cr ±=^ -esr -^3- -^ iQ_ -^ X3I -^- -O'- -Ci_ -^ TT -^ -r^ &— 76 CHAPTER XXX. Modulation. 305. Fundamental basses are rarely limitedj for any length of time, to the Game scale. The sameness which would necessarily result from such limitation is agreeably relieved by modulation. 806. By modulation is understood a change from any given scale to another related to it — such as its sub-dominantj dominant, or relative minor, or the relative minor of its sub-dominant or dominant. Change to a scale distantly related, or altogether unrelated, is generally called transition. 307. Thus the commonest modulations from the scale of Do are into the scales of Fa, of Sol, of La minor, and of Be and Mi minor. 308. These modulations can one and all be effected by slight changes in, or additions to, one or other of the chords of the original scale. 309. The easiest and most natural modulation is into the scale of the subdominant. This is effected by the addition of the minor 7"" to the tonic, which thus becon],es the dominant of the new scale. {See jig. 353.) It will be understood that no modulation is confirmed till the discord of the dominant seventh followed by the tonic (the perfect cadence) of the new scale has been heard. 310. A modulation into the scale of the dominant may be effected by makiag the 3'* of the chord of the supertonic (the 2"^) of the original scale major, and addiag to it the 7'". {See fig. 364.) 311. A modulation into the scale of the relative minor may be effected by makiag the 3'* of the chord of the mediant (the S'^) of the original scale major, and adding to it the 7"". {Seefig. 365.) Fig. 353. -Gt^ H:^ SIE T^~ -^ Chap. XXX.] MODULATION. 77 Fig. 350. 312. A modulation into the relative minor of the subdominant is effected by making the S"* of the chord of the siihmediant (the 6"') of the original scale major, and adding to it the 7'". {See fig. 366.) 313. A modulation into the relative minor of the dominant is effected by making the S"* of the chord of the leading note (the 7'") of the origiaal scale major, and its 5'" perfect, and adding to it the 7'\ {See fig. 357.) Fig. 357. -^ The foregoing are given as examples, not of the only, but of the most obvious and rapid, modes of effecting the commonest modulations. All modulations, common or uncommon, admit of iufinite varieties of treatment. {See alsofigs.363, &o.) 78 CHAPTER XXXI. Rhythm. The art of connecting choiJs together is generally used subserviently to some musical idea to some melody, or passage of melody^ which is to be clothed with harmony, combined with some other passage, or otherwise musically treated. In the mind of a practised musician, melody and harmony may be said to be insepa- rable : it is hardly possible for him to exercise his invention in the one, without some reference to the other. Nevertheless, he is often called upon to harmonize melodies or passages of melody not of his own invention : and, indeed, the power of doing this is indispensable not only as a means of study but as an accomplishment. No law of universal application exists, no recipe can be given for " putting a bass to" a musical passage. The progressions of melody are infinitely various ; nay, each individual melody may be grafted on a great vaiiety of roots and fitted with a far greater variety of basses; and the selection from these must depend on the experience and taste of the harmonist. Certain general principles, however, exist, by which this selection may be rendered more easy. The consideration of these must be preceded by a few brief explanations on iKb subject of Rhythm. 314. The word " passage" is used in mucli the same sense in relation to music as to language ; being understood to mean a succession of notes (as of words) pre- senting, in their connexion with and dependence on one another, some idea more or less complete in itself. 815. A succession of musical passages, connected together according to certain principles, is said to form a movement. 316. A movement is generally divisible into periods; a period into seclAons: a section vato 'phrases; and a phrase vaio feet. In a hng-melre psalm tune we have an example of the most simple and symmetricai form of " movement." Fig. 368 is divisible into two periods,/oMr sections, eight phrases, and sixteen feet. 317. The notes, of which a passage is composed, are distinguished as accented and Mwaccented ; and they take their places in a har, or measure, accordingly. Every bar is divisible into times or heats; the accented notes occupying the strong times or down beats, — the wnaccented, the weak times or up beats. 318. A bar of music may consist of alternations of down and up beats (strong and weak times), or of one down beat followed by two up beats — ^literally, a side beat and an up beat. In the former case, the bar is in duple time ; in the latter, in triple time. Quadrwple (or common time) of four beats is essentiaMy the same as duple. Chap. XXXI. J RHYTHM. 79 819. A. foot and a bar are often found to be of the same length, but they rarely begin and end at the same instant. Every har begins with a down heat ; almost every foot begins with an up beat ; so that a bar seldom contains an entire foot, but consists usually of the end of one foot and the beginning of another. See fig. 368, where the letters^, mark the limits of the first foot. The first foot begins be/ore the first, and the last foot ends q/ier the last complete bar. 820. A musical foot differs from a poetical foot in the fact, that whereas the number of syllables in the latter is small, and the modes in which they can be arranged not very various, the number of notes in the former is unlimited, and the modes in which they can be arranged are infinitely various. 821. A phrase consists generally of two, sometimes of three feet. See fig. 368, where the letters ph. mark the limits of the first phrase. 822. A section consists of at least two — generally of more than two, phrases. See fig. 368, where the letters sec. mark the limits of the first section. 823. A period consists of at least two — more often of many, sections. See fig. 368, where the letters ^er. mark the limits of the &cat period. 824. In the higher classes of musical movement, the rhythmical divisions are much less strongly marked than in simple melody, like fig. 368 ; since a phrase may be extended or contracted, or one phrase be made to begin before another is ended. Nevertheless, some law of proportion will be found to prevail in all well- constructed movements, the section having generally a relation to the phrase similar to that of the phrase to the foot ; such relation being perceptible even between the period and the section, and between the entire movement and the period. It may be convenient to caution the student that he will sometimes find the word phrase used in the sense asciibed above to the word section, and even to the vroid/oot. In treatises on versification, the division of verses into feet is often indicated by bars, which are placed at the beginning of e&oh foot, without reference to the emphasis (or icttcs), which, in music, governs absolutely the place of the bar. (Par. 319.) The following line appears thus in " Mason's Principles and Power of Harmony :" — " My time, | ye Mu | ses, was hap | pily spent." | Whereas, set to music, this line would undoubtedly be barred thus : — " My I time, ye | Muses, was | happily | spent." 80 CHAPTER XXXII. H armonizing. 325. Ithas been already remarked, that "the possible number of changes of root to the same note depends on the number of combinations of which that note may form part ;" and that " this number is great." {Par. 212.) 3:26. Thus, an individual note, Do, may form part of the following combinations, and of the various inversions of which they are susceptible ; aU in the scale of Do, or some scale easily connected with it, — such as its relative minor, dominant, or subdominant. Fig. 858. fig- 369. .C3I ~c->- ~T-r < > <' > < ■> <:■> e] < r> "CT" "j-y T-r ^T) -^ -^ -^s- Fig. 360. b7 \> Fig. 361. 'i -^ b: n Pig. 362. tk XX ~r~r <~) <^ 1 :ci: Gi i±3 r± G^ 4- :c± tj rt r±^ BE zx zx -^ I I 4 3 7 — 4 3 9 8 4 3 O 9 8 7 — 4 3 b9 4 8 3 1>9 7 4 ^>- 327. Here we hare four different fundamental basses to Do, and one on which it forms a discord by suspension ; three of these basses {Do, Fa, and La) will bear a common chord with or without a 7"', the 7''' in two {Do and Fa) being either ma,] or or minor ; whUe another bass {Re) to which Do is itself the 7*, may bear a major or a minor 3''''. Of each of these bass notes there are at least two inversions; making upwards of fifty combinations of which this single note Do may form a part. 328. But as a single note does not constitute melody, so a single chord cannot be said to make harmony : harmony results from a succession of chords ; and unless it can be known by what note or notes Do is followed or preceded, whether it fall on an accented or unaccented beat, whether it be at the beginning, middle, or end of a phrase, it will be impossible to select the root most fitted to it. And as in harmonizing a single note reference must be had to the phrase of which it forms part, so in harmonizing a single phrase we must consider its relation to the section, period, and even the entire melody or movement to which it belongs. Chap. XXXII.] HARMONIZING. 81 329. Melodies and phrases are of two kindsj — those whicli remain throughout, or succeed one another, in the same scale; and those which mpdulate, or imply modulation, into other scales. The process of harmonizing the former is oi course the more simple. 330. The most ohvious bass notes with which to accompany a phrase within the limits of any particular scale, are the 1" 4'" and S''-" of that scale, and, of course, their inversions ; since " in the triads of" those notes " is contained every note of the scale to which they belong" (par. 25); and "from three chords thus related every scale is said to be derived; and one or other of their roots (the 1'' 4'" or B'") will serve as a root to any note in the scale. {See par. 26 and fig. 12.) 331. Besides these, the 2"^ G'", and, though more rarely, the 3"" of the scale may be employed as roots. The 7'", or leading note (as has been shown repeatedly), is never used as a root except in sequences. 332. In harmonizing passages which modulate, or imply modulation, care should he taken, at the moment the modulation is about to be made, to use only such chords as belong both to the scale about to be quitted and to that about to be entered. Thus, on the eve of a modulation from the scale of Do into that of Sol, it would be injudicious to use the chord of Fa, which belongs only to the scale of Do; whereas the chords of Do, of La, and of Mi, all belong both to the scales of Do and of Sol. On the other hand, a bad effect will be produced by the premature introduction of the dominant of the new scale ; since, being the principal means by which modulation is made, the appearance of the dominant should in general be delayed tiU the last moment. 333. Some of the most obvious and direct ways of conducting the common modulations named above are exhibited in figs. 363, 364, 365, 366, and 367. Each modulation terminates with a perfect cadence. M(/. 3u3. Mg. 364. Mg. 365. 9- SF iJ x±^^^^:r =^ =1=:= :^ ~H~^ -€> m ixi 6 87 I 5 I'tM 56687 4 #- i H- ^^ Fig. 366. Fig. 367. -^r ~o~ ^ 8 7 334. In the choice of roots, regard must be had to the order in which they follow one another, — a subject on which much has been said in Chap. XXIX, Ir. the choice of inversions, two points have to be considered ; the combination of each G M. H. M 82 HARMONIZING. [Chap. XXXII, particular bass note with the note or notes of the melody to which it is to be set ; and the progressions of the notes of the bass itself considered as a melody. 335. As respects the former of these considerations, no rules or directions will supply the place of judgment and taste, the result of carefial study of good models : as respects the latter, one general rule only can be given with safety. 336. When the melody moves by a large interval the bass should move by a small one, and vice versa; so that an effect of contrast in the two parts may generally be produced. An examination of the three different basses under fig. 368 will show how far the principles laid down in the foregoing pages have been carried out in practice. 337. Fig. 368 ends, as it begins, in Do ; the last foot forms the perfect cadence of Do. 338. The ^xst period ends in Sol (the Dominant of Do) ; the last foot is the perfect cadence of Sol. 339. The first section of the first period ends in Do; the first section of the second period in Re (miuor) ; the last foot of each is the perfect cadence in each of those scales. 340. We are thus far assured of certain points to which the progressions in each individual section must necessarily tend, and have reference. Let us examine each individual section, with reference to the roots. The notes are numbered 1, 2, < j -©t per. 3:3 -^ <>^ 3i: xi 33i HZ -© 2U O^ -& C2 5 #6 6 -T^ 1 — nr i i -^ <-» < * 1 t-r ry > }•{ k < ; ] 1 Tl ^ J .X- < i i : 1 1 *— ' x-xl cy ,-^ 6 ■ 6 "^ 7 *6 ""■ 6 -I 1 • ! 1 LSi^ c ■) < > < \ n 1 TTTF » < ; < > ] < 1 1 c ^ J < : <-i i : CJ < ; < : 1 i— 1 J 6 6 6 4 3 6 6 6 e-jr Chap. XXXII.] HARMONIZING. 83 842. Of the second section — Note 1 is the 8'Ho Do; 2, the S'* to Sol; 3, the S'* to Sol (seeBmdc), which in the next bar becomes the tonic, or the 5*" to Mi {see A) (the relative minor of Sol). On note 4 commences {in A and b) the modulation with which the section ends; it is first the 3'" to La and afterwards the 7'" to Re, being resolved on note 5, which is the 3'* to Sol Notes 7 and 8 form the perfect cadence in Sol ; the dominant Re, being preceded (m a and c) by the subdominant. Do, with the (so-called) added Sixth and Fifth {par. los), the dissonant note of which {Sd) is prepared in the harmony to note 5. 843. Of the third section — Note 1 is the 5"' to Sol, which can be distinguished at once as the dominant of the original scale by the introduction of the 7'" (Fa tj) (see o). Note 2 is the S"' to Do, or the 3-^* to La : and note 3, the S'" to Sol, if note 4 be the 3--* to Do {tee A and c); or the 8^' to Re, if note 4 be the 8" to Mi (seeB). Note 5 is best accompanied by the chord of the (added) Sixth on Sol the subdominant to Re minor, with the perfect cadence of which the section ends. 344. Of the fourth section — Note 1 is the 5'" to Sol ; %, the 3'S and 3, the 8™ to Do ; note 4 is the 3"» to Re, and afterwards the 7*^ to Sol (see A and b), being resolved on note 5, the 3'^ to Do. The fourth section, second period, and entire melody end with the perfect cadence to Do, 12345678 1234567 31^ i i Q -ep:^ Or -^ ^^ 0| Oi 13 33 1:3: 2:3 313 -©I r2 -& '<-f xl -& -^ IZl 6 5 b 4 t 6 5 6 6 6 5 5 3 ■^ -Or 311 -©r 3ZI 21? # £2 -©r -O 23: -&^ -& JH -&^ « # « 6 5 6 5 4 3 23: -^ 23 33 0| 33 -^ — 6 6 5 6 6 jt6 ©^ 23 m -o 3q: ^ 23 — 6 6 8 7 S 23: INDEX. The mimiers refer to the Paragraphs, which form an uninterrupted series from the beginning to the end of the Work. Accent, discord by suspension distinguished from fundamental discord by its, 88, 149, 164. Accidentals, in figuring, 36 — 39. Augmenied Intervals, resolution of, 272, 273. Bass, not of necessity a root, 98. Cadence, or close, should finish on an ac- cented beat, 290; perfect, 292; imper- fect, 293 ; plagal, 294 ; interrupted, 295. Chords, the best modes of arranging, sug- gested by the harmonic chord, 29 ; con- nexion of, by common notes, 56 ; un- connected, why exceptional, 57. Chromatic Harmony, 274 — 286. Common Chord, 18 ; formed exclusively of consonant intervals, 19; major, 20; major, borne by tonic, dominant, and subdominant of major scale, 21 ; three kinds of, produced by natural scale, 23 ; doubling of notes in, 30, 31 ; omission of notes from, 32, 33; not generally expressed by figures, 36. Concord, 83. Consecutive Unisons, Fifths, and Octaves, forbidden, 60 ; allowed, 51 ; why for- bidden, 54, 65. Consonances, perfect and imperfect, 15 ; generated before dissonances, 17; perfect, generated before imperfect, 17. Diminished Seventh, discord of the, 245. Diminished Intervals, resolution of, 272, 273. Discord, 83. Discord (Fundamental), 126 ; distinguished by its place in a bar, 149; of the seventh, 126 ; of the dominant seventh, 128, 129; of the ninth (and seventh), 216 ; of the diminished ninth, 237— 239. Discords (by Suspension), 84; distinguished by their place in a bar, 88, 149; resolution and percussion of, never to be simul- taneous, 90 — 92; preparation, resolu- tion, and percussion of, to take place in the same part, 93 ; mode of preparing, 94 ; seldom fully figured, 96 ; on inver- sions of the triad, 118 — 120; resulting from delayed resolution, 155, 158, 159; on a fundamental discord, 163, 164 ; on inversions of fundamental discords, 177, 187, 193. Dissonances, not necessarily harsh, but sug- gestive, 73; must be resolved, 74; and sometimes prepared, 81. Dominant, always bears a major chord, 21, — even in the minor mode, 132 — 134 ; why so called, 131 ; discord of the seventh more often formed on it than on any other note, 170. Dovhling of Notes, In any combination, 105, 106 ; in the common chord, 31, — and its 86 INDEX. inversions, 108, 114; in discords, 152; in the discord of the seventh, 153, — and its inversions, 194; in the discord of the ninth, 219. False Relation, 59, 60. Fifths (Consecutive) forbidden, 50; when allowed, 61. Fifth, perfect, a consonance, 15; imperfect, an anomalous interval, 13; resolution of imperfect, 141 ; augmented, 227 ; resolution of augmented, 268 ; treatment of augmented, in harmony, 278. Figured Basses, 34. Figuring, not generally necessary for com- mon chord, 35; accidentals in, 36; omission of, 36, 37; contractions in the, of altered notes, 38, — of the inversions of the discord of the seventh, 170 — 174; subject to the same rules as notation, 67 ; continuation of notes indicated by straight line, 95 ; of inversions of the Ninth, likely to be confounded with that of the Seventh, and its inversions, 242, 250, 255, 260. Foot, 316 ; often of the length of a bar, 319 ; musical, differs from poetical, 324. Fundamental Basses, the most obvious the 1" 4"' and S"" sounds of scale, 330. Fundamental Basses, (Progressions of,) the most natural, suggested by harmonic chord, 297 — 299; admissible, 301 — 304; objectionable, 303; objectionable, how modified, 304. Fourth, perfect, a consonance, 16 ; pluperfect, an anomalous interval, 13,— to be avoided in progression, 65; resolution of plu- perfect, 141 ; resolution of diminished, 269; treatment of diminished, in har- mony, 278. Harmonics, 3, 4, 5; how produced, 7; imi- tated artificially, 8; consonant and dis- sonant, 9. Haifnonic Chord, 6. Harmoniiing, possible number of roots to a given note, 325 — 327; choice of root in, dependent on preceding or following notes, 328 ; most obvious roots, 1" 4"" and 5" of scale, 330; analysis of esample (Jig. 368) of harmonized melody, 337—344 Imperfect Chord, borne by the seventh of the major scale, 23; and the second of the minor scale, 135. Intervals (Diatonic), 10; consonant and dis- sonant, 10, 11 ; anomalous, 13; perfect and imperfect, 14 ; large, to be used sparingly in progression, 61 — 64; can be augmented or diminished, 228. Intervals, (Chromatic,) 226 — 230; essentially dissonant, 231 ; must be resolved, 231 — 232 ; law of resolution, 272 — 273 ; how introducible into chords, 275. Inversion, 97. Leading Note, rarely used as a root, 171, 173. Line after a Figure, 95. Licences, (see BesohUion.) Modulation, its frequent occurrence, 306 : the most common forms of, 306; various modes of conducting, 308, 313. Motion, different kinds of, 42; contrary, oblique, and similar, 43; parallel, 44; similar, forbidden between parts ia unison, 41, — or separated by fifths or octaves, 50. Movement, a succession of connected musical passages, 315; divisible into periods, sections, phrases, and feet, 316. Ninth, a dissonant interval, 11 ; not in- vertible, 12; resolution of, 78; to be distinguished from the second, 79; di- minished, 229 ; resolution of diminished, 233. NintA, (Fundamental discord of the) 216 ; octave usually omitted from, 217 • INDEX. 87 resolution of, 219; seventh sometimes omitted from, 222 ; more used in its in- verted than direct forms, 224; admits of four inversions, 240; notes omitted from every inversion of, 263 ; first in- version of, 241 — 247 ; second inversion of, 248—252 ; third inversion of, 253— 257; fourth inversion of, 258 — 262; diminished, resolved like perfect, 238. Octaves, (Consecutive,) forbidden, 60 ; why, 54; when allowed, 51. Octave, a perfect consonance, 11 ; always per- fect unless figured, 39 ; can be augmented as well as diminished, 230 ; resolution of diminished, 267 ; treatment in harmony of augmented and diminished, 276, 277. Omission of Notes, from any combination, 105, 106; from the common chord, 33, — ^and its inversions, 108 ; from dis- cords by suspension, 92, — and their in- versions, 123 ; from the discord of the seventh, 138—139, 152, 154, — and its inversions, 194 ; from the discord of the ninth, 217, — and its inversions, 263. Organ (Stops of full) suggested by harmonic chord, 8. Paris (Individual) vocal, or instrumental, 40 ; should move mostly by small intervals, 62 ; crossing of, 66. Passage, 303. Pedal Points, 287; not always produced by the bass, 288 ; most often formed on dominant or tonic, 289. Percussion of a Dissonance, 82. Period, 316 ; divisible into sections, 323, Phrase, 316; divisible into feet, 321; some- times confounded with section and foot, 324. Preparation, of a dissonance, 81, 82; of a discord by suspension, 84 ; of a funda- mental discord, 148. Prime, 5. Progression, of individual parts, 61 — 62; of fundamental basses, 291 — 298 ; fun- damental, 117. Radical Bass, (see Root) Resolution, of dissonances generally, 74, 81 ; of the seventh and second, 76 — 77; of the major seventh in a discord by suspension, 156 ; of the ninth, 78 ; of the imperfect fifth and pluperfect fourth, 141 ; of discords by suspension, 89 ; of in- verted suspensions, 1 20 ; of the fundamen- tal discord of the seventh, 142, 143, 144 ; may be suspended, 155 ; or interrupted, 287 ; of the fundamental discord of the ninth and seventh, 219, 238; of chro- matic intervals generally, 272, 273 ; of the diminished ninth, 229 ; of the aug- mented second, and diminished seventh, 234 — 235 ; of the augmented unison and diminished octave, 266 — 267; of the augmented fifth and diminished fourth, 268 — 269; of the augmented sixth and diminished third, 270—271. Resolution (Licences in the) of the discord of the seventh, 194^198, 202, 203; of the inversions of the discord of the seventh, 199, 200, 201. Rhythm, 314—324. Root, 24 ; not always the bass, 98 ; leading note rarely used as a, 171 — 173 ; changes in, on a single bass note, 211, 212. Scale, every note of a, to be found in the chords of its tonic, dominant, and sub- dominant, 25 ; derivation of, 26. Second, a dissonant interval, 11; resolution of, 77 ; compound, not a ninth, 79, 80 ; resolution of augmented, 234. Section, 316 ; divisible into phrases, 322. Semitone (Chromatic), 225 ; sometimes called augmented unison, 229 ; resolution of, 266. Sequences, 68, 69 ; tonal, 70 ; real, 71 ; motion of parts in, 72 ; of sevenths, 204, 206,— inverted, 206. Seventh, a dissonant interval, 11; resolution 88 INDEX. of, 76; resolution of major, in a discord by suspension, 156 ; added to the dominant makes a common note with subdominant, 150; following the 8'" S"" or S"" to root, 151, 176, 186, 191 ; resolution of di- minished, 235. Seventh (Fundamental discord of the), 126; different kinds of, 129, 130 ; dominant, 131; resolution of, 143— 144,— depen- dent on progression of the bass, 145; interrupted resolution of, 147 ; admits of three inversions, 165 ; notes omitted from every inversion of, 194; first inversion of, , 165 — 177; second inversion of, 178 — 187; third inversion of, 188 — 193; licences in the resolution of, 195, 203; resolution of, may be suspended, 155, — or interrupted, 147, 207 — 209 ; irregular resolution of dissonant note in, 202, 203 ; doubling in, or omission of notes from, 152, 153, 154. Sixth, an imperfect consonance, 11 ; reso- lution of augmented, 270; treatment in harmony of augmented, 279 — 282. Sownd, cause of, 1 ; why musical or other- wise, 1 ; musical sounds, how produced and controlled, 2. String (Division of), natural, produces har- monics, 4; artificial, accounts for har- monics, 7. Subdominant, of a major scale, bears a common chord, 21. Suspension (see Discords hy). Third, an imperfect consonance, 11; major, shoidd rarely be doubled in a chord, 30 — 31, 106; should never be omitted from common chord, 32 — 33, 106 ; but may be omitted from discord of the seventh, 138; resolution of diminished 271 ; treatment of diminished, in har- mony, 285 — ^286. Thorough or Figured Bass, 34. Time, duple and triple, 318. Tonic (of a major scale) bears a major chord, 21. Triad, an extract from the harmonic chord, 18 ; arrangement of, 27, 28, 29 ; inversion of, 97 ; first inversion of, 99 — 103 notes to be omitted or doubled in first inversion of, 108; second inversion of, 109 — 112; notes to be omitted or doubled in second inversion of, 114, 115 ; suspensions on inversions of, 118 — 120. Unisons (Consecutive) forbidden, 41. Unison (Augmented), resolution of, 266 treatment of compound, in harmony, 277. lua BMC).