ilii» ■:v;\'.',\'.'.'.'.''w<; of m:W^o ne - Re 1 at 1 on s ■ ■ by":-' Percj^ CoetscliliiS;Mus.Doc. CORNELL UNIVERSITY LIBRARY MUSIC J Cornell University Library MT 50.G59 1917 The theory and practice of tone-relation 3 1924 021 809 797 Cornell University Library 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/cu31924021809797 THE THEORY AND PRACTICE OF TONE-RELATIONS AN ELEMENTARY COURSE OF HARMONY WITH EMPHASIS UPON THE ELEMENT OF MELODY BY PERCY GOETSCHIUS, Mus. Doc. Author of " Exercises in Melody- Writing " — " The Material used in Musical Composition" — "The Homophonic Forms of Musical Composition" " Elementary Counterpoint " — " AppUed Counterpoint " — " The Larger Forms of Musical Composition" — "Lessons in Music Form" — etc SSrd ISSUE COMPLETELY REWRITTEN AND ENLARGED G. SCHIRMER, INC., NEW YORK Copyrighted 1892, By PERCY GOETSCHIUS Copyrighted 1900, 1917, By G. SCHIRMER, INC. 27399 /5 6^/V2>0 Kll-t^ Printed in the U. S. A. TO THEODORE BAKER, PH. D. THIS BOOK IS GRATEFULLY INSCRIBED PREFACE. I. Musical composition, in its creative aspect, can not be taught. It is a distinctly subjective expression of the individual; it comes from' within, not from without; its individuality is what gives it value. But there is a necessary medium, a technic of expression, and this technic can be taught, and must inevitably be acquired. He who would write English poetry must first learn the grammar, and other elements, of English expres- sion. No matter how great the genius, or how overwhelming his thought and emotion, he can no more dispense with technic than he could dispense with a tongue in speech. A textbook of harmony, and of the elementary technic of musical expres- sion, is, therefore, a necessary and important thing for him who desires to understand what great musical minds have recorded, and who purposes to ex- press himself in the language of tone. n. The present volume is a completely re-written and slightly enlarged ver- sion of The Theory and Practice of Tone-relations, first published in 1892. The objects of this revision were: To purify and simplify the diction; to clarify the musical illustrations; to increase, considerably, the exercise-ma- terial; and to render the latter as easy as possible of solution for the student. Particvdar emphasis is laid, throughout, upon the element of melody, since melody is the soul and Ufe of good inusic. In all outward respects this new edition corresponds exactly to the pre- vious ones, the order of chapters and their contents having been retained. Only the numbering of paragraphs and examples has been partly changed. III. Those who intend to continue their studies, after completing this elemen- tary course in harmony, may proceed with the larger and more exhaustive text book. The Material Used in Musical Composition. Their preparation will justify them in passing rapidly over the first hundred pages of this book, and this they are advised to do, beginning their thorough work at Part III. Percy GoETscnros. New York City, October, 1916. CONTENTS. DIVISION L CONCORD HARMONIES. Chapter I. Tone and Key .... Formation of Natural Scale . . . Formation of Diatonic Scale . . . Names of Scale-steps Lesson i Chapter II. Intervals . Lesson 2 Chapter III. Consonance and Disso- nance Inversion of Intervals Table of Consonances and Disso- nances Chord-construction Relation of Triads within one Key Lesson 3 Chapter IV. Rhythm, Primary Rules Melody, Primary Rules Active and Inactive Scale-steps . . Lesson 4 Chapter V. Voices or Parts .... Chord-erection Lesson 5 Chapter VI. Rules of Part-writing . Lesson 6 Chapter VET. Perfect Cadence . . . Phrase-structure Chord-progressions I-V-I; I-IV-I Lesson 7 Chapter VIII. Progression IV-V . . Lesson 8 Chapter DC. Lesson 9 Rhythmic Phrases Paqb. I 3 4 4 S 5 7 8 8 9 9 II 12 12 14 IS 18 18 19 20 20 23 24 24 2S 26 26 28 29 30 FAsa. Chapter X. Harmonizing of Melodies (Principal Triads) 30 Lesson 10 ii Chapter XL The Harmonic Minor Mode 33 Signature of Minor 34 Lesson 11 3S Chapter XII. Subordinate Triads in Major — The 11 and the VI . . 36 Lesson 12 39 Chapter XIII. Harmonizing of Melo- dies (Subordinate Triads) — II, VI, III 39 Lesspn 13 41 Chapter XIV. Subordinate Triads in Minor 42 The Period-form 43 Lesson 14 44 Chapter XV. Chord-inversion ... 44 Chords of the Sixth 45 Lesson 15 47 Chapter XVI. Harmonizing of Melo- dies (Chords of the Sixth) ... 47 Successive Sixths 48 Sequences (Concords) 49 Lesson 16 50 Chapter XVII. Chords of the Six-four 52 Tonic Six-four Chord S3 Lesson 17 55 Chapter XVIII. Other Six-four Chords 56 Lesson 18 58 DIVISION n. DISCORD HARMONIES. Introductory. Chords of the Seventh Lesson ig 62 and their Classification ... S9 Chapter XX. Inversions of the Domi- Chapter XIX. Chord of the Domi- nant-seventh 62 nant-seventh 61 Lesson 20 64 CONTENTS. Page. Chapter XXI. Melodies (Dominant- seventh and Inversions) .... 64 Lesson 21 66 Lesson 22 67 Chapter XXII. Dominant-seventh, Licenses of Repetition .... 67 Lesson 23 68 Lesson 24 69 Chapter XXIII. Dominant-seventh, Other Licenses; Stationary Seventh; Ascending Resolution 69 Lesson 25 71 Chapter XXIV. Incomplete Domi- nant-seventh 72 Lesson 26 73 Lesson 27 73 Chapter XXV. Dominant-ninth, Major 74 Incomplete Dom.-gth 75 Lesson 28 77 Chapter XXVI. Dominant-ninth, Minor 78 Faoi. Chord of the Diminished Seventh. 79 Lesson 29 80 Lesson 30 80 Chapter XXVn. Unfigured Basses . 81 Lesson 31 82 Lesson 32 82 Chapter XXVIII. Diminished-sev- enth Chord, continued .... 83 Lesson 33 84 Chapter XXIX. Second-class Dis- cords — The Two-seven .... 84 Lesson 34 87 Lesson 35 88 Chapter XXX. Other Second-class Discords 88 Discords of the Third and Fourth Class 89 Sequences (Discords) 89 Augmented Triad (III in Minor) . 91 Figured Basses 91 Lesson 36 93 DIVISION m. MODULATION. Chapter XXXI. The System of Keys and Modes 93 Key-relations 93 Fundamental Rules of Modulation 94 Lesson 37 96 Chapter XXXII. Next-related Modu- lations, Complete 96 Lesson 38 97 Lesson 39 97 Chapter XXXIII. Next-related Modulations, Transient .... 98 Lesson 40 99 Lesson 41 99 Chapter XXXIV. The Altered Chords in Major 100 Lesson 42 103 Chapter XXXV. The Altered Chords in Minor 104 Melodic Minor Scale 104 Lesson 43 107 Chapter XXXVI. Mixed Chords in Major and Minor (Chords of the Augmented Sixth) .... loS Lesson 44 no Chapter XXXVII. Extraneous Modulation, Indirect iiz Lesson 45 112 Lesson 46 113 Lesson 47 113 Chapter XXXVm. Direct Extrane- ous Modulation. The Stride . 114 Lesson 48 115 Chapter XXXIX. The Opposite Mode 116 Lesson 49 118 Chapter XL. Sequence-modulation . 119 Cadence-modulation 120 Lesson 50 iZ3 Chapter XLI. Chord of the Dimin- ished-seventh, as Modulatory Agent 123 Lesson 51 124 Lesson 52 124 Chapter XLII. Consecutive Domi- nant Chords . . I2S The Chromatic Inflection .... 126 Lesson 53 128 CONTENTS. Page. Chapter XLIII. Enharmonic trans- formation of the Diminished Seventh 129 Enharmonic transformation of the Pace. Dominant Seventh 131 Lesson 54 i33 Supplementary Exercise 133 DIVISION rV. INHARMONIC TONES. Introductory. Definition and Classi- fication 134 Chapter XLIV. The Organ-Point (Tonic) 13s The Organ-Point (Dominant) . . 136 The Organ-Point (Pastoral) . . . 136 The Organ-Point (Other Steps) . . 136 Lesson 55 137 Chapter XLV. The Suspension . . . 139 Lesson 56 141 Lesson 57 142 Chapter XLVI. Irregular Resolutions of the Suspension 143 Lesson 58 144 Chapter XLVII. Irregular Introduc- tion of the Suspension .... 144 Lesson 59 146 Chapter XLVIII. The Anticipation . 146 Lesson 60 148 Chapter XLIX. The Neighboring- note 149 Lesson 61 ij* Chapter L. The Passing-note (Unac- cented) IS4 The Passing-note (Accented) . . 154 Lesson 62 157 Chapter LI. The Appoggiatura . . 158 Lesson 63 161 Chapter LII. Embellishment in Al- ternate Parts 161 Lesson 64 162 Lesson 65 163 Chapter LIII. Harmonizing of Em- beUished Melodies 163 Lesson 66 164 Lesson 67 165 Lesson 68 (Embellished Basses) . 166 Chapter LIV. Analysis 167 Lesson 69 168 Lesson 70 169 Lesson 71 171 Lesson 72 173 THE THEORY AND PRACTICE OF TONE-RELATIONS. DIVISION ONE. CONCORD HARMONIES. CHAPTER I. TONE AND KEY. 1. A Tone, or musical sound, is distinguished from sound or noise in general, in being fixed, instead of undulating; in maintaining a certain lo- cation in the realm of sound like the tone of a bell or whistle, in distinction to the ever-varying moaji of the wind. This distinction is most apparent in our treatment of the voice in singing and in speaking, respectively; in sing- ing we produce tones, by firmly maintaioing a certain degree of tension of the vocal cords for each utterance, while in speaking no such tension is sustained, and the voice therefore simply undulates. 2. Like the tones of the voice, so all tones in nature are owing to the in- tentional or accidental tension of some elastic body, which, on account of this tension, maintains its vibration, when set in motion, at the same (incon- ceivably high) rate of speed, thus fixing the location or pitch of its tone. This fixing of the sound is the very first act in the evolution of musical science. By fixing the sound, as tone, it becomes an object of experiment, observation and association; it enters into perfectly definite relations with other fixed tones, which cluster about it as their centre, and thus it becomes an art-factor. 3. The sound-waves, generated by the vibration of the elastic body from which a tone is to be elicited, are as regular in their velocity as the succession of vibrations, and can therefore be indicated by an arithmetical ratio or num- ber. Hence, a tone, being a fixed quantity, can be designated by a number, and the relation of tone to tone is purely a matter of mathematical ratio. 4. For illustration, the sensation or tone called a?-, and written on the second space of the G-staff, is aroused by sound-waves acting upon the drum of the ear at the even velocity of 435 strokes (870 alternate condensations and rarifications of air) in a second of time. Therefore this tone, a}, is designated by the number 435. Every pianoforte string or violin string vibrating at exactly this rate of speed will be in perfect Unison with the tone aS and the arithmetical ratio of one to the other is 435 to 435, or i : i. 2 THE THEORY AND PRACTICE OF TONE-RELATIONS. Par. 5- 5. Another string of half the length, and vibrating exactly twke as fast (870 times a second), wUl produce sound-waves with which the sound-waves of the first tone obviously agree, stroke for stroke, so that there is no actual conflict of pulsation, and the effect upon the sense is that of consonance (agree- ment or harmony of sound). But the shorter string adds an intermediate wave to each wave of the longer string, thus altering the quality of what is virtually the same tone, so that it impresses the ear more acutely, and soimds (as the parallelism of sensation involuntarily induces us to assume) higher. This new tone, designated by the number 870, is then the closest relative of fli; it is therefore'also called a, but the distinction in quality, or degree of acuteness, or location, is indicated thus — c^ — and it is written on the first leger-line above the G-sta£E. 6. The relationship thus established (435 to 870, or 1:2) is called the Octave, and is the same in both directions, self-evidently. That is, a string vibrating 217I times a second, or hdj as fast as the first one (o^), wUl produce the next lower octave, a, written on the second leger-line below the G-stafi. C3 -S>- 870 ftj-a T-gg— 435- " The tone-relation of the octave does not arise from the association of two different tones, but merely indicates a distinction of register. For this reason the octave is of no other value in active harmony than to effect the dupli- cation of tones, or the extension of the harmonic body into higher and lower registers, without adding any new factor. 7. In order to find a new tone which, while associating harmoniously with the first, will stiU furnish a starting point for actual tone-combination, it is equally obvious that the next simplest mathematical ratio must be taken; that is, I to 3, or 217I : 652!. The sensation (or tone) produced by the action of 65 2I sound-waves in a second upon the ear, is e^, written on the fourth space of the G-staff, and constituting the interval of a perfect fifth with the middle a (a^, representing the ratio 2 : 3 with e*, while i : 3 is the ratio with the lower a). Thus: 4 A 1 3 a SI- Ex. 1. -PERP. FIFTH "* OOTAVE 8. From this the facts are deduced, that, while the unison and octave are the simplest and most intimate tone-relations, the perfect fifth is the simplest mathematical ratio and there- fore the closest relation that exists between two different tones. Par. g. THE SCALE. 3 For this reason the perfect fifth, which we will call a harmonic degree, must constitute the basis of the whole system of tone-combination, and the stand- ard of measurement in harmony. THE SCALE. 9. From the infinite multitude of possible tones perceptible to the ear, the intuition of man (in civilized countries) has singled out a limited number (at first 7, later 12), which, with their reproduction or duplication in higher and lower registers, by the octave relation, represent the entire absolute tone- material of the art of music. The group of seven tones forms a Key or Scale, and is collected in accordance with the above standard (the harmonic degree) in the following manner: Any tone may be chosen as "keynote" or chief of the group; with this, no other tones will more naturally and reasonably be associated than its per- fect sth above and below, as next in order of importance in the group. The next member is the perfect 5th above the upper tone; and in the same man- ner a new higher perfect sth is associated with each preceding member, untU a tone is reached which would contradict the lowest one. Thus, assuming the tone C as keynote: #■ i-ffl- Ex. 2. i Keynote *i) ^ -^ pert. 5th^,p. 5th I I P- 5th I I p. 5th I ^p. 5th ^ p. 5th, ^ p. 5th ^ *i) The tone F-sharp does not appear in the authentic group, or key, or family of C, be- cause it contradicts F^natural, the lowennost member. Why the latter, F^natural, should be preferred to F-sharp, notwithstanding it lies helow what should properly be the funda- mental tone, or basis (C), and how very frequently the F-sharp is nevertheless preferred to F-natural, and adopted as momentary member of the C-family, will be seen in time. 10. This illustration also accoimts for there being no more nor less than just seven members in an authentic scale, or family of tones, usually called a key. There is no question in this case about the six tones, c, g, d, a, e, b, all of which lie above the fundamental keynote; and as to F-natural or F- sharp, it is certain that one or the other must be admitted into the family of C, and preference is given to the F-natural, because of its direct relation to the keynote. 11. This is the true natural scale, composed of equal contiguous intervals. For the sake of convenience, the seven tones are drawn into close proximity by simply transferring certain tones down or up by the octave-relation (where- by, as shown in par. 6, their significations are in no wise altered). In this way the so-called diatonic scale is obtained. 4 THE THEORY AND PRACTICE OF TONE-RELATIONS. Par. 12. Natural scale: -(5L „ jO- Ex. "^ '^ I SI 25 f C g d a e b Transferred by the octave : or, as Diatonic scale ; Ex. -&- f C g d a e b C d e f g a b 12. This diatonic scale comprises the tones of the major mode, so desig- nated for reasons given later. Upon examination it is found that the con- tiguous intervals of the diatonic scale, unUke those of the natural scale, are not uniform, but difier as follows: »i) Ex. i 1^' , whole step wh. step \ step wh. st. wh, St. wh. st. \ st. I I U I I I I I I I I I I *i) Here the keynote is reproduced in the next higher octave, in order to complete the circuit of tones. That is, the distance between the 3d and /jih tones, and also between the ph and 8th tones, is only hah as great as that between all the other con- tiguous tones. This has no other importance for us at present than to il- lustrate the accidental relative location assumed by the seven tones * when transferred from their order in the natural scale, to that of the diatonic scale. At the same time, it is a convenient external guide to the ready mechanical formation of any diatonic major scale, and should therefore be carefully observed. *) These tones are called scale-steps (or, frequently, degrees of the scale — i.e., diatonic scale). 13. The diatonic form of the scale is that upon which all practical compo- sition is based. The names given to the seven scale-steps (numbered from the keynote upward), arranged according to their relative importance, are as follows: First step — Keynote or tonic; 5th step (perf . 5th above Tonic) — dominant (dominating tone) ; 4th step (perf. 5th below Tonic) — subdominant; 2d step (perf; 5th above Dom.) — second dominant; (also known as supertonic) ; 6th step (midway between Ton. and Subdom.) — submediant; 3d step (midway between Ton. and Dom.) — mediant; 7th step — leading-tone. Thus: Par. 14. INTERVALS. Tonic Dominant Tonic Subdom. 2nd Dom. Dom. Ex. 5. C major Mediant Submed. Leading-tone ^^ iPerf-5th| I P- 5th , , S^h , , 5th , 14. Of these seven steps, three are greatly superior to the others and are therefore called principal scale-steps. They are, self-evidently, the tonic and its two perf .-sth relatives, the domi- nant and subdominant. The 2d, 6th and 3d steps are called subordinate. The Leading-tone has specific melodic quaUties. LESSON I. A. Write out every major scale, first in its Natural and then in its Diatonic form (Exs. 2 and 4) ; use no signature, but place the respective accidental before each inflected tone. B. Write out the 7 steps of every major scale in the order of their importance, namely: Tonic, Dom., Subdom., 2d Dom., Submed., Med., Leading-tone. C. Name, mentally (in response to the teacher's question), the 3 principal tones of every scale. D. Play the 3 principal tones of every scale on the keyboard in this order: Ton., Subdom., Dom., Tonic. CHAPTER II. INTERVALS. 15. The association of any two tones is called an interval. The term interval, meaning a space, refers to the distance between notes upon the written staf. But the true musical signification of "interval" is "tone-relation" — the relation established by associating the tones. Intervals are always counted upward, along the diatonic major scale of the lower tone. The number of the step which is occupied by the upper tone is the numer- ical name of the interval. For example: Ex. 8th or Octave 7th 6th 5th 4th 3d 2d Prime or Unison 5th 2d 7th jSL. 8th V 1 /' ej ^fj 1 f(\ i ^ \> i9^^^ -h ^^; ^~*^ ~y?~ 25 -O- Maj. 6th Augm. 6th SI — ' Min. 6th -!S Z> Dim. 6th Maj. Augm. Min . Dim. *i) Not c for b-sharp. — *2) Not d for c-double-sharp. Par. ig. INTERVALS. 19. The appKcation of this rule to certain tones may result in very un- usual notation. For example, the augmented 3d of drsharp must be f-tripl&- sharp: the major 3d of d is f-sharp, and, therefore, the major 3d of d-sharp is f-double-sharp; this, augmented, becomes f-triple-sharp. Likewise, the diminished 3d of c-Jlat is e-kiple-flat. $ Major Third Augm. 3d Maj. 3d Min. 3d Dim. 3d iz ibs ibfe i Ex. 10. ^ -ggy t T^^r- is i2^ ±s iK t- Such intervals are "unusual," but quite as possible as any. They simply lie unusually remote from the tone C, which has been adopted as a centrCj or starting point, in music notation. Further, while it is natural that only the comparatively related tones should be associated, it is possible to unite any two tones, at least casually and briefly. Thus: Double-augm. 8tli Double-augm. 4th Ex. I 1. f r~rT !iac LESSON 2. A. Write out the perfect 4th and perfect sth of the following tones: C, G, F, D, B-flat, A, E-flat, E, A-flat, B, D-flat, F-sharp, G-flat, C-sharp, C-flat, G-sharp, D-sharp. — Write out the major 3d and major 6th of the same tones. — Write out the major 2d and major 7th of the same tones, in optional order. — Write out the augm. 2d, 3d, 4th, sth, 6th, 7th, and Sth of F, B-flat, E-flat, A-flat, D-flat, C, G, D, A, E, B, G-flat, C-flat, F-sharp, C-sharp, D-sharp. — Write out the minor 7th, 6th, 3d and 2d of the same tones. — Write out the dim. Sth, 7th, 6th, sth, 4th, 3d and 2d of the same tones, in optional order. B. Name the following given intervals: J2«J: !-«>- b^ M W^ Jte fife l^=* ■ ygfi^ «i) i ^ fcst- *2) •2) *2) 1 -^ .bb^ X-iS>- -6>- ^ ^ r xar -¥ ^ *i) The lower tone is to be regarded, in every case, as a tonic. The number of the upper step is the name of the interval; if the upper tone conforms to the scale, the interval is either perfect or major, according to Ex. 7; if not, it is augm., minor, or dim., according to Exs. 8 and 9. — *2) In case the lower tone is an impracticable tonic, as here, shift theintenal bodily upward or downward, but without changing the letters. Thus: i Xig ^ i!Bg ^ lowered etc. raised THE THEORY AND PRACTICE OF TONE-RELATIONS. Par. ao. CHAPTER III. CHORD-CONSTRUCTION. CONSONANCE AND DISSONANCE. 20. As has been seen, the most intimate intervals are the vmison, octave and perfect fifth (par. 8). The other interval-relations are qualified accord- ing to the same rule of vibratory ratio, which determines their respective degrees of consonance or euphony with mathematical certainty, leaving noth- ing to the faUible and unreliable ear but to confirm and accept the result; correcting itself, if need be, thereby. > The next simplest arithmetical ratio is 3:4; two sets of sound-waves ^.ctii^ upon the organ of hearing in these proportions of velocity produce the double sensation of the perfect fourth. This is illustrated in Ex. i, be- tween the upper two tones, e^ and a^. The average ear will perceive that this interval is somewhat less agreeable than the perf. sth, albeit the tones are the same, and therefore its harmonic signification is identical with that of the sth. The ratio 4 : 5 gives the major 3d; 5:6 the minor 3d; conse- quently, the former is the better (more consonant) interval of the two. As the ratio becomes more complex, the tones are observed to approach each other, and the grade of consonance gradually decreases. Thus: 'cr^ ."'^ .^'* .^'^ .^'^ Ex. 12. (at Pianof .) Consonances perf. 8 perf. 5 perf. 4 Maj. 3 Min. 3 21. The next ratio, 8:9, is the mafor 2d, which is palpably no longer consonant, but dissonant, because the conflict of tone-waves here reaches an extent which is disagreeable. Hence, the minor third is the smallest conso- nant interval. The ratio 15 : 16 gives the minor second, which is still more palpably dissonant. " ! 9 15 : 16 _ zl Dissonances Ex. IS. (at Pianof,)' i ) gjo I \> ^ Maj. 2d Min. 2d INVERSION. ^ 22. The inversion of an interval is obtained by reversing the letters, so "that the lower tone becomes the upper. i a-d As this merely involves the octave-relation, it is evident from par. 6 that an interval and its inversion are practically identical. Par. »3. CHORDS. 23. All consonant intervals remain consonant after inversion, and dis- sonances remain dissonant. The complete table of consonances and disso- nances is therefore as follows: Consonances Dissonances *i) *i) Perfect octaves, and their inversions, perf. tmisons; Perfect fifths, and their inversions, perf. fourths; Major thirds, and their inversions, minor sixths; Minor thirds, and their inversions, major sixths. Major seconds, and their inversions, minor sevenths; Minor seconds, and their inversions, major sevenths; and also all augm. and dim. intervals, on account of their obUquity to the scale. *i) Major and minor 3ds and 6ths, being no longer perfect intervals, are distinguished as imperfect consonanees. CHORDS. 24. Chords are associations oi more than two tones, in exclusively, or at least preponderantly, consonant interval-relations. Giving first preference to the perfect 5th, as a matter of course, the skeleton of a chord erected upon the tone g (for example) would be i IE This is the ratio 2:3 (or 4 : 6, which will prove more convenient). The third tone, necessary to develop the " interval " into a complete " chord," must be in consonance with each and both of these tones, therefore the simplest ratio for the three tones together is 4:5:6, which mathematically deter- mines what the ear also unhesitatingly sanctions, namely, the addition of the tone 6-natural: i This is the primary three-tone chord-form and furnishes the incontestible model of all primary or fundamental chord-structure, namely: Any tone as given basis, with Us major third and perfect fifth. 26. Other, externally different, forms can be erected, in which again all the intervals are consonant. Thus: ^^'W But these are all readily recognizable as modifications of the original form, obtained solely by means of the octave-relation, which never alters the harmonic significance, but simply effects a more or less complete inversion of the chord, lO THE THEORY AND PRACTICE OF TONE-RELATIONS. Par. a6. 26. No other forms than these can be constructed without marring the consonant condition of the chord; in other words, consonant chords, or Cofir- cords, are limited to three tones: Still, the fundamental principle of chord- structure here revealed may be extended, in order to give the chord a more copious form. Thus, the structiure of ascending thirds may be extended to a new tone, i -e- but this new tone (in this case /) must necessarily constitute a dissonant in- terval (7th) with the ftmdamental tone, for which reason chords of four tones will invariably be dissonant chords or Discords. A three-tone chord with one or more duplicated tones (as g-g-b-d, g-b-d-d, etc.) evidently does not belong to this species of genuine "4-tone" chords. Still another upper third may be added, thus: i ■^Z. tf ts — ts: s — tsr ■w -a- i -^ W but the new tone (in this case a) gives rise to two additional dissonant inter- vals, namely, a 7th with h, and a 9th with g (see Ex. 6, note *3). 27. Dissonant chords are not only admitted, but even deemed necessary in music, on account of their contrast with consonant harmonies, and the peculiar quality of activity which their dissonances involve. But the follow- ing limitations are dictated by wisdom: first, as discords are merely extended forms of the concords, their application should be deferred until the relations and progressions of the primary three-tone forms have been thoroughly mas- tered; and second, the dissonant intervals must be introduced in moderate and judicious proportion to the consonances; hence, while 4-tone chords may be unexceptionable, those of 5 tones are more rare, and the addition of still more dissonances (as six or seven-tone chords) is obviously out of the question. It is true that dissonances are often multiplied, so that occasionally even all seven letters of the scale are associated simultaneously — for example, at X, ( Mendelssohn, op. 82 ) tame. But such dissonant clusters are never "chords." Their demonstration will appear in due Par. a8. RELATION OF TRIADS WITHIN ONE KEY. II 28. The concise definition of a chord is, then: the combination of three (or four, or five) tones in thirds, or in inverted forms reducible to thirds (see par. 25). 29. The structure of thirds is the fundamental chord-form: ^ In this form the lowermost tone is the root of the chord, from which the latter takes its name, according to the name of the letter, or of the scale-step. Thus: ^ is the chord of C, or, in C major, the tonic chord, because C is its root. The other tones (e and g) are called the third and fifth of the chord, according to their interval-relations with the root. Two additional tones would be called the seventh and ninth. Thus: Ex. 16. i Chord of G w =i= -9- -^ Root Third Fifth Root Seventh Ninth 30. Three-tone chords are termed triads; Four-tone chords are termed chords of the seventh; Five-tone chords are termed chords of the ninth. Thus: Ex. 16. i Triad of C Chord of the ?th of G Chord of the 9th of D -^r -A)l •1) *i) Why the ear prefers F-shaq> to F-natuial in this case will shortly be deduced from the simple principles of chord-relation. RELATION OF TRIADS WITHIN ONE KEY. 31. Any step of the diatonic scale {excepting the leading-tone) may be a root, and develop into a triad by uniting with its third and fifth. And, as already stated, each chord derives its harmonic name from the step of the scale which its root occupies. For illustration, in C major: Ex. 17. i Tonic Triad Dom. Triad Subdom. Triad 2d-Dom. Triad Submed. Triad Med. Triad P ^ =g= :^ -^ For convenience, the triads are also designated by Roman numerals, coinciding with the number of the step on which their roots stand, and are named accordingly: The One, the Two, the Three, etc. -zg- Ex. IS. ^ EE I II III IV VI 12 THE THEORY AND PRACTICE OF TONE-RELATIONS. Par. 32- 32. The relative importance of each of the six triads of a key corresponds exactly to that of the respective scale-step, and depends upon the distance of its root from the tonic in perfect fifths; or, upon its location in the "natural" scale (Ex. 2). Assuming, as self-evident, that the tonic triad is of first and fundamental significance, the next in importance is the dominant triad, then the sub- dominant triad, and so on, precisely in the order of Ex. 17. 33. The tonic triad and its two nearest relatives, the dom. and subdom. triads, are the principal chords of the key (see par. 14), and represent THE THREE ESSENTIAL ELEMENTS OF HARMONY, among which the other three triads (the Two, the Six,. and the Three), called subordinate chords, are interspersed only for the sake of variety, contrast and embelUshment. Principal Triads Subordinate Triads Ex. ' 19. C major ^^^^^S # ? *8) V IV *1) II VI III '1) A fine distinction in the relative importance of the IV and the II will be discussed later on. — *2) To the "Leading-tone- triad" no name or rank can be assigned at present; see par. 162. From this a significant inference can be drawn in regard to the choice oif-naitirai instead oi f-sharp for the key of C (Ex. 2, note *i). F-natural can be a root in that key; f-sharp cannot. B, which cannot be a root, is the last tone admitted in C major. 34. These two classes of chords (Ex. 19) will be found, at the pianoforte, to differ in sound. The principal triads have a major third and perfect fifth, wherefore they are called major triads. On the contrary, the subordinate triads have a minor third and perfect fifth, and are termed minor triads. This accidental difference in effect is owing only to the situation of the chords in their key, and does not in any wise influence their movements or significance. LESSON 3. A. Write the major triad (as the I) on every possible tone in the octave, adhering through- out to ihs fundamental form (par. 29). B. Write the six triads of the twelve diatonic scales, in the order of Ex. 19. C. Name, mentally, the I of every key; the V of every key; the lY; the II; the VI; the III. D. Find and play these chords at the pianoforte. (The practice of 4- and s-tone chords is deferred till later.) CHAPTER IV. RHYTHM AND MELODY. 35. The images of musical art, unUke the stationary creations of the arts of painting, architecture and sculpture, are progressive; as in the art of poetry, the impressions in music succeed each other by progressive motion. There- Par. 36. RHYTHM AND MELODY. 13 fore, tmne is absorbed in the expression of a musical thought, and it is the province of Rhythm to define and regulate the diAdsions and subdivisions of this passage of time. RtTLE I. The time is divided into absolutely equal units (ieflte, frac- tions of beats, or measures, as the case may be); i.e., the respective units are of exactly equal duration (like the uniform divisions of a 12-inch rule). Rui£ II. Though the imits are alike in duration, they differ in force; i.e., some are heavy and others light (as certain lines on a 12-iiich rule' differ from others in length or heaviness). 36. The primary units (or beats) are grouped, in conformity to these rules, in uniform Measures, of which there are but too fundamental species; either a succession of one heavy and one Kght beat, in regular alternation; or a succession of one heavy and too Ught beats, in irregular alternation. The former is called Duple time, or rhythm, or measure; the latter is called Triple rhythm, There are no other species. Ex. 20. Duple rhythm: -^ T— |— p tH""? f~\ heavy, light, heavy, light, heavy, light, Triple rhythm : — ^ • • 1 — p 1* #— I heavy, light, light, heavy, light, light, etc. etc 37. Rule III. The heavy beat (caEed Accent) should indicate the be- ginning of a measure. If a heavy impression is created by any means at any other point in the measure, the rhythm is "i/rregiddr," though not neces- sarily wrong. For illustration: Mozart Ex. 21. Handel jj l j ^ I J./JUI Both of these examples are perfectly regular, because the heaviest (longest) beat, or tone, stands in every case at the beginning of the measure. On the contrary: Ex. 22. ^ =5He S ^^^^ 4=± *l) ^/4 i Beethoven 3. • Beethoven i^c 4 f fg e« m Pm =u= ^/ sf *a) *i) This is an example of irregular rhythm, because the heavier tone is where a light unit should stand. — *2) Irregular because of the sf, which transforms a light unit into a dynami- cally strong one. — *3) Like note *i). It wiU be noticed that in each of these three examples 14 THE THEORY AND PRACTICE OF TONE-RELATIONS. Par. 38. the irregular rhythmic figure is repeated. In No. i, for instance, the second measure has the same irregular formation as the first; see also Ex. 23, No. 2. Such confirmations are al- most invariably present, and they fully justify the rhythmic irregularity. 38. Rule IV. The necessary subdivision of beats into fractions, and the addition of beats, or parts of beats, into notes of greater value (Ex. 23, No. i), must consequently be so effected that the heavy beats retain the comparatively longer tones; i.e., subdivisions must take place on compara- tively lighter, as a rule not on comparatively heavier beats, and vice versa. Beethoven Schubert Brahms *i) R^ular; 3d Qight) beat subdivided. — "2) Irregular, the heavy beat being so sub- divided that the following (Ught) unit becomes more weighty. The measure seems to begin with the second eighth-beat. — *3) An unusual example of irregular rhythm. Without its rhythmically definite accompaniment, it sounds like 3-4 measure, thus: n.j ,rrin=i -)— • — etc. 39. Rttle V. For these reasons, the repetition of a chord from an un- accented beat to an accented one (i. e., over an accent) gives rise to irregular rhythm, and should be avoided. 40. All larger measures than those which comprise but two or three beats, are called Compound, and contain as many accents as there are groups. Thus: Ex. 24. I or e J J J J jg iUL^J J J ag.^ nUT^ etc. Ace. Ace. Ace Ace. Ace. Ace. Ace. The upper figure of the time-signature always indicates whether the measure is simple or compound. In the former case it is 2 or 3 (I, 4, 4, 8> ^tc.) ; in the latter case, 4, 6, 9, or 12 /4 4 6 6 9 9 9 12 ... N U' 8' 8' 4' 4' 8' 16' 8 ' ^^^J MELODY. 41. Any succession of single tones is a Melody. Its quality depends upon the choice of the tones, and their rhythm or time-values. Melody is a manifestation of tone-relations in horizontal or progressive association, whereas Harmony associates tones vertically or simultaneously; the two partly similar processes are subject to the same natural laws only in a limited' sense. The principles of Harmony, in the broad sense of chord-succession, are very distinct; those of Melody far more vague. Har- mony is the substratum of all music, and its few sturdy laws fix themselves upon the mind easily, and so firmly, that their fulfilment soon becomes almost automatic, and indeed is often intuitive; but melody is guided by more veiled and subfle conditions, which can hardly be reduced to a system, but must be left largely to the individual talent, native sagacity, or acquired skill of the composer. Largely — but not altogether: As far as the natural decrees of harmonic combination and succession influence and determine the ruling conditions of melody, the latter can be reduced to apprehensible form, and this should be faithfully observed until essentially fastened on the mind. Pai. 42. ACTIVE AND INACTIVE SCALE-STEPS. is 42. Rule I, The general requirements of good melody are: a. smooth and natural undulation (to the exclusion of awkward interval-successions); h. rhythmic variety; c. definite and symmetrical delineation — including fre- quent confirmation of the melodic figures, either upon the same steps (as direct repetition), or upon other, M^iier or Icnoer steps (as sequence — par. 128 6). For illustration: Beethoven ^t>r^irriJ | JJJJ|ij; a»c;jjj|jjj j l j jj l j-:7^ •1) - ^ -e>- -G>- -iSr -g- fe=gl -s «■— S^ -S- -K- -;s- -S-. -s?- -SI- -&- Inact. Act. Inact. Ton. Dom. Ton. Common tone, or Axis ~g?- -zr- ej fj - Fundamentals Further illustration: g ?=ii=^ i f-V f f'v ^ Ex. 29. « — ^ P t yP P^f ^^^^ ^ Since step 2 may move in either direction, no attention is paid to it. 46. Rule III. The direction of the active steps 7, 6 and 4, may be coun- teracted by approaching them along the scale from the opposite side. Thus, step 7 may descend diatonically if preceded by step 8; and the same rule applies to the others. That is, steps 8-7-6-5, or 5-6-7-8, or 3-4-5 ar^ permissible. so, 47. Rule IV. The "narrow" leap (a third) is always good. See Ex. 29, measure 2, beats 3 and 4. Any leap beyond a third is called 'Svide." Wide leaps are always good when both tones belong to either one of the three principal triads (I, V or IV, par. 33). Thus: Ex. 81. ^^^"■l^^^-i -1 _etc i The IV C major, the I The V 48. Rule V. After a wide leap the melody usually turns: Ex. 82. ^ ^^^ i T ^-^ i J - -t=v J I * •J.-J - B Par. 49. ACTIVE AND INACTIVE SCALE-STEPS. 17 49. The chief exceptions to this rule occur: a) When the melody continues in the same direction along the same good chord-line. b) When the melody turns after the next beat. c) The rule is not imperative after the inactive steps i, 5 and 3. Ex. 33. b. ^^ v=J IV- i ^^^ ^s .^*-~-v^ 60. Any wide leap is permissible (whether in the good chord-line or not) down to step 7, or «/> to steps 6 or 4, on condition that these active steps then turn and follow their natural tendency. Thus: Ex. 34. a a. Down to step 7 ^ P ^E > ^ ^. Up to step 6 -y 1 J — hn f . Up to step 4 i-g) J..;>-^lj.>iJ L^^f^ll 1 1 -^-^-' ^1 p 1 1 l-i 51. The following wide leaps are faulty (C major) : i Efe i Ex. 35. ^ w^. «1) i L^r^ »3) *i) The first nine progressions are wrong, because the two tones do not lie in a^ood chord (par. 47), and the direction of some of the leaps is contrary to par. 50. *2) Successive skips in the same direction must follow the line of one and the same good chord (Ex. 33, a). 52. The arrangement of melodic figures in uniform repetitions, or se- quences, generally justifies any reasonable irregularity. Compare Ex. 22, note *3); Ex. 25, No. 2; and the following: l8 THE THEORY AND PRACTICE OF TONE-RELATIONS. Par. 53. *i) At each bracket there is a faulty leap, but the relation of the melodic groups justifies them. *2) The octave leap, and the repeated tone, are always good. LESSON 4. A. Write out Ex. 27 and Ex. 28 in every major key. B. Write a large number of melodies in different major keys, according to the above rules, and the following: a) Each melody is to he four measures in length (as Phrase; see par. 65). b) The melody may begin with the first, third or fifth scale-step (the tones of the tonic chord); the first tone may stand upon an accented beat (as in Ex. 30, and Ex. 36}, ' or upon the unaccented beat preceding the first measure (as in Ex. 29). See par. 66. e) The melody must end upon the kejmote, on an accented beat of the fourth measure (as in Ex. 29 and Ex. 30; Ex. 36 is an incomplete sentence, as it ends on the fifth step). See par. 67. Examples of the four-measure phrase will be found in Lessons 10, 13, 16, 18, etc. CHAPTER V. PARTS (VOICES). ERECTION OF CHORDS. 63. All music is based upon chords, which succeed each other in Harmony, as single tones succeed each other in Melody. These chord-successions (chord-combinations or chord-progressions) are effected by means of a niun- ber of simultaneous mdodic Parts or voices, each of which assumes one of the chord-tones, and serves, in conjunction with the rest of the voices, to unite the chords in horizontal order, interval by interval. See Ex. 42. 64. The number of parts or voices generally employed is four. The following example indicates their respective names, their average compass, and their notation: Bass Ex. 87. ^ (-P-) Tenor 'XZ -m ? t Alto Soprano i^S^^^^ s^ Bass and tenor (male voices) are written together on the F-sta£E, and distinguished by turning the stems of their notes respectively down and up; alto and soprano (female voices) both on the G-staff, stems respectively down and up, Ex. 38. Bass and alto, tha lowest of each class, are called parallel parts or voices; tenor and soprano likewise. Bass and sopiaao are outer voices, tenor and alto inner voices. Par. 55. ERECTION OF CHORDS. 19 66. The distribution of the chord-tones among the 4 parts or voices is called erecting the chord. Rule I. The parts must not cross. Rule II. The alto should not lie more than an octave from either of its two neighbors (i.e., soprano or tenor) ; but the lower adjacent voices, bass and tenor, are not limited by this rule. For illustration: good good Ex. 38. lof C. J l ..J l .-^.l J T :^: ^ ^*i) J. J^\ J ., J , ( ^ I ■[' I f ' [' ' T *i) This sign •$■ will be used to indicate bad (wrong) examples. Chord 2 is wrong, be- cause the alto and tenor are more than an octave apart. In chord 3, alto and soprano are too far apart. — *2) According to the notation, the soprano note e lies below the alto note g. This violates Rule I. 66 a. In 4-part harmony, aU triads (3-tone chords) have to be enlarged by duplicating one of their tones. RULE. The best tones to double are the principal steps of the scale, i.e., tonic, dominant and subdominant, especially when they are roots. Thus, in C major, the tones c, g or/; Prin. chords _ Subord. chords Ex. 39. C major i :^: -sr- I(cc) V(gg) IV (ff) m n(ff) vi(cc) iii(gg) b. From which it appears that, as a rule, the root is doubled in each prin- cipal triad; and the third is the best interval to double in each subordinate triad. Further, by inference, it is imwise to double the fifth in any funda- mental chord. 67. It is possible to omit the fifth of any principal triad (if found necessary), in which case the root of the chord is tripled. Thus: ■^»i) Ex. 40, C major i ¥ Inot_ -^ :^: o I(ccc) (cece) V(ggg) IV(fff) II *i) The fifth is never omitted, however, in a subordinate chord. 68. It is always justifiable to double a root, because of its importance in its chord. Therefore, it is also possible to double the root in a subordinate triad. Thus: 20 THE THEORY AND PRACTICE OF TONE-RELATIONS. Par. 59. good , better (Ex. 39) Ex. 4t. C major "S# • II(dd) -*•- _etc.: VI(aa) III(ee) II LESSON 5. Erect (in writing) the I of the following major keys, in as many forms as possible: F, G, D, A, E, B, F#, Bb, Eb, K\>, D|>. Study the given model (the I of C), and observe the fol- lowing rules: Always place the root in bass; double the root; place either root, third or fifth in the soprano: see par. 54; par. <,$; and par. 57. Root in soprano Third in soprano Fiftli in soprano ' iJ -J J J J , , 1 , ,-J-J 'fR^rf ^ Model ^M^j.! , / i ^-H i J — f ^^^^^^ (^ (7 rji \rj o'l?. f fg nrT'f [■ ' \- ^ ^ The i of C major, root in bass CHAPTER VI. RULES OF PART-WMTING. 69. Part-writing means " writing in parts "; that is, tracing the tone-line which each one of the four parts (or voices) describes in passing from, one chord into another. Comp. par. 53. In this, which is the vital and fundamental operation throughout the art of music composition, the following rules should be observed — by the beginner very strictly. 60. Rule I: The parts, each and all, should move as evenly, smoothly (as nearly horizontal) as possible. Wide leaps should be avoided. Diatonic movement (along the scale) is best. The narrow leap is always good. A tone which is common to two successive chords is generally (by no means always) retained in the same part. The bass, which is obliged (at present) to take the root of each successive chord, is privileged to make wide leaps. For illustration, the connection I-V in C major: Par. 6x. RULES OF PART-WRITING. 21 •1) *a) "B) -^r^ & — & & \ & & I J & — s^=s — s J J:^ I J -i J J-J- -i J d=^ £ r ' T pT ^ f ! T ' r ' ^r C: I — V N.B. Each of these "measures" is an example by itself, and not connected with the next. *i) Beginning with the root in soprano. The following tone in that part is either h, or d (measure 3), because these are the nearest tones. The alto also moves to the nearest tone (e to d, along the scale). The tenor holds the common tone, g. The bass is obliged to make a wide leap, from root to root; either up or down. *2) Beginning with the third in soprano, e, which moves along the scale to d, or up to g. "3) Beginning with the fifth in soprano, g, which is either held, or makes the narrow leap to 6. *4) Narrow leaps in alto and tenor. — *$) Omitted chord-fifth. 61. Rule n: Successive perfect fifths, and successive octaves (or tmi- sons) in any pair of parts, in parallel direction, are prohibited. Successive perfect sths sound disagreeable, in the majority of cases. Successive octaves are forbidden in part-writing, because they reduce the number of independent tone-lines (voices) and create a blundering impres- sion. For illustration: It is significant, that almost all of the above erroneous progressions are due, primarily, to the violation of other simple conditions, especially that of Rule I. In measure 1, tenor and bass progress parallel from one perfect sth to another. The real cause of the error is, however, the wide leap in the tenor. — Measure 2: bass and alto run parallel in perfect sths; at the same time, the a in alto is a faulty duplication of the fifth of the chord (par. 566). — Measure 4: soprano and bass progress in parallel octaves; at the same time, the tenor makes a wide leap. — Measure s : tenor and soprano run parallel in octaves; at the same time, the fifth (o) of the subordinate chord (II) is omittfed. — In the last measure there are consecutive unisons in tenor and bass, whereby the loss of one of the four tone-lines is dearly shown. N.B. It must be remembered that successive octaves and fifths are wrong in any two parts, but only when they foUow each other in the same pair of parts. In Ex. 42, meas. i, the perfect sth c-g, in tenor and bass, does not progress mto the next perf. ^th g-d, in tenor and alto. 22 THE THEORY AND PRACTICE OF TONE-RELATIONS. Par. 62. 62. As these erroneous parallels are induced by leading the parts in the same direction (upward or downward), it is generally preferable to carry the soprano, at least, in contrary direction to the bass. i good better good J- J I U better good better Ex. 44. parallel contrary ^ I ^ f.^_ C: I IV 63. Rule ni : The leading-tone should ascend, to the tonic if practicable, in each of the four parts. The downward tendency of the 6th and 4th steps should be respected in the soprano; but this is not so necessary (though always better) in the other parts. The 4th step in bass, as root, frequently ascends (Ex. 45, meas. 7). For example: 6th step 4th step «3) «3) «3) »a) "i) When the 4th step is doubled, as here, it is likely to ascend in one of the parts. The correct progression however (downward) is given to the most prominent or most melodious voice. In this case the soprano descends, correctly. *2) Here the 4th step and 6th step ascend in soprano. This is faulty. The ascent of these same steps in tenor and alto is not noticeable (as inner parts) and therefore permissible. *3) Faulty progression of the leading-tone. — *4) Bad leap in soprano (Ex. 35). 64. A general exception to all these rules of part-writing is applicable (and often almost obligatory) in case a chord is simply repeated, instead of being exchanged for a new chord. Hence, when the chord remains the same, wide leaps are good, and even desirable; the tendency of active steps is not urgent; and "parallel" 5ths are impossible. For example: Par. 64. RULES OF PART-WRITING. 23 Ex. 46. T ^\ fi? \A\ f'" C:I i i i J. J i i ^ gg IV IV i Measure i is monotonous; meas. 2 is far better. The successive octaves in meas. i and 2, and the successive sths in meas. 3 (in bass and tenor), are not "parallels." LESSON 6. Connect (in writing) the I with the V in C major, in as many ways as possible — but al- ways with root in bass — according to the foregoing rules. See Ex. 42, and the model, below. — Connect the I with the IV in the keys of G, E, and B major. — Connect the V with the I in F, B-flat and G-flat major (with especial vigilance in regard to the first clause of Rule III, par. 63). — Connect the IV with the I in D, A-flat, and E major (observing the second clause of Rule III). — Find and play these chord-successions at the pianoforte, the three upper parts in the right hand, and the bass alone in the left. Model. Ex. 47. \ M *s) «s) «4) «a) •7) *8) j7TJJlJ^|-;hl i |:d=J^ I r^r ^'^rjk^' '^ I f^ \ ^^fWY^fi C: I-IV 7 *6) B-flat: V-I *i) The choice of triads determines the bass progression; here c-f, because I-IV of C. The soprano takes first the root or "octave"; its progression is a repetition, c-c, as no other tone of the second chord (J-a-c) lies as near as this. The same is true of the alto («-/); and the tenor moves with similar smoothness from g to a. — *2) The soprano starts here from the third (e) and moves to /, the nearest tone. — *3) The leap from e to c is doubtful. — *4) The soprano starts from the fifth (g), and reaches either o or/ (note *6) smoothly, while the leap to c (note *y) is wrong, making parallel perfect sths with the bass. — *s) The bass may rise or fall; see Ex. 44. — *6) and *7), explained in *4). — *8) The a is leading-tone, and must, when in the soprano, ascend to b-flat. — *9) In an inner voice this descent of the leading-tone is not distinctly noticeable, and therefore not strictly forbidden. 24 THE THEORY AND PRACTICE OP, TONE-RELATIONS. Par. 65 CHAPTER VII. PERFECT CADENCE AND PHRASE. 65. The phrase is the smallest complete musical sentence. It is usually four measures in length; much more rarely two measures, or eight measures. 66. A phrase which is to represent an independent, complete sentence, begins with the ionic triad, either upon the first accented beat, or upon the unaccented beat preceding this accent. The root is in bass, as usual; but the soprano may take either root, third, or fifth of the chord. The body of the phrase consists of successive chords, ending with the Perfect Cadence. 67. The perfect cadence is made upon the tonic triad, with its root in bass and in soprano; upon an accented beat of the fourth measure (possibly second, or eighth, measure). And this final tonic chord is preceded by the dominant triad (toot in bass, but the soprano optional). Thus: Ex. 48. i Meas. I Wl 5t •1) ^E & :^=^^ ' *2) •J i-J- r I C major : V I V I *i) The cadence chord (I) may fall upon either accent, in compound measure (par. 40). — : *2) Comp. Ex. 47, note *9). When the leading-tone is in an inner part, and is approached front above, as here, it may make the narrow leap down to the dominant (in order to redeem the fifth of the I). 68. The skeleton of a 4-measure phrase in triple measure, is, then, as follows: a. b. Ex. 49. C major ^ i J, p i *1) n i ^5 ■gi- i V I V I *i) The light beat (unaccented), upon which this Phrase begins, is called a preliminary beat, and must be subtracted from the cadence measure. Therefore, the final half-note has no dot here, as it had in the preceding case. Par. 6g. THE CHORD-PROGRESSIONS J-V-I, AND I-IV-I. 25 69. The vacant beats (marked | | |) may be supplied with chords in an infinite variety of successions, and it is therefore first necessary for the student to learn the rules of chord-succession. For chords have their tendencies (like the active scale-steps), and not every progression is legitimate. The rules for the three principal triads are as follows: Rule I: The tonic triad can progress, under all harmonic circumstances, into any other chord of its own, or of any other, key. This is its prerogative as chief of the harmonic system. Therefore I-V and I-IV are good. Rule n : The subdominant triad (IV) may progress either into the I or the V. Thus: IV-I or IV-V. Rule ni: The dominant triad (V) may progress, legitimately, only into the tonic chord. Therefore V-I is good; but V-IV must be avoided. Rule IV: Any bass tone (or fundamental chord) may be repeated after an accent, but not over into an accent — as a rule, not over the bar. See par. 39. THE CHORD-PROGRESSIONS I-V-I, AND I-IV-I. 70. According to the above rules, the phrase-skeletons in Ex. 49 may be filled out as follows, employing only the direct connections of the I with the V and IV (not IV with V, at present) : Any key. | I'l V | I IV 1 1 V V V [ \\\ Or: iV 1 1 IV IV 1 1 V I V |T|1 Or: IVV|IIVIVlIVV|T||Or:I*II| VII|rVIV fi\\ Or, beginning unaccented: I|VII|IVII|VVV|I|| And many more. 71. In working out these harmonic formulae, in complete four-part phrases, it is necessary first to choose a key; then to write out the bass part (in each case with the root of the chord); then, as a rule, the soprano; and then the inner parts. Thus, with formula o, in F major: Ex. 60. I f > r:I -VI IV I V I *i) Note the wide leaps during chord-repetition (Ex. 46). Everjrwhere else (excepting in bass) the movements are smooth. — *2) The chord-fifth is omitted. These are but two of very many different solutions. 26 THE THEORY AND PRACTICE OF TONE-RELATIONS. Par. 7a. LESSON 7. A. Work out the formulae given in par. 70, as shown in Ex. 5°. in as many different major keys, and different ways, as possible. B. Construct a number of additional (original) formulae, using only the progressions I-V-I and I-IV-I, and chord-repetitions; and emplosang 4, § and 2 measure. N.B. This work must all be done away from the keyboard. The text, and the given Examples, may and should be studied at the piano; but the student's work must he mmbU, unassisted by the «Etemal tone. CHAPTER VIII. THE PROGRESSION IV-V. 72. The progression IV-V is called Foreign, because here there is no com- mon tone. That is, in passing from IV to V every tone changes. In this succession: a) Wide leaps are wholly excluded. And b) The three upper parts must progress downward (opposite to the pro- gression in bass). For example: i ^ I I 6 7 *2) ,*^> I ' ' r~t \j "r*r >' r ^r *^) r r r-f ' f-f T r Ex. 61. J=i C : IV - V *i) This is wrong, because of the faulty soprano progression (Ex. 27, and par. 63). The 6th scale-step should descend (in this chord-succession, at least). And there is a wide leap in the tenor. — *2) Parallel octaves in soprano and bass. — *$) Parallel fifths in soprano and 73. By adding this progression, the phrase-formulae given in par. 70 may be multipUed almost without Hmit. Thus (still in triple measure) : Any key: I I'l V I I IV V 1 1 V V |T|| iV 1 1 IV IV V I IIV V |T|] i'|vii|virv!viv |T|i i'| iv iv v 1 1 iiv | v v v l?!| And many more. 74. Formula a may be solved as follows (in G major, | measure) : Par. 75. THE PROGRESSION IV-V. 27 Ex. 52. fe ^ 1 P^ \ [^ 1 1 A i '^- JI J J r=f^ 5 -J5l-i ^ JSi. ±z r ?^ £ J- ¥^ i g '' G:I - VI IV VI V- I 76. The following solution, while technically faultless, would be unmusical, because of the monotony of the soprano. ? 1 Ex. 53. i a=^ ii^^ T f-T=r ^ J , ^ --^ J , j j—j- it ^F^ e ?^ Such versions must be avoided. It is of the first importance to obtain a good, interest- ing, soprano; for this is the chief melodic part, and melody is the soul of music. 76. In duple measure the possibilities are again greatly multiplied. For example: Any key: I I I V I V 1 1 IV IV V V ri IV V V I I II I'l IV V I I IV V 1 1 V V I IV I V vT|| c. ^ I I I IV V I I IV i V V I i II And many more. A solution of a (in B-flat major, g measure) : i Ex. 54. ^ iS ni^ OiJ^ r ■rx »i SE I *i) Here there is a wide leap in the tenor; but it is a permissible leap {down to step 7 — E'X. 34); and it obviates other awkward conditions that are worse than the leap. An oc- casional wide skip may, therefore, be justified. 77. A few exceptional connections, permissible for variety; or in order to avoid worse conditions; or as a means of securing a better melody in the soprano: 28 THE THEORY AND PRACTICE OF TONE-RELATIONS. Par. 77. •1) 1 i feiw^^p^ i TTmrft^^ ^f f^^^ f^ ^ Ex. 65. te jiji tet JJ^iiiij ^ e;^ f r I ' 'r^ |E r-^-r cadence cadence #3)1 i i^i^ it *7) V-l ^ i^^a f Tf S^=PP ■i i r i r ■«)-! ( ^^nTTr^tfHHHf r rir r K i ? P?^ V IV V V IV Y IV "i) The leap in soprano (from g up to c) makes octaves with the bass; but they are not parallel octaves, because the bass moves down from g to c. Therefore they are permissible. In any case, if there is, as here, a wide leap in both soprano and bass, it is important to make the leaps in opposite direction. The second measure is wrong, because the octaves are parallel. *2) This leap in the soprano is most common at the perfect cadence. See Ex. 57, a, end- ing. — *3) Here there are successive fifths in soprano and bass; this is wrong, although they are not parallel, because fifths are more sensitive than roots, and are always objectionable in proportion to their prominence. Opposite sths may be excusable in inner parts, but not in the outer ones. — *4) This is like Ex. 54, note *i); not wrong, even in soprano, but to be avoided. The next measure is similar; the leap in soprano from step ^ up to 6 is permissible. *S) Here the 6th scale-step ascends in soprano; permissible, but not good. Comp. par. 63. The next measure is faultless, because the chord remains the same. — *6) This measure is immelodious, in soprano, according to the rule in par. 48. The preceding measure is good. — *7) Here the V progresses into the IV, contrary to par. 69, Rule III. It is rare, but possible; best when, as here, the V immediately returns. Note the soprano. — *8) In this soprano position the progression is not good, because c in the soprano, as fifth of the IV, does not sound enough like a tonic to satisfy the progression of the leading-tone. — *9) The I may be repeated over the very first bar in a phrase, as here, since the unaccented beat is only "preliminary." See par. 6g, Rule IV; and Ex. 49, note *i). LESSON 8. A. Work out the formulae given in par. 73, and par. 76, in a number of different major keys, and with different soprano. B. Construct a number of additional original phrases, in all kinds of measure. Review Lesson 7, N. B. Par. 73. RHYTHMIC PHRASES. 29 CHAPTER IX. RHYTHMIC PHRASES. 78. By altering the time-values of the chords (instead of the uniform values used in the preceding Lessons), still more variety, harmonic and melodic interest, can be obtained. The student should realize that these three principal triads constitute the broad, and only, basis of all music composition. No chord, or group of tones, can be found, which is not a derivative of one or another of these three; precisely as there is no shade of color in the universe that does not originate in the three primary colors. See par. 33. Of all the various methods of treating these fundamental chords, which result in the infinite variety of styles of music, the most significant and prolific is diversified rhythmic manipulation. The work of this chapter is therefore directed to the very fundament of the whole musical struc- ture, and no amount of time spent upon it can be considered wasted. Review the chapter on Rhythm (par. 35 to 40) very thoroughly. 79. Rhythmic animation is secured simply by the use of different time- values. For illustration: i. . *a) *a) Ex. 56. j-J-iji J ^J. ^^^::t. \ a-. I A | | fir f E J i ? F r" r ' I f "i) The dot, applied to the accented beats (par. 38), represents one of the simplest means of modifying the rhythm. — *2) Here the beat is divided, the chord remaining the same. This is applied to the unaccented beats (par. 38). — *3) Chords which represent the sum of two or more beats should occupy accented beats. — *4) The cadence-chord is usually more than one beat in length. In duple measure: i * » S3 i^ Ex. 57. 9^ D: I T I VIVV *i) See Ex. 55, note *2). — *2) The chord-fifth must be omitted, because the leading- tone, g, must, in this case, ascend. — *3) See Ex. SS, note *7). 30 THE THEORY AND PRACTICE OF TONE-RELATIONS. Par. 80. LESSON 9. Construct a large number of original phrases, in different major keys, in triple and duple measures, and with rhythmic diversity (regular), imitating the above examples. CHAPTER X. HARMONIZING OF MELODIES. 80. As stated in par. 41 (which review), Harmony or Chord-succession is the substratum of all music; it is the source from which all melody is derived^ be it with or without direct and conscious intent. Hence, the system adopted in the above Lessons, of constructing phrases upon the basis of primary chord- succession, is obviously the most natural and correct one. Nevertheless, the process is often reversed; that is, the melody is generally conceived first, off-hand, apparently without reference to the underlying harmony; especially in the actual practice of composition, when the observance of harmonic con- ditions has become, so to speak, automatic. 81. In working out a phrase from the melody downward (i.e., in harmoniz- ing a given melody), the following facts must be recalled: The melody will not contain, at present, any other tones than the seven steps of its scale. Of these, the ist, 3d and 5th scale-steps belong to the I of the key; the 5th, 7th and 2d scale-steps belong to the V; and the 4th, 6th and ist scale-steps belong to the IV. Thus: Ex. 58. C major Step I Step 2 Step 3 Step 4 Step 5 Step 6 Step 7 y • y' ^ or i-' '^ * • ^ fr ■v * • /v \- 2 /? *' or <5 / or IV IV V or I IV 82. The tonic and dominant tones (steps i and 5) each belong, as is seen, to two different prin. triads, while each of the other steps represents but one. The choice between the two chords, at these points, will be dictated by the rules of par. 69, and other familiar estabUshed principles. For example, applying Ex. 58 to the following given melody: Steps: Ex. 59. C major ^ i tff I : I I I IV I I V V V IV *1) *8) *3) *4) V IV V V I IV »6) 'i) Of these two chords, the I must be chosen (par. 66). — *2) The choice falls upon the I; the V should not progress into the IV of the next beat (par. 69, Rule III). — *3) May be either I or V, because the following beat will be the I, chiefly because of the wide leap in Par. 83. HARMONIZING OF MELODIES. 31 soprano, which almost always calls for chord-repetition. — *4) The IV is not possible, as it •would give rise to successive sths (sopr. and bass) with the following V. Comp. par. 72 h. — •5) The IV is canceled by par. 67. 83. The chords (and the bass part) will therefore be as follows: I I I I IV (V) I V I IV V I I I I J (^y Ex. 60. frr gii (^ 111 ^ I *i) Ex. t,i, note *9). 84. Another illustration, in duple measure: Steps: r^ Ex. 61. D major i fe 4- X i: ^B Chords: I V I V I V I IV IV V I V V 1' (IV) (IV.) (IV) (IV) (I) (IV) »i) »2) *2) »3) *a) *i) The triads in parenthesis are canceled. — *2) The IV should not follow the V. — *3) This may be either the I or the V; the I, because of the wide leap in soprano; or the V, which is the better of the two, because it is wiser to change the chord ctt an accented heat — though not imperative at the secondary accent. LESSON 10. Harmonize the following major melodies, according to the above directions: 1. " 2. ^ S P S 3. i=p= :^sid= •a) FFPf 5#: B -t* 4 * i » ei.\ VA.d h fii¥i- ±iU Se b . o » p iiL , I r>^ JHJ j jj j j i %] : flt i^ ttct i s^ =i=F tt g. ^^^ -is>—^ 32 THE THEORY AND PRACTICE OF TONE-RELATIONS. Par. 84. - 10. '-'^ ' «a) 11. =P=PE y-r-r^^ ^ *4) 12. i lA :^^=^ ft ffi: ^^Ebf-rT^-j p*=^=^ EM^^ ^^^S a F^ «5) 13. 14. S tf T-f^^ g^ -F r5==F=p g «6) tf-P^R 15. ^ fe^^4-t =p=-» #^ »e) •7) ^^^ ^^ |tfi.r-r rir r r jii ^ s^glg^ EP ^ ^?=f=-^ "^m ^^E^ g •i) Turn all stems upward. — *2) The wide leap (and slur) usually indicates that the chord remains the same. — *3) At this wide leap the chord must be changed, because of the scale-steps represented. — "4) Here the chord must be changed, despite the wide leap in the melody, in keeping with par. 69, Ride IV. Beware of parallel octaves in soprano and bass. Review Ex. ^$, note *i). — *s) Here, also, the wide leap must be harmonized with diferent chords, because the phrase should begin with the I. Again, see that the bass skips in op- posite direction to the soprano. — *6) See Ex. 55, note *9).— ■*7) When the leading-tone descends, as here, with a narrow leap to the sth step, it is evident that the chord must re- main the same; for only chord-repetition justifies the melodic licence.; see Ex. 46, meas. 4. *8) Compare Ex. 46, measure 1. The chord should be changed for each of these four beats. — *9) In this chord it will be found necessary to double the third {b-flat). This licence is the only means of counteracting the very unusual wide leaps in the soprano (which cannot be harmonized with the same chord). Par. 8s. THE HARMONIC MINOR MODE. 33 CHAPTER XI. THE HARMONIC MINOR MODE. 86. The line of research and argument in Chapter I, leading up to para- graphs II and 12 (which see), proves that, of the two modes recognized and employed in modern music, that one known as major (because its prin. triads have a major third) is the natural one. 86. The other, i.e., the minor mode, is consequently to be regarded as an unnatural or artificial mode, and is accounted for as an arbilrary modification of the natural major mode. 87. This modification affects the two mediants, namely: The third and sixth steps of the major scale, which are lowered (by an accidental) so as to transform the corresponding major intervals into minor intervals. No other steps are changed. In other words, the minor scale is derived from the corresponding major scale by lowering the third and sixth scale-steps of major. Thus: C, major mode (Ex. 4) C, minor mode 13346678 IS34:SG787G54331 88. The scale thus obtained is called the harmonic minor mode. It is the only theoretically accurate minor scale, and is the same in both ascending and descending succession. Still other alterations, rendered necessary by melodic considerations (to be explained in due season), are based upon this harmonic minor mode, which must therefore be first thoroughly mastered. 89. It appears, then, that a minor scale is derived from the major mode of the same keynote — C minor from C major; A minor from A major, etc. And the lowering of the 3d and 6th steps results from transforming the prin. chords I and JN from major into minor triads (comp. par. 34). Thus: C minor Scale C minor Chords Ex.^§i^^^ I IV V«i) "i) Observe that the dominant chord is not changed. N. B. The best reason that can be given for the lowering of these particular scale- steps (3 and 6), is, that these alterations do not impair the essential consonant quality of any one of the three principal triads, and therefore do not interfere with any legitimate function of the scale and chords — as any other changes would. It is true, the 7th step might also be lowered without injuring the dominant triad, but it would interfere with the significant fimction of the leading-tone, and therefore it is not done in the legitimate, harmonic, mihor mode. (The lowering of the 7 th step, and other alterations, belong to the domain of Altered chords.) 34 THE THEORY AND PRACTICE OF TONE-RELATIONS. Par. go. 90. It is significant that, while the tonic and sub-dominant chords are major in major, and minor in minor, the dominant chords remain the same (major) in both modes. SIGNATURE OF MINOR. 91. The minor mode has no specific signature. For convenience (and foi that reason only), signatures for minor are borrowed from major, and the choice falls upon the third scale-step of the minor scale, that proving to be the most convenient. That is, the signature of a minor mode is taken from its third step: For c minor, the 3d step being e-flat, three flats are adopted. Thus: •1) i C minor Sig. of e-^ai (3d step) fc g ^^ Ex. 64. S 5 *i) The accidental before b (the leading-tone) shows that the adopted signature, though the most convenient one, does not exactly fit the scale. It must be remembered, then, that in the notation of the minor mode with its customary signature, an accidental is necessary at the jth scale-step. N. B. The major key represented by this minor signature, is called the relative major — in this case C minor and E-flat major. The relation is significant, as will be seen; but it must not be confoimded with the still closer relation of derivation. 92. The treatment of the principal triads in minor corresponds in every respect to that of major, excepting only that the succession of the 6th and ph scale-steps (in either direction) should be avoided, as it is an interval of the augmented second — an unnatural melodic movement. For example: C minor augm. 2. Good i Ex. Se 1^^ ^^^ i Bs.,^ sz. 65. rS-^ 19-^' . iJ g O ^"S-g V V 'S. '/■ 93. This succession (6-7 or 7-6), has not appeared in any of the foregoing exercises in major (comp. Ex. 51, note *i); therefore, any phrase in the pre- ceding chapters may be transformed from' major into minor with no other changes than those of accidentals. For illustration, Ex. 52 : G, major mode G, minor mode Par. 93. THE HARMONIC MINOR MODE. 35 *i) Compare these at the piano. — "2) The signature is that of B-fiat, that being the third step of the G minor scale. — *3) The leading-tone of G (major or minor) is f-sharp; as this is not in the adopted signature, the accidental is everywhere necessary. LESSON 11. A. Write out all the major scales (excepting D flat £uid G flat) and place their corre- sponding minors below them, using no signatures, but accidentals, as follows: i C major -Si-x -«- C minor S) ^ f^ I o o etc. The minor scales of c-sharp, g-sharp and d-sharp are derived from the corresponding major scales, in the same manner. This is a little more difficult than the process with the more familiar scales, but must also be included in the lesson. B. Harmonize the following melodies, as before. The choice of chords is governed by the selfsame rules (Ex. 58). Do not neglect the accidental before each leading-tone: i *i) *a) 2. *1) Ml 4 J J i+»=^ a. u ''ff ■ tta 1 "<■'> — 1 it 1 / • Tl h ^ r * (^ • * f( \ \ jtJ * • J r V ) 1 . £1 LI fl^ U — ■ — 1 &—' Li * J 1 m ^P 3 iit =r^ itat ##tg ^3: •— • ' S'^ 'p^ 5. i teE Wf '*-• — i~ I I I W |i=t*==?=^ ^i=^ 6. Is te^ II la p^i *3) irrrr^^-^rhrrtf i ^^ ^ &^=^4 1:^ tb» tf ^^^gj lA f -KO - Sh:^ ^^=F <=^— »- lite: i 10. 5 •; i^ ^, t 1 «4) b t. .5) 3 '^ ^_ 1^ J :/ 36 THE THEORY AND PRACTICE OF TONE-RELATIONS. Par. 94. i w ^ 12. IA% n f-r» tq=t rr-TT ^^^ 13. 1^1 I , J^ J W— ^ =^ *i) As a rule, the wide leap is harmonized with the same chord. — *2) Since the last tone is a, as keynote, this phrase is in A minor, which is treated like A major. — *3) There is no alternative here but to use the same chord for both measures (an exception to par. 69, Rule IV, induced by the skips in soprano). — *4) Like Lesson 10, note *7), which see. — *5) Here the IV must follow the V, because of the succession of steps in the melody. C. Construct a number of four-measure Original phrases in minor, exactly as in Lesson 9. CHAPTER XII. SUBORDINATE TRIADS IN MAJOR. 94. The triads upon the subordinate scale-steps (the II, VI, and III — see par. 33), are not to be regarded and employed as new and independent chords, but as the parallels of the three principal triads, in the place of which they are re- spectively used, chiefly for the sake of variety. 95. The relations are as follows: The VI is the parallel of the I (Tonic element) ; The II is the parallel of the IV (Subdom. element) ; and The III is the parallel of the V (Dominant element). In other words, the VI is the subordinate representative of the tonic element; the II is the subord. representative of the subdom. element; and the III the subord. representative of the dominant. For illustration: Principal ; *l) Subordinate ; Parallel relations ; P^l^ Ex. 66. ^EEi^EF f: IV *2) n VI m -VI IV- -II -in *i) Comp. Ex. 19. — *2) It will be observed that the parallel chords represent relative major and minor keys (Ex. 64, N. B.) — that is, keys with corresponding signatures (C major — A minor, etc.). Par. g6. SUBORDINATE TRIADS IN MAJOR. n THE n. 96. The strongest of the subordinate triads is the II, because it follows the V, in perfect-fifth succession, as second-dominant (see Ex. 5). Assuming the I and V to be the two vitally important chords of the key, it follows that the perfect-fifth relatives of these, on either side, constitute the most im- portant secondary rank. For illustration: The II is thus very closely allied to the IV, and is very nearly, if not wholly, equal to the latter in importance — though perhaps somewhat less frequent. The II is therefore a semi-principal chord, and has, in its treatment, many of the traits and privileges of the principal triads. This will be more clearly seen further on. 97. The best interval of every subordinate triad is its third. The triad is at its best when the third is in the soprano. And, as shown in par. 566 (which review), it is usually best to double the third, although the doubled root is always good (par. 58). 98. The II often takes the place of the IV before the perfect cadence. Thus: *3) «5) Ex. 68. C major gffpTiVr ' r'ff'r ' f f ' r' ' fi ' r-" J -i. 4 nv— I II I n n 11 v ' "i) Doubled root. — *2) Third in soprano, and doubled third; this is better. The 4th step, in soprano, should descend. — *3) A good leap, according to Ex. 34. — *4) This is one of the very rare cases where the 6th step ascends to the 7th in the soprano. Note the chord-succession, II-V. — *$) Like Ex. 55, note *3). 99. The progressions of the II, in the order of preference, are as follows: From the II ; n— V n- -VI n- u — ^iv Into the II ; IV — u VI — n -n V — n g^ 3 Ex. ■2=*^ 39. *l) »3) »8) ?? •4) »6) *e) *i) The best progressions from the II are a perfect fifth down and up: II-V and II-VI. — *2) This is a "Foreign" progression (par. 72). It is stiff, and imcommon, and should be avoided. — *3) No subordinate chord can legitimately precede its own principal triad. There- 38 THE THEORY AND PRACTICE OF TONE-RELATIONS. Par. loo. fore II-IV is not good. — *4) This, on the contrary, is an excellent progression, ahnost equivalent to chord-repetition, since IV and II are parallels. — *5) The I can progress in all directions (par. 69, Rule I); therefore this foreign progression is perfectly good. — *6) Simi- lar to the doubtful progression V-IV. Compare par. 69,, Rule III. N.B. This table of chord-movements must be thoroughly memorized. 100. The connections of the II, in four-part harmony: 3 33 3 *^^ m Ex. 70. I ^bBa ^3^ C; n-vi *l) n — I IV— II vi-n I— n The best progression, II-V, is illustrated in Ex. 68. *i) Doubtful, because the II rarely soimds well with its fifth in soprano. And the so- prano progression is inferior. — *2) This is the only plausible form of the very rare pro- gression II-I; each chord has its third in the soprano. — *3) The wide leap in soprano is perfectly good, because the connection of parallel chords (here IV-II) is practically the same as chord-repetition. — *4) The strict rules of the foreign progression IV-V, given in par. 72, are somewhat less rigorous here, because one of the chords, being a subordinate, may have either a doubled root or doubled third. In this measure, the soprano moves upward, in 3ds with the bass. In the last two measures, all three upper parts run contrary to the bass. THE VI. 101. The VI is the counterpart of the I, and is used exclusively as in- ferior representative of the tonic harmony. 102. As in the II, the best interval is the third of the chord, which is usu- ally doubled, and which appears most frequently in the soprano. 103. Being a tonic chord, the VI can also progress into every chord of its key (par. 69, Rule I), excepting into the 1 (Ex. 69, note *3). Therefore, the VI may also precede the perfect cadence. Thus: «i) «i) 661 .5 Ex. 71. C major m ^-^ J^tLhUa PFfPf -f—0- *3) m *3) -zH frrPf, ± ilA-JJJ.. .f ii:^:i lA Ui,r/\r\^^^H^^^^ m ww^ r~n~T-r VI V— I VI VI VI VI *i) In the first measure, the third of the VI is doubled; in the next measure, the root. — *2) Extremely rare, and scarcely permissible. The VI should never be used with its root in soprano. — *3) A faulty leap in soprano; and inexcusable, because a foreign chord-pro- gression (par. 72a). Par. 104. THE VI. 39 104. The full table of connections of the VI is as follows, in the order of preference: ■$■ Into the VI; From the VI ; S r^'-e'- Ex. 72. ^^ VI — V VI- -II VI— rv VI- »i) -VI V — VI n- -VI rv— VI *i) A subordinate triad preceding its own principal chord. See Ex. 69, note *3). — *2) This progression is correct, according to par. 6g, Rule III, because the VI is a tonic chord. N.B. This table, also, must be thoroughly memorized. 105. The connections of the VI, in 4-part harmony: a ^ j J i J-JW JiJ^r' J i 'j"-J|J J | J I I rrrvrn r ' fT^ Ex. 73. r f r r r r r 7 r r , . a i i™- i r nr r i r i ' r i ' r ^3^ C: VI— n VI— IV I — VI V— VI *i) The fifth of the VI is rarely used in soprano. — *2) Two wide leaps in parallel motion (soprano and alto) ; good, in this case, because they are parallel sixths. — *3) Compare Ex. 70, note *3). This, again, is practically chord-repetition. — *4) A foreign progression. Note that two upper parts run contrary to the bass. Compare Ex. 70, note *4). LESSON 12. A. Write out the following chord-successions in the usual manner, without regard to rhythm (uniform quarter-notes or half-notes), in a number of different major keys: rv-ii-v-i II vi-ii-v-i II i-ii-v-i II iv-ii-vi-v-i II i-ii-vi-ii-v-i II I-V-II-V-VI II I-VI-IV-V-V-I II I-V-VI-VI-V-1 11 1-IV-II-VI-VI-IV-V-I II N.B. A part of the Lesson may be done at the keyboard, the three upper parts together in the right hand. B. Construct a number of Original 4-measure phrases, in different major keys, similar to Lesson 9. CHAPTER XIII. SUBORDINATE TRIADS. MELODIES. 106. In applying the subordinate triads to the harmonization of melo^ dies, the following facts must be recalled: that the VI takes the place of the I (par. 95) and therefore harmonizes the ist step of the scale (more rarely the 3d step); that the II takes the place of the IV, harmonizing the 4th 40 THE THEORY AND PRACTICE OF TONE-RELATIONS. Par. 107. ste^, (rarely the 6th step); and that the II may also be used as independent harmonic factor (par. 96), harmonizing its own step — the second — (just as the I harmonizes the ist step, the IV the 4th step, and the V the sth step). Thus: Chord; VI »l) [yij VI II «3) *l) 11/ V— I v-i ii-ii V V VI n V *3) V— VI (V-n)ii V v^v (n— VI) *i) Always the best step for this chord. — "2) Rare; Ex. 73, note *i). — *3) Very rare; but see Ex. 68, note *4). And remember that abnost any condition is possible, when the chord remains the same. 107. Applying these rules to Melody 18 of Lesson 10, the following sub- stitutions may be made: Step Ex. 75. C major Step Step J "^ ^v, I ^ ; i f i r r r . i . r ^ VI *i) (I) I n (IV) VI (I) *i) Not the II. — *2) Not the VI. 108. Furthermore, with special reference to the second scale-step: ^ ^J=U 4: U^ r ' r I f TT Ex. 76. J- i J i J i -^ i J §3 «a) ^L^P- r " ' :. f T «i) C VI (IV) (D VI (I) »3) n (IV) *i) Whether the 2d step is to be harmonized with the V, or with the EC, depends largely upon the next melody-tone. This d might be either V or II, as the VI follows. — *2) This d cannot be a V, because the latter would not be repeated over the bar. — *3) The following tone (e) must be harmonized with the I; therefore choice falls upon the V for d, as II-I is objectionable (Ex. 69, note *2). — *4) Must be the V, as the II shoulAnot be repeated from the preceding (light) beat. Par. log. THE III. 41 THE m. 109. As shown in par. 32, and Ex. 19, the III is the last, and weakest, of all the triads of its key, as it lies most remote from the tonic centre, in the chain of perfect fifths. It is therefore very rare, and limited in its connections. The only way in which it may safely be used (and, in fact, must be chosen) is in harmonizing the leading-tone, when the latter descends into the 6th scale-step. In this case the III is followed by the IV. In very rare cases it harmonizes the 5th step, and may then be followed by the VI or the IV. For example: a. b. Vfiri rare ; 6 *1 6 6 Ex. 77. C major r^^ -J I J ^ ^rm ^ -X vrvrv?. "^^ ni IV VI III IV III VI m IV 110. The following table shows the application of principal and subor- dinate triads to the seven steps of the scale: Steps : Ex. 78. C major i Exceptions: *3) 6 7 7 Triads; yi I (Ylf IV V V7' »i) rrr ■tT n in *i) Note that steps 3, 6 and 7 are limited almost entirely to the principal triads I, IV and V respectively (each with its third in soprano). — *2) These irregular melodic progres- sions are explained in par. 46. Each of the melodic irregularities is attended by a correspond- ing harmonic irregularity; steps 6 and 7, when they progress properly, are always harmonized with the IV and V; but when they move improperly, the parallel triad of each (II and III respectivdy) must be taken. LESSON 13. A. Re-harmonize, with the material of this chapter. Lesson 10, Nos. i. 2, 3, 4, 7, 10. Refer constantly to Ex. 78. B. Harmonize the following melodies: 1. 2. m ^9 s -^+* 3. tt fj^^^' i Qj^mM^ms VI •1) 42 THE THEORY AND PRACTICE OF TONE-RELATIONS. Pat. iii. 5. g a 7 ■zn Ifc 6 It -SP-fS- ^ #■ -.•- -i=H=^ f^ P ^ «i) .3) *8) 7. ^ m ^^^ m^ »iig ^ ;^ yr^HTT ^ tt «4) 8. 7 8 **) p ^^^ fe i ^ m ■•-■-SH «4) ttf 7 a ifc_ _a 7 .1) ^^ IfK PPSB ^s f^ -*-•- lO. -^— ^ -rn. :ffl: « 11. w i^EE? ^ ft • — m- ■d-\-» m Bt Crr j r ! '^ ^t 12. 11; ^^^ m ..) tf: 13. =(C^C H^^q i ^ ?c:p= 4=1=4 3t=* »s) m i 4= r • — p — p- P 1= P c t=tfe^ *=tti IV »3) ' *5) *i) Ex. 78, note *2). — *2) At each of the repeated notes in this melody, the chord must be changed. — *$) The III is possible here (followed by the VI). — *4) Each of these half- notes may be harmonized either with one chord, or with two (as quarter-notes), at option. — *s) This second step must be harmonized with the II (not with the V, because of the wide leap, and foreign progression). CHAPTER XIV. SUBORDINATE TRIADS IN MINOR. THE PERIOD-FORM. 111. The notation of the II, VI and III in minor must conform to the harmonic minor scale. Thus: Ex. 79 C minor .or^ i -^ a t/ s ±Z %= ^ u tsi- n VI m Par. 113. THE PERIOD-FORM. 43 a) The II, having a diminished fifth, is a diminished triad. It occurs very rarely in its fundamental form (as triad, with root in bass). b) The III, having an augmented fifth, is an augmented triad. It is even less frequent in minor than in major. c) The VI is a major triad, and is of equal importance in both modes. Review ihe'notes to Ex. 63, N.B., and observe the effect upon the subordinate triads of lowering the 3d and 6th steps. 112. The II and III in minor are, therefore, Discords, and cannot be used here. Of the three subordinate chords in minor only the VI may be used at present. See par. 92, which appUes also to the VI. THE PERIOD-FORM. 113. When a musical sentence is eight measures in length, it usually sep- arates into two four-measure phrases. The first of these is called the Ante- cedent phrase; the second, the Consequent phrase. 114. The division is made by a cadence in the middle of the sentence (on an accent of the fourth measure), which is called the Semicadence, and differs from the .perfect cadence in being made upon some Ughter form of harmony. 115. The semicadence is most frequently made upon the V (preceded by the IV, 11, VI, or I). But any other chord may be chosen, excepting the ni; and it is sometimes the I itself, with third or fifth in soprano (not with the root). The semicadence chord must be longer than the adjacent chords (similar in length to the perfect-cadence chord), in order to interrupt the rhythm, and mark the end of the Antecedent. More rarely, the whole Period is only four measures long, in which case the Antecedent phrase will contain only two measures. Comp. par. 65. The following illustration is a small (two-measure) Antecedent; that is, the semicadence falls in the second measure: Antecedent : Ex. 80. T 171 "I ii f III 'I r M^ III n r p^E^M^^ nv IV V IV *8) VI n •4) I I V »i)VI *i) Or the VI, by taking a in bass. — *2) The semicadence chord. — *3) The semi- cadence on the VI is called "deceptive," because V-VI is substituted for the expected V-I. — *4) This semicadence, on the I, is sometimes called an " imperfect cadence," as it is prevented from being a perfect cadence only by the absence of the root in soprano. 44 THE THEORY AND PRACTICE OF TONE-RELATIONS. Par. ii6. 116. The second phrase (the Consequent) should begin on the same beat as the Antecedent (with any convenient chord), and must close with the perfect cadence, on the same accent as the Antecedent, which it must ex- actly equal in length. The Antecedent sketched in Ex. 80 might be contin- ued as follows: y Consequent *3) | Antecedent ir^'^^^h^ ^ i l'r]n l . \ -zi- s' ^ ^^^r ' frr ' r r' r r " rr ' r ^ g?f=f Ex. 81. *1) I 'jjj,jj ^ rjJJ , j J J , ^-J | j--Jr i ^^ J * §ie^ £ £ ^^^ P ^ f- .1 V. V I, tZIiL .V I, *3) «4) *2) *4) *i) Compare these 4 measures with the 4-measure melodies of Lessons 10, 11 and 13, and observe the distinction between the Phrase (as uninterrupted chord-series), and the Period (or Double-phrase), with its semicadence in the middle. Not the number of measures, but the presence or absence of a semicadence defines the form. — *2) Semicadence. — *3) The melody of this Consequent phrase runs parallel with that of the Antecedent. This is favorable, but not obligatory. Comp. par. 42c. — *4) Perfect cadence. LESSON 14. A. Re-harmonize Lesson 11, Nos. 6, 7, 9, 11, 12 — introducing the VI at least once in each melody. B. Write a number of Original 8-measure Periods, in major; and a few in minor, with the three principal triads and an occasional VI. C. Write out the following series of chords, in 4-part harmony as usual, formulated in Phrases of 4 measures: i-v-vi-rv-v-i-v-i Use the following forms (the rhythm, location of bars, and chord-repetitions being optional) : 1. C minor, 2-4 measure, beginning on heavy beat; 2. A minor, 3-4 measure, beginning on light beat; 3. F-sharp minor, 4-4 measure, beginning on heavy beat. DntECTioNS: 1. First fix the Jofi. These may be drawn between a«jr 0/ ife gii;eji cforif J, almost unlimited option being possible. But care must be taken to preserve the sum of four measures, and to locate the Cadence properly. 2. Determine the number of melody- tones for each measure; this will decide the number of chord-repetitions that may be neces- sary, and the rhythm. 3. Write out the bass; then the soprano; and then finish. CHAPTER XV. CHORD-IITVERSION. 117. The fundamental forms hitherto employed (with the root in bass) are naturally strong and heavy, but also to a certain degree inflexible and ungraceful. Therefore it is not only admissible, but often desirable, to modify the form of a triad Par. ii8. CHORDS OF THE SIXTH. 45 hy placing either its third or its fifth in the bass, instead of the root, thus effecting the inversion of the chord. This is touched upon in par. 25, which see. 118. This alteration of the lowermost part affords the bass similar op- portunities for smooth and graceful melodic progression (instead of the almost constant succession of wide leaps). 119. When the bass thus assumes the third of the triad, the latter stands in the first inversion. For illustration: Chord of C Chord of C 4-^ ±^ Chord of G of D of F . 1 I ^ I J U43 1 i ^i i 4- ^ ^ ^^ =#-THIRD- Fund. form First Inv. -^-BooT- 1 r Fund, form First Inv. First Inv. 120. The first Inversion of a triad is designated " chord of the sixth," because the shape of the triad (as regards its component intervals from the bass tone upward) has changed from "root — ^d — Sth," to " bass tone — Sd — 6th": Triad (c-e-g) First Inversion (e-g-c) Ex. 83. i •J : BOOI-0- The figure 6, when attached to any bass note (usually below it) will therefore serve to indicate that the first inversion of the chord is required; or, in other words, that the bass note in question is not the root (as hitherto), but the third of the chord; — the root must there- fore be sought a 3d below the given bass tone: a Chord of C Chord of A CHORDS OF THE SIXTH. 121. Rule I. In a chord of the 6th, the soprano usually takes the root — or, if more convenient, the fi,fth of the chord. But rarely the third, which should not appear simultaneously in both soprano and bass. Ex. 840. Rule II. Double, as usual, any of the principal tones of the scale (tonic, dominant, or subdominant — par. s6a). That is, either the root or the fifth; or even the third, in a subordinate sixth. In other words, the rules of dupUcation, in the first inversion, are less strict than in the triads, and subserve, chiefly, the purpose of good, smooth melo- dic progression. Ex. 84J. 46 THE THEORY AND PRACTICE OF TONE-RELATIONS. Par. laa. Rule III. In an inversion, no internal should be omitted. Rule IV. Change the bass tone at each accent, and change the chord also if possible. For illustration: i. Chord c-e-g d-f-a a. Chord c-e-g g-M e e «4) 6 6 e ni»a) ffTf a 6 a e e Vi«3) *i) In C major, c-e-g is the tonic chord, or I. With e (the third) in bass, it is the ist inversion; this is indicated by Ii (spoken: One-one), and figured 6. — *2) The II (d-f-a) with / in bass; hence IIi (Two-one). — *3) The V (g-b-d) with 6 in bass, hence Vi (Five- one). — *4) Doubtful, because e is doubled. — *$) These three duplications are all ad- missible. — *6) Doubled leading-tone — always wrong. 122. The first inversions of the I, V, IV and II are excellent, and should be freely used. But the first inversion of the subordinate VI and III must be shunned. 123. Appljdng the principle of first inversion to the following chord-series, 1 1 v-i I rv-n I v-v 1 1 H the results would be: Ex. 85. C major *i) »a) «3) «4) "s) *b) *6) ifc AUJ-, AAA J. jj. A Al J. AAj.J,j ,j/" r2i :££: ^ m p^ -IZ- iS>--P- pw *i) The V (g-b-d), with the third in bass and fifth in soprano. — "2) IV (f-a-c), third in bass, root in soprano. — *3) Vi — root in sopr. — *4) Ii — root in sopr. — *s) Hi — root in sopr. — *6) In a complete phrase, neither of the two cadence-chords should be inverted. Furthermore (the bass alone) : »i) *a) o Ex. 86. Bass *8) # *4) i 1=^ 1= H=- ■?5l- -zr- a a e e or : *5) S^ [•y e ft > Par. 124. CHORDS OF THE SIXTH. 47 *i) In a complete phrase, the jirsl chord is not inverted. *2) This descending leap to the leading-tone is admissible. See Ex. 34. — *3) This progression violates par. 63. — *4) The ascending leap to the leading-tone is wrong. Comp. note *2). — *5) This version illustrates how hoth chord-fotms may appear, as repetition, during the same beat. LESSON 16. A. Construct complete 4-measure phrases in A major, E-flat major, F major and D ™^Jor, 3-4 measure, with the following chords: 1 1 1-I-VI I V-I-IV I i-n-v 1 1 II using occasional chords of the 6th (i.e., the third in bass) as shown in Exs. 85, 86. Remember that the VI is not to be inverted. Also, that the first chord and the last two chords are not inverted. Place the figure 6 below the bass at each first inversion, as in Exs. 85, 86. B. Construct complete 4-measure phrases in E minor, D minor, B minor and F minor, 4-4 measure, with the following chords: 1 1 V-V-I-I I IV-IV-V-V I I-VI-IV-V 1 1 11 utilizing the first inversion as before. CHAPTER XVI. CHORDS OF THE SIXTH. MELODIES. 124. The chord-basis of the given melody is defined in the usual manner, according to the Table in Ex. 78, without reference to inversion. This being done, choice is made between the root or the third of the chord, in bass, as shown above. The root is generally chosen in bass when the soprano has the third (or fifth) of the chord; the third is taken in bass most commonly when the soprano has the root of the chord — more rarely, when the fifth is in soprano. Re- view par. 121, Rule I. 126. Assmning the chord-basis of melody No. i, Lesson 13 (slightly modified) to be as follows, ^ I — the bass voice might run thus: IV IV V I Ii IV, VI IV V V n IVi Hi Ex. 87. Bb major (iSe J J ■J i b) ^^ i-J^r ? ^ a n) a »a) •s) a a f= 48 THE THEORY AND PRACTICE OF TONE-RELATIONS. Par. ia6 II J J (1 ,j J J. i J i i i r^f=rP^^ e ' e *i) ♦a) 6 a »2) a a *i) Root in soprano, third in bass. — *2) Fifth in soprano, third in bass; good, but less common, and only in principal chords. 126. Another important advantage of inversion is, that it facilitates the chord-progressions. All objectionable triad-progressions become possible when the second chord of the succession is inverted. For example: i ? good J , I J.I good good. or; J i J J . J JiJ ^faj IE r r ' r r ■ rT ^ ^-^v^-H— f =^ Ex. 88. i J -i V IV V iVj u I n ij VI VI SUCCESSIVE SIXTHS. 127. From the above it follows that chords of the sixth may be connected each other, in any order. Such "Unes of 6ths" are common in music, and very effective; but they are subject to the following rules: a) The bass should move smoothly along the scale, or, at most, with a narrow leap. A wide leap, from one 6th to another, is very rare (but see Ex. 85, third version, chords 3 and 4; and Ex. 86, chords 1-2, 4-5-6). b) The root should always be in the soprano, so that bass and soprano run parallel in 6ths. c) Care must be taken to avoid absolute parallel movement in all four parts. d) Further, even the forbidden VI] and IIIi (par. 122) may appear in such a line of 6ths — that is, when followed by another chord of the 6th. Thus: Par. laj. SUCCESSIVE SIXTHS. 49 •a)VIi 1*8) in, m, m. ^ iiiitij If'i'i i/i''.','J,iA','. V i' /i^ | >11>' J-P- ij J:il :^i-ij *i) F^ AAA' a e a a a a a e a *i) This might also be a 6th (Ii), but the triad is better, after so many inversions; and the progression IIIi-VI is correct. — *2) Par. i2-jd. — *3) Par. 1276. — *4) Par. 127c. Note how the tenor is obliged to leap, in order to avoid parallel octaves and fifths with the other parts. — *5) Par. 127c. Such absolute parallel movement in all four parts is tempting, but wholly wrong in strict part-writing. — *6) Par. 127a. SEQUENCES. 128. a. The reproduction of a cluster of tones on the same steps consti- tutes a simple repetition: Beethoven, Symphony No. i. ^ Ex. eo. re Rep. I I I I Figure modified repetitions J. The reproduction of a figure or cluster of tones upon other, higher or lower, steps, is called a sequence : Beethoven, Sym. No. 2. Ex. 91 #" J. .^J-^ ^ Figure Sequence J L^sj Li!5u 129. Such symmetrical recurrences as these justify any reasonable irregu- larity of mdody, harmony, or rhythm. See par. 52. For example: Melody; Harmony: i *i) *i) u f i ij j J i £ Ex. 92. m -<9 — 'S> % -& — s — e- Seq. Seq. Bhytbm; n *a) IV "c|t2 J J- p fl p - It ^^ *i) This extremely irregular melodic progression (7-6-7, see par. 63) is justified by the sequence. — *2) An exception to Ex. 69, note *3), permissible because of its sequential re- lation to the preceding measure. — *3) Like Ex. 22, note *3), which see. so THE THEORY AND PRACTICE OF TONE-RELATIONS. Par. 130. 130. When the sequential fonn is adhered to in all jour parts, the re- sult is a complete harmonic sequence. Such chord-clusters in sequential succession are generally good, regard- less of the rules of regular chord-progression, excepting when the triad on the leading-tone (Ex. 19, note *2) is involved. When this occurs, the sequence is either abandoned, or altered. Sequences rarely extend beyond three (or four) recurrences. In minor they are less common than in major. For illustration (sequences, with triads and chords of the 6th): < j^j , J-J J 2J. i^ ii \ iU f=^ r Ex. 83. ij Aj. fr"-i ^ .^ i i J ^ kAT i 9-1 V r r^ f^i fi Seq, Seq. «l) ( J J , t- J ^ S i: r=^^ ^H i J »a) etc. UA r f- 1 s ^^ -r ^^ 'I Seq. H *i) Leading-tone triad. In this case the sequence would be altered to the next higher step. — *2) This is the connection of a triad and 6th upon the same bass tone. The figure s (before 6) is necessary, to indicate the change in shape, and the progression 5-6, which occurs in the soprano. — *3) Here the sequence is shifted to an unexpected higher step. At the same time, the relative position of the inner parts is altered; but the harmonic form as a whole remains the same as in the first group. — *4) The inner parts are altered. LESSON 16. A. Re-harmonize, with triads and chords of the 6th, Lesson 10, melodies i, 2, 3, 4, 8. Lesson 11, melodies 2, 4, 6. — Lesson 13, melodies 2, 3, 5. B. Harmonize the following: 1. 2. t m^ ^ J N r J ^¥^T ffi w t=r=t ±j p# -^ r 1 f^^ r 3. k^i * . > r [TT-T r r 1 c- h' 1 ' ' -1 * -^ -J n. -«> — J-Z_Li P—J! — 1 — -.-^^-^ Par. 130. CHORDS OF THE SIXTH. 4. 51 ^ m p 4^^-h#— ^ *8) i fe »3) ge -# — •- g>— *— # ^F^ 7. *4) H -f— r w — * e- e e e iFrn^ tt «4) -I* •^— (t ^ P ^=*= tf »4) ^s 5^ f^^3 ^ • I ^ 1 ^ 6 a • -^ ~t7 a — is e e 6666 ea'-*- e O 6 6 6 8 Seq. Seq. *6) 8^ F^^^ .1) v-n. 11. ^m s I-Vi a E^ ^ 3t 111 12. '«5) n I 1 a see I 1 itaH-^-L* ^^E* n. I IjIV Seq. Seq. IlVjlIiSeq. 52 THE THEORY AND PRACTICE OF TONE-RELATIONS. Par. 131. 13. i ^ •7) ^i f^^ -ei- Seq. VI fcr I S ^ fl< fli ^ *i) The semicadence (par. 115). — *2) The II may be freely used in minor, when in- verted. See par. 112, and comp. par. 126. Also par. 1660. Even the inverted III is available in minor, but the occasion for it is very rare. — *3) This may be the VIi, if the following chord is the Vi. See par. 127^. — *4) The tones under the bracket are to be harmonized with successive 6ths. Review par. 127. — *5) To be harmonized as harmonic sequence of the preceding figure. — *6) An example of irregular rhythm, justified by re- currence in the following measure, and in measures 5 and 6 (par. 129). — *"]) A different hass lone for each repeated tone, throughout this melody. C. Extend the following measures in exact sequences, at the Iceyboard: 1. 2. 3. 4. i j=i 0;in:i,'' f-|tf i Vl -gj- W r etc. m^ etc, ^ i^' ■±. J.^*^- ^^^ m. Tf I 6 4 times a 4 times e 4 times 6 4 times CHAPTER XVII. CHORDS OF THE SIX-FOUR. 131. When the bass assumes the fifth of the triad, the latter stands in the second inversion. Compare par. 119. For example: Chord of C Chord of F Ch. of D Ch. of A i T ^ W Ex. 94. I i J. -I ^ -FITTH— CI ^^ -|*-EOOT- -^FIFTH- It -^-PIPTH- -^FIFTH- Fund. triad ist Inv. 2d Inv. 2d Inv. 2d Inversion 132. The second Inversion of a triad is designated " chord of the six- four" because the shape has changed from "root — 3d — 5th," to " bass tone — 4th — 6th": Par. 133. THE TONIC 6-4 CHORD. S3 Triad [cre-g) ; ist Inv. (f-g-c) ; *-> -19-BOOI ^ _ . B The figures 6-4, when attached to any bass tone, therefore serve to indicate that the second inversion is required; i.e., that the bass note in question is not the root, nor the third, (as hitherto), but the fifth of the chord. The root must therefore be sought a 5th below the given bass note: Ex. :9i Chord of C 6 Chord of A I Compare par. 120. Chord of F THE TOinC6-4 CHORD. 133. The second inversion is the weakest (though not the least useful) form of a chord, and is therefore subject to many restrictions. A second inversion is never employed to represent or substitute its own fimdamental chord, but only for the purpose of harmonic embellishment. The best six- four chord is the second inversion of the tonic triad ; i.e., the I2 (I in second inversion; or "One-two"; comp. Ex. 84, note *i). 134. The tonic 6-4 chord may be connected (preceding or following): With the triad on the same bass tone, namely, the V. This may occur anywhere in the course of a phrase or period, but it is of pe- culiar importance at the semicadence, and at the perfect cadence. For illustration (both major and minor) : Ex. 97. C major and minor i i iJ | J ^ iAl-^^ir\^.^r] y f{iM , f=^ y— ^ — X=^ m p—p—p rr~ i r- r ir i f *3) ^ % *i) This chord does not produce a genuine tonic impression, but merely that of a casual embellishment of the dominant harmony. — *2) Note the figuring. When the shape of a chord changes while the bass tone is held, sufficient figures must be used to indicate the change, and where it takes place. Here, § denotes the triad form. — *3) The bass tone is repeated over the bar, contrary to par. 121, Rule IV. It is therefore evident that this connection, V-Is-V, can not take place over an accent. 136. The use of the connection I2-V at (or near) the cadences, is shown in the following 4-measure period: 54 THE THEORY AND PRACTICE OF TONE-RELATIONS. Par. 136 Ex. 98. nzzj — — «. j-j-V- ij • — ^- ^3 aiBEs 3 V « i 136. The tonic 6-4 chord is furthermore connected, before or after: With any other form of the same chord, as repetition. Thus (major and minor) : I I2 Ii I Ii I3 I Ex. gg. C major and minor . 1 e a I 6 a 4 " ■ 4 This, and the preceding connection, together: I Ii I9 V I I2 V Ex. 100. C major and minor J- i^^ V lol, f f=^ 3& -*-^ ^^ P 9i i ^ J J- ij j-j- /::^i Ji -t eE ^ ^1 Ef g |e 137. The tonic 6-4 chord may, finally, be also connected, before and after: With the triad, or chord of the .6th, upon the next higher or next lower bass tone ; that is, along the scale, in bass. For illustration: *i) *i) IV, n, Ex. 101. C major and minor i i^ i J- J. :^=t 4-:,-4- i HZ -4- J- i I -J- Par. 138. THE TONIC 6-4 CHORD. 55 i J r J i- •$• "a) ^ 'a) M | J J J JZEJ ^m ^sf I f ' f f not: i i X I ^ g i-i i i ^ 1= EE 4: E^ ! "i) VI-Is, and Ili-Ia. Both exceptional chord-progressions, justified by inversion. — *2) These parallel sths are very insidious. More than ordinary caution must be exer- cised in M connections of I-II or II-I in major. In minor, however, one of these 5ths is "imperfect" (the diminished 5th in the II), and the parallels are therefore not objectionable. — *3) Six-four chords cannot appear in succession (unlike the 6ths), because of the weakness of the successive chord-fifths in bass. 138. These three connections of the tonic 6-4 chord constitute the basis up>on which the movements of all second inversions are regulated. Hence the following deductions are applicable to second inversions in general: Rule I. Six-four chords can neither enter nor progress with a skip in the bass voice, excepting when a repetition. That is, the bass is either stii- tionary, or is limited to diatonic (step-wise) progression, or leaps along its own chord-line. Rule II. Six-four chords must be connected with triads or 6ths; not with other 6-4 chords. Rule III. In six-four chords, the bass tone (the chord-fifth) is almost invariably doubled. See also par. 121, Rule III. 139. One exception to Rule I, above, is applicable to the tonic 6-4 chord only, in the major mode, namely: A leap in bass from the II to the I2, when the latter is accented. Thus: n la Ex. 102. Il-Ia i * 1 i J i^ ^ f- j ,-i J J i J ' e 6 ^ e s 4 8 4 8 I § LESSON 17. A. Write out the following chord-progressions in. at least fotr major keys, in 4-part harmony: V-I2-V; I-I2-I1; IV | t-V; VI-I2-I1; IV1-I2-VI; IIi | I2-V; II | %-V. B. Play all the above chords (excepting the last one), in the corresponding minor keys. C. Construct 4-measure phrases in G minor, A minor, F-sharp minor, and B-flat minor, (3-4 measure) with the following chords: 1 1 V-I-V | I-I-I | IV-I-V 1 1 1|, substituting Ij for I at option. D. Construct 4-measure phrases in F and D major (4-4 measure) with the Mowing chords: 1 1 IVi-I-ni-I-V 1 VI-IV-I-V | VI-I-I-I | I-V-I ||, substituting Ij for I where desirable or necessary. 56 THE THEORY AND PRACTICE OF TONE-RELATIONS. Par. 140. CHAPTER XVIII. OTHER SIX-FOUR CHORDS. MELODIES. 140. The next 6-4 chord in order of importance and frequency is that of the subdominant (IV2). Its treatment is as follows: Connection 1 (par. 134) Connection 2 (par. 136) Connection 3 (par. 137) ' J^J ■ I , .J J C : I IV3 I 141. The dominant 6-4 chord (V2), though a principal chord, is one of the weakest and least common of second inversions. Unlike the I2 and IV2, which appear equally well accented or unaccented, the V2 is usually unac- cented. It is limited chiefly to the diatonic progression (scale-line in bass). For example: Con. I Con. 2 Con. 3 (good) m hJ J jj J J ij m i TT P f r r f I «3) ' J J J Ex. 104. V, *i) 1 •$• 'Al ji n- ^ lA -^-F- m ■f » i I § C:n V3II a 4" 6 4 *i) Wrong, for obvious melodic and harmonic reasons. — *2) The 6-4 chord stands, as passing chord, between a triad and its first inversion. This is always effective, when possible. It is seen (with the I2) in Ex. loi, group 5. — *3) The 6-4 stands, as passing chord, between two chords of the 6th; also good, but less frequent than the preceding. 142. The subordinate 6-4 chords are rare. The best one is, probably, the II2, which is connected as follows: Par. 143. OTHER SIX-FOUR CHORDS. 57 Ex. 105. i Con. I ^ p ^ Con. 2 -J— Con. 3 (rare) S i ^^ i (^ iij- j;jij J rc;T Ljr f — f I •iT' I ' I s i I § §Si° C ; VI Ha VI •i) See Ex. 104, note *2). I il 1 i ^ na 5 V 8 a a 0^^ 4. a > 4. 4, 143. The VI2 is fairly good, especially as passing chord. Review par. 122, and nate that while the first inversion of the VI is very rare, the second inversion may be used effectively. For example: Con. 1 Con. x Con. 3 (good) Ex. 106. VI9 <^^# ^ f "r^ «l) ii= 5 a s V I 11,1 II — ^ VT s 5 "^ a a 8 4 3 ^ a ''■'■43 4 TTT -TTT -rrr 4 ilj ^ i ^?6^^ S±±^ :^ a 4 VI I I ' ? 8 8 c:inviam *i) See Ex. 104, note *2). 144. The III2 is extremely rare; it may be used only as passing chord, after the triad I. Thus: Connection 3 Ex. „ 107. < Ilia *l) I J J. J i PSt *i) The 6-4 chord passes diatonically downward from a triad; this connection is generally made in a Single beat, and it will be noticed that the root of the triad is not doubled -~- in order not to interfere with the bass tone of the 6-4. See also Ex. loi, group 6; Ex. 103, last measure; Ex. 106, last measure. 145. The above examples refer to the major mode. But they are valid for minor also, excepting where the II or III occur, and where the 6th and 7th steps appear in succession; these are Umited to major. For instance, Ex. 103, connection 3 — doubtful in minor, because the II is not inverted; Ex. 104, last measure — steps 7-6 in soprano; Ex. 105, connection 3 — steps 6-7, 7-6, in so- prano and bass; Exs. 106 and 107 are good only in major. S8 THE THEORY AMD PRACTICE OF TONE-RELATIONS. Par. 146. 146. When a six-four chord occupies an accented beat, it evinces a strong incUnation to progress into the triad of the same bass tone. Thus: Ex. 108. ij^jiij-j i J ^J: J-i ^ji i7r-n-iH7r-]f : I a C: I * ~f a e 4 a 5 IV I i VI 4 » m a n 4 *i) This IVi sounds like an interposed chord which only defers the natural progression I2-V. LESSON 18. A. Re-harmonize, with triads and both inversions, Lesson 10, Nos. i, 2, 3, $, 16. — Lesson 11, Nos. i, 6, 12. — Lesson 13, Nos. i, 5, 6. — Lesson 16, Nos. 2, 4. First review par. 138, especially Rule iii. B. Harmonize the following: 1. 2. -K^4_| — 1 — 1-4- \ 1--- "^ 4 * -* * -*~F~"I — — ^ 4. 2*1) y^y r-with thi same in G minor, I « following ending l ^l^'llj-ifM m ^s =p=p 1= — r ^=t==^=t ^ »3) « ^ i^^^^^^ W: -D »a) ' ■ IlT^ 7. #^iiJrfr i ^ ^ s -«-i- 1^^ Par. 147. DISCORD-HARMONIES. 59 *i) These figures indicate that a 6-4 chord may be used. But this is wholly optional; the student may ignore all these figures, and harmonize the melody according to his own judg- ment and preference. — *2) Par. 13s. — *3) The semicadence. — *4) Par. 127. DIVISION TWO. DISCORD-HARMONIES. INTRODUCTORY. 147. The possibility of extending tji'e 3-tone fundamental harmonies, by the addition of another (higher) third, was demonstrated in par. 26, which review. The 4-tone chords thus obtained are designated "chords of the seventh," because the new interval (which distinguishes its chord from the consonant triad in extent, harmonic effect, and obligations) is a seventh: Seventh i 96>- "^^ 148. The 7th is a dissonant interval (par. 23), and its adoption transforms the concord into a Discord; the pure and simple triad, an independent pri- mary chord, into a restless and dependent harmonic body. The general conditions associated with a discord are given in par. 27, which review. Be- sides the latter, the following special obligations must be observed: 6o THE THEORY AND PRACTICE OF TONE-RELATIONS. Par. 149. 149. Rule I. A chord-seventh must progress diatonically downward. This is called its "resolution." Rule II. The interval of a 7th should not be followed by an 8th, as the succession 7-8 (or 8-7) is usually quite as objectionable as 8-8. Rule III. A chord-seventh need not, and should not, be doubled. For illustration: j T-^r^X'y^ Major Minor Rule II i w ^ *3) *i) In the chord g-b-d-f , the tone / is the chord-seventh, and it is therefore this tone to which the rules apply. — *2) Called "Unequal octaves." DISCORD-CLASSES. 150. Any step of the scale — excepting the leading-tone — may become the root of a triad, as has been seen (par. 31). But only four of the seven steps may be the legitimate root of a discord. These are found, and at the same time classified, in conformity with the law of tone-relation, in degrees of the perfect fifth, above the tonic. Thus: Ex. 1 10. C major i Dominant, or First-class Discords Second-Dominant, or /3d class Atla. class \ Second-class Discords / jo^ \ I « a ! *l) Tonic i± I perfect 5th perfect 5th VI m perfect 5th U perfect 5th *i) It might be supposed that the tome-discords would be the First, and best, class; but it must be considered that the tonic would inevitably forfeit its independence, and the attribute of repose peculiarly essential to it as "Tonic," the instant it became alloyed with a dissonance. Hence the tonic harmony is exclusively consonant, and for that reason the First-dass discords must be sought beyond the tonic, namely, upon the dominant. (When another 3d is added to the tonic triad, above or below, it ceases to be a tonic-harmony and becomes a Third-class discord.) — "2) The 3d and 4th discord-classes are extremely rare, and scarcely maintain any appreciable connection with their key. Par. 151. THE CHORD OF THE DOMINANT-SEVENTH. 61 CHAPTER XIX. THE CHORD OF THE DOMINANT-SEVENTH. 151. The chord of the seventh upon the dominant is obtained by add- ing one higher third to the dominant triad. o) In keeping with par. 69, Rule III, its natural inclination is toward the tonic harmonies. Therefore it resolves into the I (or inversion), and into the VI (triad-form only). J) The resolution of the dominant-seventh chord into the I is called normal. The resolution into the VI is called deceptive (comp. Ex. 80, note *3)- c) The form and general treatment of the chord are identical in major and minor (comp. par. 90, 92). d) In the progression V-I, when both are /M« ejo - 165. These various forms of the dominant-seventh chord are extremely important in harmony, and though differing apparently but little in effect, they possess, respectively, marked indiiddual characteristics, which are of significance to the discriminating composer. Their treatment is governed as follows: Rule I. The chord-seventh resolves as before, diatonically downward. Rule II. In the inversions, no interval should be omitted. Rule III. The inversions of the V are limited almost exclusively to the normal resolution (into I or Ii); that is, only the V itself can pass into the VI. Rule IV. The treatment is identical in major and minor. First inv. (Vj) «l) Second inv. Ex. 1 14. C major and minoi i m *2) , »3) (Va) Third inv. (Vb) m 3 ^^ r7 y ^ ? r ^^T^f'r^rVf=rPr=PF *4) «s) j-ij J-J-^J^ f I I t i ^if VI| I I IjS i^ *i) Vi — spoken "Five-seven-one." — *2) An awkward skip from the leading-tone (in bass). — *3) The Deceptive resolution of the first inversion of the V^, into the VI, is pos- sible in major only, and very rare. The parallel sths which must result (in this case they are in alto and bass) are not inadmissible, because one of them (b-f) is not a perfect sth. — *4) The second inversion of the V' may resolve into either the I or Ii. In the latter case, the third of the I must be doubled. — *s) The third inversion can resolve only into the Ii, on account of the seventh in bass. 166. The introduction of the inversions corresponds to that of the V itself. For illustration (comp. Ex. 112): 64 THE THEORY AND PRACTICE OF TONE-RELATIONS. Par. 157. 7 *i) *i) 7 Ex. 1 15. C major and minor i YJLl T=^ d==t -J^i- ^-^i J- *3) ^=]= *i) 6 S 7 *3) *3) ^ 1 *4) I -i- — ^ It t =t =^ t *i) In each of these cases parallel sths occur; they are all allowable, because one of the Sths (6-/) is not perfect. — "2) Ex. 34, a. — *3) Ex. 112, note *3). — *4) Major only. LESSON 20. A. Write out the following chords, in 4-part harmony as usual; the soprano optional: 7 7 7 (G major and minor) I-Vi-I; (F major and mdnor) Ii-Vi-I; (D major and minor) IV-Vi-I; 77 7 (B-flat major) VI-Vi-I ; I-Vi-VI ; (A major and minor) I-V2-I1 ; (E-flat major and minor) 7 77 7 I1-V2-I ; (E major and minor) IV-V2-I ; Ili-Va-Ii: (A-flat major) V-Vs-Ii; (B major and 7 77 minor) I2-V3-I1; (F-sharp major and minor) I-V3-I1; (D-flat major) IV-Vs-Ii; (G-flat 7 major) IIi-Vs-Ii. B. Find and play these chords at the pianoforte in the usual manner. CHAPTER XXI. DOMINANT-SEVENTH AND INVERSIONS. MELODIES. 157. In appljmig the dom.-seventh chord and its inversions to the harmon- ization of melody, the following facts must be recalled: 7 a) First: that the V is simply an extended form of the dominant triad; therefore it harmonizes the sth, 7th and 2d steps of the scale, as substitute for the V. For illustration: Ex. 1 16. C major and minor t i With dominant triad > J I J J ' ^^ ^' ^J J .ilOE Par. 157. DOMINANT-SEVENTH, AND ITS INVERSIONS- 65 The same melody with dom,-seventh r "■ - J. m m j-^ J J 1 |j 5^^ i 1 a ^ ia Elfc^ 7 Vi 7 7 V 7 V Compare these two versions carefully; note that the chord basis is exactly the same, but the seventh is simply added, in each case, to the dominant triad. This is not always feasible, or necessary; but generally so. 7 J) Second: that the V contains, besides the tones of the dom. triad, the additional chord-seventk, which is the fourth step of the scale. Therefore the 4th step may be harmonized, not only by the subdominant chords IV and II as heretofore, but also by the dom.-seventh chord. The choice is determined chiefly by the direction in which the 4th step progresses; it is 7 only when it descends diatonically that the V can be employed for this step. 7 In other words, steps 4-3 are favorable for the V and I (or VI). The in- version depends upon the melodic movement of the bass; the third inversion is impossible, because of the chord-seventh in the soprano. For illustration: With Subdom. chords * 4. lY IVi a The same melody, with Dom.-7th chords i .^ A « A I m m M ^ ^ ■ ^ ■ ■» ^ f= mJT-T^^ ( ^rn^jni im j .jr^ Va ■^ ^1 *i) V Va « i^* 66 THE THEORY AND PRACTICE OF TONE-RELATIONS. Par. 157. *i) It is not advisable to use a dom.-jCTe»/A at the semicadence; the dom. concord (i.e., the triad) is preferable for this point of repose, because less active. — *2) A line of 6ths (Ex. 89). — *3) Here, the 4th step in the melody must be harmonized with II or IV, because it leaps downward to d. LESSON 21. A. Harmonize the following melodies, with the V and its inversions; and with reference to this summarized table: S*«P==1 2 3 8 4 iTHL 6 C major i N. B. N. B. W -19- sxl 10 a ^ s VI eto. V. flto. IV, 7 n V 7 .1.. y^ 7 V3 ^ ^ IV tf.i J ! i i r:! i ! I m \ -^.. Ji -m^-j^ 4 v» ni-iT 4 a «-- F f • #JrjJ l ^-|fe •i)V iS"— ^ lg- fg l g ^2- ■SI--3I- n. :P3^^ ^ ^ ^^ ■^-^ *a) *i) This mark indicates the semicadence. See Ex. 117, note 'i). — *2) At each of these rests, the bass begins on the first beat (as whole note), and the three upper parts follow on the second beat. B. Re-harmonize Lesson 10, Nos. 2, 7, 11, 16. — Lesson 13, Nos. 4, 9. — Lesson 16, Nos. 2, 8. — Lesson 18, Nos. 2, 5, 7. Vw. lH. DOM.-SEVENTff. LICENCES OF CHORD-REPETITION. 67 LESSON 22. n) 1. m «l ^ fir =P=?c: -f—r ^^ -z^ i^t P « | g • f I ig- :i sJ "» -'S' — ^ I « __v ^ gf^ m ^ ?H*Tr fe ^^, P • — •— -s>- «a) ^1 i ffi A a a^^^^ -p — •- S3i ^ *3) m s >-r!* ^ -• ^ te4-44|-^j=^ 5 PI m Is-- F— r £^: P^ff^ *— #- *4) *i) One chord, or two, at option. — *2) One bass tone (e-j?aO for both of these notes. Comp. Ex. 93, note *2). — *3)' The slurs indicate, as usual, that the chord remains the same. The lower parts may change, or may be simply held; the latter is preferable, almost regardless of duplications, as such active melodic figures should be harmonized as quietly as possible. — *4) At each repeated tone throughout this melody the bass note must be changed. CHAPTER XXII. DOM.-SEVENTH. LICENCES OF CHORD-REPETITION. 158. When the chord of the dom.-seventh is repeated, the following liberties may be taken with the chord-seventh: a) During the repetition of the V, the seventh may pass downward to any other interval of the chord. This is possible in any part, and is equivalent to resolution. 68 THE THEORY AND PRACTICE OF TONE-RELATIONS. Par. 158. IP -^^- i ^ i =iq=J: P fvrtTT tSI-i- Ex. I 18. :^-ii 9^ ^ f=F *s) O 7 V- *i) The seventh disappears; V becomes V — another form of the same chord.. — *2) Here the seventh reappears, in another part. — *3) Carefully note the manner of figur- ing the bass. These figures should indicate all the essential tones, and, generally, the man- ner in which they move. b) Much more rarely, the seventh may pass upward, when the chord is repeated, but only in an inner part, as a rule. If the seventh passes upward, in soprano or in bass, it should immediately turn back, if possible into the resolving-tone. better : Wfrm *i) Better, because the seventh, after ascending, returns to the resohing-tone. — *2) The seventh resolves where it last appears. — *3) In the outer parts, the resolving-tone must follow immediately, as here. — *4) This is wrong, because both parts aim for the resolving- tone, and make imequal octaves. — *$) The ascending seventh, in bass especially, must re- turn to the resolving-tone. LESSON 23. i ^ :^ W *i) ^^^^^^^ p=F ^ ^ > ^ 'w==i^ *i) 3. «i) &E 1^ a -•— -/L *l) e 4 Par. 159. 4. OTHER LICENCES. 69 i fe^n-^ ^^(t- S^ ^E ffi Si3=:e ^cp: ly=t =B=5--P m *3) i fer *a) i=:1: i T? I ig- S ?|i^ C — S>- -S — (9- -S- e) eJ T^i—z J- ^'Tr -^ - ■ei—r)- w ^ $ m ^=F'^ ^ aw^ - a^Fs ■p—F- -•=^ WeE^ -^;» *i) « ^ ••--(=- g I f ? ^- ^s-- -<2- ^ IV ^ tt :^ ]^ ;^ 1^ 4=3t :^zt if^ »i) »3) *l) i ■ta* ^=fe ^ :S^fc:^ S F^= * ^ i'-=a '»- :^«=t S I ^ =^ II ^ -^ ' *8) I *i) One bass note, at each of these slurs. — "2) A different bass note for each repeated tone, throughout this melody. — *3) The lower parts as quiet as possible. . A single bass tone is possible, though not imperative. An occasional irregular duplication is freely permissible — even that of the chord-seventh and leading-tone — when the melody thus "breaks" the chord. LESSON 24. Construct 4-measure phrases with the following chords, in duple and triple measure alter- nately, and in at least 4 alternate major and minor keys; the rhythm, the chord-form and the inversions (bass) of every V optional, as usual. See directions. Lesson 14 C. I-V-V-V-I-V-I-IV-IIi-V-V-V-V-I. CHAPTER XXIII. OTHER LICENCES. THE STATIONARY RESOLUTION. ASCENDING RESOLUTION. 159. Besides the above licences, naturally attendant upon chord-repe- tition, there are two others of a more irregular nature, namely, the station- ary seventh, and the ascending resolution. 70 THE THEORY AND PRACTICE OF TONE-RELATIONS. Par. i6o, 160. The chord-seventh may be hdi (in the same part) while the V pro- gresses into either of the subdominant chords (IV or II). The harmonic 7 7 progressions V-IV, and V-II, are exceptions to par. 69, Rule III; but they are rendered feasible by the connecting-link which the stationary seventh provides. Being "irregular," however, they produce the best impres- sion, as a rule, when followed by a return to the dominant harmony. Rule. The chord-seventh, during this change of harmony, must remain undisturbed in the, same voice; and it must not be doubled. For example: *i) J_J_J , , , "^ . J_J_-^ Ex. 120. iE i =t i 1 1 f^r t i 11111 ^ m 7 C: V- -IVi- 7 -V 7 V II V, I ni 1 . ^ i i ^ ^ p^^^ W=f=t J— J-4- *2) I J J- f r *s) ^ J=T^-^-4: J i J i «3) I jL ^ 9^ r-^ry a IV IV 7 V »4) II3VI 7 V IV, 7 7 *i) After the irregular progression V-IV, the V returns. — *2) The stationary 7th is possible in any part, but rare in bass. — *3) Here the stationary 7th is followed by a tonic chord; but the V soon after reappears. — *4) The / in bass doubles the stationary 7th in soprano. This always disturbs and mars the characteristic effect of the progression. See the Rule, above. — *s) In this progression the chord-seventh must remain in the same part. 161. A singular, but not uncommon, exception to the strict rule of reso- lution occurs when the seventh ascends, diatonically, in parallel thirds with the bass. For illustration: *i) ± ^ r -4- T -4- •3) T T r f k^ ^ *i) The parallel 5ths, in soprano and alto, are not perfect. — *2) Here the bass does not run in thirds with the ascending seventh. This licence is Umited to the second inversion of the V (fifth in bass). Par. i6i. OTHER LICENCES. 7» LESSON 26. A. Write out the following chords (in 4-part hanuony, as usual) with imiform quarter- notes: (Major) V-IVi-Vi-V iT — (Minor) Vi-IVj-Va-Ii. — (Major) Vi-IIz-V | IVi-Ij-V. |'l^. — (Minor) V,-IV-V,-Vi |T — (Major) Vz-H-Vi 1 IVj-I. — (Minor) V-IVi-Ii-V. |T. — (Major) Vi-V 1 IIj-VI. — (Minor) I-Va-Vj 1 IVj-I. B. Harmonize the following melodies: 1. ■i M r 1 Vr ^ ^^ -• m- *-0 d =t=W^ •1) a. i B^ m S d ^ -* P- 9^ ?=i= tlB -¥ •1) V3-I1V2 VI m s »3) ^ '**! T^ t^* «2) »l) ' =*t p^ i i ^^Oi^jl IS ^s=f=& ^ o) p^ «3) V I9 i M jJ^TT^ ;ff rr..r i r^ egg :^c=i: n) *i) n. fiiJ i JJJ i JJ «4) 5=F=^=FF='^ T^V ^V - JVJ-^ , -^ ^ J | J ) | J s *i) At each bracket, throughout this exercise, the stationary resolution is to be applied (par. 160, Rule). — *2) Three bass notes to this e. — *3) The ascending resolution (par. 161). — *4) Two bass notes. — *$) This melody is in the tenor. Add the other three parts, according to the same principles. C. Construct a number of'original phrases and periods. ^2 THE THEORY AND PRACTICE OF TONE-RELATIONS. Par. i6a. CHAPTER XXIV. THE INCOMPLETE DOM.-SEVENTH. 162. A chord is called "Incomplete" when its root is omitted. This omission occurs, occasionally, in the chord of the dom.-seventh, and the result is a triad upon the leading-tone. See Ex. 19, note *2). For illustration: Ex. 122.- C major and minor V Complete & ih V Incomplete ig Inversions 7 V 7 7 *i) Leading-tone triad (sometimes called the VII). The o denotes the Incomplete! form. 163. The proofs that the leading- tone triad is simply an Incomplete domi- nant-seventh chord consist in the facts that it contains the most charac- teristic feature of all dominant harmonies, namely, the leading-tone; and that its harmonic movements coincide in every respect with those of the' 7 Complete V. 164. The qV is a diminished triad (because its fifth is diminished) ; there- fore, like the II of the minor mode, it requires inversion to become available. Comp. Lesson 16, note *2). The hest form of this and all other diminished triads is the ist inversion (chord of the 6th). The 2d inversion, and the triad-form, are both possible, but very rare. 166. Rule I. The qV is alike in major and minor, both in form and gen- 7 eral treatment. Its progressions correspond exactly to those of the V itself. Rule II. Any interval may be doubled, excepting the leading-tone. Rule III. The dissonance (dim. 5th) generally descends, but may freely ascend, especially when doubled. For illustration: *i) »a) »3) *4) *s) «e) *?) *i) Triad-form: rare. — "2) First inversion. This is far the best form, almost always; namely, as chord of the 6th, with the leading-tone in the soprano. Either d or f may be doubled. — *3) The dim. sth (/) is doubled; comp. par. 560; one ascends and the other Par. i66. THE INCOMPLETE DOM.-SEVENTH. 73 descends. — *4) Comp. Ex. 68, note *4). — *s) Comp. Ex. 770. — *6) The 2d inversion; treated like any other 6-4 chord. — *7) A succession of 6-4 chords, contrary to par. 138, Rule II. This is always permitted when one of the 6-4 chords is a Discord, as here. — *8) Also applicable to minor, excepting where the 6th and 7th steps are melodically con- nected — as in measures 5, 6, 7, 8. 7 166. The Incomplete V , and the II in minor, are the only two legitimate, diminished triads in harmony. To what has already been said about the II in minor, the following may be added: a) The best^form is the first inversion. The second inversion is also avail- able; but the triad is very rare. See, again. Lesson 16, note *2). b) Either the root or the third may be doubled. c) The diminished 5th resolves downward. 7 d) The best progressions are: IIj-V; IIi-V; IIi-Ii; Hi-Ig- For example: Ex. 124. II in minor ^^ iM m n 6 6 7 V 6 6 6 6 *i) Comp. Ex. 123, note "7). LESSON 26. A. Write out the qV of every major key (with its inversions), and note the Relative minor key in which it is the II, thus: 1 j»_ «i" ~y 1 / ifV " u \ \/Ja ffl s." MP 1 L_|? J oVof G B. Find and play these chords at the keyboard. II of E min. LESSON 27. 7 Harmonize the following melodies, using the qV {pt option) at each *: 1. i V •!) 2. •1) ^ II* le i^ V ^m eS s^ «i) •a) 74 THE THEORY AND PRACTICE OF TONE-RELATIONS. P«r. 167. •3) V i «4) *4) =i^ fe ^ ^ i *3) »1) ag^=^ *3) ^^^ j^ i *s) tf 6. ^ -m W n IV, *i) Review Ex. 123, note "2), and observe that the leading-tone in soprano may, under 7 all circumstances, be harmonized as chord of the 6th (qV ). This is, of course, not obligatory — for the Incomplete V is, at best, a comparatively rare chord. — *2) Observe how service- able this chord of the 6th is, when the melody has the irregular succession 6-7, or 7-6. This is amply shown in Ex. 123. — *3) One bass tone. — *4) Successive 6ths (par. 127). — *S) Par. 161. CHAPTER XXV. CHORD OF THE DOMINANT-NINTH. MAJOR. 167. According to par. 26, chords of the seventh may further be extended from 4 to 5 tones. In the latter case they are termed "chords of the ninth," because the new and distinctive interval is a ninth from the root. 168. A five-tone chord may be erected upon each of the four fundamental steps (V, II, VI, III) as defined in Ex. no (which review, with context), and they are classified accordingly, that of the dominant belonging to the First class. 169. The chord of the ninth upon the dominant is obtained, then, by adding one higher third to the dom.-seventh. This demonstration of the origin of the uppermost interval is significant, as it determines the correct location of the ninth, in relation to its root. For illustration: in the 5-tone chord * — « — Par. 170. CHORD OF THE DOMINANT-NINTH. MAJOR. 75 obtained by superposing one more third (over the 4 tones g-h-dr-f), the tone a is removed from the root (g) by a distance exceeding an octave; the a immedi- ately above the root ^Saz has no legitimate place in this chord. Hence the distinction which must here be made between a second and a ninth (see Ex. 6, note *3). 170. Like all dom. chords, the dom.-ninth tends toward the tonic har- mony. The details of its treatment are as follows: Rule I. The chord-ninth may never lie less than 9 tones above the root. Li major, the ninth of the dom. is rarely placed in any other voice than the soprano. Rule II. The ninth resolves diatonically downward, like the seventh. Rule HI. In the Complete chord, the root is generally given to the bass; and the sth (never the 3d, nor the pJi) is omitted. For example: Ex. 125. C major Complete V •a) -»- '^ ■$■ ■$"$■ Resolution »8) .^ I .^ I *^) J I - 17~T r rir [ U. - T T VI «=. eta. Vi y7 w. o • ^ IV VO J II - V V III— IV (T7) jjV» ^ !J} oV V7 V — VS oV^ V-oVe SE^SE nv'^-^n^ m m w^^ \ *i) «a) ^^^ ^ ^n ^ij^pfe «i) -?»— ^ »3) « s ^-l-s- m- m litat -^=5- ±=i: ■•— #- :tt *-^" ^ ■ *l) *3) i *!= SeS ^ IE : >'— i^- g *3) ^ J^T^^ P^gl ^Tg ^W^ P I !^t^? «i) ICJ fg--fg 1^ fg •4) ^ it tS" IS) i© «>■ f^-nS-- ?^ ■29 — I* g o *i) According to the rules, and the above Table, the V and qV in major are limited almost exclusively to those points in the melody where the sixth step occurs (descending). — *2) One bass note through each slur. — *3) Two bass notes. — *4) A different bass tone at each repeated note. 78 THE THEORY AND PRACTICE OF TONE-RELATIONS. Par. 173. CHAPTER XXVI. CHORD OF THE DOM.-NINTH. MmOR. 173. The ninth of the dominant chord, being the 6th step of the scale, undergoes modification in the minor mode (par. 87). Therefore, the dom.- ninth is the first dominant chord which differs in major and minor. Comp. par. 90; par. 151 c. Thus: Ex. 12s. i -^- W ^- mi C ; V in major V in minor 174. The transformation of the 9th from a major to a minor interval does not alter, but rather confirms, its obligations, and facilitates its treat- ment in many respects. The rules given in par. 170 (which carefully review) are also valid for the minor dom.-ninth, with one exception, namely: The ninth of the minor chord may lie in either inner part, quite as well as in the soprano. But the 9th is not possible in bass. And, as usual, it lies never less than nine tones from the root (in the Complete form). For illustration: Complete V. (Compare Ex. 125.) Ex. 129. C minor i m §^ r r r =y _^J 4 J — E. -J— ^ m -^L -1 — r -5— P-^^-i ^ «i) J- *a) -*n^^ s^ s V »3) 7 V fri=fj 11=^3^ ?= r 1 '-t N. B. ^ H — j- -W m o 9 V 9 I e V *i) The third inversion of the Complete dom.-ninth (i.e., 7th in bass). Extraordinary as this chord looks (and sounds), it is nevertheless perfectly correct. — *2) The first inver- sion of the Compl. V^. These unusual forms are somewhat more easily obtained in niinor than in major. — *3) Stationary dissonances. Here, a 6-4 chord is exceptionally introduced with a leap in bass. It resembles Ex. 102. Pir. X75. THE CHORD OF THE DIMINISHED SEVENTH. n THE CHORD OF THE DIMINISHED SEVENTH. 176. The difference between the major and minor chords of the dom.- ninth is most marked, and most significant, in the Incomplete form, which, here again, is by far the most conunon. 176. The Incomplete dom.-ninth, or the chord of the seventh on the leading-tone, in the minor mode, is a chord of the diminished seventh. It bears this name because it is the only legitimate chord which contains the pecuUar interval of a dim. 7th. It is one of the most frequent and im- portant forms of the dominant harmony, distinguished alike for its great tonal beauty, and its almost incredible flexibility. 177. The treatment of the chord of the dim. 7th coincides with that of the Compl. V®. The 9th (i.e., the 7th from the leading-tone) may lie in any mice, either above or below the leading-tone (but it should be avoided in the bass voice, as much as possible); and it resolves diatonically downward. For illustration: Ex. 130. C minor Diminished ?th (pV) i *i) W m ii± 7— rr i m J-.-i-^ T^ H-B , ' — ^ J . i J_J>J , I J ^^ ^ r^^ IVo s O T »a) , ( i ' I TJT^ 8 T i I *3) *4) ^^^^ J u yt±*= -fig- i J. i —» E m i i i i mrVr ^j^tti^ s m VI, N. B. 7 V *i) The false melodic progression from the 6th step to the 7th, in minor, is here jttstified by chord-repetition. — *2) Even in minor, where one of the sths is imperfect, these parallels should be avoided. Comp. Ex. 126, note *3). — *3) The/ in bass is actually the 7th of the chord, wherefore its best progression is diatonically downward. But comp. Ex. 123, meas- ure 7 (alto). — *4) The original gth in bass is objectionable, because it gives a very weak chord-form. It is hest in repetitions. 8o THE THEORY AND PRACTICE OF TONE-RELATIONS. Par. 177. Additional illustration, for analysis : Adagio tfp \ ^ « ^ -*- -*■ ^ ^ ^ il Ex. 131. ( V I ^ II Vg I IV^ IV IV Ii Ii V3I gt rj: :gd^^ ^g ^^ig :?=i^ * -n- 5 n tf i ?=^ ^^ %—^ ^^ir#t gi ai^ nV g o W=^ s Later : i tf=j^ Later : ,_^ BEETHOVEN. O p. lo6. etc. -,111 1 1 — g^ etc. ^© ( ^^^ i&i f «=i=^ % VV V laV la 799 V V V V I„ LESSON 29. 9 A. Wnte out the V Complete in every minor key. — B. Write out the chord of the Dim.-7th, and its inversions, in every minor key. — C. Find and play these chords at the pianoforte, without notes. LESSON 30. A. Re-harmonize, chiefly with the dim.-7th chord, Lesson 11, Nos. 1, 5, 6, 7, 10. — Without reference to any directions there given: Lesson i6, Nos. 5, 10. — Lesson 18, Nos. 4, 6, ro. — Lesson 2t, Nos. 4, 5. — Lesson 22, Nos. 3, 4. B. Harmonize the following, using the V^, occasionally Complete, hut chiefly Incomplete. A dom.-ninth chord (or dim.-7th) is possible, but not obligatory, at each *: Par. 178. 1. UNFIGURED BASSES. 81 i*n J J M^-^^^ ^^^^^fe^^ 2. T^"^^: i •1) e ?^ :P^ :*N 5*- n. i ff 3. .2) ^m fe •2) ^ *t -?y 2^ *i) Two bass notes. — *2) Lower voices may be held through the measure. — *3) Lower voices J 1 I ; and the same in the next measure. CHAPTER XXVII. UNFIGURED BASSES. 178. In adding the three upper parts to an unfigured bass, the same general rules must be observed as in adding three lower voices to a given melody. The two processes, though inverse, are nearly identical. The following table (which compare carefully with that given in Lesson 28) will therefore suflSce: I IT, 7 V 7 n M.i. o ^ (II Uiii.) o T "' oV fil, IV 7 V 7 «I 0" V 7 T IT, (11,) \i" m -bv- .^-aA-ig-. iSsz Ex. 132. C major andmlnor Steps: la 38844 6087 179. Besides which, however, the following genera;lities must be recalled and borne in mind: The bass note is not as likely to be the chord-fifth as it is to be the root, third or seventh. The leading-tone is not likely to be a "root apparent" (see par. 164), as qV. And in minor, neither the 2d nor 3d steps are likely to be roots. In all minor basses, the Incomplete dom.-ninth (chord of the dim.-7th) is to be used very freely. 82 THE THEORY AND PRACTICE OF TONE-RELATIONS. Par. 179. LESSON 31. Add soprano (and then alto and tenor) to the following basses. 1. »i) »a) *8) ^ ^ -&z^ d2ii=s l±^tp P'—p- *8) »4) 4. S ^»=F^ ifc =P=i: =^^5=? .±^ 4JTrr^ *5) «s)- #-i= ^^^^^^ »i) •a) •s) «3) fe te ^ ^g^Ete -•t Pi= »3) *3) *S) ♦8) ^=S I ^5^ F^ rg'n '- ' *4) ^' *i) All stems down. — *2) Basses i, 2, 3, 7, in minor also. — *3) Two melody-notes (at option). — *4) When step 2 is followed by step i, as here, it is far more likely to be a dominant chord, than the II. — *$) All minor basses in at least two ways. — *6) One melody-note to each slur. *i) *i) LESSON 32. *i) a^i is -^ — — £>- t=^ m -g^-&- ri—d-d- *8) *3) 3. ^m ^ ;j | J J I jl4^ ^^ f=3i li ' VI ■♦• •4) d^ Par. 180. CHORD OF THE DIMTNISHED-SEVENTH, CONTINUED. 83 ^W 5^=Q=g ^ IS * -■-^ 1 -iSt *4) (t) (I) (?)(!) 6.»4) S5te±t i fi=^ ^ — ^- m. ii:i=* ^^ i *i) Three melody-notes. — "2) In two ways. — *3) Also in minor. — *4) The three upper parts together on the G-staff. Pay strict attention to the slurs; one melody-note to each slur. CHAPTER XXVIII. CHORD OF THE DIMINISHED-SEVENTH, CONTINUED. 180. In working out this lesson, all in the minor mode, the student will put the broadest possible construction upon the term "Dom.", and deter- mine at his own discretion the form (V, V, qV, V^, or qV®), and the inversion (bass note), of each dominant chord, giving preference, however, to the chord of the dim.-seventh. The rhythm (arrangement and repetition of the given chords in the measure and beat) is also quite optional. The following ex- ample will serve as a model: Given the chords (minor mode) : IlDom.iI-IV|l2-Dom. ll Solution: D minor, duple measure e* ^-- W4-i f r If Ex. 133. (s * 7 9 V V oV IV o V 7 V 84 THE THEORY AND PRACTICE OF TONE-RELATIONS. Par. i8i. E minor, triple measure ^S f- f r 'r ^ ^ =^ ^ J ^ ^j J J^ -J — ^ i^g * f=^ 7 S 7 V IV 7 7 V V V 7 V LESSON 33. A. Construct two phrases (at least), in different minor keys, with each of the following chord-series. The required number of beats (or of melody-tones) will be obtained by chord- repetition. Study the above model closely, and review the directions given in Lesson 14C: (I and I) I-Dom.-I | Dom.-VI-Dom. ] I-Dom.-I-IL | Dom.-I || (ig and I) I-IV I Dom.-IV-Dom. 1 1-II-Dom. 1 1 1| (I and I) 1 1 Dom. | I-IIi \ Ij-Dom. 1 1 11 B. Construct two (or more) periods, in minor, with the following chords, using the dim.- seventh at each *; everything else optional: (I and I) I-*-I I *-IV-V 1 1-*-I | V^l *-IV-* | * *-I | II1-I2-V 1 1 11 Some experiments may be made with these chord-series in major also. In this case the dim.-seventh wiU not appear, although the qV^ (with the Umitations of par. 171) will be available. C. Construct a number of original 4-measure phrases (both major and minor), following the above process. CHAPTER XXIX. SECOND-CLASS DISCORDS. 181. The fundamental tone of the Second discord-class must be sought one perfect sth higher than the dominant, or two perfect sths above the tonic; it is therefore the second step of the scale. Review Ex. no, and context. The Second class comprises the same number and forms of chords as the dominant class, namely: The triad; the chord of the seventh. Com- plete and Incomplete; and the chord of the ninth. Complete and Incomplete. Thus: Ex. 134, C major b^Z g Second-Dom. Concord Discords *3) »3) - 7 7 n •!) n Compl. II Incompl. or IV ;z?- -;g~ ~g^ 9 o II Compl. II Incompl. or IV Par. i8a. THE CHORD OF THE SEVENTH ON THE SECOND STEP. 8S *i) " Two-seven." — 'a) The IF without its root proves to be the subdominant triad (the rV). See next paragraph. — *3) Called "Four-seven," instead of qII^, because of its relation to the IV, the name of which is established. 182. It is now necessary to revert to Ex. 19. note *i), and par. 96 (which see), and eluci- date the apparent contradictions which are presented by the subdominant or Second-class body of chords. About the discords of this Class there is no uncertainty, but the concords (II and IV), as has been seen, do not, in practice, preserve their actual theoretical co-rela- tions with fuU emphasis. From the above example it is theoretically apparent that the triad II is the principal representative of the "subdominant" harmony, while the IV is only an Incomplete form of the 11''. This confirms the theory that no chord-root can be accepted upon any perfect sth below the ke3mote. Practically considered, preference is likely to be given to the IV, because of its direct perfect-fifth relation to the tonic. The degree of promi- nence which either of these two equally important chords assumes, depends upon the acci- dental emphasis given to the tones d 01 f respectively. The following table illustrates this (in C major), and demonstrates the coincidence of the subdominant with the Second-class chords, in the tones /-o-c: Third rank — Second-Doln. (7th) d-f-a-c. Sth Second rank — Dominant g-b-d. Sth !^= First rank — Tonic C-E-G. Sth (Third rank ?) — Subdominant f-a~c. One significant deduction for the student is, that the Second-dominant and Subdominant chords hear the same relation to the dominant harmonies, that the dominant does to the tonic. Therefore the term "Second-dominant" is peculiarly indicative, and preferable to "Sub- dominant." 183. The distinctive external characteristic of fundamental Second-class chords is their minor third — in C major the tone/ instead olf -sharp: C major i M 1125 nz This interval distinguishes them from the dominant or First-class chords, whose major third, being the leading-tone, is their most significant feature. THE CHORD OF THE SEVENTH ON THE SECOND STEP. 184. The chord of the 7th upon the second step, the IF, and its inversions, resolve most naturally into the preceding chord-class, namely: Into the dominant chords, whereby the chord-seventh descends diatoni- cally, as usual. Ex. 135. C major and minor ^KRz^H r ^ ^ 7 7 V 7 oV ; i^i n -j^. ^ e V 86 THE THEORY AND PRACTICE OF TONE- RELATIONS. Par. 185. i -^—^ — ^ *3) -(J)^- ^^ i^\ J- -J- J 1^^^^^^^ I ^^ g V 7 V g *i) A-natural in major, and a-/ai in minor. — *2) These first five measures illustrate the resolution of the II'' into each of the five dominant chord-forms. — *3) The second inversion of the IP is best in minor. Otherwise no distinction is made between the two modes. 1 . . , , 185. The II and its inversions, like the dominant discords, are also en- titled to the licences of chord-repetition (review par. 158); and those invol- ving the stationary seventh (review par. 160). For the progressions with stationary seventh (into the tonic chords I or VI) the Second-class discords all evince great preference. Ex. 136. / C major and minor, i 45- 1*1) -4^^- ^^ ^ VH^ i^ *4) f- *2)' ^ W^ m ^^ I ,iJ.,UM^^-A^.ii W W^^^^ ^ 1^*3) I a « I, *i) A curious example of parallel sths (perfect) in both pairs of upper and lower parts. They are justified by chord-repetition. — *2) It is not unusual for the 7th of the IP to leap downward, thus, to the dominant, to avoid doubling the leading-tone, when the latter is in bass. Here it is the tonic — a tone whose importance gives it certain privileges. — *3) Comp. Ex. 102. — *4) Wrong, like Ex. 120, note *4), which see. 186. The introduction of the dissonances in Second-class chords demands closer attention and more restriction than in dominant chords. Review Ex. 112, and limit the seventh of the IF to strict introduction, as much as possible. Thus: Prepared Ex. 137. C major and minor. II it N.B. rrn Repetition of chord f^at ^ ^ ^^ e a 7 5 s VI IV Jj etc. U— ^-^ T n n Par. 187. THE CHORD OF THE SEVENTH ON THE SECOND STEP, ij *i) In the II'' itsdf (root in bass) the chord-fifth may be omitted, and very frequently is. In the inversions, however, there are, as usual, no omissions. — *2) These sths are wrong in major only; in minor they are not perfect. Comp. Ex. loi, note *2). In passing from I into II' it is usually necessary to omit the fifth of the latter, especially in major. 187. Especially unique is the introduction of these chords after dominant harmonies, thus: V-lV, V^-II'', etc. This is merely another version of par. 160 (which review), and involves the following rules: a) The 7th (or gth) of the dominant chord remains stationary. b) After the Second-class chord, a dominant chord must return, in some form or other. Ex. 138. i *i) iS^ s^=rf^pf=pw tat^t t^ ^^ ??»3) f- 1 ^ i^^ i J i i id . 7 ■V ? ^ i J ! >. ikj iij 1 t 77777 7 V II V II V oV I 9 V o ^m 7 7 V n 'qv ¥±atxx»o* '0*0' vxxl *i) These first 2 measures are applicable to major and minor. But the others demand modification, as usual, wherever the 6th and 7th steps are melodically connected. — *2) Two stationary 7ths in succession are objectionable. Further illustration: Presto. I 1 I , 11 I I m Ex. 139. i a FD min. JJ ^ i X ^^ \^M 7 V, 7 7 Mendelssohn. Op- 38- s (^ etc. 7 Ha 7 V LESSON 34. 9 oV- Write out the following chord-successions in different keys, in 4-part harmony, with uniform quarter-notes. All inversions are optional, unless specified. Resolve all sevenths properly. See Ex. 137, notes *i) and *2) : (Major) I-II-V-VI. — (Minor) Vl-ni-Va-Ii. — (Major) Ii-IIi-Ij-V. — (Minor) I-lVoV-Vj-L — (Major) I-lVvij-il-oV-I. — (Minor) I-IVs-IIa-Vi-V.-IV-oV-oV-I.— 8777797 777779 7 (Major) I-Vj-II-Vs-II,-oV-V-I. — (Minor) I-V-n,-V-V,-IIi-oV-Ii-II-Ii. — 88 THE THEORY AND PRACTICE OF TONE-RELATIONS. Par. i88. LESSON 36. A. Re-harmonize Lesson lo, Nos. i, 2, 3, 8. — Lesson 11, Nos. i, 4, 6. — Lesson 13, Nos. 2, s- — Lesson 18, Nos. 2, 4. — Lesson 21, Nos. 1,2. — Lesson 27, No. 6. N.B. The in is possible (not obligatory) at those steps where either the IV or n would be used. B. Harmonize the following melodies. Some form of the IH is possible at each * : 1. P<'' r r 1 ^ * ^ r I f r r f \ f=^7TT\i 2. -.\\\>fi r 1 — -^ i— J — iVhp — r-i^f-f—pr-t- 4:Y^4. ' *• * J — J — ^ ^ • ^ f 1 1— 1 1 ' —d— CHAPTER XXX. OTHER SECOND-CLASS DISCORDS. 188. The 5-tone chord upon the second step (second-dominant) is ex- tremely rare m its Complete form, but is available and not uncommon with- out its root, as chord of the seventh on the fourth step {IV, or Incomplete II* — compare Ex. 134, note *3). The treatment of the IV corresponds in every essential particular to that of the IV, but is more rigorous. Licences of introduction and resolution are almost entirely precluded. Review par. 184, 185 and 187. The seventh descends, as usual, or remains stationary; and there are no omissions. Thus: Regular resolution: N. B. Ex. 140. C major and minor •4) li So- I fe ^M- i a a a a a \- 1 m^ - — i J — a T O 7 7 T 7 ' ' II r I r \ ^ J. J *t i 1 i £-A 1 n IV iVi IV3 iVg 7 6 4 8 m i t=t ^^ 7 T IV V 8 4 Par. i8g. THE THIRD AND FOURTH DISCORD-CLASSES. 89 i *a) g Stationary dissonance Par. 187. r rT^f^ y^ =^ -f- X *s) i j.iii^ijj_j h Mr i r i ^ffS ^ ^ :t=/ 7 7 7 8 7 6 IV I9 * 7 7 7 V— IV— V *i) The IV rarely resolves into the triad-form of the dominant, on account of these 5ths, which disappear when the dominant-seventh or ninth follows. — *2) The inverted forms of the IV' are rarely used. — *3) The resolution into the tonic, with stationary seventh, is very frequent and effective, and removes the danger of parallel sths. — *4) In minor, e-flai and ti-flat. THE THIRD AND FOURTH DISCORD-CLASSES. 189. Of these extremely rare chords, the best is. the seventh upon the 6th step — VI'. Its connections are as follows: Ex. 141. C major *l) *3) »3) •4:) N. B. T=q: i VI U VIII 7 7 V VI ' ' "r I f 77 777 nvi n VI V *F=?= rP 7 O Q Via oV V VI "i) Principally in major; possible in minor only where the melodic connection of the 6th and 7th steps can be avoided. — *2) Third-class chords resolve "regularly" into those of the Second class (II, IF, etc.). — '3) Analogous to par. 187. — *4) An "irregular" (but very common) resolution, into dominant chords. SEQUENCES. 190. All the rest of these remote Discords are least objectionable, be- cause most comprehensible, w]ien used in sequence-relations with better chords. Review paragraphs 128, 129, and 130, with their examples. The possibilities here are more numerous than in the former lessons, because the sum of chord-forms and inversions is much greater. But, as stated in par. 130, sequences are far less common in minor than in major. All questions of quality or admissibility must be left to the ear. A few random examples will suffice: 90 THE THEORY AND PRACTICE OF TONE-RELATIONS. Par. 190. b. Ex. 142. C major 3 4^ ^z.-:^ ^ u -gy jffTffljr^ jji g S^p^ l.rr TT r . iJ I , IjJ ,JJ, rf 7777770777 7 O in VI II V I IV oV m VI V I vi n qV .ttfUj ^ — r -is't • — V -J- -i e i -i. I * • ^ J J. ^ e: 9 II V g 7 ni VI II- S 7 »V I- 7 9 / Wh^fh^ ^ K I • s :J. p^=|r=f^^ r=T r J- etc. CI i^J -j-.J ^"J , J- J J J etc. ^^ §3 ^—f^ Further illustration: Presto. i .#. .«. *l) ^ *3) # • — >-»- *=HC ^ Ex. 143. (at the piano- forte) / bI? Maj. ^ LrJ tLrJ m ^ Efc:^ Si OS 5^^ =i^p^ -M;:^^ 1 i i ^^aiS^^ 7 .VI- 7 -II- 7 -V- 7 -IV— Par. igi. FIGURED BASSES. 91 m * — V*—* ^. Schumann. Op. 20. a ^ -^^ ^^ o oV- ^^+^S^W ^ 1^ etc. 7 ,ni- 7 ■VI- 7 -II- 7 -V- *i) When the tempo is so rapid, successive beats, of similar harmonic import, blend; therefore these chords are defined by grouping both beats (represented by each bass figure) together. — *2) The figure in J^ -notes continues throughout, as in the first and last measures. The pupil is to play it in its correct form. THE AUGMENTED TRIAD. 191. One unusual chord, of the Fourth discord-class, claims special men- tion, namely: the triad upon the third step, in the minor mode. It is an augmented triad (par. 1116), and is treated thus: Ex. 144. C minor »^7-Bg- i 4- -6i^=l»->^ ^ J- t I ' I ' a Ti, FIGURED BASSES. 192. The student is now sufficiently familiar with the figures placed be- low the bass tones, to work out an exercise from a figured bass. The figures indicate the shape of the chord; that is, the intervals which accompany the given bass tone, reckoned upward from the latter. The most important aim is to secure a good soprano melody. The following fairly elaborate model should be carefully studied: Given bass, figured Ex. 145. ^^ e sa s a a a a s 4 r Solution: 87 87 66 4S i % J i j J J n .BA ^^ ^ ±: te 4-. n. ^j 687428 sa 3 B 6 r 6 6 7 5 4 ° IS 92 THE THEORY AND PRACTICE OF TONE-RELATIONS. Par. iga. each ' LESSON 36. 7 7. A. Harmonize the following melodies. A Second-class discord (II or IV) is possible at i. 2. m m ! r f \ P- m :& -P P- =it=^ i ^ti=s -^•=-^- ^ eS !*== ^ atz±3t ■•-v-i ?& ^ Eigi » I 11 » liii.i i h.^n'^ ^w^^m ^m a^ I I IV invvi #%^ ^g^feg f ^— «'-4f i»^; ±i=K f— ^^- =tf4 ^ VI IVj *i) The brackets indicate sequences. B. Work out, and analyze, the following figured basses: 1. 2. S*l) . 3 8 Jl ! 7 IV ^g =t t #-!-•— !*• ^e i: 7 3. a 4 a 5^ m ■«• f2- ^© 6 76 4 1*2) i » « *i ''a a 5 g^ -(2- ftffeig iH: yrn^'ir trS^ 87 6 5 OS 4 J e 8 7a „ 34 7 <*u 8 a 2 a a a 6 4 7 g« ^ 7a 7a -P=S S tat e 7a 2 a 8 7 7 7 a fe =9±*| m ^ ■75»- -si — s>- -^-*- 77 367 767 677" *i) The figures above the bass indicate the interval the soprano is to take. — *2) The Sharp is a necessary reminder of the accidental before the leading-tone, in minor. Par. 193. THE SYSTEM OF KEYS AND MODES. 93 DIVISION THREE. KEY-RELATIONS AND ASSOCIATIONS. MODULATION. CHAPTER XXXI. THE SYSTEM OF KEYS AND MODES. 193. The relation of key to key is precisely the same as that of tone to tone, and is measured by the interval of the perfect fifth (Jmnnoaic degree, par. 8). Keynotes which he a fifth apart have adjacent signatures; for ex- ample, e-flat (3 flats) ; b-flat, its upper perfect fifth (2 flats) ; a-flat, its lower fifth (4 flats). As shown in Ex. 64, N. B., the relative minor of a major key has the same signature as the latter. 194. From this it appears that , The degree of relation between one key and another is indicated directly by their signatures. The following circular arrangement of keynotes and signatures illustrates this dearly: *i) The distance from point to point is a perfect 5th, or harmonic degree, along each line — major and minor. The outer circle represents the major keynotes, indicated by capital letters; the inner circle, minor keynotes, small letters. The difference between the size of the upper and lower arcs serves to illustrate the actual difference between g-fiat and i-sharp (e-flat and d-sharp), but is intentionally exaggerated. 94 THE THEORY AND PRACTICE OF TONE-RELATIONS. Par. 195. 195. Each key is seen, in the above chart, to be surrounded by five other keys (major or minor). These are called the attendant, or next-related, keys. For example, from C major (natural signature) : 1. The Relative key, a minor (same signature); 2. The Dominant key, G mMJor (i-sharp signature); 3. The Relative of the Dominant key, e minor (i-sharp signature); 4. The Subdominant key, F major (i-flat signature); 5. The Relative of the Subdom. key, d minor (i-flat signature) ; All the rest of the 24 major and minor keys are more or less foreign to the key of C. The so-called remotely-related keys will be defined later. MODULATION. 196. Modulation is the act of progressing from one key or mode into another, or of exchanging one key for another. 197. The process of modulation, while subject in general to the foregoing rules of part- writing, is furthermore regulated by the following special rules : RULE I. Modulations are limited ordinarily to the five next-related keys. A transition which extends beyond the next signature is called "extraneous," and is always subject to special conditions. RULE II. The desired key is most easily and legitimately reached through one of its dominant (first-class) chords (V, V', qV, V®, or oV° in any form). RULE III. The key may also be entered through any second-class chord (II, 11', IV, IV) in any form. As a rule, it is not satisfactory to enter a key through any tonic chord; but there is one notable exception, namely: the tonic 6-4 chord, when ac- cented. This is due to its intimate relation to the dominant harmony; comp. par. 135, and 146. RULE IV. It is always best to dose the original key upon one of its tonic chords (I or VI in the usual forms). It is also possible to abandon a key at some other, non-tonic, chord, but often awkward, and always conditional. Hence the following fundamental modulatory formula: 198. Abandon the first key at one of its tonic chords, and enter the de- sired key through its dominant class; more rarely through its second class; or through the accented tonic six-four. Illustration of these rules: , , , , *2) Ex. 147. From C to G *5) # I *1) -TJ-'jS- ■^ fe J- J -ii C I, GV P=f ij J'JT LQ fF^ ij-j^i J. a ii'i eS T^TfTTWTT C I G v., C laGoV Par. igg. MODULATION. 95 •a) r ^'r rr' v r ' r f f T^"f iA^ (^P frf=^'. rirfr^^ffrnfTT * C VI GV C IiGoV C IjG II Vi *4) ( ^^ ^ JT+W * t=i 3: :8 r^r ' i^-r F # f^ r r rr i jjjhJ: I J i-l^ ^ ij i^i!; i ' , ': i i i M 1 7; [ pn-f-T r l ^-^-^T ? C IGII V C IiGIV 11 oV C VIjGIa V *i) The modulatory transition is effected by the connection of the two chords under the I 1 ; the first one is the Ii of the original key (C), which brings the latter to a sufficiently marked close, leaving no impediment to the change of key, or modulatory digression; the second of the two chords ushers in the desired key (G), through the agency of its dominant chord, which contains the leading-tone. — *2) It is evident that the rhythmic location of the modulatory chords (on heavy or light beats) is of comparatively little moment. — *3) The new key (G) is entered through one of its Second-class chords (the II); this resolves into the dominant, and therefore merely serves to protract the modulatory process. — *4) G is en- tered through its accented tonic 6-4 chord. — *s) These examples are also valid for the modulation from C minor into G minor, with the usual reservation (par. 92). 199. The last chord of one key may, in many cases, be at the same time the first chord of the next key. If this is the case — if this chord has its place and name in the coming key — the modulation is called diatonic. But if the last chord does not belong to the next key, one (or more) of its tones must be inflected chromatically (by an accidental). The modulation is then known as chromatic. For illustration: Diatonic mod. Chromatic mod. i -^ S J- -«• ^;^ -& gi- EHE -l—tS- 1 — r Ex. 148. fe J- J «l) «3) -J. J -i J ^^ -^pl- C: I F; V 7 V C: I 7 aV 96 THE THEORY AND PRACTICE OF TONE-RELATIONS. Par. 200. *i) This chord, the last one in C, is, at the same time, the V of the coming key — F. (In Ex. 147, the modulations are all diatonic. Analyze carefully, and note the double name of the last chord in C, in each case — as above.) — *2) Here, the last chord in C does not be- long to the coming a minor, because of the g; therefore, this g must be inflected to g-sharp. 200. The rules of chromatic inflection are as follows: a) As a rule, the chromatic change should be made in one and the same part (as above, in alto). b) If, however, the two chromatic tones are not in the same part (caus- ing the so-called "cross-relation"), it is simply necessary that the first one of these .tones should not skip. i ,^ ^ L-U ^ J M ^m ^ ^s^ ^ Ex. 149. C toa •4) 4- ^fr^/Pf^/Pr*=Pf 1 I C IjaV •1) *a) *i) The chromatic inflection (g — g-sharp) is divided between two different parts. — *2) The alto note g skips to e, while its duplicate in tenor is being chromatically inflected. *3) This measure, and the following ones, are correct, because the g progresses diatonicaUy to / in one of the parts. — *4) That is, C major to a minor. LESSON 37. A. Name the s next-related keys of every major and minor key, mentally. B. Write out the following chord-progressions, in ordinary 4-part harmony, as usual; each in several different ways; all chord-forms (inversions) optional: G I-C V *i) f I-Eb n-v I > "^ ,, I^Vil. e I-a V *i) II F I-d V I DI-eoVllEI-fifl-V d I-F oV II llgil-EVl A I-E V f# I-c# o' 7 Abi-cii-v! bb I-Gb oV II c 1 1 Bb Ij-V II b 1 1 f» *i) Capital letters represent major keys, small letters, minor keys, chord of each group into its I. Resolve the last CHAPTER XXXII. NEXT-RELATED MODULATIONS, COMPLETE. 201. A modulation is distinguished as complete, when the prospective key becomes the final aim of the digression, and is confirmed as such by a complete perfect cadence in the new key. Such transitions require, as a rule, a whole phrase or period. ^ Par. aoi. NEXT-RELATED MODULATIONS, COMPLETE. 97 LESSON 38. Harmonize the following melodies, with a change of key at each ' .,1. ^ * ^^ 2. m s 1^ ■±=± Ato/JK »i) ftoA^ 3. g W: 9W^ P m ifi¥V=^ ^==4 *i) %-B], ■ 4. i fe^ ' ' I LJ »JJ I ^m=m W- 5. 4 ^ =P=I^ m 5 -^ J I :22: ^ £-^ S-'l *i) This is the first chord of the new key; either a dom. chord, or a Second-class chord, may be used (par. 197, Rules II and III). Review par. 198. LESSON 39. A. Harmonize the following melodies, as in Lesson 38; each in at least two different ways: 1. ^^ : iJ4,^J4C4V4.-[| -^ • tn Gi>-i\> n) 0^ « Bft^E^fe -?^ SI ^#-^# #2) B-<:!Jt « ^^SBBIS L^?^ ^^ i: ^f*^^ ^bp: P =t=±t *l) *1>-Gl» »8) 7 7 7 7 *i) n. — *2) These two as may be either I2-IV, or IV-I2 of the new key. — '3) V or II'. B. And the following basses. Analyze the keys and chords: 98 THE THEORY AND PRACTICE OF TONE-RELATIONS. Par. 203. ^S -w=^ ^ S ^ ^^ 4*4 1)7 87 ess 4 a i ^^ flii I ^^iSS I £ I T 65 I V 6 6 7 4: 5 C. Construct original 4-measure phrases, each with one complete next-related modulation. CHAPTER XXXIII. NEXT-RELATED MODULATIONS, TRANSIENT. 202. A modulation is distinguished as transient when the new key oc- curs in the course of a phrase or period, and is followed either by the original key again, or by some other next-related key. Transient modulations are frequently very brief, extending through only a few beats, sometimes in- cluding only two chords, but not less than two. Because: 203. A modulation is never consummated until the new dominant chord has been resolved into (and confirmed by) its tonic harmony; no key can be tmmistakably represented by less than these two chords, V-I (or V-VI), in some form or other. The modulatory process is the same as in complete transitions. For il- lustration: Ex. ISO. Haydn 204. Transient modulations often assume the form of sequences, whereby, as usual, certain irregularities are tolerated. For example: Par. 204. NEXT-RELATED MODULATIONS, TRANSIENT. 99 Mendelssohn. Op. 7 Ex. 151. Presto I 1 I I I I I £ major *i) etc (^^^^ E^^ ^^^Pl E I c#oV I V VI fjfoV I E 11 V I I I I I I *i) The meaning of this c-natural is explained in par. 207, No. i. LESSON 40. Harmonize the following melodies, introducing transient modulations as indicated (at each *) : 1. 2. ^ ± ^ ^ » •- fz±^ ^^3 C-a-c f T-r ^ II, g-d-g 7 V« ^3^5 tt g 4=* S ^i^±^^^^, fzj^i^:* S^ ^1 ^ n ■•-^ztf- IIl F f^ l ^ 3t±i ;t^rt J — L ^ 1^*^ • It — . -•— i n VI ^S P S9^E^^ ^-J-s- ^^wU-teAVFt^ ^^ Bi "i) The sequences define the keys. LESSON 41. Harmonize the following unfigured bases, with transient modulations at each '-. 1. «: ^iftirfrrJrffe ^ z^ifa^ ? *3t P *l) *l) o oV •l; lOO Tim THEORY AND PRACTICE OF TONE-RELATIONS. Par. 205. a. ^ \ rir 'r s *i) n) 3- .3) ^-«}i rPtH^ i ai^wi i ^ PP 7 113 e gft $^ I t I f - w -%r r T r -#-» P=-¥ IS ^ »i) 5. 3 o oV J^;] i|Pi; -rj^i^.rrn^ ^ ^ l^ti: ^ 6. *2) g ii a 'a- ' r f -i ^^^ /» ^ 8 *i) Two melody-notes. — *2) One melody-note to each slur. The three upper parts together on the G-staff. CHAPTER XXXIV. ALTERED CHORDS IN MAJOR. 205. Altered chords are such as contain one or more tones foreign to the scale m which they appear. They represent the most fugitive grade of key- association; or, more strictly, they are only incipient modulations, not con- summated by regular resolution into the key to which they legitimately belong according to their notation. From which it is to be inferred that an Altered chord is distinguished from the legitimate chords- 63/ the manner in which it progresses. 206. An altered chord is always followed by some chord which unmis- takably characterizes and confirms the prevailing key, i.e., usually by the I; sometimes by a Dom.-Discord ; rarely by any other chord. For illustration: C minor C major G major C major Ex. 152. w •1) ^^ fe *8) ^^ -g'z^-fc -^^^^ 7 V 7 n Par. 207. ALTERED CHORDS IN MAJOR. lOI b minor C major *i) This is the legitimate Incomplete V (chord of the dim. 7th) of c minor, and is con- finned as c-minor chord by its resolution into the I of that mode (c-e-flat-j). — *2) Here the very same chord progresses (resolves) into the I of C major (c-e-natural-g), thus iden- tifying itself as a C-major chord, in which the 6th scale-step, a, has been casuaUy altered {lowered) to a-flat. — *3) This chord appears to be the dom.-seventh of G major, and is con- firmed as such, by resolving into the G-major I; the f-sharp is indispensable. In the next measure its appearance (notation) is not confirmed in this marmer, but, progressing into the I of C-major, it proves to have been a, C-major diord. Altered; the f-sharp (4th step raised) in this case is arbitrary, and optional. The other examples are demonstrated similarly. Com- pare par. 203, and observe that the identity of a chord depends upon what it does (i.e., upon its progression). 207. The most frequent alterations in major are: 1. The lowered 6th scale-step, in all chords which contain that step; 2. The raised 2d step, in the dominant triad; 3. The raised 4th step, in all Second-class chords (Ex. 134); 4. The raised 2d and 4th steps together, in the 11'^. For illustration: Ex. 153. C major Lowered 6th step •!) ixjwerea oin siep »x/ I I 1 1 f «3) Vb s oVb IVl, 7 7 IV1> III. 7 VIb 7 7 V Raised 2d step ^ Raised 4th step i^ 4-^-4 — ^ Rused 2d and 4th steps * $ ^ H-^-t " i tf-r^ ^g^ f^ v# I iv# I n# I im I •2)V *i) The chord of the dim. 7th can thus be used in major as well as in minor. Comp. par. 176, last clause. — *2) A very exceptional, but not uncommon, resolution. — *3) Ob- serve the manner in which the alteration is indicated in the chord-name. The inversions are not marked. 208. Other alterations are possible, but far less usual. Namely: 1. The raised ist step (in the I or VI', always resolving into the dom.-^th). 2. The raised ist and 6th steps together (only in the VI', followed by the I02 THE THEORY AND PRACTICE OF TONE-RELATIONS. Par. ao8. For example: Raised tonic Ex. 154. C major •PT *1) Raised ist and 6tli steps ^^^^^m '\r nrr-^r d min. 7 rj ' *2) I# V VI# V VI## V i) i\ro< thus, into the 11 of C, as this would corroborate the preceding chord as a legitimate dom.-7th chord in d minor. — *2) In connection with altered chords, such unusual interval- progressions as c-a^, etc., are permissible. Additional illustrations: 1. Lento I Ex. < 155, ''i^f^ %.^-^^if^^^^ ^ ^'^ C major gft i c n## " I n«# I ■SH ^ -J. ^ ^. -f Later ; El < f < [' I a — -^ ^ * -iS<-=- >^ g -e ^^T^ ja I I ^ #frfi ^^^ ^ u^ c ii#r enV- 7 -V- 2. Allegro ^m Schumann. Op. 21, No. 4 W-^ii.^444 4 i^ «6)i" :^ f' l r f NLi =£^ ft r D major. Par. aog. ALTERED CHORDS IN MAJOR. 103 *i) The altered 11' of C major (raised 2d and 4th steps) ; repeated two measures later. — *i) Here a transient modulation is made into i minor; — *3)and here C major is re-entered, through its IV. — *4) The lowered 6th step of C major. — *5) *5) The comparison of these two measures illustrates the distinction between an altered and a legitimate chord. At first, the ^ I J I r 4-J K^V ^ 4 ^^Tg 4. m rJijjjijj g^p -' i rrirr i '^ ii ^Hij ^ g ^ m SC: 7. i ip= jjj fHJJ i Kiitig^ s t- f i ^S- 9. 4 f ^4 J J J \^^i^pt^^^-^^ ^ ^tO^ ^ 11. i ^^ ^5 ^ =!«=Ff- IS * i \ ^ w^^=^ 104 THE THEORY AND PRACTICE OF TONE-RELATIONS. Par. aio. 19. ^ tS f=^ ^ ;5==P=xp: zj g- 13. 14. ^^^ te^ te ^f f=F-i-^ J:t K-i|J-LJ- ^ 15. i fe^ ^ Ifffe ffl:rWFK g ife J rf * sg i3 Gt.— Db- »l) *2) 16. » * » *i) Ex. 153, note *2). — *2) Par. 208; resolution into the dominant-; CHAPTER XXXV. ALTERED CHORDS IN MINOR. 210. Review, carefully, par. 88. The alterations in minor are defined on the basis of the harmonic minor scale. Their most obvious purpose in harmony consists in obviating the awkward interval-progression between the 6th and 7th steps of the harmonic scale (par. 92), by substituting a melo- dious succession which gives rise to the melodic minor scale. 211. For this purpose, The 6th step is raised in the ascending scale, and the 7th step is lowered in the descending scale. Melodic form ; Ex. 156., C minor i •1) *2) IE -Bi= tts^gg- -^^^ zhsz -bs- Comp. Ex. 65. , *i) By raising the 6th step from ob to ai}, the awkward interval of an augmented second (between steps 6 and 7) is reduced to a simple, melodious, major second. This is the only reason why the alteration is made. It is done only in the ascending scale, which thereby assimies the original major form (at those steps). — *2) The same change from an augmented second to a major second is made, in descending, by lowering the 7th step from jjj to b\>. ^This descending form of the melodic minor scale exactly agrees with the adopted signature 91). Pai. ai2. ALTERED CHORDS IN MINOR. lOS 212. The external proportions of these various minor scales may be systematized with- out confusion as follows: I. The first five tones, from tonic to dominant, are ihe same in all the forms of minor, and contain the lowered {minor) third step. C minor, harmonic form i ^5©= ^ -Bi= •tpSr 2. In the melodic scales, the upper series of tones, between dominant and upper tonic, consists of "whole step, whole step, half-step" in both directions; thus: C minor, melodic form I 1 i =s^ Itta-B^ nMi 1 1 J -^^b'S-H 1 1 213. From this the important deduction is made, that the third scale- step is the only distinctive tone between the major form and the various minor forms; it is major in major, and minor in minor. 214. The raised 6th step is applied and treated as follows: Ex. 157. C minor ^^' '^^i\\iij] ryM^ytVr^H^ I I < J — f M^ •a) ' I f r •8) -i.1 1 ^ n . j I ir-i,i-H-h-^i Jit ^ p^frf p f¥^^ i viU 7 VI, nJtv I nil V ivlj iVJtVo •i) The progression of these chords is defined by the resolution of their altered step; not rigidly by par. 206. Here, dominant chords must follow. — *2) The resolution of this 7th (c in alto) corresponds in this case to Ex. 121. — *3) The ai| in soprano is followed by ab in tenor. See par. 200 b. 216. The raised 4th step often accompanies the raised 6th step, in Sec- ond-class chords^ In tliis case only the 4th step requires the ascending resolution; the 6th step may rise or fall. For illustration: I 'a) I , , *5) *a) Ex. 168. C minor ^^SSS^ ±=4= m¥ 4 ^ -U4- 1 CTysi^t i=3 ii#il V I nift mm r ^^ J J. i*^t iJ- =..J_ t^^ o ™V ii#it V I iiijj mtti V o' *i) See Ex. 136, note*2). — *2) Resolution into the I; stationary dissonances. — *3) Analogous to Ex. 153, note *2); rare. — *4) Comp. Ex. 157, note *3). — *s) The reso- lution into the triad V resembles a modulation. The dominant discords, or the I, are more genuine. Comp. par. 206. io6 THE THEORY AND PRACTICE OF TONE-RELATIONS. Par. 216. 216. The lowered 7th step is applied and treated thus »i) , *a) , , , «3) Ex. 159. C minor ^^^ t^ fe^ :\=X ^^ hr^ J-J ^ t 4^ irdz ^ lb IV mblV VblVj VboV oVb VblVg *i) Comp. Ex. 157, note *i). — *2) Compare Ex. 77. — *3) The lowered 7th step is rarely employed in dominant chords; especially so in the discords of the dominant. 217. Aside from these alterations, which are identified with the melo- dic minor mode, there is one other very common alteration, namely, the lowered 2d step, which occurs in the ist inversion of the II (more rarely in the II itself). For illustration: «l) *2) Ex. I60. C minor fcid:^ e t-r ^ I I W^ lizf: h ^ yhl-U t-rr i =t=j= -p— t- ^£=MM i s*^ ni, I V IIMVSlt "i) See Ex. 154, note '2). — "2) Two different altered chords in succession; observe that they both belong to the Second-dominant class, so the progression is practically chord- repetition. Additional illustrations: , .„ .. Mendelssohn 1. Allegretto ^^^ Ex. 161. m r'i m^\i-i-m < f# minor i i t^:t 5: Jf (Hi # s 2. Prestissimo \- w_ m etc. VI7 iV ^-ivr J 7 V- Beethoven Par. 217. ALTERED CHORDS IN MINOR. 107 (^ 8- AlUgre ■^=-% ^ I. m Beethoven < d minor *8) »8) ^^m ■f-r- -t i 0- ^^^ ^-^*--L^^ 4. Len/o 7, 7 -VlJtoV I *6) ^ V VIJI oV I Chopin 15= "^ »6) ^ a minor »4) . . j I I I I J P¥i» l j'fM | T 1 1 r — ^r• I r'Tfi^-^*'^ 77 **) o 7 I UiKII) V VI V Ii Uib VV V *i) Lowered 7th step. — *2) Raised 6th and 4th steps. — *3) Raised 6th step.— *4) Lowered 2d step. — *$) Embellishing (neighboring) notes. LESSON 43. Harmonize the following nunor melodies and basses, introducing altered chords at each * (in some cases definite, in others optional); and m6dulating as indicated: 1. 2. i I * £fe#^£ ^^f¥^^^ ^ gFFp i^ zitzM: 4. i g m g=fe ^ P^l9- S & P ^ ±at g * M 1* Vi D — 'Pt P^^^^^^ ^^ g ^ ^?hi^ -g)-^ ;«c^ ^t tf: ~1 f# min.' 6. fTr~;r:fi p:i2y ^Igi 1 ^-*- I,»l) VI (8 a e) Io8 THE THEORY AND PRACTICE OF TONE-RELATIONS. Par. 218. 8. , , C ~ I a min. I I I i tf rrf^Tf w =^a^ P^ ^^ ^^ IKZ D- »3) a 10. ft 1 ^ ^ t=* *<=& «•- tT7 VI 11. ^._^ • fi » • a **) L* i.'" ^ ^ :^ •hd-i — *i) One bass note for the beat. — *2) Like Ex. 160, note *2). — *3) These irregular key- relations (contrary to par. 197, Rule I) are justified by the sequences. — *4) The three upper parts on the G-stafi. One melody-note to each slur, strictly. CHAPTER XXXVI. MIXED CHORDS IN MAJOR AND MINOR. 218. Mixed chords, usually called chords of the augmented sixth (be- cause they all contain that peculiar interval), have an illegitimate or de- formed shape, resulting from the more or less unnatural association of steps which are pecuUar to different scales. They are very effective, frequent, and easy to manipulate. Besides the rules in par. 206, 209 (which review), which apply literally to the mixed chords, also, it must be observed, that The interral of an augmented 6th is rarely inverted; and mixed chords usually resolve into the tonic chords. 219. Mixed chords in major are obtained, first, by raising the 2d step of the scale, in dominant discords; second, by lowering the 6th step in conjunc- tion with the raised 4th (or raised 4th and 2d) steps, in Second-class chords. Par. 220. MIXED CHORDS IN MAJOR AND MINOR. 109 Third, and very rarely, by lowering the 3d step in the dominant seventh. Mixed chords of the dominant class: Ex. 162. C major *^> *^>IA 1 J I *•> 7 Mixed chords of the Second class: *e) f-rM=4-i| with the leadmg-tone b. — *4) The augm. 6th (a|>-/#) is here agam inverted (to a dim. 3d, /jt-ob). — *S) When the augm. 6th is inverted beyond the octave (i.e., as dim. tenth) the effect Is much less objectionable. — *6) The d^ in these chords is quite frequently written el>, erroneously. The latter could appear only as distinctive tone of the minor mode (see par. 213). 220. Mixed chords in minor are limited to the Second rlass (II-II''- IV-IV'), and are obtained by raising the 4th scale-step, while the 6th step remains minor. For example: *i) *a) Ex. 163. C minor i HJ-4n^ m ^ i •3) »i) n) 4 1= ti IVS I r r V I ^^^ ^ ^J tfe ^-f =F 7 II# i i-H^-^-J il^-^^ I ^-^H^ IV# I T 7 7 IV n H *i) The identity of these chords in C major on one hand, or in C minor on the other, de- pends, as usual, upon the resolution, — here solely upon the tones e-flat, as above, or e-natural, as in Ex. 162, measure 6. See par. 206, and 213. — *2) For the reasons given in note *i) , the progression into the dominant (instead of the tonic) chord is indefinite; the I must im- mediately follow, at all events. — *3) The augm. 6th (o|>-/#) is here inverted, as dim. loth. Comp. Ex. 162, note *s). — *4) These perfect sths are so seductive, that unusual caution must be observed in using the mixed IV; the only reliable safeguard is the resolution into a tonic chord. See Ex. 140, note *i). In the following measure, the 5ths are inverted (as 4ths); and the last measure shows still another method of avoiding them — by resolving the 7th (eb) alone, into the IP. no THE THEORY AND PRACTICE OF TONE-RELATIONS Par, aao. Additional illustrations: 1. Moderate *\) *a) Schumann. Op. 42 s ■*-, -i-. Ex. 164. ^Et ^ 1 ^ s it ap^ etc. i^ ^ ^ ^ ^m -»~=- ^ ^ ^ d I (C Vb 1) FIIbl| — V FVS FI a Hi V- 2. Allegro t i «4) M. S j=j=^^ ^ 'Ifflg *5) ^ ^ Jf Jf- ^=tf :£ f f t^ §^te I I ^ 1 1 11 ^ Eb V- (Bb V Eb n I) V Eb V I AbVlj Beethoven 3. Allegretto Mendelssohn J-TA»i:t rX l 1 ^ gi3Eri=4 |W=Mg ^ It tt»s) 1^ ■n^- *a) ^^ J^^-?l =^ i^ V. I i ^ ^^^m — r Eb V EI A V#— I E n##. A V#-I *i) Possibly the lowered second step of C major, but more likely a lowered 6th and raised 4th step of F major. — *■£) Raised second step. — *3) Raised^ 4th step. — *4) This, like note *i), may be analyzed either way, but E-fiai major is far the most plausible, because the lowered second step in major, is very rare. — *5) Mixed dom.-yth of A-jlat major. — *6) Here the modulations are both effected through altered steps. LESSON 44. A. Harmonize the following melodies and basses, with altered or mixed chords (as marked Al. and M.), and modulating as indicated: M. M. ~-li>i ^ liJ a S «i) »3) Par. »20. MIXED CHORDS IN MAJOR AND MINOR. 1 1 1 Al. 3. Al. M. M. Al. i 7. ^^ riT^\^ ¥ 1 — I — \ d * ^ r r I s^ V F \B\, 1 Eb- ' — ■ Al. Al. M. g oV II, Al — S M. M. ■ g e i p=t i m. -1 fr M. 8. i > •\p t P i'H J»J Al. *3) # ^ M. IIjM. Al. M. M. 2 M. M. 9 A*. 8A1. °A\.%A].l- ■^ ^ ^cii: m 11. Lowered 6th step throughout Al. 8 Al. 8 Al. I A].| 2 »5) ^ ^ s 6 4 6 S 5 8 M. I Al. "^ *4) Al. Al. Al. M. |A1. 1 ■^ §''2 g "i) The raised second step in soprano is most suggestive of a mixed dominant chord. — *2) The raised 4th step must be in some Second-class chord. — *3) The mixed chords in minor are exclusively Second class (par. 220). — *4) Begin with the high third in soprano. — *5) These last two chords, which follow the perfect-cadence chord, constitute a Plagal cadence. B. Experiment with original 4-measure phrases. 112 THE THEORY AND PRACTICE OF TONE-RELATIONS. Par. aai. CHAPTER XXXVII. EXTRANEOUS' MODULATION, mDIRECT. 221. Extraneous modulations are such as extend beyond the next-related keys, in any direction. Compare par. 197, Rule I. The remote key is usu- ally reached indirectly, by modulating through the next-related keys which in- tervene, i.e., from signature to signaiture in the direction of the desired key — whereby either the major or minor mode of the intermediate signatures may be taken. For illustration: from C major (or a minor) to A -flat major (or/ minor), tlie following signatures will be involved: Jj — 1> — 2\> — ^\> — 4.\> (see Ex. 146). The modulation may there- fore represent any of the following lines of keys: C (a)— F— Bb— Eb— Ai7 (f) (Capital letters, major; " — d — g — c " " small letters, minor) "— F-g — Eb— "— d— Bb— c — "— F— Bb— c — "— d— g — Eb— Or: from B\> (or g) to A (or/S), through the signatures 2b — ib — 9i — 1# — 2# — 3S. Or: from ZJb (or 6b) to E (or cfl) thus: sb— 6l' = 6#-S*-4#. LESSON 46. Harmonize the following melodies (Nos. 2 and 4 in several ways), modulating at each *: N.B. Use the dim.-ph chord very freely — in both modes (Ex. 153, note *i). ^ ^ * ^^^P ^ =F=^ c a d ^ ^ b ^ F d Bb g Eb c i IE d2t Ab f Eb =#=|ii UJiLi_b Jr:yi bb- ^-P- ibE ^^^ g 2F=i: m ^^ 4. G e ^ D b f=f=^ A H Par. 321. EXTRANEOUS MODULATION, INDIRECT. 113 LESSON 46. Harmonize the following melodies, each in at least two ways, with a modulation at each * (major or minor) : i a 1. ^ *A *i) a s^ -^ g f Tm E B F#- g# d#- -Gb bb -el, ^mit^^vj I I ^ 11 ^ j: , ]ff g ^^ A D G b e F d 3. g ^^^'-f^=P p^ - g -g ll ^ t =^ :#t Eb c 4. Bb g F d *i) ^ tta Nr^-^^L^^^ J J l iffrr-1- p ^ V=^=¥ B E A a E * *i) Where the key is not specified, the student can easily define it. LESSON 47. Harmonize the following basses, each in at least two ways, with a modulation at each * (major or minor) : 1. m is =P=F^ f=ii J=^ W=fa «i) a. F d Bb Eb c Ab f Eb ^jjf Ir r Is^ ^^ k^Ui^-irm Ab Eb f Bb F g *2) E Bb g F d C G »8) a e *i) Use the dim.-7th chord freely, especially in minor. — *2) Lesson 46, note *i). •3) Raised 4th step of D major. 114 THE THEORY AND FRACTICE OF TONE-RELATJONS. Par. aaa. CHAPTER XXXVIII. DIRECT EXTRANEOUS MODULATION. THE STRIDE. 222. Under certain favorable circumstances a remote key may be reached directly; that is, without passing through the intervening signatures. 223. The first and best of these cases is a direct transition of four degrees (or signatures), for which the author has adopted the term "modulatory stride," and which is defined as follows: The "stride" is a perfect fifth downward from any major keynote, and upward from any minor keynote, with a change of mode. For example: from C major down to / minor; or from c minor up to G major. The Stride-relation is therefore represented in both directions by any perfect 5th, the upper tone of which is a major tonic, and the lower tone a minor tonic. Ex. 165. i Stride-relations -12— El. -bi»— Kb ■ -bl9 — tb-'9 nl" i ^-g-gj jE^DJ^b" etc. 224. Upon reflection it will become apparent that the remote transition called the Stride results simply from an exchange of mode (minor for the ex- pected major, and vice versa); without the change of mode it would be an ordinary dominant or subdominant modulation, respectively. That is, the Stride from C major is / minor instead of F major; . and from g minor it is D major instead of d minor. Confusion can however be avoided only by mechanically observing the formula in par. 223- The Stride-modulation is made in the usual manner, according to par. 198. For example: i Moderato ^^ ^P^ ^3 ^ Ex. 166. s 7 t s r r r i« -^i— I- I I y 9-^ =? -*■ 7 g V- 7 -II- 7 -V- Par. aa4. DIRECT EXTRANEOUS MODULATION. THE STRIDE. II5 Chopin. Op. 23 m ^ x i— ^« ¥ ^% « f r » Ji4 r r- • s. g^=:^ - i^ I I ■ ' , f f ' 4 -. ^ D V- gV- *i) With f-natural (instead of f-sharp) it would be the next-related key, d minor. That f-sharp should however be preferred to f-natural, in the vicinity of g minor, is very obvious, and affords the best demonstration of the practically close intimacy of the Stride-relation, notwithstanding the actual difference of four degrees in the key-signatures (g minor — D major). LESSON 48. A. Indicate the Stride-relation (by ke)motes) from every major and every minor key. B. Harmonize the following melodies and basses, introducing the modulatory Stride at each *: fc fe m fc W^ :*: ■^-G^ I I 4 5. I Ab maj. . maj. M Pf^^ ^^te atf^p -r ^ p^ li^ n) M * y * I e min. I » 7. ii^ J2I j g [^ ^ •3) e.a ba qa as bs {6 .8 bs ,7 „7 a ^ u Bo ii6 THE THEORY AND PRACTICE OF TONE-RELATTONS. Par. 225. 8. 8 ^ ■& ^^ ^3i '^ ^ I R na Ufa #s. r #« »3 es 43 H «a a t|3 #g #8 ' Jta 87 *i) The Stride from A\> major is db minor, or its equivalent, <;# minor, which is more con- venient. — *2) When the last chord of a key is, as here, the dominant chord of the coming key, the latter may enter at once — apparently through its tonic. — *3) The basses must be thoroughly analyzed. CHAPTER XXXIX. DIRECT EXTRANEOUS MODULATION. THE OPPOSITE MODE. 225. The next best direct transition to a remote key is the change of mode (from major to minor, or vice versa) upon the same tonic; for in- stance, from C to c, or d to D, or G-flat to f-sharp, etc. Although this tran- sition into the opposite mode actually effects a change of location in the modu- latory circle (equal to 3 degrees — C — c), it is hardly to be regarded as a modulation in the strict sense of the term; for it is only a modification of one and the same tone-family or key, as was demonstrated in par. 86 and 89, which review. 226. The possibility of thus changing the mode of any keynote is trace- able to the coincidence of the dominant chords (V, V^, qV) V* altered and oV° altered) in the two modes. (See par. 90; 151 c; 165, Rule I; Ex. 153, note *i): By reason of which any dominant chord may be resolved at option either into tlie major or minor tonic chord of the corresponding key. See Ex. in, note *9). The resolution into major is, however, always the more natural. For example: 167. *i) The tone upon which this exchange of mode devolves is the mediant (third step) of the key; in this case etj for C major, and eb for c minor. See par. 213. 227. Any dominant chord, then, which enters from major (i.e., as major- key dom.) may resolve into the corresponding minor tonic (by substituting the minor mediant for the expected major mediant); or, inversely, a domi- nant chord which enters from minor, may resolve into the corresponding Par. aaS. THE OPPOSITE MODE. 117 major tonic; thus effecting an eocchange of mode. This may be done at any point in a phrase, and is subject only to such conditions and limitations as are patent to a cultivated ear. 228. The coincidence of the dominant chords in major and minor is fre- quently utilized as a means of reaching other remote keys directly, by sub- stituting the Opposite mode for what would otherwise be a next-related key. This is always the case with the Stride (see par. 224); and also with such examples as the following: 7 V Ex. 168. o -I 1- -K -^ H— ® — -^^^^^—^^^ -^ -? *^ *i) With b^ it would be G major, a nextHrdated key of the C major which precedes. Sub- stituting the minor mediant Vv makes the modulation remote. — *2) With /I] it would be the next-related key, d-minor; with/# it is a remote modulation. — *3) The Stride. 229. Further, the exchange of mode may also be accomplished by the simple chromatic inflection of the mediant itself (Ex. 169 a) ; Or, perhaps best of all, through altered chords with the lowered 6th step (Ex. 169&): Wagner Ex. 169. i -J—hJ- ^ r c- ^^ f igyi Gb- f- -(f)S- i d. IE -IVb r j b-i. ^ -IV(CIVb)-C Additional illustrations: 1, Lento ^ :>j/ i P/;jM.. i ;':Aji-n^nM i e£ Schubert 3^ sr^ Ex. 170. «i) »2) ^ r r^^ ^ ^-i ^ij^fa=a j 11^ :::t -AI- r Il8 THE THEORY AND PRACTICE OF TONE-RELATIONS. Par. 239. 2. Adagio Beethoven. Op. 22 M t • g^ ■ ■ ik i- J <- - Lf ^ T ^ g- ^ e ^ F^frTi te^^^ *4) T -t -^M^ ^ *3) *s) H •e) m £ s= * Eb I- B|> major bl> minor -oVblVboV V 1 Ilib IVUlj V Bbmaj. 3. Andante Brahms. Op. 10 i tai 4-^ i^^ ^ ^-i "inn etc. b minor B major "i) The dom. triad of o minor, resolving into A major. — *2) A direct chromatic tran- sition from major to minor. — *3) The g-fiat is the lowered 6th step of the next-related key, B-Jlat major. — *4) The dominant chords of B-jlat major resolve here into b-Jlai minor. — *5) See Ex. 160, note *2). — *6) B-jlat major here finally asserts itself. — *?) Direct chromatic transition from h minor to B major. LESSON 49. Harmonize the following melodies and basses, introducing the Opposite mode at each *: 1. i ft ^^ JE ^ 2. ^^ff=fp=^rFr ^ I f s= ?= b J a f\ p=¥=^ P«I. 230. SEQUENCE AND CADENCE MODULATIONS. 119 bb—Bbc— C d— D -E f# fc^ r< j WiJ i J jjiJh^TrTT^rrrt^rirrirr i i A|> major e. »8) Mkv-H^ »4) t •!) t V: !^^ 7. Pffy ip g-t>a^ e o§ o qs 7 5i a^0a~5s^ba Qa 1,7 g^ 3 ^ tS ^ i^ «3 ba 1.8 bs bs ba . bi 17 5 6- pa ba I SS 03 «3 *i) At each t> the foregoing dominant chord is resolved into the opposite mode of the expected (next-related) key. — *2) Lesson 48, note *2). — *3) This is the Stride (G-e), simply because minor is substituted for the expected major. — *4) The cross-relation (see par. 2ooi) is often unavoidable in sequences, as here; but, as usual, the sequence justifies it. — *S) The signature is omitted here, and in No. s, because the notation, during such extensive modulation, is more convenient with accidentals. — *6) Analyze the basses thoroughly. CHAPTER XL. SEQUENCE AND CADENCE MODULATIONS. 230. In all the foregoing modulations, both next-related and extraneous, the fundamental rule given in par. 198 has been strictly observed. But more abrupt and irregular modes of transition are possible, under favorable circiunstances. The most auspicious conditions are afforded by the momen- tary breaks or interruptions which occur between sequences, or at (i.e., after) cadences of any kind. Hence: 231. Upon passing into a sequence, or into a new phrase, or distinct member of a phrase, an abrupt transition may be made into the desired key (whether related or not) without necessarily interposing the usual dom. (or second-dom.) modulatory chord. For example: , ^ 2. Ex. 171. Sequences SE :± ? i A. etc. i 11 I 4H»= -I dl- E I- n) I20 THE THEORY AND PRACTICE OF TONE-RELATIONS. Par. 932. d# min. II "i) The transition is made abruptly from the I of the old key, into the I of the new (comp. par. 197, Rule III, second clause). There is no conmion tone connecting the keys (see par. 232), but the sequences are so dose and coherent that the connecting-link may be dispensed with. — *2) This modulation is made in the regular way, but the keys are not related. — *3) Here there is a succession of tonic chords, and one single chord must suflSce to represent a key. Comp. par. 203. It is all accounted for by the sequence. — *4) The old key is abandoned at its dom.-7th (comp. par. 197, Rule IV). The connecting-link into the first sequence (which is a very close one) is the tone cx = d (leading-tone becoming a tonic). 232. The limitations for such abrupt modulations are: That there shall be a reasonable degree of coherency between the keys; and, as a general though not strict rule, that at least one tone be sustained from the old key into the new one, as connecting-link. Of these "pivotal" modulatory tones the best are the tonic, the mediant, or the dominant of the old key, which may be exchanged at option for either the dominant, the mediant, the tonic, or the leading-tone (perhaps the 4th or 6th steps, as seventh or ninth of the dominant chords) of the new key. Illustrations of abrupt cadence-modulations, and "pivotal" modulations: 1. Presto D'Albert V >-. > Ex. 172. Cadences n i i rg-g q^g? p I ^ m H5 :?i=r4=?: :tt P ^ ^=^ •1) _^ ^^ — i;^ ett. a minor I- -II f minor I- -VI- Par. 232. SEQUENCE AND CADENCE MODULATIONS. 2. Allegro 121 Brahms A' e& Pi^gi ^.^,-f::^-^:-k/TJ egg*- - d d d - W9: i etc. ^^^^ g ? D I- -V II C I- 3. Vivace i x^^^a *—m-4 Jz ^-± Vli i n# I us# I HUMMEI, ^S ^ ^^ ^ I ^^=T-_ -s- ,^ «3) -k h etc. D I A V 1 II CI V I D I A V- 4. Lento 122 THE THEORY AND PRACTICE OF TONE-RELATIONS. Par. 232, *i) Cadence (semi-) in a minor, followed by the abrupt announcement of the /-minor I. The coimecting-link is c-c (mediant becoming dominant). — *2) Dom. semicadence in D, followed by the I of C. Cormecting-link e-e (2d step becoming a mediant). — *3) Tonic cadence; connecting-link e-e (dominant becoming mediant). — *4) Transient tonic cadence; connecting-link c-c (mediant becoming tonic). — *s) Connecting-link a-a (mediant becoming dominant). — *6) Dom. semicadence in a minor, followed by the I of B-jki major. There is no common tone; this is a typical ca<^e»<;e-modulation. — See also £z. 201, No. 2, a typical feguem^e-modulation. LESSON 60. Harmonize the following melodies and basses, with abrupt modulations as indicated: Seq. Seq. Seq. m ^ f r r i r 1 r f± 1 r n r ~1 Dom.= rrr^r ^ t \>i^ 4: ^ Med. 7 III Med. :=; Ton. Bl, Med.^ Dom, Ton.=: Med. i Med.= Dom. ^ ^^i=^i -P P- ^ jUi^-' "-^ 3^ 1 ^^ J Gb h 2- .3 te Bb la Ton. = Med. Med. = Dom. Eb C Ldg-tone = Ton. C f r i »rrr \ -^ v y^jj \ * im Bl, G *•! I F# Bl» Ldg-tone ;=; Ton. G «3) ^ A=^'> I . ^^J ^ n&^ fe 3' E V I G (Seq.) m (jjjt min. I I L. « B (Seq.) E g# niin. E 1=2^^— (*- c# I A V I E lilt I ivij I 1 ■e> — '—-& — I — & — ' — &■ I I •s) I I L. «4) Dom.= 6th step Ton.= Leading-tone mia ., rT i[J ^ Med.= t^l LJlX^ l ^tU^^;^ Bl, Ton. Bb Db gg^tolf^E^^^^-^^^^ Ton. = Leading-tone P«r. 133. SPECIAL APPLICATION OF THE DIMINISHED jTH. 123 *i) The bass begins on the first beat; the three upper parts follow on 'the second. — *2) Like note *i) throughout. — *3) This irregular rhythmic form of the perfect cadence (unaccented) is not unusual, and is justified here by its agreement with the semicadence. — *4) Plagal ending. Comp. Lesson 44, note *s). — *s) The three upper parts on the G-sta£[. One melody-note to each slur. CHAPTER XLI. SPECIAL APPLICATION OF THE DIMINISHED- 7TH CHORD, m BOTH MODES. 233. The most efficient and attractive form of the entire dominant chord- class, and the most flexible chord in the whole range of harmony, is the chord of the diminished 7th. It is very frequently employed for the purpose of modulation, and, on account of the unlimited facihty of its connections, it serves as a transitional medium between any keys, regardless of mode, and almost entirely irrespective of the ordinary consideration of key-relation. 234. The following points must be borne in mind: a. The chord of the dim. 7th is the Incomplete form of the dom. ninth, and is found upon the leading-tone of the minor mode (par. 176). b. Though legitimately a minor-mode chord, the dim.-7th is equally avail- able (as altered chord) in the major mode; i.e., it may resolve indifferently, either into the minor or major I. Ex. 153, note *i). c. A dim.-7th may be introduced, in some form or other, after the tonic chords (I or VI) of any other major or minor key. The choice of inversion will depend upon the form and location of the pre- ceding chord. d. The notation of the dim.-7th must conform to the new key (into which it resolves). See the table made in Lesson 29, B. Whatever chromatic in- flections appear, must be effected according to the rules in par. 200, which see. For illustration: •1) ^ J J J h^ *i) ^^^S^ Ex. 173. =F«F =r=^ f — r- j. i i°'=j. i 1 i\>X j."=j. C G maj. g mio. C F maj. min. *») 124 THE THEORY AND PRACTICE OF TONE-RELATIONS. Par. 234. »i) i=bi: IE -f— »r f — r- -feJ j- i ^'- ^ i j- b^ -^ ^ =t t=T -l;a- C d mm. maj. »3) B|? maj. min. 3zr--L^j I ^ ^^'^ -^ I ^ t^ 5 »— V— fr f=F ^^ P^ J- ^^ -^0- g I I r ^ ^r fei£ J<«-i,J_ etc. s i ,.a ) P l ^-M^-L-l C a min maj. C Eb e min. maj. C f^ min. maj. *i) With e-fiat, instead of e, the first chord will represent the I of c minor also. — *2) Avoid that form of the dim.-yth in which the 7th (the original 9th) lies in the bass. See Ex. 130, note *4). — *3) In this example the VI of C major is used. It represents, at the same time, the I of o minor. LESSON 61. A. Connect the I of every major and minor key, with the dim.-7th of C major (and minor), in the maimer of Ex. 173. — B. Connect the I of G major with the dim.-7th of every other major (and minor) key, as in Ex. 173. All inversions optional. LESSON 52. Harmonize the following melodies and basses, introducing a dim.-7th {choice optional) at each' i PJ^r^ &, r" a -jg=ga,-:^z^ |J4^tf^ nS—lh^ «— ; ^ *l) *3) *3) 2U,J J I I fTlHtl gjfe^Eg^S » u* * ^ ^ — Vt^ ■I =-tH — fj^^^ i- ^Jj^ jig^f^:^^^^^ «4) K^- Par. 235. CONSECUTIVE DOMINANT CHORDS. 125 *i) The dim.-7th of d minor, D major, or F Tnajor, at option. — *2) The dim.-yth of C major, c minor, ot E-flat major, at option. — *s) The choice here is Umited to c-sharp minor, in view of the approacliing cadence in that key. — *4) The choice here is limited to D major or d minor, in view of the following slur. — *s) Place the three accompanying parts together upon the bass staff, and use one chord to each slur, strictly. The choice of key is rendered evident by the slurs. — *6) The three upper parts rest on the ist beat of each measure, ex- cepting the cadence, and enter together on the 2d beat. Thus: J? J J I — together on the G-staff, throughout. CHAPTER XLII. CONSECUTIVE DOMINANT CHORDS. 235. The most notable exception to the fundamental law of dominant chord-progression given in par. 69 (Rule III), is encountered when the domi- nant chord, instead of resolving into the tonic harmonies of its own key, digresses into another dominant chord (of some other key). This irreg- ular but by no means infrequent progression may be demonstrated on the ground that the obUgations of the first dominant chord are simply trans- ferred to a chord of exactly similar obligations in another key. And the con- nection is moreover usually effected by means of one or more chromatic in- flections, which is the smoothest of all modes of melodic progression, and justifies every irregularity.. 236. The chromatic inflection is directly opposed to the diatonic progression, and consists, as has already been seen, in simply raising or lowering a certain letter or scale-step by an accidental, without effecting an actual progression from one letter or step into another. It does not conform to the line of the diatonic scale, but is oblique to the latter. It is an abrupt digression from the natural order of tones, and its effect is therefore to cancel the key instantly and completely. No resolution, and no diatonic chord-progression of any kind, within the same key, can include any chromatic inflection (only excepting the possible chro- matic introduction of altered tones). Consequently, the chromatic inflection {unless in- cidental to an altered or milled chord) invariably executes a change of key, as abrupt as it is inevitable, and usually so quietly and smoothly that this species of melodic succession, i.e., "Chromatics," is properly regarded as the most powerful and seductive factor in modula- 126 THE THEORY AND PRACTICE OF TONE-RELATIONS. Par. 937. tion. The fundamental principle of chord-analysis, that "the identity of a chord depends upon its progression" (Ex. 152, note *3), is also canceled by every chromatic inflection, which, as stated above, instantly severs the connection of the chord with its key. From this, the peculiarity, but at the same time the extreme importance of the cliromatic inflection, and the frequency of its employment, especially in modem composition, may be inferred. A great number of curious chord-progressions may be and are effected through the agency of chro- matics, which dude all rational demonstration, and can be accounted for in no better way than as a manifestation of seductive chromatic agency. Therefore, the chromatic inflection must be accepted as one of the chief excuses for the peculiar harmonic connection of which this chapter treats, namely, the direct succession of different dominant chords. 237. This principle of chromatic Dominant succession is to be applied in the most general and comprehensive sense; i.e., the dominant chords of one key in any form (V, V, qV, V* or ©V^) can progress into any form of the dominant of another key (V, V, qV, V° or qV^), either major or minor. This sweeping rule is tenable in theory, but in practice it is limited. By far the best and most common successions are those in which the third of the first dom.-chord is chromatically lowered, or its root chromatically raised. See Ex. 174, measure i (lowered third), and measure 2 (raised root). 238. The new dominant chord may resolve properly into its tonic, or it may be followed again by another dominant chord. When the series of domi- nant chords is thus protracted, either the soprano or the bass is likely to pro- gress in continuous chromatic descent or ascent (Ex. 174, B); 239. Rule I. The seventh of each dominant discord should be cor- rectly resolved (diatonically downward), if possible. Rule II. The chromatic progression should be approached, if possible, in the corresponding direction. Review par. 200, and par. 60. A.»i) *a) »3) *4) «6) «6) «e) Ex. 174. i 4- L-,i—4- r-[ f->— T ^? i < 1 1 1 1 1 *==t ? C V FY c A C Bb C D C Et c a c bb c d c el> 1 il p ^ ^ •^ or: m- i ^ i 1 ii'» f=*f=H= c c A], C c B b C c Db C c G g C E c e Par. 239. B. »b) J. I CONSECUTIVE DOMINANT CHORDS. »io) 127 ^ ijJ_ | J bJ ,J 1.;+^ ^ i i'iii ^v^^n ' " ' i ^" /f ii ^ b» p- « I ' I I 7777 V V V V 7 7 V V 7 7 V V 9 9 9 oV oV oV oV 9 9 oV oV oV oV *i) May also be c minor. — "2) May also be any other form of the dom. hannony of C (VjoV, V®, qV^). — *3) Maybeorejio^Aerdom. chordotF. — *4) May also be/ minor. Note that in this succession the third of the first dom.-chord is lowered chromatically (6 to 6b). See also measures 5, 6; and B, measure i. — *s) *$) In both of these cases there is no chro- matic inflection involved. — *6) Here the seventh of the dom. chord remains stationary. — *7) The substitution of the diminished-jth (qV^) for the dom.-yth, is an effective means of facilitating all such awkward successions as these. — *8) *8) In both of these cases the 7th is obliged to ascend. See par. 239, Rule I. Therefore the connections are somewhat objection- able. — *g) See par. 238; and par. 239, Rule II. The identity (i.e., the keys) of each of these chords can be determined only by conjecture. Comp. par. 203; and par. 236. — *io) The notation of the diminished-yth, in chrom. succession, cannot be definitely regulated, be- cause the keys represented are only conjectural. In descending succession flats, and in as- cending succession sharps, are apt to prevail. — *ii) Comp. par. 2006. Additional illustrations : I- Andante Brahms 2. Andante Brahms qfff^dfe f i^S : ^. • ;\'yW tit Ex. 175. i ■ij :^ J- J m ^tfr'r> i r- i2ft: S BbV g V C V-VF V Bb V— I Bb V- o i idi J i £ 3. Allegro Brahms ^g m m ^ t&T Hjt f^ w^* ^ ^ w rbg^H ^r • J -tj r -^ 7 B O 7 BbV g<,V FoV BbV- FIV I CVFV — I 128 THE THEORY AND PRACTICE OF TONE-RELATIONS. Par. 239. 4. Moderato Schumann ^j^^^p:^^^ ^^! V zj^^^r-^ ^ Se^ ge^^ 1^ i M Q 9 9 doV CqV— oV 5- Allegro I aoV BboV — oV I goVBl,IVtl-I Schumann ^rt =#* 4^-A- % ( P*^^^^^^^ simile i §^ 1" — '..-rt * ^ig fiV V- fSoV O 8 oV oV 9 oV LESSON 53. A. Connect the following chords, in 4-part harmony, inversion (bass) optional: A maj. V— D V *i) ; Eb V— c V; D V— F V; £ qV— Db V; E V— C V; Bb V— Ab qV; '~ii 7' ' 7 o"' ' 9 g s 3 I o s 9 o^ G V-A V; B V-f# qV; g oV-d oV-a oV-e qV; ci oV-fS oV-b oV-e qV. B. Find and play these successions at the keyboard, the bass alone in the left hand. ' C. Harmonize the following melodies, with successive dom. chords, as indicated at each * (inversion optional) : ,.1. 2. _ajiJi * » » i m ^S ^ a^^^fi^ *3) i A D G C A fc ^j^.^=fcihfa E «3) ^ lli % * In # Bb G— a! SE^t iffi CAD G C- C Db Bb Eb Ab Db Ab- * --t -0 f. =f=^ ^^3:^ *3) D F d- i ^a=^ P cp= ^ Tsr-a^ *3) O 9 V D V Par. 240. 5. ENHARMONIC MODULATION. 129 i ^ M\ S C d g c F bP fc ^ — 1»^ «4) *i) Resolve the last chord, in each case, into its tonic. — *2) The V at each * in these melodies. — *3) Either V, V, or qV'^ at each *. — *4) A dim.-7th at each *. CHAPTER XLIII. ENHARMONIC TREATMENT OF THE CHORDS OF THE DIMINISHED- 7TH AND DOMINANT-7TH. 240. The enhaxmonic change (or exchange) is obtained by inflecting the next higher or lower letter so that it agrees in sound with the original tone. Thus, the tone g-jlat is "enharmonically identical" (in musical practice) with f-sharp, and either of these two tones may be enharmonically ex- changed for the other. The enharmonic equivalent of b is c-flat; of /, e-sharp; of d there are two enharmonic equivalents, c-double-sharp and e-doubk-flat; and so on. Review Ex. 146, with its note. 241. The enharmonic exchange involves an inevitable change of key, or modulation, as the two enharmonic equivalents cannot belong to the same key. 242. This modulatory factor is most commonly applied in the chords of the diminished-yth, which admit of the enharmonic exchange to a very remarkable extent, and with that facihty and flexibility which characterize every movement of these extraordinary chords. 243. The wonderful ambiguity of the dim.-7th is owing chiefly to the peculiarity of its structure, consisting, as it does, of equal contiguous intervals (of three half-steps each), which divide the 12-tone chromatic octave into four equal parts. This is best seen and understood at the keyboard. Thus: DoV i J^^^^ '(f &L^ -^c^ Ex. 176. |gr^ Cprz^Z^ In consequence of this uniformity of structure, there is no external mark of recognition by means of which the various forms or inversions of the diminished-7th chord might be dis- tinguished in sound from each other. The four forms (inversions) of the above chord: bg H^ , gg — 0^^ all present the selfsame external form, upon the keyboard, and are not distinguishable from each other as chords of the 7, f , % and a, respectively; because the actual difference in the size of the interval h-jlat — c-sharp (augmented second), while recognizable on the paper, in the notation of the dim.-7th chord, disappears in the sound of the chords, on account of the en- harmonic coincidence of the augm. second with the minor third. I30 THE THEORY AND PRACTICE OF TONE-RELATIONS. Par. 244. 244. As the different inversions of the dim.-7th chord can therefore not be distinguished from each other in sound, it follows that the identity of the separate intervals is not distinctly definable, or recognizable by ear. That is, it is impossible to determine, by ear, which of the four tones is the leading- tone, which the original pth, which the ph, etc. Hence, each tone of the dim.-7th chord may be assumed in turn to be a leading- tone, whereby it will represent in each case a different key, and will be sub- ject to a corresponding alteration of notation. As the alteration in notation does not alter the sound of the interval or chord, it will simply be an enharmonic exchange. For example, adopting the dim.-yth chord of b minor: =B5= =Bi= Leading-tone a-sharp, resolving into B minor or B major : Leading-tone c-sharp, resolving into D minor or major : Leading-tone e, resolving into F minor or major: Leading-tone g (orfiC), re- solving into A-flat (or G- sharp) minor or major : *i) The form and notation of each chord of the dim.-yth is defined by the formula given in par. 176 (which see); namely: it must constitute a chord of the seventh upon the leading-tone of each key, respectively, and correspond in notation to the minor scale of its key. — *2) Here the |-form of the original chord ( qV^ in h minor) on c-sharp, is transformed into a chord of the 7th on the tone c-sharp, whereby an enharmonic change from a-sharp to b-flal is involved. The selfsame procedure gives rise to the other two enharmonic exchanges which follow. 246. The same system of enharmonic exchange is applied with similar results to the other two chords of the dim.-7th, which lie respectively a half- step above and below the one upon a-sharp (manipulated in Ex. 177). For illustration: Ex. 178. At the keyboard, g ■^^^h^ te -SHIS USS' — g I,.eading-tone : a f# d^ Keys: bKBb) g (G) e (E) ci (C#) = ^1 iE te^i^fc^fe Leading-tone : b g^ Keys : c (C) a (A) e# ex f# in) (d#) d eb (Eb) Par. 846. ENHARMONIC TRANSFORMATION OF THE DOM.-7TH. I3I 246. The application of these exchanges in enharmonic modulations is made as follows: The chord of the dim.-yth is introduced in its own key (i.e., in the notation corresponding to its scale, — but in minor or major, indifferently), and, upon repetition, or during a series of repetitions, the notation is altered, according to the given tables, to agree with that of the de- sired key. For example: Ex. 179. »l) a 4=ft -I •s) ^^ •4) Brahms J J *3)l I 1 I i -i -J .M>A p g |ff^:pf:E^ ^aBg 9 '8 ' 00 c min.0^ — * o^ — I s min-oV — B^oV — I ft- m etc. fftff boV =DoV-I *i) Or C major. — "2) A-flat is enharmomcally exchanged for g-sharp. And, as is here shown, the exchange need not be made in the same part. — *3) Or A major. -^ *4) The en- harmonic coincidence of the chords (practically chord-repetition) renders all peculiar melodic progressions, as here in soprano, excusable. ENHARMONIC TRANSFORMATION OF THE DOMINANT-7TH. 247. The chord of the dom.-7th is identical in sound with a mixed Second- class chord of the minor and major keys upon the tonic immediately (i.e., a half- step) below the original tonic. By means of this enharmonic exchange, a modulation may be made, in other words, into the next lower key (the lead- ing-tone becoming a tonic). For example, from C (or c) to B (or b); from B (or 6) to A# = Bb (or 6b). Thus: Ex. ISO. At the keyboard ^XJ **) »3) * Eg j y-r -l_ | f II r -f — S|^ tMEa ^=^-r — •4) f f=F 7 V b IV#— I «i) r :«pt=«F«^- V Bil#x-I *a) r B b 7 V bIjIVJt ii- I.F^»*f= b V Bbilttjj-I 132 THE THEORY AND PRACTICE OF TONE-RELATIONS. Par. Z47- *i) Raised 4th step in minor (IV). — "2) Raised 4tli and 2d, and lowered 6th steps, in major (II'). — *3) Generally, the 7th, or the 7th and sth, of the dominant chord are en- harmonically changed (see the first measures); but here, owing to the unusual location (or signatures) of the keys (B major progressing into a^sharp minor), the 7th remains, and the lower intervals are changed. — *4) The resolution into the I is the more legitimate progres- sion, because these are mixed chords. But the progression into the dominant chord is wore common, in practice; in which case, the parallel 5ths must be guarded against (usually by omitting the 7th of the mixed IV — reducing it to the IV). See Ex. 163, note *2), note *4); and Ex. 181, measure 4. Additional illustrations: 1. Allegro Et> major Par. 247- ENHARMONIC TRANSFORMATION OF THE DOM-'-jTH. 1 33 LESSON 64. A. Harmonize the following melodies, introducing a chord of the dini.-7th at each *, with enharmonic exchange at the following *, as indicated by the key, and according to Exs. 177 and 178: i ^SF^iR ^ : — Bb l^^l <*- 2. *- M ^-4- % % % % % % % % i ggl^ ^^i ^b "=-"— #- d f- -Ab- -B- i IS ^^P^ rijm fe^fl a ^M ^ifc^i ® *i) c C a- .Eb- -eb- -Gb- *i) The three lower parts together on the bass staff. B. Transform the dom. 7th-chord of emery key, enharmonically, in exactly the manner shown in Ex. 180. C. Harmonize the following melodies, with an enharmonic change at each *, according to Ex. 180: 1. , 1 e i ± *= ^ ^^ I ^H^^^ i^. g j * «N=|^3jfi 7 V f#- 7 7 -IV# G V- 2. II ritard. SUPPLEMENTARY EXERCISE. Harmonize each of the following fragments, in as many keys as may be found to contain the notes, either as legitimate or as altered steps: 2. 4. 5. tFt ^ -gH7s>- *i) *i) *l) An excellent general rule for chromatic successions is, to harmonize the first tone with some (almost any) 3-tone chord, and the second tone with some dominant harmony. 134 THE THEORY AND PRACTICE OF TONE-RELATIONS. Par. 248. DIVISION FOUR. INHARMONIC TONES. INTRODUCTORY. 248. A chord, as a cluster of accordant tones, is defined in par. 28 as the combination of 3, 4 or 5 tones in thirds, or in inverted forms reducible to thirds. The simultaneous association of more than five different tones; or the as- sociation of even 3 tones in any other interval-relations than those embraced in the definition; or, in a word, the addition of any tone which is foreign to the legitimate (harmonic) chord-structure, results in a so-called inharmonic discord. For illustration: Chords Inharm. Discords — 3 r^ S «< 1 — G> — I 1 1 1 — • S" n 3 ; g | :z=i:etc. _|_J_ -^ g- • — =g:^^etc.=i| Ex. 182, -^ '^^ s>- -&- -&- -e- *l) *8) «3) «4) «S) *i) Six different tones can not accord. — *2) Association of two seconds {c-d and S g- ^ *i) rtt. ^M ■G-r- f'r rr r i Jl . ii! -^pJL^^¥^ ^ ^ 3. Allegretto f^^ # S^^ Sg ^^:g *2) etc. mmju t ^mM mm^ m rit. (i *i) Plagal ending. Comp. Lesson 44, note *5). — "2) One inner voice will suffice, ex- cepting at the two cadences, where the harmony should be fuller. C. Construct a number of original phrases and periods, with Organ-points. Par. as7. THE SUSPENSION, 139 CHAPTER XLV. THE SUSPENSION. 267. The suspension is a tone which becomes foreign, or inharmonic, by being held over from the preceding chord. The tone which is thus sustained past the limits of its own chord, dis- places or defers (Uterally "holds in suspense") the expected legitimate tone of the following chord, hence the appellation Suspension. The displaced tone is called the suspended tone, and it must obviously follow immediately, as resolution of the Suspension. The Suspension is the Neighboring-note (par. 249) of the tone which it defers. 258. For this reason, the prolongation of a tone as Suspension can take place only in a voice which has a diatonic (stepwise) progression. And unless the prolonged tone becomes foreign in the following chord, it will not produce the impression of suspension. For illustration (given the chords tonic-dominant in C) : Ex. 189 C major aiid minor •S) i :^ 7 V The e of the I, by being held over into the V, becomes ; inharmonic. It "suspends" d (the fifth of the V) whose place it u- suips, and to which it must sooner or later give way. Thus: S.*i) S. ^ , j=M s. «3) ^ ^m *a) J Al »8) TT s. ^ f^P=EE^ rr o oV s. »*) *i) E is the suspension, and d is the suspended or displaced tone; the Suspension is re- solved (stepwise) by progressing into this d. — *2) *2) The form (or inversion) of the chords has no essential influence upon the Suspension. — *$) The same Suspension may occur in either inner part, nearly or quite as well as in soprano. — *4) In bass, Suspensions are somewhat rare. — *5) Play each example in minor, also. 269. In these same chords (I-V), the tone c may be held over, as Sus- pension of b (the third of the V or V), to which it will diatonically descend, as resolution. Thus: Ex. ISO. C major and minor /■ ■ i;jjj|.uj|JUj j|,7 i :jVj u fT^fT-^r^m^f^Tr?^ ^ J J I J J I J J , jj , jj n T^ T 7 I V r f2-TS>- I V t-r I V J--J-I AA:J=A ^^^^ I40 THE THEORY AND PRACTICE OF TONE-RELATIONS. Par. 260. *i) Comp. Ex. 189 (note *2). The effect is substantially the same whether the dom.- seventh or the Aonv.-iriad is employed. 260. If the toneg is held over from the I into the V or V'', it will not become inharmonic, because it is the common tone. But if held over into the V®, the g will be a Suspension. And the tone e can be sustained, as Suspension of/ (the seventh of the V), in which case it will resolve diatonically upward. Ex. 191. C major and minor *a) B. «3) ■J^J>^ -r ^^i^^ : gfe^= -P>-(s> — ==[= =3= Tr~f7 ^^ fe 4 ^.U-^-J .-^J ,^j. 42 G)- ■f=2-!S'- I V 9 I oVb (^ 7 V e f^^ =?^ *4) *i) G is the common tone between I and V, or V'', and does not produce the effect of a! Suspension. — *2) In connection with the dom..-ninth, however, the g becomes inharmonic. — *3) This Suspension, e, resolves M^iaar^i into/ (as well as downward into d — Ex. 189). — *4) Ex. 189, note *4). 261. The tones c and e, in this same chord-progression, may both be sus- tained, as double suspension. And, on the same principle, triple and even quadruple Suspensions are obtainable. For illustration: Ex. 192. C major and minor i 3 ■^-Ur^ »i) f^fr=n f -»U4 *2) *3) ^f ^ r-r ^ -(=^ 7 I V s ^^m -(2- :(^: eg ? I V 7 o V VI Vb I (D *i) If the c and c are held over into the IriaA V (instead of the V or V ) they do not become inharmonic, and therefore do not create the distinct impression of a Double suspen- sion, though virtually they are nothing else. Compare Ex. 108, numbers i, 3, 4, 5. — *2) Triple suspensipn. — *3) Quadruple suspension. 262. Rule I. Any interval of any chord, in any voice which progres- ses diatonically (downward or upward), can be sustained (or repeated) during the change of chord, as Suspension. Compare par. 258. Rule n. The Suspension usually appears on an accented beat of the measure; or, if not, it must always be at least more accented than its resolution. With this exception, the length (or accentuation) of the Suspension is op- tional. Par. 262. THE SUSPENSION. 141 Rule III. The Suspension and the suspended tone (its resolving-tone) should not, as a general principle, appear simultaneously in different voices. This, however, appUes only to those cases in which the suspended tone is an inferior step of the scale, the duplication of which would be avoided in any case. For illustration: m RULB II -^-^H-j- hJ^-h4 r«i Ttt Rule III *a) «3) *4) *6) H^ W -r-f Ex. 193. 1*1)1 &E J- J Ji ^ JTlA m^^ ± =f^Ff *i) Suspension on the unaccented second beat, and resolved on the accented third beat. — *2) Palpably wrong to anticipate the resolution of the Suspension in soprano by the simultaneous d in alto. This example would be correct, however, if the Suspension (e) were to ascend iato /. — *3) This is equivalent to a doubled leading-tone. — *4) Good, be- cause the duplication involved is that of the tonic (c). — *$) If there is any doubt about the case, simply suspend the tone in both parts (as here the e in both soprano and tenor). Additional illustrations: 1. Allegro Schubert. 2. Moderato Schubert 3. Largo Beethoven 1^ h f^M fe^^^ g^ *4? ■^ i P^ W iiXi= ^ Ex. /, 194. \ P^ i 1 < C I V I II iV V g -^—f- p t=t^ ^=-|S- i^t i±=t C I III Ig V I AlaV VI LESSON 66. Write out the following chord-progressions, in 4-part harmony, introducing a Suspen- sion on the accented beat; at first a single Suspension in each adapted voice, successively; then Double, and Triple suspensions if practicable. The rhythm, and (unless indicated) the inversions, are optional: G major: I ] V |1 D minor: 1 1 qVO || F major: V 1 1 1| B minor: qVO ] 1 1| El. major: V^ 1 1 1| C# minor: V | VI || A major: IV | Ij || C minor: IV | V 1| Dl> major: IIi 1 12 1| 142 THE THEORY AND PRACTICE OF TONE-RELATIONS. Par. 262. LESSON 67. A. Harmonize the following melodies and basses, with reference to the subjoined ex- pkmatoiy notes; modulate freely, as indicated, and at option: 1 Lesson 10, No. z. 2. Lesson 10, No, 7. I i s s m Jjjjj J --=' — ■=" — '-'-•-i-U s p 4 — 4 d O td^ «i) «a) *3) i SI r"F~rrT « II S^^-H f f i ^^ 4. »a) »a) «8) *a) •2) *a) i « #4#.:^- ^FJ^m^ ^^ S±fe IP^ ^t^ v=U= *a) «a) «a) ^ •3) m^^^^m. 1^ I 7 =3=*=^ -«>— 1*- ■•— #■ *4) i * *6) e 1 D" D- SEEtzcJtitiSfefe II i ^m -*-i^ ^ 1 ^ * r,VS r,V» fe^^Ciifl F^ i^J ^4^ft^£ ^^^ S. *6) VI m IV b|? min c S f min, i m gzzte »7) »8) ^S f \ff a \ a- g *— #- iE^^ s: 9. *a) nV8 te «7)- I ^ I * ■'g a:)- 10. VI m IV *9)_ .*3) ^77]7¥ ^ ^ £ W *+*-^ ^§ 11. 76 8 '.^ e LJ ^ B- 6- a 7 - „^ Q tl^J ft j * s«i«5^iii ^"»-»»r»» Par. 263. IRREGULAR RESOLUTIONS OF THE SUSPENSION. 143 *i) The first two melodies are taken from Lesson 10, as shown. Compare them with the unimbellished originals; and make similar experiments with other former melodies. — *2) Every note that is thus repeated (whether tied or struck) may be treated as Suspension, by harmonizing the following tone in its place (exactly as in Exs. 189 to 193). The original, simple, form of the third melody, before it was embellished by Suspensions, was thus: 1^ W^ *3) Susp. on the ist and 4th beat of each measure. — *4) The dot is a Suspension. Comp. note *6). — *s) In this melody. Double suspensions may occasionally be used. — *6) Each dot is to be a Suspension, as if the notation were Jn...^J J throughout. — *7) Suspen- sion in alto. — *8) Susp. in tenor. — *9) Double suspensions in soprano and alto. B. Construct Original phrases, with Suspensions. CHAPTER XLVI. nUlEGULAR RESOLUTIONS OF THE SUSPENSION. 263. Simultaneously with the diatonic progression of the Suspension into its resolving-tone, the other voices may make any smooth progression which does not interfere with the resolution of the Suspension. This progression of the other parts, 'at the moment when the Suspension is resolving itself, may be limited to a simple alteration of the form or inversion of the same chord; or it may effect a change of chord, or even of key. For illustration: s. "a) s.«2) g 7 3 7 7 V oV C VaoV C V eV Modulations *i) While the Suspension (e) is resolving to d, the bass progresses in such a manner as to alter the Aom.-triad to a dom.-seventh; in the next measure, to a Aom.-ninth. — *2) During the resolution of the Suspension (c), a modulation is made. 264. Other licences of resolution, such as the prolongation of the Suspen- gjon — the indirect resolution (through an intermediate tone of the same chord) — and the exchange of Double suspensions, are possible, but of com- paratively rare occurrence. For example: 144 THE THEORY AND PRACTICE OF TONE-RELATIONS. Par. 265. S. S. ■ Sj— - res. Ex. 196. C major and minor , m ^^^ f=r res. S. J. i J »i) ^^^ *3 4-^ 77 7 CIV IISl, V V 7 V f *4) 7^ f=^ *i) The Suspension (c) in soprano is prolonged for 3 beats, before its resolution into 6 takes place. — *z) All three Suspensions are prolonged, while the bass progresses. — *3) The Suspension (S) is resolved indirectly to c, through the lower %, which is a part of the same (re- solving) chord. — *4) The Double suspension {i and f) changes voices. LESSON 68. Harmonize the following melodies, with reference to the subjoined explanatory notes : 1. i *i) 1= & =p=tp= ^ X t=tt .1) I, I, ^^i^ I ^^ g ^ ?i^= jaiiUc^^fag^ S li^^ P »3) IF *i) The accented note becomes a Suspension by harmonizing the following note in its place, as usual. Biii the preceding (unaccented) tone must be harmonized with some chord which contains, or might contain, the Suspension. See par. 265. — *2) An additional (Double) Suspension, in alto or tenor, may in many places accompany the soprano Suspension. — *3) Triple Suspension. CHAPTER XLVm. THE ANTICIPATION. 266. The Anticipation is a tone which appears in advance of the chord and beat to which it properly belongs. It may appear in any part, but al- ways sounds most natural in the soprano. Though possible at any point in the course of a phrase, it is perhaps most effective at the cadence. RtTLE. The Anticipation invariably appears on an unaccented beat, or unaccented fraction of its beat. The more brief it is, the less danger there will be of a misapprehension of the harmony and rhythm. Comp. par. 262, Rule 2. Par. 267. THE ANTICIPATION. 147 For illustration (given the chords tonic-dominant in C) : Ant. A. A. Ex. 199. C major and minor The h is inhar- monic, or for- eign, in the I. It "anticipates" the third of the V, into which it —^ is immediately —— repeated. Thus: r£ *i) Double anticipation. In the next measure, triple. 267. The Anticipation is usually, hut not necessarily, an inharmonic (for- eign) tone. Being in reality only a modification of the rhythm, its relations to the chord-progression are comparatively immaterial. It is even possible to anticipate the whole chord, in all of the voices. The violation of par. 39, which this occasions, is generally counteracted by making the anticipating chord very brief. For example: 1. Menuetto Beethoven 2. Mehuetto Beethoven »3) »2) S. Ex. yi 200. \ ^^ ^ W i ^ *i) ^^m -#--«- -f i tSz ^ TTmrm G I V Eb I 7 V 3. Andante «3) *3) »a Haydn *3) »3) *3) *3) "a) D V 1 -n, la V 1 4. Presto Mendelssohn I i M Pfe -«-i- ^^ ^ It? ^ «3) *3) «l) Later ; E I- 7 -V- ^^ Eel- 148 THE THEORY AND PRACTICE OF TONE-RELATIONS. Par. 268. *i) An inharmonic Anticipation, — foreign to the chord. — "2) An Anticipation which is not foreign to the chord in which it occurs; but nevertheless an "anticipation." — *3) An- ticipation-cA(W(fa; because they are too short to create the impression of true chords. 268. The free or irregular Anticipation is one which, instead of remain- ing upon the note which it anticipates, progresses into another tone, usually with a skip downward. The anticipated note should appear in some other voice, in the following chord, or it must be understood, as possible interval of the latter. See par. 265, Rule, of which this is exactly the reverse. For illustration: 1 Haydn 2. Andante_ Brahms 3. Brahms Ex. 2U1. ^Pi^ mm \'^m ^a X\l [ f a iA-^ ■bH^P- G I- 7 -V VI #=t=^^&^ g# I V- I f# I V-1 =# CoV- *i) The c in soprano is an Anticipation of c in the following chord (tenor). The irregu- larity consists in its progressing with a leap. LESSON 60. Harmonize the following melodies, with reference to the subjoined notes: 1, Lesson 10, No. .i. 2. Lesson 10, No. 8. i^^ »2) ^*^ w *i) »a) (S.) 3. Allegretto *3) ^S a III 4. Andante *3) 3F ^m ^ C r-1>lr- J «3) ?=H^=^ m^^m 9 i g minor — 5. Maestoso EbVi «4) ^m u s Se P -r*--Pzi. ^m ± *s) 6. Lento •a) g oV S. »3) ^- *8) -,- Eb- 1 y »! SES :ij ; ^1 * '^ jt^ iH-»h Tonic Organ-point in bass_ ai> V Eb V Ab V[] I Far. 26g. THE NEIGHBORING-NOTE. 149 7. Larghetto 6ths- ff\\ &1^T^\l^^ "^ »8) S. ■W-ii- Tonic Organ-point in tenor_ I* * *i) The first two melodies are taken from Lesson 10, as shown. Compare them with the miembellished originals, and make similar experiments with other melodies. — *2) Each i6th-note is to be an Anticipation; that is, it is not harmonized at all (see Ex. 199). — *3) Each 8th-note an Anticipation, throughout. — *4) The altered IV of B-flat. — *%) Each single 32d-note an Anticipation. — *6) Irregidar Anticipation (par. 268). — *^) Anticipation- chord (all four parts) at the end of each slur, throughout. — *8) Mixed IV of d minor. CHAPTER XLIX. THE NEIGHBOIUITG-NOTE. 269. As stated in par. 249, every inharmonic tone is the upper or lower diatonic neighbor of one of the legitimate chord-tones. The special designation Neighboring-note has been adopted by the author to indicate that simple form of melodic embellishment in which either the upper or lower inharmonic neighbor alternates briefly with the prin- cipal (hannomc) tone. *i) The Neighboring-note is everywhere indicated by o. The harmonic interval which it embellishes is called the principal tone. 270. This alternation of harmonic and adjacent inharmonic tones may be appUed to any interval of any chord, and in any voice, subject only to the general conditions of rhythm. It gives rise to a number of different melo- dic groups, promijient among which are such conventional "grace-notes" as the TriU (long or short), the Mordent, the Turn, and other familiar Em- bellishments, but embracing also a great variety of special ornamental figures, whose importance and efficiency in enriching, adorning, and enlivening the primary harmonies can not be overestimated. ISO THE THEORY AND PRACTICE OF TONE-RELATIONS. Par. 271 271. Rule I. The Neighboring-note enters from (i.e., follows) its own principal tone, and always rettirns to the latter. Rule II. The upper Neighboring-note is generally used when the di- rection of the melody, into the next tone, is downward; and, inversely, the lower Neighbor when the direction is upward. In other words, the Neighbor- ing-note should he opposite the next essential melody-tone. The accented Neighboring-note is more prominent, and sometimes more efiective, than the unaccented one; otherwise the rhythmic location of a Neighboring-note (on or between the beats) is immaterial. (Comp. par. 275.) Rule III. The upper Neighboring-note should agree with the scale repre- sented by the momentary chord (more rarely, with that of the next beat). The lower neighbor may also agree with the scale, but it is usually the half-step. The leading-tone, however, is almost invariably embellished, both above and below, in accordance with its scale. For example: Rule I „fe-E^^^S ^T=^ _g Q o o ^M^m^M. C »a) A|,*a) E major *7) B|7 major N, B. Leading-tone (C maj.) *i) The Neighboring-note d must return to e, its principal tone. — *2) The unprepared Neighboring-note will be explained in a later chapter. — *$) The embellishing group may be thus extended by any leaps which conform to the chord. — *4) The upper Neighboring- note, before a descending progression. — *5) The lower Neighboring-note is possible, but less smooth in this connection. — *6) Whether the upper Neighboring-note is to be a whole step or half-step, depends upon the momentary key. — *^) These lower Neighboring-notes all agree with the scale {fi-Jlal major, in this case). — *8) A half-step, contrary to the scale; Par. ays. THE NEIGHBORING-NOTE. ISI this is more common, and more graceful. — "g) The Neighboring-notes must invariably rep- resent the next higher or lower letter. — *io) C major; but also valid for c minor, with e-flai and a-flat. 272. These embellishing tones may appear simultaneously in two or more parts, as double or triple Neighboring-notes; or even in all the parts, as Neigh- boring-chord. These and other forms are exhibited in the following example: Allegro CZERNY 2. All". Jensen C I Vi IVi I3 Mendelssohn i ei3 t: ^r Bb I V EboV V I cV I V I 4. Allegro Clementi A I 5. Andante Beethoven Eb I •152 THE THEORY AND PRACTICE OF TONE-RELATIONS. Par. 972. e. Allegretto Beethoven o 00 F I- V. Andante Brahms u^nr^^n^:^ 4 -f- u *i) Double Neighboring-note. — *2) Neighboring-chords; they are too brief to be essen- tial. — *3) Accented Neighboring-chords. — *4) Here all| and a\> appear together — ab as 7th of the dominant, in bass, and at| as lower Neighbor of b\> (the root) in soprano. It wOuld be impossible to define the multitude of combinations, or tone-clusters, that result from add- ing Neighboring-notes to the legitimate chord-forms. In his studies in Analysis the pupil will encounter many extraordinary tone-shapes, which are easily accounted for in this simple way. Glance at Ex. 211, No. 6, for instance. LESSON 61. 1, Lesson 10, No. 4 Soprano Par. a7a. TffE NEIGHBORING-NOTE. «53 8. Soprano «8) — f Bb V S|^4-^^-i-^ ' ^ ^ i ^-J ^H"^""^ ^ 6. Tenor •s) y-—^ -iT—^v ^^~^^ '■' ^ *i) This melody, in its original unembellished form, will be found in Lesson lo, No. 4. Add the three lower parts, in the usual manner. — *2) Add the three upper parts to this "running bass," together on the G-staff. One melody-note {and chord) lo each slur, strictly. The Neighboring-notes are readily definable. — *3) Harmonize this embellished soprano in the usual manner, one chord, to each slur. — *4) Add soprano, bass and tenor to this running alto. It will facUitate the task, to reduce the given part first to its original, unembellished ■ Q h M I etc. — *s) Here the alto pauses and the tenor takes up "tcT)^^^ - • I* • f *"^ the embellishment. — *6) Add soprano, bass and alto form each slur. First reduce it. 'f to this running tenor; one chord (and soprano note) to IS4 THE THEORY AND PRACTICE OF TONE-RELATIONS. Par. 273. CHAPTER L. THE PASSING-NOTE. 273. The Passing-note is an inharmonic tone which is touched in "pass- ing" step wise jrom one chord-tone to another. Hence it serves to connect 1x00 diferent chord-tones. (Comp. par. 271, Rule I, for the distinction be- tween the Neighboring-note and the Passing-note.) 274. a. This connection is almost always made diatonically, along the momentary scale; but occasionally it is also made chromatically, especially in ascending succession. Descending chromatic Passing-notes should, as a rule, be avoided. b. Two, or even more, Passing-notes may occur in immediate succession if they follow each other stepwise in the same direction. This will depend upon the size of the harmonic interval to be filled out, and also upon the choice of diatonic or chromatic Passing-notes. For example: *i) + Ex. 205. t- p, C major ts n n ^ , i -a- ^Lurj^ =k *a) f^ r C I IV Ji-J;. i + + ^&i •^ ^ -^ -tl ^^^s^^^ p -r^ f r «3) r *4) *S) *i) The Passing-notes are indicated by -|-. — *2) Two Passing-notes in succession. — *3) Descending chromatic tones are generally written with flats, excepting the one immedi- ately below the dominant of the momentary key, which is written, as here, as raised 4th step (in C, as f-sharp). — *4) Four chromatic Passing-notes in succession. — *s) C minor; the change of notation in the minor mode is significant. The notation of chromatic Passing- notes should conform to the scale of the momentary key, or to its altered steps. 276. In the above example, the Passing-notes are all unaccented; i.e., • they stand between the beats, as Ught fractions. But they may also occur at the beginning of the beat, as accented Passing-notes, and are then usu- ally more effective than the former, because more conspicuous. For illus- tration: Ex. 206. C major i -J n ^ d n^ i=E *i) C-Tr r Par. 376. THE PASSING-NOTE. IS5 *a) ^i^^^j^^f^ t WW^ l^a J J J J. *i) The accented Passing-note is indicated by X.— *2) These measures are all valid for c minor (with e-fiai and a-fiai), excepting this beat and the next, which would read a-jlal and h-fiai. 276. Rule I. Unaccented Passing-notes are admissible and effective in any part. Accented Passing-notes are best in soprano; in the inner voices, or in bass, they are apt to obscure the harmonic sense, and must therefore be carefully tested, by ear. Rule II. Passing-notes usually necessitate the subdivision of their beat, and are therefore subject to the rule of rhythm given in par. 38, namely, the light beats must be broken first, so that the unbroken beats (if any remain unsubdivided) are the heavier ones of the measure. Rule III. Successive perfect 5ths or 8ths, which may result from the insertion of Passing-notes, will be objectionable only in case the second, sth or 8ve is perfect and harmonic. For example: --F^ s »— ■ ^ — INT£BC£FTED' FIFTHS AND OOTAVfS; 7 V r- V I 4- vi^rv CIVVVV I ■$• A few of the very numerous forms of embellishment with Passing-notes, accented and unaccented, are exhibited in the following example: 1. Ailegreito J. S. Bach hi m Allegro E^ _ ^ 1 ^ ■^- trtf^# r Org.-pt. 9; I fU. ( Wi t ' ^ i 7 V T I 3^ 7 V Beethoven -J J J I J ^ ^' ^- f- IS6 THE THEORY AND PRACTICE OF TONE-RELATIONS. Par. 276. Chopin « 3, Allegro + X m 4^ 8va Efe -•-^•- * £ -•-hA- 1 — I — \ ^ + X i^ *1) ,-•- yt cit nij- 4. Lento 7 -V- Chopin (^ 5. Alleero Chopin I + X Sg^^S ^^& 04 - 'l»— I ■* V «I3) O O X r-l W^-^ X ♦2) i iiS fcKai « Sp ^ 7 C V- 7 -V- DH' 6. Allegro Chopin 7. Allegro J. S. Bach 8. Allegro S Chopin pg»2r I f r r ? f^^i^J=^i=Mc^ [ | ip~4 ^ft 4t »6) ^a r^"^n c#V- 9. Allegro 8va CZERNY tr liSLss i X X «s) "g. Par. 376. THE PASSING-NOTE. 157 *i) The lowered second step {d) of c-sharp. minor. — *2) Double Passing-notes. — *3) Passing-chords. In such rapid tempo they are too brief to be essential. Comp. Ex. ' 204, note *2). — *4) The descending chromatic tones are intercepted Passing-notes, sepa- rated by the reiterated e. — *s) Repeated Passing-notes. — *6) Comp. Ex. 204, note *4). LESSON 62. Elaborate the following melodic sketches as Running soprano, in a uniform rhythm of first 2 notes, then 3 notes-, 4 notes or 6 notes to each beat, as indicated; using Passing-notes, unaccented and occasionally accented, Neighboring-notes, and (when unavoidable) harmonic (chord) tones. The lower voices need not be added. By means of Neighboring-notes, any single tone develops into a group of 3 or s (7, 9) tones, thus: without involving the question of space (interval to the next essential tone) at all. These groups can then easily be extended to 4, 6 (and more) tones, by addfng Passing-notes or harmonic (chord) tones: Given : Embellished : .,— ». -^ A Given ; 0' J * M 1 1 ^ dT — 1 LrT r :"=r=f=T=fT=f=f^:E "^^ ^^- t^ |14 ILUJ L -LU ^ H — : — Li_| 1 u ^g Embellished ; + barm. P m P w EXERCISES. i , therefore the upper neighbor of g must be a-flat. — *4) Continue the given rhythm during the first beat of the cadence-measure. LESSON 66. A. Elaborate the following phrase three times, as in Lesson 64, with first two, then three, and then four notes to each beat. Review par. 271, Rule III: hhUnt:^ tkk ( r r r 7^ ^ ^^ i I J -nj 1 r r B. Elaborate, similarly, some of the completed (4-part) phrases of the earlier Lessons; or construct Original phrases, in embeUished form. CHAPTER LIII. HARMONIZING OF EMBELLISHED MELODIES. 282. Before determining the chords for the harmonization of a florid melody, it is necessary to reduce the melody to its original unembellisked form. Such notes as are obviously (or probably) only ornamental inharmonic tones will not be harmonized at all, and may therefore either be omitted or im- agined absent, while choosing the harmonic basis. 283. Tones of short time-value, especially in diatonic or chromatic suc- cession, and tones with accidentals (unless distinctly indicative of a modula- tion), will probably be inharmonic, and unessential. On the other hand, all comparatively longer tones, and all tones which progress with a ship, will generally prove to be harmonic, and essential. The indications of a Sua- l64 THE THEORY AND PRACTICE OF TONE-RELATIONS. Par. 283. pension or Anticipation have already been given. Aside from these very general principles, the pupil will be best guided by his judgment, experience and taste. LESSON 66. Hannonize the following florid melodies, with reference to the subjoined notes: 1. Allegretto rtijrr •• » p-m-P- ^ ^ *1) 2. Andante hai \r-^^ mfrm ^i !\A nnin ^^ *i) 4. Moderate m w=^ ^^^^ UT ^ '4" i j t4' i\ :i *i) 5. Maestoso ^ ^ ^^g # f-gr-r-ff^tl^ ^fW^5=^i^^ ^=^4^==fe an. 6. Allegretto n# ii ^m & 3^^ s -^ — — I- ^s fc tt •a) *i) Par. 883. HARMONIZING OF EMBELLISHED MELODIES. 16S i w ^ ^ -M. W^ ^ ' \^ m Dl, V I Abia *i) One bass note (and chord) to each slur; or, the student may ignore the slurs, and use his own judgment. An inner part may move, at any time. — "2) During six measures, the rhythm of the accompanying lower parts will be I "^ f "* f I • — *3) The three lower parts together on the bass stafi. LESSON 67. Continuation of Lesson 66: 1. Andante g ^^^^^B ^rr j , . OMT m t w w I m ^ ^^■i ^*.l^ e w Ant. -J-''' P^ 2. Allegro miir^\^m^^mrti^^i^\mwi w ^^^i:± ♦1) BI9 m ^^ G ^^^^^^^^^^S ■!■-*-««— MIF=#- semi-cad. C S X f A !^nV \ ^J!^ ^^^ F o o o ffjt^.m j P^^ 1^ E e SUfi-tT^ d ' * s s f# rail. .S. D cad. l66 THE THEORY AND PRACTICE OF TONE-RELATIONS. Par. 283. 3. Grazioso *i) One bass tone (and chord) to each slur. The three lower parts together on the bass staff. — *2) One chord to each slur. — *3) At each of the next 4 bar-hnes the embelUshment alternates, as indicated. — *4) Bass, In the next measure, soprano again. Plagal ending. LESSON 68. Harmonize the following embellished basses, with reference to par. 282, 283, and the sub- joined notes: 1. *i) Par. 384. 3. ANALYSIS. 3. ^-^ Bl, ^ 167 D Sf b ^ ' ■— I 1/ e IT--/ ^"^^ 1^^ I Q •■ 5. Allegro f^m *i) The first care must be to obtain a good, melodious soprano, throughout, before adding the inner parts. Use one melody-note to each slur, and place the inner parts (the number of which may occasionally be more or less than three) together on the upper staff. CHAPTER LIV. ANALYSIS. 284. The following sentences are to be copied out and analyzed. The keys (modulations), chords, and inharmonic tones (Organ-points, Sus- pensions, Anticipations, Passing-notes, Neighboring-notes, Appoggiaturas) must be accurately indicated, in the manner shown in the foregoing examples, and given in parts of Lesson 70, No. i. Rule I. Place the simplest construction upon every chord; i.e., de- fine it as tonic or dominant chord if possible; not overlooking the possibility of its being a Second-class (subdominant) chord, especially if Altered or Mixed. i68 THE THEORY AND PRACTICE OF TONE-RELATIONS. Par. 284. Rule II. Look forward. The identity of a chord depends upon what it ioe$, i.e., upon what follows. Rule III. Take the tempo into consideration. What will produce the effect of an essential tone or chord in moderate tempo (or upon a full beat), will probably be an unessential embellishing tone or chord, in very rapid tempo (or upon a short fraction of a beat). Every note must be accounted for. LESSON 69. A. Mark every inharmonic tone in the following extracts, with the usual signs (Org.-pt., S., o, +, X). The keys and chords are given: 1. Allegro 8va.. Chopin 2. Allegretto ^^^m Chopin 3. Lento fe^, ^^^£|££MMa aJ-j r H ^ ^ -»*-*- ^ etc m ^^ a^^E ^m S 7 -V ^V— I- 7 aV- -i¥ Par. 284. ANALYSIS. Chopin 169 4. Largo ^l' t j- j* I ' lj = J I ' ^ I t^^^ ^ J ^~^ WTJ>' ^^ ii^ ^ uLjcr/LJi;::; -V(E I)- BI- « ^ ^ S it Chopin i (H J •s) V V -I *i) Intercepted Passing-notes. — *2) The upper Neighbor of the Neighboring-note — tare, but sometimes fully recognizable. — *3) The -J-J+./.^.^.Liaa ^^:ilc:^,=^M W^^ gf^^^ffmDTF^s fct i topsa p ^te^^g ^^ ■•j}*=S3ti±=^S i ifeife =£: Havdn. (Symph., E-flat) f=F?= !^E3 L± f?~f= fa^a^E tes ^ etc. f^^L ^ S^ 3. Adagio molto tr Beethoven. (Variation) "i) The analysis of a few measures is given, as a guide. — *2) At this point the second Part of the chorale begins. The melody is an almost exact reproduction of the first Part; but note the remarkable changes in its harmonization. The latter is prompted throughout, as will be seen, by the independent melodic progression of the individual voices. — *3) A good example of cadence-modulation. — *4) E-flat major (or minor) V^. — *s) The modulation into C is effected at this place, through what proves to be the IV of the new key. LESSON 71. Continuation of analysis 1. Moderato assai (gfe m mwmm ^ mi ^ rtffl-imlTr^ ■xxru± "^KTT^ cl w^ 172 THE THEORY AND PRACTICE OF TONE-RELATIONS. Par. 284. JTOT a^^^Mk irn B rn J. B. Cramer. (Etude) m^ 5£^H^-Mr^^^ <^ I <^ ^ p I g^ p ^=ff^f ;^^ ^ f# fff^g^ r I 2. Allegro W'l^ I J J J# J ^m VTi ^ i ^-llJU^J' V^ ' ff- ^ ;te=^ 1=13 r^ P ^ . rri ^; ^1 3; ^^£?Tff^^^ ^T^ ^^ fuj^y. !e Mk. Chopin. (Mazurka) 0^ . ■^ — =^ 1^ F=^ t±=td*=i i -ItJt^tiL jji etc. I aiff ?^ *i) The g-flat in tenor is a Passing-note, which might be written f-sharp. — "2) Like note *i). The chord isf-tainor I, with c-Jlat (b-jiatural) as Passing-note. Par. 284. ANALYSIS. LESSON 72. 173 Continuation of analysis: 1. Lento ^g i w^. 4-pt §Se 1 ^ 1 =f — =1 — — -=1- -1 i ^ 1 -=1 — = — =1- Efe ^yv^ te *i) J^ 'CfT — * * N» "P — : * p m • *~^ ^^ f ^ ^P -? ^ ^n: — ¥ Schumann. Op. 23 fe^^^-^^iTT^ liJUi^ I ^ J-rJ J ?^& T^ ^ 2. Moderate fci ^^S ssiP i ^ la i^ fe H n rp o * ^ *3) gj^i^j^t^L:^ fzidS: GI- ; -»■ yJ- 01 Glazounow. Op. 75 \ r~n~~r"n liLAZOUNOW. up. 75 ^e^^rf l ir m:l ^ I II 111 „1 J i« I ^ -| I etc. 174 THE THEORY AND PRACTICE OF TONE-RELATIONS. Par. 284. 3. Allegro ^ -a c ^J2- H^^ \Z Wagner. "Meistersinger" w^ 11 ^ipc^i Jd= X — Tg - SI- f ^- - T. I JL-^ 1 etc. &E ^ -^ f C V 4. Grazioso, poco vivace ($4^ d^^d =g ^^=5 ^^- — c i, —sir r i ^ I 1 ^T>. f— g - ggE J ^H^ ^ i^ i ^^^^Eterf ^ r^f f ^^^^^ I ^V.