Cornell University Library MT 50.J21 1893 A manual of harmony / 3 1924 022 485 548 CORNELL UNIVERSITY LIBRARY GIFT OF George H. Sabine MUSIC 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/cu31924022485548 NINTH EDITION A MANUAL OF HARMONY BY S. JADASSOHN TEACHER IN THE ROYAL CONSERVATORY OP MUSIC AT LEIPSIC. Translated from the Third Augmented and Carefully Revised German Edition BY Dr. Th. Baker. NEW YORK: G. SCHIRMER. Copyrieht, 1893, by G. Schirmer. I09J.1 PREFACE TO THE FIRST EDITION. Yielding to oft-repeated and urgent requests for the publication of the method according to which I have for years given instruction in the Theory of Music, I have decided to publish the fruits of my private study and experience in teaching, in the form of three in- struction-books. The first of these will be entitled "A Manual of Harmony," to be followed as soon as possible by a second on "Sin- gle and Double Counterpoint," and a third on "Canon and Fugue." An attempt to give an idea of the new features which I have in- troduced, both as regards the elucidation of the chords and their combinations, and the plan of instruction, would take too long ; the matter is fully set forth in the following pages. But I will not ne- . gleet to call attention to the additional examples given in the Ap- pendix, which are worked out conformably to rules found in the corresponding chapters. I have learned from practical experience in teaching that it does not suffice, in many cases, to show the pupil how the rules are applied in isolated instances, i.e. out of all connection with some piece of music, however small, which forms an organic whole. Almost any pupil can learn a rule more easily and thoroughly when its application is clearly illustrated in the compact form of one or more little pieces of music. The manifold and peculiar difHculties besetting instruction in musical theory ren- der this method almost indispensable. We derive what we call our rules from the works of the classic masters ; but at the same time we find so great a number of exceptions to the rules, that the latter often seem doubtful to the pupil. Take one instance : The pupil learns at first that the seventh in a chord of the seventh must resolve by a step downward. Presently he discovers that in very many cases it may also progress upward by a step, or be held, or enharmonically changed, or even led down by a skip to tones be- longing to other chords. Thus nothing is left him of the rule first laid down but the principle that the seventh is to be led down- ward by a step, when the following chord and the correct leading of the parts permit of so doing. Now, if one were to show the pupil examples from classic masters, whenever one of the above-men- rv PREFACE. tioned numerous exceptions turned up — pi-oviding that the neces- sary material was always at hand — he would hardly be able at first to judge of and understand such examples taken from large compo- sitions, and might possibly be inclined to regard them as liberties permitted to genius, whereas these liberties take their rise, exactly like the rule, in the nature of the case. It is therefore better to show the pupil the application of and the exceptions to the rule by means of examples specially constructed for the purpose ; although such little pieces, written merely to teach certain points, possess neither the value nor the charm of artistic compositions. Though I have termed the present first part of my work, con- formably to general usage, a "Manual of Harmony," the words "harmony " and "harmonic " are not used in the body of the book ; the terms "chord" and "chordal" being substituted for them throughout. This step, too, was dictated by experience in teach- ing. Before the pupil enters on the study of theory, he has become familiarized with the term "chord" from the beginning of his prac- tical study, whether instrumental or vocal. Everyone knows what- this word means in music. The term "harmony" is mostly known in a sense different from that in which it is used in the earlier in- struction-books. The pupil finds it strange that dissonant chords., such as the augmented and diminished triads and all chords of the seventh, are also called "harmonies." He finds it strange, more- over, that the term "harmony" is employed only for chords in the fundamental position, and that their inversions are always called chords and not harmonies, whereas both terms are applied in just the same sense to the fundamental position of the chords. The ex- pressions "chord of the sixth," "chord of the fourth and sixth," "chord of the fifth and sixth, of the third and fourth, of the sec- ond," are all used as technical terms. Here we need not discuss whether and to what extent the terms "harmony" and "chord" are interchangeable; my sole object has been to make my text-book as simple, clear, and intelligible as might be to the pupil, without superfluous verbiage, and without regard to elegance of diction. Then why use two terms, one of which can be employed only with restrictions, and is strange and indefinite to the beginner, while the other, which he knows from the outset, suiGces in every case .? And now one word to the pupil. Whoever wishes to get real benefit from this book, must not be satisfied with merely learning PREFACE. V and understanding the principles and rules given in it. He must also learn to apply them practically with the freedom of an artist. For this reason I have provided the book with a very large number of exercises for practice, advancing in each individual case from sim- ple, easy tasks to more complicated and difficult ones. Let no one be content with working out only a fart of these exercises ; each of them is so arranged, that the pupil learns the application of a rule in as many and various lorms as possible. A thorough and complete knowledge of the chords and their inter-combination, such as the artist needs not only for original free composition, but also for preluding and modulating, and for a correct and intelligent ren- dition of master-works, can be attained solely by means of earnest, diligent, and persevering work. Nor should the pupil be content to treat the exercises for practice as dry school-exercises, and to work them out merely from this point of view ; for even in them a talented student will find opportunity to display the qualities of an artist, such as taste and refinement, a striving after euphony, and a good leading of the melody. It will therefore often be well to work over one and the same exercise several times and in different positions, even in cases where a given pitch appears most con- venient and suitable. In this way alone can the pupil attain to a sure and perfect mastery over the technicalities in the inter-con- nection of chords, which form the groundwork of the studies in counterpoint and of all work in composition. S. JADASSOHN. Leif sic, July, 1883. PREFACE TO THE SECOND EDITION. The second edition of the "Manual of Harmony" has been care- fully revised, and augmented by explanatory notes and hints for working out the exercises contained in the book. These explana- tions have been added in the shape of a second Appendix of six- teen pages ; they will essentially facilitate the teacher's task, and be a welcome aid to the pupil when at work ; and will prove, more especially, an efficient help to and a reliable guide for the self- *""^'^'- S. JADASSOHN. Leifsic, March, 1887. TABLE OF CONTENTS. Chapter I, pp. 1-9. §1. Natural and derivative tones. §2. Intervals; diatonic major scale. §3. Greater and lesser semitones. §4. Exacter definition of the intervals. §5. Measurement of the intervals upward. §6. View of the intervals. §7. Modes. Enharmonicochromatic scale. §8. Perfect and imperfect con- sonances ; dissonances. Chapter II, pp. 9-12. §9. Intervals both above and below ( inverted ). Chapter III, pp. 12-24. §10. Classification of the chords as triads and chords of the seventh, inde- pendent and dependent chords. §11. Major and minor triads: fundamental triads in major. §12. Interconnection of the fundamental triads in four-part writing; compass of the voices in the chorus. §13. Exhibition of the triads in the four-part vocal chorus. §14. Common tones in two chords. §15. Pro- gressions between the triads on the 4th and 5th degrees. Parallel octaves and fifths. §r6. The three styles of motion. §17. Exercises, close and open harmony. §18. Forms of the close. Chapter IV, pp. 24-35. §19. Subordinate triads in major. Dissonant, diminished triad. §20. Pro- gressions between all triads in major. §21. Covered parallel octaves in the outer parts. §22. Connection of two neighboring triads by contrary motion. §23. The leading-note. §24. Examples. Exercises. §25. Sequences. Chapter V, pp. 35-45- §26. The minor scale, and its triads. §27. Dual form of the minor scale. Augmented triad. §28. Step of the augmented second. §29. Connection of the triads on the 5th and 6th degrees in minor. §30. Thorough-bass nota- tion. §31. Examples. Exercises. View of all triads in major and minor. Chapter VI, pp. 45-58. §32. The inversions of the triad. §33. Successions of two or more chords of the sixth. §34. Chord of the fourth and sixth. Examples. Exercises. Chapter VII, pp. 59-70- §35. Chords of the seventh. Dominant chord of the seventh. §36. Nat- ural resolution of dominant chord of the seventh. Covered parallel fifths. §37. Perfect cadence. Examples. Exercises, (vi) TABLE OF CONTENTS. vii Chapter VIII, pp. 70-77. §38. The inversions of the dominant chord of the seventh, and their nat- ural resolutions. Examples. Exercises. Chapter IX, pp. 77-86. §39 The secondary chords ef the seventh in major, and their natural reso- lutions. The tritone. §40. Preparation of the seventh. Exercises. Chapter X, pp. 86-89. §41. Interconnection of the secondary chords of the seventh in major, in the fundamental position ; their inversions and progressions. Exercises. Chapter XI, pp. 86-98. §42. Secondary chords of the seventh in minor, and their inversions. §43. Diminished chord of the seventh, and its natural resolution. Exer- cises. Chapter XII, pp. 98-108. §44. Non-cadenced progressions between the chords of the seventh on other degrees and in other keys. Deceptive cadences. Modulation. Freer leading of the seventh. §45. Necessary leading of the seventh upward. Exercises. Chapter XIII, pp. 108^117. §46. Progressions between the secondary chords of the seventh and chords on other degrees and in other keys. Permissible succession of a perfect and an augmented fifth. §47. Free entrance of seventh and root in contrary mo- tion. Exercises. Chapter XIV, pp. 118- 128. §48. Altered chords. Triads with altered fifth. Exercises. §49. Chords of the seventh with altered fifth. Open harmony. The old clefs. Examples. Exercises. Chapter XV, pp. 128-144. §50. Augmented chords of the sixth, of the third and fourth, and third, fifth and sixth, and their resolutions in major and minor. Augmented chord of the sixth belongs to two major and two minor keys. Exercises. §51. Indirect resolutions of the augmented chord of the fifth and sixth. Direct modulatory resolutions. Exercises. Leading of the parts by a skip. View of all chords. Chapter XVI, pp. 143-164. §52. On suspensions. §53. Entrance and resolution of suspensions. §54. Suspension in the bass. Thorough-bass notation of the suspension. Examples. Exercises. Chapter XVII, pp. 164-175. §55. Suspensions in several parts. Upward resolution. §56. Freer pro^ gression of chords in a suspension. On suppositious chords of the ninth, eleventh, and thirteenth. Exercises. viii TABLE OF CONTENTS. Chapter XVIII, pp. 175-182. §57. Passing-notes and passing-chords. Changing-notes. The organ-point §58. Organ-point on the tonic, on the dominant, and on tonic and dominant together. Examples. Exercises. Chapter XIX, pp. 182-194. §59. Covered parallel octaves and fifths; cross-relation. §60. Covered parallel fifths with a whole-tone step. Chapter XX, pp. 194-208. §61. Employment of the chords for accompanying a cantus firmus in four- part writing. Leading of the bass. Inner parts. Examples. Exercises. §62. The cantus firmus in alto or tenor. Melodic leading of the soprano. Examples. Exercises. Chapter XXI, pp. 208-221. §63. Modulation. Means of modulation. Dominant chord of the seventh. §64. Augmented chord of the third, fifth and sixth. The \ chord on the strong beat. §65. The diminished chord of the seventh as a chief means of modulation. §66. The augmented chord of the sixth, and other means of modulation. More extended modulations. Chapter XXII, pp. 221-233. §67. Closing cadence. §68. Chromatic change of tones in the chord on the 2nd degree in the closing cadence. §69. Chord of the seventh on the 2nd degree as introducing the closing cadence. Triad and chord of the sev- enth on the 4th degree, with chromatic change of the several tones on begin- ning closing cadence. §70. Chromatic alteration of chord of the seventh on the 4th degree. Concluding remarks. Chapter XXIII, pp. 234-240. On the Musical Hearing. Chapter XXIV, pp. 240-246. Subject-matter and Form. Appendix I, pp. 247-272. Explanatory examples. Appendix II, pp. 273-288. Index, pp. 289- 292. A MANUAL OF HARMONY. PART THE FIRST. CHAPTER I. The Intervals. § I. The number of primary or natural tones employed as the building-material of music is limited to seven, from which we derive five further derivative tones. Taken in natural succession, the seven natural tones form the Diatonic Major Scale. i l¥. ZISZ I ^ -Sh '^ From these natural tones are derived, by means of raising the first, second, fourth, fifth, and sixth tones by a semitone each, the derivative tones 2. %-^=^^^^^ lying between the naturals. We can also get them by lowering the second, third, fifth, sixth, and seventh natural tones by a semitone each. 3. fc^^=^^^^l All twelve tones may therefore be written in chromatic suc- cession, either with the following signs : g I ll-===^=:^=i^==^=is=%^==^-=^^^^ or with these others : i zzzT-— ^ iE^ ^=g^-^^^'^^=g^^^^l;= B We assume that the pupil already knows that tones can be enhar- raonically represented in still other ways, which we do not require for our present purpose. (I) A MANUAL OF HARMONY. §2. The difference in pitch between two tones we term an In- terval. Within the diatonic major scale, erecting the intervals in every case on the first or key-note ( tonic ) , the second note will form the interval of a Second with the key-note ; the third note that of a Third ; the fourth note that of a Fourth ; the fifth that of a Fifth ; the sixth that of a Sixth ; the seventh that of a Seventh ; and the eighth, the interval of an Octave. The key-note itself we call a Prime. i 6. zsz -&-S- tS^-' -s^ '^ -&- Prime, Second, Third, Fourth, Fifth, S- - be - i The lesser semitone is found only between two neighboring degrees. Thus the interval from c to the d\f next above it, from c# to the next d, from a? to e\> ; or, from a? J to e, is a lesser semi- tone. Remark. The falsity of the contrary opinion expressed by earlier text-books, that the change produced in a natural tone by a chromatic sign is the lesser semi- tone of the natural tone, and that the minor second is the greater semitone, will at once be revealed to the practical musician by the different resolutions of the like- sounding chords _/^-(r-^b 3inAf-ar-c—d%. i -bg- m^ -feg* £\> being the nearer to D, tends to D, and Dt to £. Louis Lohse, in his essay " Contra the New Keyboard" ( Musikalisches Wochenblatt, 1883, No. 2), ex- presses his views on this head with great clearness. He observes : " The opin- ion thatc-ct is the lesser semitone, and c-i/b the greater, is doubtless productive of serious mischief. The reverse is true. Assuming c' at 256 vibrations, an absolutely pure db has 268.04, while a pure ct has 273.0375 vibrations. The minor second is therefore materially narrower than the augmented prime." This observation furnishes an easy explanation of the natural progression of the leading-note, and also of the natural resolutions of all the altered chords and chords of the seventh. §4. The intervals lying within the major scale, which we named, as erected upon the key-note, the Second, Third, Fourth, Fifth", Sixth, Seventh, Octave, and Ninth, become essentially dif- ferent intervals when either of the two tones forming each interval is raised or lowered a semitone by means of a chromatic sign. The sixth C - A, for instance, appears narrower or wider according as we change c into cff or cb, or a into a f or a b. 11. 3 ^ ei ~rf fi Z::itfS %a. ^ «J '^ g-«>- b-s^ fr«i- "^ 4 A MANUAL OF HARMONY. These changes in the tones of an interval by chromatically raising or lowering either or both of the tones, render necessary a preciser nomenclature of the intervals so obtained. Measurement of the Intervals Upward. §5. We named the intervals of the major scale either -perfect or major. By raising the higher tone of any such interval by a greater chromatic semitone, the perfect or major interval so changed becomes an augmented interval. This also holds good of the Prime, which in itself is no interval, but a unison. Unison. Interval. i Perfect Prime. Augmented Prime. I By lowering the higher tone of any major interval by a greater chromatic semitone, we change the major interval into a minor one. By raising the lower tone of any minor interval by a greater chromatic semitone, we get a diminished intei-val. By raising the lower tone of a perfect fourth, fifth, or octave by a greater chromatic semitone, the perfect interval is changed to a diminished one. §6. We likewise get the diminished fourth and fifth by lowering the higher tone of a perfect fourth or fifth; the interval c-g^ is thus exactly equivalent to c%-g. Diminished primes and oc- taves do not occur in pure chords ; neither are diminished seconds, augmented thirds, diminished sixths, augmented sevenths, and di- minished ninths employed in building up chords. 12. i View of the Intervals. Perfect Intervals. ~Z7- i Prime (Unison), Major Intervals. Fourth, Fifth, Octave. I i 13. -&- Second, Third, Sixth, -iS>- Seventh, Ninth.) 14. 15. i A MANUAL OF HARMONY. Augmented Intervals. ;^^=B!gEEgg^ B -j^r^i^ :fl2= i -&-Jlj-&- -&- tt^ "^^ '"-IS- -&- -»■ -&- -e>- Prime, Second, Third, Fourth, Fifth, Sixth, Octave, Ninth. Minor Intervals. ^fe- i ife: -^^ a -rS'- " tSi- Second, Third, Sixth, Diminished Intervals. Seventh, Ninth. itts: i 16, ■^P=il Third. 1^- . ' F:ourth, -1^ Fifth, Sixth, Seventh, Octave. Remark. In melodic succession, diminished primes also occur ; c. g. i p = frg — ffi^ d?2 eI The intervals which may be used for the erection of chords, or in occasional chord-formations, are given in regular order in the fol- lowing : i Primes. perfect, atfgm. major. Seconds. minor. augm. I 17. ~^ -t^- it*- i Thirds. major, augm., minor, dimin. Fourths. perfect, augm., dimin., dimin. ^m :1= =#t -M lia '-^ -^i^ -&' W^' w^~ i Fifths. perfect, augm., dimin., dimin. Sixths. major, minor, augm., dimin. S m =«t iM =is: i^- "f^ s-^ i Sevenths. major, minor, dimin. Octaves. perf., dimin. Ninths. major, minor. E ^ — f4 =a ^- ^ ^ §7. We have now learned all the intervals necessary for build- ing up chords, and have erected them on and above the tone C. 6 A MANUAL OF HARMONY. To this end we chose the diatonic scale of C-major as a normal scale for our basis of operations. Although we may take it for granted that the student beginning the theory of music is practi- cally acquainted with all the scales, we pause to remind him that we recognize two musical genera or modes, the major and minor modes, and two diatonic scales corresponding to the modes, called the major and minor scales. These latter are formed in ac- cordance with definite laws, and can be erected on any tone what- ever with a precisely similar arrangement of their tones. This arrangement we have already learned from the C-major scale (comp. No. 8).* When we start from any tone but C, we have to use chromatic signs for building up the scale ; thus the scale of G takes one sharp (jf) ; that of D, two ; A, three ; E , four ; B, five ; and -^It, six sharps. The scales of ^, B\f.i E^, A\>, D b, and G i? take from one to six flats (t*) respectively. Consequently, the scales having a signature are to be regarded simply as transpositions of the scales of C-major or a-minor. For scales beginning a perfect fifth above or below C or a we require one chromatic sign to ob- tain a similar arrangement of the intervals. Advancing either way by fifths, to get key-notes for beginning new scales, an addi- tional chromatic sign must be added for each skip of a fifth, in order to build up scales exactly like the model scale. This is il- lustrated in the figure, which is called the " Circle of Fifths." 9rB^, C-EP B-i ,A-t» Mtf l£-t^ 'The formation of the minor scale will be explained at length further on. A MANUAL OF HARMONY. To get the major sixth above F $, we have to find the sixth tone m the scale of Fijrmajor, which is Z>J{. The minor sixth is therefore Z>, and the augmented sixth 2?x. 18. i ^ =Se: ^ :#ei xg -la^ i major sixth, minor sixth, augmented sixth. To get the major sixth of ^ b we have to find the sixth tone in the scale of ^l^-major, v/hich is F; the minor sixth is therefore F^^ and the augmented sixth F%. 19. i dfe -bs- ite ±sz J^ i major sixth, minor sixth, augmented sixth. For the exact determination of all the intervals we have to em- ploy all the chromatic signs — the Double-flat (tt?), the simple Flat (t>), the Natural (Jj), the simple Sharp (jf), and the Double- sharp (x) — in order to raise or lower the tones chromatically. To show this quite plainly to the pupil, we give below a view of the intervals as erected on the tones G b and F%. From the signatures it is evident that the scales of (? b and F% are taken as a basis. ^ Primes. perfect, augm. Seconds. major, minor, augm. I 20. m^'^ e > g \ o Bg V^ " I g -Wcr 332= i Thirds. major, augm., minor, dimin. HE Fourths. N.B. perfect, augm., dimin. ^^ =5S li^ itto: :l2i2s: -)9- W- ^ S^' 1— 0dJ perfect, -tr:r :;r-i IFTHS. augm.. N.B. dimin. 1 B»— major, f3 &1XII minor. IS. augm., 1 1^ dimin. p^— -iff ^ — » -«> -g, 1^ 1^ A MANUAL OF HARMONY. i major, Sevenths. minor, SS ■^- diinin. ^ Octaves. perfect, dimin. feffl- i w 1^ te= i bfcl Primes. perfect, augm. major. Seconds. minor, augm. t\ li P i2z: 3^ — S5=2=^=^^=}^==S^ ^z=tta=z ^fe'- — i l >r^^~~ag ' • ^ I~g^~B A MANUAL OF HARMONY. 9 Hence we see that the minor second is a narrower interval than the augmented prime ; that the minor third, C-e 7, is narrower than the augmented second, C-d%; and the diminished fourth narrower than the major third, etc. §8. Finally, we will observe that the intervals are classified as perfect consonances, imperfect consonances, and dissonances. The perfect consonances are the perfect prime (unison), the perfect fourth, the perfect fifth, and the perfect octave. The imperfect consonances are the major and minor thirds and the major and minor sixths. The dissonances are the major and minor seconds, major and minor sevenths, major and minor ninths, and all aug- mented and diminished intervals. 22. i Perfect Consonances. •Ep i 23. i Imperfect Consonances. =1^ =2= i Dissonances. 24. ^_S- — p — ttgg— '^^^^ — ^^o. --i^tfe? — ^4=" ^ =^ -e> \>o — ^- lits: m g ft g - =Ss:: «■*■ H* -is>- -&- f»^ S-iS^ -s- CHAPTER 11. Intervals both Above and Below (inverted). §9. We are obliged, both in the theory of chords and in our studies in counterpoint, to consider the relations of two tones con- tained within an octave when either of the said tones is uppermost. For example, the tone E above A forms the interval of a fifth and below A that of a fourth 10 A MANUAL OF HARMONY. By erecting the intervals in the scale of C-major above C, and then inverting the intervals so erected above two-lined C by an octave, we obtain the following scheme : . . . J i i ^ 25. 3 .,; SX- — fg* a f3 a a a^ r>m J g ^Y~r r r-f r f " " By inversion into the lower octave the perfect prime becomes a perfect octave ; the major second becomes a minor seventh ; the major third, a minor sixth ; the perfect fourth, a perfect fifth ; the perfect fifth, a perfect fourth ; the major sixth, a minor third ; the major seventh, a minor second ; and the perfect octave, a perfect prime. Thus all perfect intervals (perfect consonances) remain perfect after inversion to their lower octave ; major intervals be- come minor ; and minor intervals become major. V 26. i iE 5W- ^ ^i ^1 'r^ ¥ ^ I All augmented intervals become diminished : 27. m ^fit d=F=i -'Sr -s=tzt^- P- li?: pi All diminished intervals become augmented : J ^J- bi ei 28. ~^ts-- =pp=p^^ Jt ^tty— To render the matter quite clear, we append a view of all the intervals, together with their inversions to the lower octave. The pupil should now write out in like manner all the intervals as erected on each of the other tones, in doing which he must take each of the other eleven major scales in turn as a basis. A MANUAL OF HARMONY. 11 Intervals Primes. perfect, augm. =31 ::^ Intervals Below. OpTAVES. perfect, dimin. s=^= Seconds. major, minor, augm. g^^ :rft i Sevenths. minor, major, dimin. -w- ~g- -p- eB Thirds. major, augm., minor, dimin. i =^ ±iL=n=i±i Fourths. perfect, augm., dimin., dimin. ^ :^i- isz — :^)p2- az= g fg_ P jS 1 (2- i Sixths. Fifths. minor, dimin., major, augm. perfect, dimin., augm., augm. :«^ js. — ^fts — rUfg- r=='=^==^^r^r^T=^f='*T=^ Fifths. perfect, augm., dimin. i W , a-l , kI Sixths. major, minor, augm., dimin. J- U ji_ ^- a jp2 JI_/2, -a z%sL Fourths. perfect, dimin., augm. Thirds. minor, major, dimin., augm. ^^-+^ ZE^^g^ major, I Sevenths. minor, Ir-L dimin. Octaves. perfect, dimin. I H I I =»s: =tf^ Seconds. Primes. minor, major, augm. perfect, augm. I 12 A MANUAL OF HARMONY The other inversions of the intervals by a tenth or twelfth can be ,ps.ssed over for the present. But for the exercises in double coun- tfefpoint we shall be obliged to pay special attention to them. CHAPTER III. Theory of the Chords. The Fundamental Chords and their Inversions, and Also THE Altered Chords Derived from Fundamental Ones. §io. All chords are classified either as Triads, i.e. those com- posed of three tones ; or as Chords of the Seventh, which have four different tones.* We divide the triads, to begin with, into independent and de- pendent chords. We call triads independent which are composed solely of con- sonant intervals, having either a major or minor third and a perfect fifth (reckoning from the fundamental). On the other hand, triads are dependent which contain a dissonant interval, a diminished or augmented fifth. All chords of the seventh are dependent. Every dependent chord seeks and calls for progression to an in- dependent chord. t As we have to occupy ourselves first of all with the triads, we give for the present examples of independent and dependent triads only. a. b. c. d. 30. *At the close of the chapter "On Suspensions" we shall -explain in detail why it is that accidental chord-formations, which earlier text-books termed chords of the ninth, or even chords of the eleventh and fifteenth, cannot be treated as dis- tinct chords. By that time the pupil will have reached a standpoint from which he can intelligently follow our explanations. t Two or more dependent chords can, however, occur in succession, only the last one most resolve to an independent chord. A MAIfUAL OF HARMONY. 13 a. Has a major third E and J)erfect fifth G, reckoned from the root (i.e. the tone on which it is based), and is an independent triad. b. Has on the contrary the dissonant augmented fifth Gf, to its root C, and is therefore a dependent triad. c. Has a minor third and perfect fifth reckoned from the root, thus Being an independent triad. ^ d. .Though having a minor third F^ this triad is completed by a dissonant diminished fifth ^t?, reckoned from thd root, and is consequently a dependent triad. §11. Every triad is formed by the addition to its root of the third and fifth above it. According, as the third is major or minor we obtain, provided that the, fifth of the root is perfect, either the Major Triad, having a major third and perfect fifth, reckoning upward from the root ; or the Minor Triad, hitving a ipinor third and perfect fifth. Major Triads. 31. 32. i Minor Triads. By altering -the relation of the fifth to the root we obtain other Varieties of triads, which we shall take up further on. A triad can be erected on any degree of the scale ; the most im- portant ones, the Fundamental Triads, are found on the ist, 5th, and 4th degrees. The above three degrees of the scale, i. e. the Prime, Fifth, and Fourth, have -also received the special names of Tonic, Dominant, and Subdominant respectively. 33. m Tonic. Dominant, a.. -s>- s Subdominant. 14 A MANUAL OF HARMONY. The triad on the first degree is therefore called the Tonic Triad ; that on the fifth degree, the Dominant Triad ; and that on the fourth degree the Subdominant Triad. The closeness of their relations to each other will be seen by the following grouping. Subdominant Tonic Dominant triad. triad. triad. 34. JL - 2^ -=^' — n From the apex of the tonic triad, the fifth G, the dominant triad is evolved upward ; while the root of the tonic triad forms the apex or fifth of the subdominant triad. These three triads contain all the tones of the C-major scale, and display, in their grouping and artistic combination, the characteristics of the key. All three fun- damental triads are major triads. §12. For effecting the interconnection of these triads according to the rules of musical art, we take a mixed four-part vocal chorus as the most suitable medium, consisting of Soprano and Alto (fe- male voices), and Tenor and Bass (male voices).* The compass of the high female voices (called soprano or treble) in a chorus may be assumed in general as reaching from c' to ^, or even to l^^ The range of the low (alto) female voices is from *Our reason for choosing a four-part mixed vocal chorus as the imaginary exec utant of these as well as of all following exercises, is easily apparent. All our exercises are preparatory studies to Counterpoint. Counterpoint, however, re- quires the independent leading of each part, and its innermost essence is vocal. In It we have nothing to do with harmonic masses, with chords, or with a predom- inating principal melody to which all the rest occupy the subordinate position of a chord-accompaniment, as is often the case in modern compositions for the piano- forte, the harp, the organ, or orchestra. In all contrapuntal compositions, on the contrary, even if not intended for singing, every part must be melodious, and its leading governed accordingly. And as our preparatory exercises in the inter- connection of chords are in closest touch with the later studies in counterpoint, even containing, though the pupil does not realize it at first, a. great deal of con- trapuntal work, we are obliged from the outset to assume the vocal chorus as the executant of all our exercises, and to work them out in this sense. A MANUAL OF HARMONY. 15 a (or even g) of the small octave up to c', or d'. The high male voices (tenor) correspond to the soprano an octave lower, reaching from c of the small octave up to ^' or a'. The low male voices (bass) have a compass from G or even F of the great octave up to c', or occasionally to cP'o or (f, of the one-lined octave. We term the soprano and bass the outer parts, and the alto and tenor the inner parts. The range of the voices of a chorus may therefore be exhibited thus : 35. Soprano. m -e> — ffl- Alto. W-- -g — •- -z^ ^ ^ ~o — s>- 11 Tenor- ■m i tr-25'- I Bass. -&- -»- -gg- I §13. When a triad is to be sung by a four-part chorus, one of its intervals evidently must be doubled, and sung by two different vocal parts either in unison or in the octave (or double-octave). The following rules apply to such doubling : Any tone of the triad may be doubled ; the root is best suited for doubling, the fifth less so, and the third least of all, because this latter, according as it forms a major or minor third with the root, is most sharply prominent in characterizing its triad as major or minor. We can write the tonic triad of C-major for a mixed vocal chorus in a great variety of forms ; e. g. 16 36. Soprano. Alto. Tenor. Bass. A MANUAL OF HARMONY. g a. 9 i b. c. d. t. ra s- h. i. k. r '^ 1 fS m. «^ > — -s- 9- Us'-J -&— « fa ^ 1 1 LfS^ Lis-J Ls*— 1 -&— -&- -»• etc. ^z: .az- i i w- -&-^—s- ^ -O- C: I This style of notation, in which each part has a separate staff, is called a Score. But as we do not need it for our first and very simple exercises, we shall choose instead the style of notation on two staves (short score) with the violin and Ijass-clefs, which will afford the pupil a more convenient view. Written thus, No. 36 ap- pears as follows : 37. A a. b. c. d. e. /■ g- A. i. k. I. in m. f3 <- \j fZJ PS r^ IJ 1 J( m » " H 1 ifh II 1 \a} g_" S S 'S '9, ij S- ^ -&- -s>- cs 1 C\- n \ n 1 /3 <2 1 1 T. /2 in 1 1 ^ /% ^ iri ^ a in fp ja. 1 \ - 1 1 ' J At a the root is doubled in the soprano ; at h and c, in the alto ; at «, in the soprano ; at g, in the tenor ; at k and m, in the alto ; at d and /the fifth is doubled ; while the third is doubled at^and «'. The triads of the dominant and subdominant may be written out in the same way. 38. < T / 1 /5 1 7 z? 1 ^ 9, 1 (c S fi> *^ a 1 * "^—i ^ 1 \s T ^ % 1 ■fii 1 t^ -Sl- -s>- -s>- etc. Si in ej in etc. f-x. ^sS 1 ^ ^ n in <* 1 ■^ 1 1 1 LgJ L-s> — ' J C: IV C- V A MANUAL OF HARMONY. 17 §14. In order to effect the interconnection of these three triads according to the rules of strict composition, the first and leading prin- ciple to be kept in view is to lead the parts in such a way as to render execution as easy, convenient, and natural as possible for the singers. For this reason, when one tone belongs to two suc- cessive chords, we prefer to keep that tone in the same -part, and lead the other parts to those tones of the new chord which lie near- est to them. Thus Ex. 39 shows us some progressions of the tonic triad to the dominant triad, both being in the fundamental position, i. e. the position in which the root of the chord lies in the bass. h. c. d. e. ^ ^\, 39. < i p -^-t-^ afcb±H etc. f^^ ^^ m ^ I C: I V In Ex. 39 (a) the alto holds the tone G, which belongs to the tonic triad as fifth, and to the dominant triad as root. In Ex. 39 ( 6) the tenor holds G, which the soprano holds in 39 c, etc. Ex. 40 exhibits progressions between the triads of the tonic and the subdominant. C: I IV §15. But if we wish to let the triads of the subdominant and dominant follow in succession, the connecting link of a tone com- mon to both is lacking. In this case we must lead the tones of the first chord into those of the second in such a manner, that no part shall progress in unison with, or in parallel fifths or octaves with, any other. The following progressions are entirely wrong. " b. c. d. ^.^ 41. -tS>- s^r^= ^2!^ IZ> S^ I 18 A MANUAL OF HARMONY. In 41 (a) the tenor and bass progress in unison from f to g., and at the same time in parallel fifths with the alto, which progresses from c' to cP^. At b we find parallel octaves between the sopran» and bass, and parallel fifths between the bass and alto ; at c are parallel octaves between the tenor and bass ; besides, both parts progress in parallel fifths with the soprano. Finally, Ex.41 {<£) shows parallel octaves between the soprano and bass, and parallel fifths between the tenor and bass. Our sole resource for avoiding these gross mistakes is, not to lead the bass in parallel motion to the other parts, but in contrary mo- tion, leading the higher parts to the tones of the new chord whict lie nearest them ; e. g. 42. Pa ^ C: IV -w a^ip IV etc. l -^-g — j ^z-^-<9— |=a=[ — g— I Ex. 42 (a) shows correct progressions from the triad of the sub- dominant to that of the dominant ; Ex. 42 (b) shows like progressions from the dominant to the subdominant triad. §16. The pupil therefore has to distinguish between three dif- ferent styles of chord-progression, namely : a. Parallel motion, b. Oblique motion, and c. Contrary motion. Parallel motion is the progression of two parts in the same di- rection by either a step or a skip. Under certain conditions even three parts can progress, stepwise, in the same direction. In the interconnection of triads, the leading of four parts in par- allel motion will always yield faulty progressions, and should be carefully avoided later, when effecting progressions between other chords ; it is permissible in only a few rare cases. Ex. 43 shows parallel motion between two parts. 43. id=^iH^^^ ^ etc A MANUAL OF HARMONY. 19 Ex. 44 shows parallel motion between three parts. 44. i X I Oblique motion is brought about when one part ascends or de- scends, while another part remains stationary. Thus in Ex. 45 45. i -J- llLZ 4- H=- r I both the higher and the lower parts progress in oblique motion to the middle part. In Examples 42 {a) and (^) we have already had instances oi con- trary motion. By employing either oblique or contrary motion we can best avoid faulty progressions in unison, or in parallel fifths or oc- taves. We must also avoid leading three, or even all four, parts by a skip from one chord to another. This is allowable only when a transposition of thejirst chord is obtained thereby. .good. good. bad. bad. 46. i w isz ~W i -&- _|2- i C: I C:V C:\ IV C: V Parallel unisons, octaves, and fifths can occur, of course, only in parallel motion. The above three modes of progression in the parts are combined in the following example. ^^^^eeI 47. I C: I V 20 A MANUAL OF HARMONY. Here the soprano ( c ) and tenor ( e ) progress together in par- allel motion, but in oblique motion to the alto and in contrary mo- tion to the bass ; the bass at the same time moving in oblique mo- tion to the alto. Kemark. An explanation of the reasons for prohibiting parallel unisons, oc- taves, and fifths, in strict composition, would be incomprehensible to the pupil. §17. Exercises for the interconnection of the fundamental triads of the tonic, dominant, and subdominant. To begin with, we mark the bass with the degree-numbers I, V, and IV, because the triads in question have their seat on the ist, 5th, and 4th degrees of the scale respectively. The Arabic numerals over the first bass note indicate the place of the soprano as the third or fifth of the chord. When the soprano is to take the octave or double-octave of the bass, it requires no distinguishing mark ; though in some cases where it appeared necessary or desirable a figure 8 is written above the first bass note. 48. < i w i3 C: I ^2 ^ IV C:\ IV 122= I I IE =S= I =1= Eg^ i^ i G: I IV F:\ V IV pj»iEEEp; I ^t>: I IV The notation of all these examples is such, that the three high- est parts — soprano, alto, and tenor — are kept close together, not A MANUAL OF HARMONY. 21 spreading beyond the compass of an octave. This is called the close harmony of the parts. In our first exercises we shall use close position exclusively. Opposed to close harmony is of en harmony, in which the three above-mentioned highest parts are spread out beyond the compass of an octave. The following chords are writ- ten in open harmony. 19. i ^— s.- o -19- -Wr- etc. Open harmony may be changed to close harmony when any part can be transposed by an octave in such a way as to bring the three highest parts within the compass of an octave. Thus the chords of Ex. 49 may be brought into close harmony by transposing the soprano into its lower octave, between the alto and tenor. 60. i s^— -g-- -er- I i By transposing the tenor into its higher octave, between the alto and soprano, we again obtain close harmony. 51. A } /-3 r-g 1 rS— 1 a II t i* n i> 1 S g II 1 ^ 1-3 ■2 SJ 1 S II I } 9, <9 1 — 1 ■■ 1^ Sl- 1 , 1 II ■ •- • i 1 II 1 J ^ n /3 . _ 1 II VJ iJL — L^— .. _, . '— zr- -»—& 1 L-« — U 22 A MANUAL OF HARMONY. Ex. 48 can be written out in open harmony as follows, by trans- posing the alto into its lower octave. 52. I sa C: I IV sr- Z^ C:\ IV I i 1 s w 5 i^ G: I IV F: I IV i I 3 _(2_ I -5- V ^b: I IV On the basses given below, which contain the roots of the funda- mental triads in different keys, the pupil should now write out ex- ercises in the interconnection of the tonic, dominant, and subdomi- nant triads in close harmony, after the model given in Ex. 48. Un- der the several bass notes he should set the figures I, V, and IV, as a constant reminder that in all the different keys he simply has to do with the triads on the ist, 5th, and 4th degrees. From the very outset he ought to accustom himself to consider, when work- ing in C-major, the triad P- ^ - C as the triad on the 4th degree, and not as the triad on the ist degree in -F-major. The triad F- A- C becomes, in -F-major, the tonic triad ; in JB\^ major, the dom- inant triad ; and in C-major, the subdominant triad. In ^-niajor it has its seat on the ist degree, in Bb major on the 5th, and in C-major on the 4th. §18. Before taking up the exercises, attention must be called to the different forms of Close, to be employed in these and in all suc- ceeding ones. The closing chord of any piece must always fall on A MANUAL OF HARMONY. 23 a strong beat, just after the close of a metrical phrase or period, and must consequently have the effect, both rhythmically and met- rically, of a beginning, in order to form a complete close, and not an incomplete or half-close. Only thus will the hearer obtain the Jmpression of a satisfactory close . 53. i i^ gi^ I I Ex. 53 satisfies us because, following a metrical group of two measures, the chord of C-major enters on the first or strong beat of a new group. The next Example exhibits the direct opposite of this. 54. < l^ 9 ia d= =3= i I Here no one can obtain the impression of a satisfactory close, because the last chord falls on the second or weak beat of a two- measure metrical group. It is self-evident that the closing chord must always be that of the tonic. It may be prepared (preceded) by either the dominant or subdominant chord. In the first case we get an authentic close, in the second a plagal close. Authentic Close. Plagal Close. 55. IE I c»f- 5^ Wi I IV Further on, when discussing the authentic close, we shall take up this point in detail. 24 A MANUAL OF HARMONY. Exercises. i 56. ^ :^==ra ^ I IV I V I -^:, ;|t |g \ s> \ M 1 1 1 1—2, u Also transpose into G and /"J, ^e Se ^ 1— - g a^ I— ffl — J g. . — etc. -(2- ^m^ IV vno All triads, the roots of which are either a fourth or a fifth apart, possess one tone in common. In one exceptional case, however, we must forbid the holding of this common tone, as the following ex- ample shows. The leading of the outer parts (soprano and bass) in Ex. 5g{a) is entirely unallowable. These two parts progress in so-called Covered Parallel Octaves. §21. Covered' octaves arise when two parts progress from differ- ent intervals, and in parallel motion, to an octave or double-octave. In our next exercises we shall prohibit the pupil from writing cov- ered octaves only between the outer parts, and in case one or both parts progress upward by a whole tone, as shown in Ex. 59.* * In downward progression, however, the unpleasantness of such covered oc- taves, even in the outer parts, is far less apparent ; e. g. in the progressions given in Ex. 60, ' ^^.■a — I - ig:5!sE= i 60.' EEE :s:iC r-*:; 3E I no fault can be found with them ; even the upward progression in Ex. 59 (^) is per- missible, because the near relationship of the two chords — the triad A-C-E is the subdominant triad in ^E-minor — materially softens the effect of the covered octaves. But the triads D-F-A and G-B-D are not directly related, because in the key of af-minor, in which D-F-A is the tonic triad, the triad G-B-D does not occur ; neither is the triad D-F-A found in G-major. This matter, and also the subject of covered octaves, will be treated at length in the Second Part of this book. A MANUAL OF HARMONY. 27 The above-mentioned covered octaves are permitted between the bass and an inner part, when the inner part reaches the octave of the bass by a step ; e. g. Covered octaves having an ill effect can therefore arise only in case both parts reach the octave by a skip from' different intervals, 62. i 3^ i which is entirely unallowable, or when one reaches the octave by the step of a whole tone, and the other by a skip, as Ex. 63 .shows. 63. On the contrary, any covered octave in which one part enters the octave by a skip, while the other reaches it by the step of a semitone, may be written without hesitation between any two parts, even the outer parts. Such a progression of chords has no harsh or unpleas- ing effect, but (especially upwards) rather a very agreeable and nat- ural one. 64. i BE 1 ^0 - -m±i ^ lr:^g fe=|E= j^^^g=|:| -Z?'^^'^- -I ^a — I — g-f-^ =tt5 -^s- I 28 A MANUAL OF HARMONY. §22. Common tones are never found in two triads on neighboring degrees of the scale, as we have already seen in progressions between the triads on the 4th and 5th degrees. In such cases contrary mo- tion must always be employed, to avoid open parallel fifths and oc- taves. A few progressions of this kind are given below. 65.. i =g= C: I or thus : ^^ 3& -g- :g— :.2^i i: :s: -&- -Cl- i IV 1^^ -tS^}- - Q'lS' ^— ^ r-^ i i N. B. in this way : i iE 9^ --^ T V — I I letting the soprano close on the fifth of the tonic triad. §24. In the second measure of Ex. 6S we find an instance of con- trary motion in the progression of the triad on the 2nd degree to that on the 5th, in order to avoid covered octaves with a siep of a whole tone between the outer parts ( soprano and bass ) , which octaves would have been produced by leading the two triads, instead of in contrary motion : N. B. The skip in all three parts is entirely correct in this case, where merely one and the same chord is transposed. a2 A MANUAL OF HARMONY. i i=id=3 ^B^ in this way : iSfe^P^ gg^g^ In the latter case the soprano ascends by a whole tone at b. Hence the covered octaves between the bass and soprano have a bad effect. In the last measure but one the three highest parts are held, while the bass skips down by an octave : -^- i ^ A progression of the highest parts is quite unnecessary in this case, as the bass in the low octave again calls for the same chord on the 5th degree. The leading at the close is such, that the soprano takes the third of the triad. Thus the pupil will perceive that the soprano is by no means obliged to close on the octave of the root of the tonic triad in every case, as many beginners wrongly suppose. The soprano may also close on the third or fifth of the triad. 68. fcgi B^: I -^-. -zd- f-- j^ — IV II v~H i I Before the pupil begins working out the exercises at No. 69, he should transpose Ex. 66 into ^b, ^, and ylt?-major, and Ex. 67 into Z>, Z», ^, and ^-major. By this means he will learn the triads of the major scale in other keys much more thoroughly than by merely writing out the View of the Chords given at No. 57 in C- major. In No. 57 the chords are only written out disconnectedly ; A MANUAL OF HARMONY. 33 in Ex. 66 and 67 he sees them as naturally inter-connected. The exercises at No. 69 are likewise to be transposed into the keys indicated. 4- Exercises. 69. ^ aa tS"- ? p Also transpose into Z>b. 3 gS I ^ Also transpose into P, Ft and Gb. 3 asa :z:^- Also transpose into ^4, B\) and ^. 3 N. B. ^ zz^: ii =t I -s*- -«'— '-Z5'— Als^ transpose into />. §25. The last exercise in No. 69, at a?, calls for a few observa- tions. At N. B. in measure 5 the leading-note must be doubled, be- cause this gives the best leading of the parts above the bass, which continues through several measures in skips of one and the same in- terval. Such an undeviating leading of the bass, to which the lead- ing of the highest parts must conform, is termed a Sequence. Ex- ercise d would therefore be written thus : Sequence - — — — ___ 69 ercise might also be worked out as follows : 69^. i IE itS: -s>- f- r^ T etc. 5 1 T- / i ^ ^ ( / ^ 1 Us 1 LJ 1 L© the pupil may finish it himself. If we were to let the soprano begin on the octave of the key-note, this exercise could not be written as a sequence conforming to the leading of the bass, on account of the covered octaves which would then occur between the outer parts ; quite apart from the fact, that the highest parts would be forced to overstep their range. 69/. m i^ b:-J=F^d= ■31- etc. Remark. In certain sequences we may, for the sake of the sequence, depart from our rule of retaining in the same parts the tones common to two chords. E. g. the following bass : Sequence ^^=^f=^ -f2- I :t might be worked out thus : 70. < i^ ^^ i =s rf^ -■&- -z^ I i A MANUAL OF HARMONY. 3& or in this way ; — ig 1 — gy ■^^^^ -&■ ^-^--i-- i or, in G-major, as follows : ^IH i a^^i= ^ i ^i— ii3rg=^: (9 g- -(S^ -t9- ^•— ^ ^ ?^ i -z^ g- CHAPTER V. The Minor Scale and its Triads. §26. Tlie minor scale most nearly related to any major scale has the same signature as the latter ; it begins on the sixth of the major scale, or, what amounts to the same thing, its key-note lies a minor third below that of its relative major. Thus a-minor is the relative minor to C-major, <^-minor to ^-major, e-minor to G- major, ^-minor to ^b-major, etc. According to the signature, the tones of both scales would therefore be just alike, and the peculiar character of the minor scale would be due simply to its beginning the same series of tones in a different place, i. e. on the 6th degree in major. 71. i W — p — is>- I This change in the arrangement of the tones forming the scale of C-major lends to the scale of a-minor, beginning on the tone a, a totally different character. The intervals between the successive 36 A MANUAL OF HARMONY. tones of this series are, from the first tone to the second a whole tone ; from the second to the third, a semitone ; from the third to the fourth, a whole tone ; the same from tlie fourth to the fifth ; from the fifth to the sixth, a semitone ; and from the sixth to the seventh, and seventh to eighth, a whole tone each. 72. i -&- IE I \ \ But as the authentic close, shown in Ex.55, can be formed only by the aid of a major dominant triad preceding the closing chord, we could employ only a plagal i WE^ -^ I close for pieces in a: IV minor keys, according to the minor scale as exhibited in Nos. 71 and 72. To make a major triad of this dominant triad, so as to obtain the authentic close in minor by its aid, we raise the 7th degree by a greater semitone. Now, through its relation as a minor second below the octave of the key-note, this tone takes on the character of a leading-note, and makes itself very sharply felt as such in the three triads of the minor scale in which it is contained.* Thus the minor scale necessary for the erection of the chords is as follows, the intervals between the several successive tones be ing indicated by figures : 73. -¥- i \ IJ I We call the above the harmonic minor scale, to distinguish it from the melodic minor scale,,in which, for the sake of melodic *The chromatic raising of the 7th tone of the minor scale must be specially in- dicated in each case where this tone occurs. To write it once for all at the head of the piece would be apt to give rise to mistakes, and would also be self-contra- dictory. Minor keys always have the same signatures as their relative major keys. A MANUAL OF HARMONY. 37 progression, the 6th and 7th degrees are raised in ascending and lowered in descending. 74. i £J S>- rs JSU-^— ^-ttffl-|g- g o- i -p— g- - g— zg- The reason for not raising chromatically the 6th degree of the harmonic- minor scale, which is used in erecting the chords, is plainly to be seen in the plagal close ; for this close could never be formed in minor with a major triad preceding the tonic triad. The progression at 75 75.' m. p* ^ I is unnatural ; that at 76 76, I i natural. §27. The fundamental triads of the minor scale are found, as in major, on the ist, 4th, and 5th degrees. Those on the ist and 4th degrees are minor. 77. i -^—a — «■—#=- w -jCI- The dominant triad becomes, through raising the 7th degree, a major triad. i V :fti:^»=fe: I It therefore is formed exactly alike in major and minor; E- G%-B is the dominant triad of both ^-major and a-minor. These 38 A MANUAL OF HARMONY. ithree fundamental triads in minor are related in just the same way z& the fundamental triads in major, as shown in Ex 34. Fundamental triads in minor. 78. i -ftt- W ^g==^ I On the remaining degrees of the minor scale the following triads are found. 79. i srSE -- a: iio III' ^ i VI viio Those on the 2nd and 7th degrees are diminished, that on the 6th .degree is major. On the 3rd degree we find a new form of chord, .a triad having a major third and an augmented fifth. P This we call the augmented triad. It is indicated by III', as was ■shown in Ex. 79. In Ex. 80 the triads of the minor scale are given in regular order. Fundamental triad of the Tonic. Minor triad. g Subordinate triads, dimin. augm. Fundamental triads, minor. major. .60. w -M- IlO III' i Subordinate triads, major. dimin. "^m w- VI vno In the minor mode there are only four independent triads ; ■namely, the three fundamental triads on the ist, 4th, and 5th de- grees, and the secondary triad on the 6th. The dissonant triads on the 2nd, 3rd, and 7th degrees are dependent ones. The greater number of dissonant triads in minor — three as compared with the 39 one in major — arises from the necessary chromatic raising of the 7th degree in minor. On account of these dependent dissonant chords, and especially of the interval of a whole tone plus a semitone be- tween the 6th and 7th degrees, difficulties arise in the interconnec- tion of the triads in minor, which we shall examine with care. Progressions between triads like those m Ex. 81 81. 4- ^- m ^^m a: lio III' iio III' 11° III' i will occur in none of our exercises, although in these cases no ob- jection to the leading of the parts can be raised.* §28. The step of an augmented second, between the 6th and 7th degrees of the minor scale, is a melodic progression not easy to take with purity and confidence. f It must therefore be carefully avoided in progressions between the chords on the 6th and 7th de- grees, and also in all other progressions where it might occur. The following progressions are altogether wrong. 82. p^ =rF^g^f=T =i ^"i ^^ a: lio V III' IV III' VI VI V li" V V VI *In strict composition the rule obtains, to prepare dissonances and resolve them to consonances. The succession of several dissonant triads, the first of which is not prepared and the second does not resolve to a consonant chord, should there- fore be avoided as transgressing the rules of strict composition. fThe difficulty is most apparent in ascending progression, when the 7th degree is to be taken as a pure and strongly accented leading-note following the 6th. Itis easier, to be sure, in descending progression, when the octave of the key-note is followed first by the 7th degree and the 6th sung next in order. But we must forbid the pupil to make use of either the ascending or the descending progression in the exercises of this text-book. 40 §29- The step of an augmented second can be avoided, between the 5th and 6th degrees, when the dominant triad is followed by that on the 6th degree, only by doubling the third of the latter. Where the triad on the 6tli degree comes first, its third should be doubled. A few examples of such progressions follow. i^ii^i^ mm^^^ a: V VI V VI VI V VI VI 4 ti^ ^^m^m ^= -^ =g= 5Jfe VI V VI V VI V VI V VI V m In case of a progression between the triads on the 2nd and 3rd degrees, which however rarely occurs, the step of an augmented second is to be avoided by contrary motion, which the stepwise pro- gression of the bass calls for at any rate. 85. < i ^ =^ -«i- etc. a: I IV 11° III' VI For progressions between the triads on the 2nd and 5th degrees, and those on the 4th and 5th, contrary motion is also to be em- ployed, although open parallel octaves could not arise in parallel motion between the 2nd and 5th degrees. A MANUAL OF HARMONY, i. 41 -^ ii3=s 86. -zi- ^^=d-li d= s=l-^3ii ^= ill ^^E=ll « f2- a; 11° V 11° V -ts> — (=- s In Ex. 86 (a) we have to depart from the rule of letting a tone common to two chords lie in the same part ; for we can not (in close harmony) let the tone £ lie, and lead ^ to G^. Progressions like this must always be avoided.* §30. As the chromatic alteration of the 7th degree in minor must be indicated in each separate case, we shall mark it, wherever contained in a chord called for by the bass, by writing the required ^•g" (tl> 8) o*" I'l) ^'^^^ ^^^ ''^^^ note, the sign thus written always re- ferring to the third above the bass note. Should it refer to some other interval from the bass — which in our next exercises can be only the fifth — we write the number of the interval over the bass note, and add to it the required chromatic sign ; when this sign is a sharp, it suffices to draw through the figure a stroke slanting up from left to right ; e. g. 87. i- ^ 5| III' III' B Although the triad in its fundamental position is not usually in- dicated in the figuring, in this case it becomes necessary to indicate •Taking the same in open harmony, B might be held in the same part; e. g I I I But for the present the pupil should work only in close hat > II I rtony, so as not to be perplexed by the difficulties of leading the parts in open harmony ; besides, we do not need the latter for our present purposes. 42 A MANUAL OF HARMONY. the fifth of the bass to be raised by a figure and sign, cr figure and stroke. As we have seen before, it may also be necessary to figure the first triad, in order to show the position of the soprano and, by implication, that of the other parts as well. We can use the single figures 3, 5, or 8, or the combinations g, f , or in the following case |. 87. ^.< i i IB Thus the figuring of the following bass calls for 3 I 88. i3 -P- III' VI 11° 1 . An arrangement of the highest parts in which the soprano takes c", the alto a', and the tenor e'. From this the leading of the highest parts can be deduced according to the rules given for the leading of the parts. 2. The sharp over the third bass note E, which has no figure, shows that the third of the bass note (in the dominant triad) is to be chromatically raised. 3. The crossed figure over the fourth bass note shows that the fifth of the augmented triad must be^J. The example is worked out below. 89., i HI --J- -^- rM. f—f< I a T5l- I III' VI IlO The pupil should transpose Ex. 89 into c-minor, ^-minor, b'^- minor, ^J-n>inor, ^-minor, yj-minor, and y-minor, that he may also become familiar with the triads of the minor scale in other keys. To this end we write out the transposed basses, wth the chromatic signs proper to each key. ^ manuai of harmony. 43 All figures ana signs written above the bass notes belong to Thorough-bass Notation. 3 8 4- sa I 9o.:i5S^ ?= 3 8 5 I EiteES 3 8 5 5Q I iSasEa -(=2- 25 -=i- 3tf ^ P=£ -s<- gfcffi: I Ei -s< 'g- gsEg :^= I ^ §31. The following bass requires, in measure 2, a progression between the triads on the 6th and 5th degrees, and in measure 5 a progression from the dominant triad to that on the 6th degree. 91. rv- T r-r — — • — - ■ ^ R i " 1 I J 1 d: I VI V Ill' I IV I ^i I VI IV 11° III' VI In measure 2 the figure and chromatic sign over the third note F might be omitted, and also the sign over the second note A in 44 A MANUAL OF HARMONY. measure 5. In both cases the chromadc raising of the 7th degree of the scale had already been indicated. We will observe, that in these exercises we follow the universal practice of letting each chromatic sign affect its note throughout its measure. Two workings-out of the bass given at 91 now follow, which the pupil should carefully study and then transpose into eb-minor and cj-minor, before undertaking to work out the basses given at Nos. 93' 94' and 95. (Comp. also App. II, p. 273 ). 92. i ^4=g4 r4=F^ d: I 5 i^ VI V III' I :,!= VI IV iio f eBj=i ^ Ei^ ii=«i n^ ^f=rT i^ ^ III' V VI • IV iio V isk- III V VI IV 11° V i # 11 VI V III? 3 m r^'~r~ It s; I :t VI IV 11° III' V VI IV iio V A MANUAL OF HARMONY. 45 Exercises. I 93. m X The position of the' first soprano note is to be retained when transposing this example into c, 3, ^l7, g%, ^jyj.andy-minor. I «4-^S^ 1= -(2- When transposing Ex. 94 into elf and (/-minor the soprano should begin on the octave of the bass, and on the fifth in the transposition into e and el?-minor. sq 95.^^gg^^Pg ^ EEiL-a Below is a view of all the triads of the major and minor scales. Triads of the Major Scale. 96. 97. 1/ -, « ■* II 1 ^~l ^ '^ f^ ■#, 1 1 ffK „ «> S % S IS II \!. ; % &t ^ /> ^ ' 11 I 11 m IV V VI Triads of tlie Minor Scale. VIlO ■ / ^11 " / J J-^ '^ J* ■ 1 f( \ #^ (V ifg r3 jtS II v^ } ^ e> BS! (^ WS; « *»^ II t^ ' ^ ^ S- ^ '=^ "f" 11° III' IV V VI VIlO. These triads differ in structure. We found major triads on the 1st, 4th, and 5th degrees in major, and on the 5th and 6th in minor ; and minor triads on the 2nd, 3rd, and 6th degrees in major, and on the 1st and 4th in minor. Diminished triads occur on the 7th degree in major and the 2nd and 7th in minor. The augmented triad is on the 3rd degree in minor. CHAPTER VI. Inversion of the Triads. §33. The reason that all the exercises heretofore given were more or less constrained, stiff, or actually forced, even when worked our quite correctly, was, on the one hand, because we worked with 46 A MANUAL OF HARMONY. triads only, and on the other, because we could use these chords only in \ht\r fundamental position, i. e. the position in which the bass always takes the root of the chord. But the bass may also take the third or fifth of the triad. The position of the chord is then no longer the fundamental one, and we term a chord thus al- tered in position an. Inverted Chord, or an Inversion. We call the two practicable inversions of the triad : a. When the bass takes the third of the triad, a chord of the sixth. b. When the bass takes the fifth of the triad, a chord of the fourth and sixth. Any triad can be used in the position of a chord of the sixth, or as chord of the fourth and sixth. These are of course no new chords, but merely different forms of one and the same chord. As we know, the fundamental position of a triad is marked by figures — 3, 5, 8, |, |, | — only in exceptional cases, e. g. at the beginning of a piece (to indicate exactly the position of the soprano or of all the parts) ; in the midst of a piece such marks have oc- curred only in the shape of a chromatic sign over the bass note for the third, and of the figure 5 with a chromatic sign for the fifth, where a chromatic alteration of these intervals (in minor) was needful. But we must mark the chord of the sixth with a figure 6, or with^g, or with a 6 and a chromatic sign below it referring to the third above the bass (in case the third requires to be altered chromatically) . For the chord of the fourth and sixth we always write 2 over the bass note. We now proceed to erect on the note C (without ^ figure, or marked with a 3, 5, 8, etc.) the triad of C in its fundamental posi- tion C- E- G. C with a 6 (or |) over it calls for the chord of the sixth of that triad, in the fundamental position of which the note C is the third. C marked | calls for the chord of the fourth and sixth of that triad, in whose fundamental position C is the fifth. ^ Fundam. pos. Chord of the sixth. Chord of the fourth and sixth. ?5 — r " ^ ~h — ^ H 98. 6 I ^ a IS. & ji C: I A MANUAL OF HARMONY. 47 Supposing this example to be in C-major, the C in the first measure gives us — as the figures under the bass indicate — the triad on the ist degree ; the C in the second measure, the chord of the sixth derived from the triad on the 6th degree ; and the C in the third measure, the chord of the fourth and sixth derived from the triad on the 4th degree. The following example show^s all three triads in all positions. 99.. y <^ II / " « « 1 '^ /* II /•^ 1 n n II v^; g s rD ■ ^ - A ■■ i) » e 1 6 1 6 s- % a* ^ 1 II T- r3 1 " \ II 1 n 1 '^ II 1 >n n II C: I I I VI VI VI IV IV IV In the chords of the sixth we intentionally neglected to double the bass note, the third of the fundamental chord ; this we shall ex- plain later. First of all, the pupil should study attentively the no- tation of the chords of the sixth in the View given below of the triads on all degrees in major and minor, and in all positions. We have intentionally doubled the bass note, the third of the funda- mental chord, only in the chords of the sixth on the 7th degree (in major and minor) . An explanation follows directly after the View. 100. r\ "■■ 1 f^ 1 /3 r3 1 " ■D V /" n , 1 S ^ ' s S=. o_ ' .* lO 1 t^ a I 6 -Sl- 6 6 4 r^ . 1^ --. ^ 1 1 P J* ir> 1 " V 1 1 r- 1 ' — s — 1 .'^ . C: I III i W- e -h- -&- IV IV 48 A MANUAL OF HARMONY. but not : N. B. =^ -19- -19- VIlO vilO VIlO vno viio viio viio viio vno i rare : better : ^ =i- - ^ I tfg ; 4tai Is: 11° 11° 11° iii: III' III' III' i eI3£ P^ -^ 6 ^ I 9^ i or thus : i ^E ^i tS^ gt I -^ VI VI VI VIlO viio viio viio §33. The previous remarks (§13, p. 15) on doubling the tones of the triad in its fundamental position also hold good, for the most part, for the inversions of the triad. The third of the major and minor triads, which characterizes the mode, being the most promi- nently felt interval of the triad, gives us a special reason for not doubling it in the chord of the sixth, because it then lies in the bass, which, as an outer part, renders any interval which it takes pecu- liarly prominent, much more so than the inner parts. Conse- quently, we double the third in the chord of the sixth only when we thereby : — A MANUAL OF HARMONY. 49 a. Obtain a smoother leading of the inner parts by holding a tone ; e. g. 101. |=fc3 |^^j JB I is quite as good as •'^Sr -h-^ ■s- 6 I ^ i C: I However, we must not forget to keep a sharp lookout for the leading of the leading-note ; thus the following progression is not to be recommended : better. rgi 102. a i i C: V b. For the same reason (progression of leading-note) we must avoid, in chords of the sixth derived from the triads on the 7th de- gfree in major and minor, doubling the root of the fundamental chord (this root being the leading-note of the key) . Hence the rule, in four-part writing, that In chords of the sixth derived from the triad on the 'jth degree either the bass note (the third of the fundamental chord), or the third above the bass note (fifth of the fundamental chord), is to be doubled ; e. g. 103. < sr- e C: vno viio vn° -| — gg — a: viio — s — VIlO -ft*'— VIlO i i 50 A MANUAL OF HARMONY. c. Besides, the third of the fundamental chord must be doubled when, in the case of two or more successive chords of the sixth, parallel fifths and octaves cannot otherwise be avoided, or when an unconstrained leading of the parts renders the doubling of the third more natural than the doubling of the root. 104. i C: I =f= VII° —js — — "S"- i I In measures 2 and 3 of Ex. 104 we have in succession the chords of the sixth on the 7th and ist degrees, and both with doubled third. The chord of the sixth derived from the triad on the 2nd degree (meas. 4) could not double its third. Hence the following rule : In two or more successive chords of the sixth, progressing by steps, the third of every second chord must generally be doubled, to avoid faulty progressions (parallel fifths and octaves). 105.- C: I =3= 4_l _J_ iaiii^iaiii^i^g -St- 6 feEj^g ^jtoi ^i^l VI Vlio I o ; I viio IV III' VI V 106. i Sequence of Chords of the Sixth. i W=^- i -jA- 4__1 -^- :iM: — -■g^- ^±^=^=d 6 6 It ¥^ C: I vii° I vno I i^ etc. i II III II III IV A MANUAL OF HARMONY, i)l i .-J= ^ etc. 9- C: IV §34. With choi'ds of the fourth and sixth it is usually best to double the bass note, i. e. the fifth in the fundamental chord ; though the fourth of the bass (root of the triad) can also be doubled. The sixth of the bass note (third in the fundamental chord) can be doubled only in very rare cases (where the leading of the parts de- mands it). 107. rarely : -G>- rarely ; / J r3 n 1 ">= ■ 1 ( / 1^ A ^ A 1 i-i ?$ n '^ II \ (c ^ X . 1 >5 55 % II I \s:t7---'^ ^ II K. 6 4 6 4 -'S- 6 4 S I 1 1 1 % f r> . ^ n ''J rj ■ II r I- ^ a n in " 11 \ If 1 — s) 1 II C:\ In the case of inversions of the triad the highest parts may be grouped above the bass at pleasure, just as Ex. 37 (§13) shows for the fundamental position of the triad. It follows, that in chords of the sixth, and of the fourth and sixth, the highest parts can assume very different positions with reference to the bass ; e. g. 108, Chord of the Sixth. Close harmony. Open harmony. -G- 6 ^s- f^z: -G- 6 si- a 6 C: I 52 A MANUAL OF HARMONY. Chord of the Fourth and Sixth. Open harmony. ^K-" "" """"J- f / ^ /S 1 ^ 55 n *' 1 1 \ 1 1 ) ^ S S ^ 1 *- i -Br e 4 6 4 a 4, 1 -Br e 4 6 4 S- I etc. 1 1 r • 1 rj 1 1 ■> * 1 VJ 1— &- 1 (S — 1 1 iS 1 L-« — f — «. 1 — g S— ^ ^^Ei f=Ff : n g ^ -s>-^ F: I VI IV II VI IV II VI V I V Below w^e give another example ; I I 112 a.. i w o -z) — g- T ■z^z -si gv l i 7^ -5-f? ^ -gi—Q- -zt- ^s*— «^ iS= i= d. 3 6 6 |ga^ ^ ^ ga =*^ ^ 6 I 6 4 t i^ 3z:d P9^ -51- 4 6 (t / =gg =1^ s E^ 4 # a i A MANUAL OF HARMONY. More Difficult Exercises. 8 8, O e s e 118 i. ^ -i^ -^ : t Also transpose into Z)b, D, £b, and E. 67 ^iia^ IS>--F- -s-^ Also transpose into F'i, F, and E. a 6 s 6 6 4 6 4 3 §^ m ^gg ^ -.^^^ K-- Also transpose into B and C. k. 3 ^ =I5= ^^ ^ j= Also transpose into B, Bb, A, Ah, and G. ^- 8 sO 6 6 Q 6 N.B. ^a^ 3 ^Ir^- :^ -&^ The tj at N. B. suffices in this case to indicate the dominant triad 5 8 with raised third. The full figuring of this last G would be J or ft" This Exercise is to be transposed into c$, d, cl7, and e. X :^^ Fl=2- Transpose into/ and ^b- '•8 # '-<5>—^ ^—(2- s-^ is ^ $:t^ ^=t Transpose into e and £-J. -S^ ^ 6 . 4 « isa P^ Transpose into ^J( and a. 58 A MANUAL OF HARMONY. e e p^f^ fii- e i=i l« ^ -z^ . S> 6) iS wards : ^^^^^^B^^^ES^^^^ <-&-■> -O- I 7 Et C; Vif r; V, i iiil e|^|^^ fc^ I 1t^i:is g ^^_g>g^ t3=^i^=^%^ E^ ~zp — P ^ !E?E 9^ i 33= 12?! ^; V, Vt a: V, V, In this natural resolution of the dominant chord of the seventh the tonic triad appears incomplete ; its fifth is lacking. In any triad or chord of the seventh the Jifth may be dropped, and some other interval doubled to replace it. In the case of triads, as Ex. 124 shows, this doubled interval may be either the root or the third; in fact, any interval of the triad may be doubled. In chords of the seventh only the root can, in the great majority of cases, be doubled in four-part composition.* •With chords of the seventh exceptional cases occur, the third, and even the seventh, being sometimes doubled in four-part writing. This may happen, in particular, when several chords of the seventh follow each other, as the next ex- ample shows. 5: ^ -r- f I 9^ c.-i i 117 Even the third may sometimes be dropped from the chord of the seventh, though very rarely. i^B I A MANUAL OF HARMONY. The chord then assumes the followingf forms : 63 125. -zyg- C.-V, -I — ggg- =sr '^ _<5Z- 7 s V7 a.-V, 3gz -.nth the root^i which is doubled in one of the higher parts, is held in the same part, thus becoming \hejlftk of the tonic triad. The resolution of the chords at 125 IS given below. 126. "T=»?Z -s"^ - V7 I -^ Such covered parallel fifths (also called hidden^ concealed., or consecutive fifths) are to be carefully avoided as incorrect pro- gressions 1. Always when, as at 131 ( a), both parts skip-to the per- fect fifth ; 2. Generally when, as at 131 (3), the higher part pro- gresses by a skip, and the lower by a step., to the perfect fifth. Other covered fifths, such as those in which the higher part progfresses by a step, and the lower by a skip, may be permitted for the present without reserve, provided that they are accompanied by no other faulty leading. For instance, the progression at 132(a) is entirely correct, whereas 132 (3 ) is utterly wrong on account of 66 A MAHOAL OF HARMONY. the covered parallel octaves in two skipping parts, which accompany the covered fifths, and by reason of parallel motion in all the parts. Compare on this head §21 and §16. 132. good. b. bad. i^^^^ §37. After all we have said, it is not a matter for surprise that, in practical four-part writing, we meet with the dominant chord of the seventh oit^n^x ■without its Jifth, and with doubled root., than with its fifth. Indeed, it is clear that the chord of the seventh, with its four tones, can better spare its fifth than the triad, which contains but three. In closing this chapter we may add, that the natural res- olution of the dominant chord of the seventh to the tonic triad is called a Cadence. When, in this resolution, a dominant chord oi the seventh on the -weak beat is followed by the tonic triad on a strongh&aX., this progression forms a Perfect Cadence. 133. i p •z:&: C: V7 --3-- 7 t m ::2i mm I a ; V7 t 7 l^i^ 1 A MANUAL OF HARMONY. 67 If we desire to let the dominant chord of the seventh follow the dominant triad, we figure the chords as follows : I. When the octave of the root of the dominant triad is to progress to the seventh by a step, with 8 7 over the bass : 134. ■--^^ T I =H G: I The line under the 7 means, that the chromatic sign con- tinues to affect the third of the chord of the seventh. Within one and the same measure, however, the line may be omitted. 2. When the fifth is to skip to the seventh, with 5 7 : 135 «. i t=^ m, T D: V V7 ^-I b: V Occasionally even the third may skip to the seventh : ^— J- 135 b. i -■o — ' — 3 7 C: V V7 -&- 11 I The following bass 3 a 57 e9i^: -S> (=- I 68 A MANUAL OF HARMONY. should therefore be worked out thus : 136. I 3 g F^p— g- -73- S- a -iS>- ^ I 6 7 C: I IV V V, II V V7 I The examples given in Appendix I, p. 247, bearing on this point, should first be analyzed and accurately figured, as No. 136 shows. Also comp. App. II, p. 275. Exercises. 7 137. g^ It G> (=- ^ ^ ^=- 3^ 12 a -& — (^— Iff- 4 6 8 7 -1=2- -(=2- - S>— <9 2- N. B. In this exercise the pupil must take care not to treat the fifth of the triad on the 7th degree as if it were the seventh in the dominant chord of the seventh, and lead the tone C downwards accordingly. The fifth of the triad ; can be led up just as well as down. ~( In the above example it is better to lead it up.) The seventh of the chord i must, however, be led downwards. <:■ 3 6 7 6 6 % 6 8 7 -t^T — yts — «'— ^— IS— ^- __| — 1 1- — t— — 1 ^- -s> — 1 ^I^^ =^4^- -«— si- M=^ -d-^^ :>-J- y. ^ Z^_| d. gw A MANUAL OP HARMONY. 69 =2^=13- -zgi- /• ^ 7 ?; 7 I EE -s*- N.B. N. B. In progressions between the triad on tiie 6tli degree in minor and the dominant chord of the seventh, the former chord must likewise double its third, to avoid incorrect progression to the dominant chord of the seventh (compare §28). In the measure before the last, the downward parallel motion in all the parts is not good : A. it is better to write the dominant chord of the seventh without its fifth : B. "?p" -^ I I The leading of the parts at B would also be preferable if the tone a were held iiv the bass; because the simultaneous downward progression of the three highest parts from a perfect to a diminished fifth has an unpleasant effect without con- trary motion in the bass. w not so good. ^== i 1^~ ^ better. EE i 70 A MANUAL OF HARMONY. s- 3 6 7 6 7 e s 6 « 7 C\' K ^ tt^ (^ 1 * 1 . 17 / k ft^ ^ \ /r> 1 ■^ h t J 1 ffl -1 -a' 1* - 1 P ' 1 1 sU fii « -~ C: V7 V7 V7 V7 V7 V7 Compare close of §35. The natural resolution of these inversions of the dominant chord of the seventh to the tonic triad is such, that the root of the original chord is held in the same fart; all the other intervals progress, in the resolution of the inversions, to the tones of the tonic triad in precisely the same manner that they did in the resolutions from the fundamental position of the dominant chord of the seventh. It follows, that the first inversion of the dominant chord of the seventh, the chord of the fifth and sixth, in which the third of the chord lies in the bass, must resolve to the fundamental position of the tonic triad. Close harmony. Open harmony. 140. ii_^^ ^=zF%--S^i =F -c^ eB iS= --^- -Z5»- 11 C: V7 ^ ^^3 ■_ -zf^ etc. eI^ The pupil will perceive, that in all these resolutions the root ( G) of the original chord is held in the same part. The bass note B of A MANUAL OF HARMONY. 73 the chord of the fifth and sixth goes to C. The seventh (i?) of the original chord progresses one step downwards ; while the fifth, Z>, may be led either a step downwards to C, or a step upwards to E. For this reason — that the fifth in the dominant chord of the seventh can be led by a step either upwards or downwards — the second inversion of that chord, the chord of the third, fourth, and sixth, admits of a double resolution. It can resolve either to the fundamental position of the tonic triad, or to the chord of the sixth derived from the latter, according as the bass is led up or down by a step. The third in the chord of the sixth derived from the tonic triad must then be doubled. Let us examine the resolutions of the chord of the third and fourth given below. 141. Close harmony. ^3^ ^ -s^- g^ C: V, y I zgztnl ^^t si- Open harmony. -A. iN J- gte'- =-1= -^ etc. l -i*- -(2- The third inversion of the dominant chord of the seventh, the chord of the second, in which the bass has the seventh of the orig- inal chord, must always resolve to the chord of the sixth derived from the tonic triad, because the seventh must be led down by ^ T4 A MANUAL OF HARMONY. Step. A few such progressions are given below. (Comp. App.II, p. 275). 142. i IS*: Mk C: V7 d. eJ~-^' ' =F= it /. N. B. m -^ --^-^ -s- etc. In minor the chord of the third, fourth, and sixth must always be figured in full with |, and the chord of the second with at least | over the bass note ; because the sixth of the former and the fourth of the latter require, as the seventh degree of the minor scale, a sign that they are chromatically raised. Consequently, though formed exactly alike in major and minor both in its fundamental position and its inversions, the dominant chord of the seventh requires a more detailed figuring in minor, as we have already seen in its fun- damental position. Example 143, on the dominant chord of the seventh and its inversions in minor, will furnish a sufficient illus- tration. 143. i w ^ a: V7 n- :iii ±. EE!i ise :fe .; V, -SL-a 9.43. ell t" N. B. In this case the leading-note, even though in an inner part, can skip down- wards, because parallel fifths do not arise from this leading. A MANUAL OF HARMONY. 75 i Egl ~ys?~ "SJ- X g%- V7 V, In the following exercises, the triad is also specially indicated by 3 or g whenever a second chord follows to the same bass note ; thus the figures 3 2 side by side call for the triad of the bass note and the chord of the second on the same note ; 3 f or 5 | for triad, and chord of the third and fourth ; 6 f for the chord of the sixth followed by that of the fifth and sixth ; as shown in Ex. 144. 144. i ^i: 3 i=i= C: IV ^= ^! -#- IV IV ^^ ^ -SK'- ^=r='=7=f= -(2- 6 6 5 etc. V7 Before working out the exercises, the examples in Appendix I, p. 348, bearing on this subject should be carefully analyzed, and accu- rately figured both above and below the bass ; the same obtains of all succeeding exercises. 76 145 A MANUAL OF HARMONY. Exercises. "■ 3 8 e 626 326 ' ia^ t=|: e S , 3 6 ■S 1=- -fi- e 8 7 4, 6- 15EE^ 3 6 6 ^^ hS2- s ■« g a) -«- 6 6 4 7 8 6 6 3 3 6 I^ifc to^^^^^tf^^ rf. l ^fegfeS ^ -B^ — ^ ■^2-©- 6 e 3 e f t 6 3 3 3 6 l7 r^* h , 1 1 • 1., 17 k , , 1 1 ^ U^uP £> *? 1 f* i J e> 1 P 17 — ' '•^ ^ r?* 1 g^ 3 3 6 4 8 7 ^ <= «> (Z- -JZ g-SS. /■ I 3 e j-^j— ^- 7 6 (t ^5*i3Ei ■ z^— 'g— Hg— z;!- ^ it=tis -r- il ^1 6 ' 1 7 6 % (2. r^ (^ 1 1 • 1.. / » ^ ^ r^ ! !^ ('■' -" ^ 1 > U I / ig' c f.^ '^ /S J O 1 L| — _ 1 >s. f 6 t 6 6 5 »,- ^^fE^^=^ -g^'g A MANUAL OF HARMONY. 11 ^S s i T. a I ^ (2 <9- -e>- ^ '— pi I g l ^^ 5 fx e r i ^ e ^I t=^ ffi^ g £j - I" §11 5 7 a - ga^g P ^ ' ^ >3 II If ^ ^ in 1 Ks) g n II C: I7 IV7 as chords of the seventh with minoi triad and minor seventh, on the second, third, and sixth degrees of the scale : i 27~ C: 1I7 I 11I7 VI7 and as the chord of the seventh with diminished triad and minor seventh on the seventh degree : '^ C: vn07 We may observe here, that major triads with a minor seventh will always be dominant chords of the seventh ; e. g. :1s '■^- ^ I 147. ^E F: V7 G: V7 A: V7 B\,: V7 C: V7 D: V7 E: V7 The natural resolution of the secondary chords of the seventh in major is effected in all cases — excepting that on the 7th degree, which admits of a double resolution — in precisely the same way as that of the dominant chord of the seventh. The root skips up- ward by a fourth or downward by a fifth ; the seventh, whether major or minor, progresses downward by a step. The third goes up a step, in case it is not preferable to let it skip down a third in opposition to the ascending bass ; the fifth, in the secondary chords of the seventh on the ist, 2nd, 3rd, 4th, and 6th degrees, may progress in resolving either a step downwards or a step up- wards, at pleasure. It is only in the resolution of the secondary chord of the seventh on the 7th degree to the tonic triad, from the A MANUAL OF HARMONY. 79 fundamental position, that the fifth must always be led downward a step. All these natural resolutions of secondary chords of the seventh are called cadence-like resolutions. To clearly illustrate the above we append a View of the secondary chords of the seventh in major, with their cadence-like (natural) resolutions. 148. good. IIE^^^ ^= IV IV IV IV fifth omitted and root doubled. bad. ,S»2- bad. e I e^^eeI^^I^I: ==l ^ -- — I ^^ =4 — — T ■ Bin ■ ^ ^i *■ 7 I I ±^ -a- IV IV IV I7 IV 149., good. less good. not good. bad. ^1 -fS"- C: \l^ V "7 1^^ 117 V i bad. -S'-' Li2_ bad. tolerably good. good. -sz i -g— g= -■gy- -zr ~sr- ^ i 1I7 V -19- 117 V 117 V 1I7 V 80 A MANUAL OF HARMONY. good. -6L- J _, ^ 1 1 1 ^ ^ 1 150, -iS>- ^^ -ffl- I C: 11I7 VI 11I7 VI 1117 VI O- III7 VI ^m III7 VI less good. bad. very bad. i^ ^- — 1» — » — ' ' — 7s — ^ — ' — zj'^'*^ — ' — -o — e— " tr~ ^; •^ If: I l-^^--,^l=g ^ C5,-! 5»i: le III7 VI 151.< tolerably good, but rare. rare. bad. tolerably goo -g?-^ ■^- 7 — g — C- IV7 viio ^ F^T=P ^3 IV7 viio IV7 vno IV7 —s» — VII° — g — IV, viiO I None of the resolutions in 151 are good, on account of the doubled leading-note in the triad. A cadence-like resolution of this chord of the seventh on the fourth degree to the triad on the seventh degree occurs but seldom, and always has a rather unpleasant effect. Any such resolution necessitates a doubling of the lead- ing-note in the triad on the fourth degree ; moreover, the bass can be led only downward, because the skip upward from Fio B embraces the interval of a so-called Tritone, i.e. an interval containing three whole tones. [The author terms the interval between the fourth and seventh degrees, in either ■direction, a tritone. TV.'j Note-I Such a tritone between two different chords is to be avoided in ascending progression, when it forms an augmented fourth; because all augmented intervals in upward progression are inappro- priate to the strict style of vocal composition, being hard to sing correctly, and not properly vocal. On the other hand, it is entirely correct within one and the same chord in either direction; it may likewise be employed without hesitation in downward progression, even when the chord changes, whether in the shape oi a.a augmented /burth or diminished fifth. A few examples follow, in which its employment both within a chord, and between two different chords, is entirely allowable and correct. A MANUAL OF HARMONY. 81 TJ z? ^ ■ ^ * -fZ- J-+.-J -ffl. i^i^i^i ^ 152. 7 — -(S- 7b E i =^F pa j^a=^ r^ 153. C; V Vy good. V V, V, — II V, II Vyj^-III V, -«»=- 7 C: w-j II VI7 II bad. VI7 II I -2p- I is: ^^ VI7 II VI7 II VI7 II Below are cadence-like resolutions of the chord of the seventh on the 7th degree, which are seldom employed. to be used not to be used. 154. VHO7 III VIIO7 III VIIO7 III VII°7 III VII°7 III VII°7 III Another and far more frequent resolution of this chord is that leading to the triad on the ist degree. It is based on the natural tendency of the leading-note, the root of the chord of the seventh on the 7th degreej towards the octave of the tonic. This resolution, however, is dependent on various conditions. When the root as- cends a semitone to the key-note of the scale, the seventh goes down a step, pro '5'— - g — H ' '" which case the third of the chord of the 82 A MANUAL OF HARMONY. seventh can progress a step upwards to the third of the tonic triad, 7U ca -^ — ; but the third can also be led down a step, in case the ^ -&— -1— ° \^ seventh is not a fifth above it, but a fourth below it When the interval between third and seventh is that of a fifth, it is impossible to lead the third downwards, on account of the parallel The fifth of the chord of the fifths then arising seventh must always be led down a step to the third of the tonic triad. It cannot progress upwards, because the interval of a di- minished fifth subsisting between it and the root of the chord of the seventh forbids their progression to the perfect fifth of the tonic (Compare §23). The resolutions of the chord triad of the seventh on the 7th degree to the tonic triad may therefore be exhibited as follows : 155. i Close harmony. Open harmony. C: vii°7 I vno„ VI1O7 VI1O7 i i IE I V11O7 V11O7 vn07 All these resolutions are good, and often occur in practice. As a general thing, however, the employment of the secondary chords of the seventh, more particularly in the cadence-like resolutions to triads shown above, is very much rarer than that of the dominant chord of the seventh. We shall meet most frequently with the sec- ondary chords of the seventh on the 2nd and 7th degrees, — the latter chord with the resolution to the tonic triad. Still, in the exer- cises on these chords, we shall now and then introduce its cadence- like resolution to the triad on the 3rd degree. A MANUAL OF HARMONY. 83 §40. As most sevenths, especially the major ones, are sharply dissonant intervals, they require not only resolution, but prepa- ration. We say that a tone is prepared, when it is present in the same part of the preceding chord as a tone proper to that chord. This preparation must be at least as long as the following dis- sonance. The preparing tone may, however, be longer than the dissonant tone which it prepares ; it occurs very rarely that a dis- sonance is properly prepared by a tone of shorter duration than itself. good. not good. 4- =S; ^ 156. ^1 i*= 4- -^ Zt3t ^S r + C: I i ^m ^ i 117 V I 1I7 V I 1 1I7 For preparing a seventh, or any other dissonance, any interval of a triad or chord of the seventh will serve. The seventh can, therefore, although itself a dissonance, serve in its turn as a prepa ration for a new dissonance,* when it has itself been prepared. We connect the preparing note and the dissonance by a tie, as shown in the foregoing example. A preparing note can therefore always be tied to a note of equal value J <=) ; or to one of shorter duration than itself o J, J J ; but with less propriety to one of longer duration J eJ, J <=>. 157. i 3 etc. 9^ C: V "7 IV * For instance, either a major or minor seventh may be employed to prepare a suspension : ^ 1 Efc ■^S- -23- ■^^^ lS>- 6 QSI ■&- Efczfi G: I IV7 V7 c: I iiff: vn°7 «4 A MANUAL OF HARMONY. The preparation of a seventh, or of any other dissonance, may be effected on any beat ; on a strong beat quite as well as on a weak one. Preparation on a strong beat. 158. 159. i :Si "^ §3 -Sr- 7 PpB i C- V I7 IV VI1O7 III VI7 II Preparation on a weak beat. ^= -^- :Si -fii- -Z5l- 3F ^ §3 -fS2- :^ -^ C: I "7 11I7 IV 1I7 -^- I The seventh of the dominant chord of the seventh may enter by a stef without preparation. 160. i ^^ C: VI Ei W^=^- -f-- "Z?- "Z?" -si- sr I It may enter similarly by a skip: I . When the seventh is preceded by some other interval 0/ the dominant triad, as the octave, so that the unprepared skip- ping seventh merely amplifies the triad, as it were, by making it a full chord of the seventh : 161. I =E 15^^^ f^- C: V V7 -4- J- -27- V V7 I I A MANUAL OF HARMONY. 8» 2. When the root of the dominant chord of the seventh is prepared by being present in any other fart: ^ d^-L-,- j rl=- 162., -zf ^m ^ -4S. — e>- C: I V, I V, I V, idt A i 3. When progressing in contrary motion to the bass.' 163. < Ml S ^ ^^ C: II V7 ^^ I 7 1 =^ t=r: IV v. i The seventh of the chord of the seventh on the seventh degree requires no preparation, and may enter freely. 164. ih d=-j= C: I VI1O7 4 -<2- IS -J- -za- =3= VIlO, -is*- i i The figuring of the secondary chords of the seventh with Roman numerals to which an Arabic figure 7 's added, may be learned from the foregoing exercises. (Also comp. App. I, p. 250). 86 165. A MANUAL OF HARMONY. Exercises. 6 a e 7 s 7 ^^ ■!*- :P^^P=P -gj- 6 7 7 i 7 6 8 7 ^^ 7tT -(= jS> 1- ^5 ^^ — j 1— ^•«tt(' o— i 7i- -F — -^ -^ T^- -«) sJ- -^ "i — h ~*^ — - ■■■ A LsL-^L. 1 d. 3 6 7 §a Ej ^it i g ^ -T5l- ■;=>- -!— SL /• 12=21 3 6 7 ^^g^g :f= g 6 8 7 i CHAPTER X. Interconnection of the Ciiords of the Seventh in IVIajor in their Fundamental Position; Inversions of these Chords, and their Interconnections. §41. We have already obsei-ved, that cadence-like resolutions of the secondary chords of the seventh to triads seldom occur. Such progressions are often somewhat stiff. The effect is much smoother when several successive chords of the seventh are written in cadence* A MANUAL OF HARMONY 87 like progression, i. e. when each chord of the seventh resolves to another chord of the seventh on the degree a fourth above it or a fifth below it. Where the resolution of the first chord of the seventh to the second is effected according to the familiar rule, that the seventh is to be led downwards, we simply have to let the third of the first chord lie, this giving us the preparation of the seventh in the second chord. When several chords of the seventh follow each other in such cadence-like progression, a sequence of chords of the seventh arises, in which the fifth of every other chord will be dropped. 166 a. i Vl s C: I -zjs- -Tljr- IV7 VIIO7 III7 VI7 II7 I or, with the same chords. 166 ^. C: I r^J-rJ J sr- g IV7 VIIO7 III7 Vl7 II7 I I In Ex. 166 a the first chord of the seventh in each measure appears complete with its fifth, while in the second chord the fifth is dropped ; the leading of the parts at 166 b gives the same series of chords, but here the first chord of the seventh in each measure is incomplete (without a fifth), while the second chord is complete. In either case the third of one chord of the seventh was always the preparing tone for the seventh of the next chord, the third of this latter then preparing the seventh of the next chord, etc. The cadence-like progressions of these chords, whether with_triads or chords of the seventh, become far more diversified by the em- ployment of the inversions of the secondary chords of the seventh. Like the dominant chord of the seventh, each of these chords may be written in three inversions : As a chord of the fifth and sixth, of 88 A MANUAL OF HARMONY. the third and fourth, or chord of the second. These inversions are formed in the same way as those of the dominant chord of the seventh, the bass taking, in the chord of the fifth and sixth, the third of the fundamental chord ; in the chord of the third and fourth, its fifth ; and in the chord of the second, its seventh. 167. C: I, 1I7 -TT 1 / 1^ P " n l(\ % g J r* n V^) 2 >3 7 I t a <3 7 % r-v. <-J P )• /5 ^ « "7 EE St-_=gz ^ etc. 1I7 1117 11I7 III7 III7 The cadence-like resolutions of these inversions, whether effected to the triad or to the chord of the seventh either a fourth higher or a fifth lower, will in every case yield either chord named complete with all its intervals. 168. Cadence-like resolutions of the inversions to the triad. ^-> -e- ^&- -e>- -^ -Si- ^ -^ ^^m^^^^^^m. C: I7 IV I7 IV I7 IV I7 IV IV I A MANUAL OF HARMONY. 89 Cadence-like resolutions of the inversions to the chord of the seventh. 169. < -251- 3 6 • =f= -■g — X 2^Sr 1 ^ <2- C: 1I7 117 117 (For the following Exercises comp. App. I, p. 251, &nd App. II, p. 276.) Exercises. 170.^3 -^- S '^^ e 5 2 f 2 a 6 S3 s 1^^ -z^—^ gg^3 7 7 7 7 ]?:& ^ EO ^= -?=)- ^^ ss I ^ b'M ^ r -iS'— N.B. N. B. The three highest parts may be held to the descending bass of this mea'ure. ^ e e 53 6 5 ~a—\—is>- 6 6 8 7 7 7 7 -Zp—'—i9- -si-'S'- /• S 6_ 3S^g'— 1=±= =^r:5-.^: SS a 777 6 6 4 6 6 4 3 48 7 1=^ 6 3 6 4 S -fS— |S5- tfL-=t -&-—^- 5 S -«- 6 S g^ii 36 677 77 7777 ^ fer= -f=- ?^ I 90 A MANUAL OF HARMONY. CHAPTER XI. The Secondary Chords of the Seventh in Minor, and Their Inversions. §42. Tlie most important and most frequently employed secon- dary chords of the seventh in minor are those on the 2nd and 7th degrees. Chords of the seventh can, to be sure, be erected on the other degrees of the scale, but they can seldom be used in cadence- like resolutions. On examining the following group of secondary chords of the seventh in minor 171. i w^. ^E "ST Jil sr iiiV i 1V7 VI, VI lO- we find three new forms of these chords, namely, a viinor triad with major seventh on the ist degree, an augmented triad with major seventh on the 3rd degree, and a diminished triad with di- minished seventh on the 7th degree. The chord on the ist degree is not adapted for resolution according to the rules we have hitherto learned ; its seventh ^, the leading- note of the scale, cannot be led downward by the step of an aug- mented second. For this reason we shall omit this chord in our present exercises.* The chord of the seventh on the 2nd degree takes a cadence-like resolution to the dominant triad or, with the third held, to the dom- inant chord of the seventh. In these resolutions the fifth of the chord of the seventh on the 2nd degree must always be led down- wards, and the upward step of an augmented second avoided ; e.g. m \ 1^ 7 -19- T -fi&- i ^^E^E^^^m *We shall return to the secondary chord of the seventh on the ist degree in minor when treating of the free resolutions of the chords of the seventh. For it admits of a cadence-like progression, although not with a descending seventh, to the triad on the 4th degree both in its fundamental position and as a chord of the sixth, as well as of various other non-cadenced progressions; in modulatory reso lutions its seventh may also be led down to G or F% (compare Chapter XIII §46, Ex, 199 and 200.I A MANUAL OF HARMONY. 91 Jti 172., -^- isi -Ml -Ml -6t- 7 -^ Ml -t- 6 -f--^^ -^ a: I7 IV7 IV I7 IV7 n°7 W^^ Mr- igi 3^ -:#-- -iS^ -iS'- VI, VI i II7 The chord of che seventh on the 3rd degree is also little used. It must be resolved to the triad on the 6th degree in such a manner that its fifth g^ (the leading-note) always progresses upward. 173. g^=l EEI^ -&- a: III'7 VI Iir, VI III', VI III'7 VI li^^ "^ ^I --gr- ift^ ^i: HI', VI III'. VI III't VI A cadence-like connection of the chord of the seventh on the 4th degree with the diminished triad on the 7th degree is impracticable 92 A MANUAL OF HARMONY. on account of the constrained and incorrect leading of the parts necessitated thereby. 174. a: IV7 viio On the other hand, a cadence-like resolution of this chord of the seventh to that on the 7th degree may be effected by leading the bass down by a skip of a diminished fifth. An upward ^ip in the bass of an augmented fourth would give us a tritone in upward pro- gression (comp. §39), and must consequently be avoided. The pro- gressions between these two chords are easiest, when the fifth of the chord of the seventh on the 4th degree is omitted. 175. i -^ W=-w- -^^ r 9± P i a: IV7 vil° H^PI ^~ IV7 VII07 IV7 VII07 ^w- VII07 Hi m t- I :& r etc. ^ -e>- ^ =S3= V11O7 -pi- V11O7 1V7 VHO7 1V7 1V7 Carefully avoid doubling the leading-note in the chord of the seventh on the yth degree. — The inversions of both chords are also adapted for interconnection. 176. E^ 3a?! I a: IV7 VI1O7 1V7 V11O7 ^ V11O7 A MANUAL OF HARMONY. 93 A cadence-like progression between the chord of the seventh on the 6th degree and the triad on the 2nd degree is possible, but of rare occurrence ; the bass (in order to avoid the tritone) can onlj skip down by a diminished fifth. Nevertheless, the progression is more easily effected in minor than that of the same chords in major (4th and 7th degrees). For in minor the root of the diminished triad on the 2nd degree is not the leading-note of the scale, and therefore can be doubled (comp. §39, Ex. 151.) 177 i I 7 r J==J: -ia_ ■S- _ — zl a I iv etc. gigiSi | Eg^=|i^ EgEJ iEgg|;BE | a: VI7 11° VI7 lio VI7 11° VI7 11° VI7 iio VI7 11° We more frequently meet with progressions between the chord of the seventh on the 6th degree and that on the 2nd. They are effected in minor, both in the fundamental position and in the in- versions, precisely the same as with the similar chords on the 4th and 7th degrees in major. 178. i IE SE^l i =P ^liill hF4=^.- ig g= l ^^ ^ It -&- etc. ^^^m VI7 1107 VI7 11O7 VI7 1107 VI7 1107 VI7 1107 §43. The most frequently employed and most important of the secondary chords of the seventh in minor is that on the 7th degree, called The Diminished Chord of the Seventh. becau-se it has, in addition to a diminished triad, a diminished seventh (reckoning from the root) . It can in no case progress in 94 A MANUAL OF HARMONY. cadence-like resolution to the triad or chord of the seventh on the 3rd degree. Progressions like the following i79.< i ■»■ ^ X =^ i r H^ Sg— g — s^- iSe: J- -S- i\ '-t^ ^^^m a: vu°T IIi; viiOt VI1O7 III' VI1O7 vii°-j III' viio^ can never be regarded as resolutions of the chord of the seventh on the 7th degree to the augmented triad on the 3rd degree.* A reso- lution to this triad in its fundamental position is impracticable, on account of the bad leading of the parts invariab^«' resulting. 180. i s d=E^: « m I ^^ IS ■^ 7 -X ^ VI1O7 III' VI1O7 III' vno^ III' The ascending Skip of a diminished fourth p@ ^^ ^-I is to be prohibited, as an unvocal interval, as strictly as the ascending tri- tone and the step of an augmented second ; whereas in descending, the skip of a diminished fourth is always alloivable and of good effect. Even within the same chord it can hardly be sung in as cending progression. S -zi- -- B The natural resolution of the chord of the seventh on the 7th de- gree in minor can lead only to the triad on the ist degree, exactly as in major. (Comp. Ex. 155, §39). Its resolution is effected pre- •Further on we shall meet with these progressions under the name of accidental chord-formations (passing chords). A MANUAL OF HARMONY. 95 cisely as in Ex. 155. Its root (the leading-tone of the scale) pro- gresses upwards by a semitone, its seventh downwards, its third ascends a step when it forms a diminished fifth with the seventh ^ gg— "^ 1 ^ but can also be led downwards when it forms an augmented fourth with the seventh i^ The fifth of the diminished chord of the seventh must always be led downwards (for reasons, comp. §39 and §23). The resolution of the chord of the seventh on the 7th degree in minor is never in cadence-form. (Comp. Ex. 179, and 180, 181 and 182). The diminished seventh of the chord of the seventh on the 7th degree in minor requires no preparation ; the chord can always enter freely. 181. g IE 'jSZ j2- — s— -e- IJSZ -i*- I We hardly need remark, that a resolution of the diminished chord of the seventh to the chord of the seventh on the ist degree is im- possible in minor, although the resolution to the triad on the ist degree is so natural. A few progressions of the diminished chord of the seventh to the triad on the ist degree now follow. 182. < i p=^ i ^ 1 ^ -^- a: vvPr, I VI1O7 VIlOv :J^ V11O7 r =l=Ji^^^B= s :^ ^t: -ftsJ •^ ^ etc. -1=- VIlO, VIlO, VIlO- VIlO, 96 A MANUAL OF HARMONY. The seventh of the chord of the seventh on the 2nd degree in minor may also enter without preparation, because it is combined with a diminished triad. When two or three chords of the seventh occur in succession, in minor, and in \h& fundamental position., the fifth of every other chord must be dropped. 183. i w -A 9^ d= 4- a: IV7 VI1O7 VI, 11°, VI, 11O7 I When a chord of the seventh in the fundamental position is fol* Itwed by the inversion of another, or two or more inversions occui iti succession, the complete chords can always be given. 184. < m. -i W- ^t -g- E^ -SiS- ^ a: Vio, 11, IV7 VH°7 VI7 11O7 (For the following Exercises com. App. I, p. 252, and App. II, p. 276.) 185.gi3^ -4^- Exercises. 6 7 =1= -Si- =13- -zJ — - ^—t 7 7 t ^ fe& llE e x 5 3 6 ?^ 6 4 3 .JS— EE3 -(=2- A MANUAL OF HARMONY. 97 6 3 S 6Q 6 S I" 6 % I ig zta -19^^(9- ^^Fg -^g i»= ~z^~l~zy 8 12 t» a^ SI ./• s 3i^i^ 8 P 5^ =fl^ =F= -g — z^ - gl— 'g- /■ 3 6 ^ f _3t! 1 t" 6 7 7 6 i P f fn' '(O ^ • 1.. 17 U /» 1 ■ r P* ^ P^ ^ wJ'. i 1 1 * . PJJ.^ AJ 6X 3r a 7 5 6 8 7 5 X - -^:g SAa ?5 — «■- -«2 «? -/5 1 -^ — 1 -:^ ^tt g »'j ■ ^ -(2 1 s( — — 1 o • 1 +*■ ^ Lj €i 1 Lfil — a 1 1 i3s3t « a f a 7 P»S 2=S :^ N.B. I t a I §a^=^^ Ei -1©-=- i-g^- In the exercise before the last we have, at N. B., the chord of the seventh oti the 3rd degree with a cadence-lilie resolution to the triad on the 6th degree. The inversions of this chord of the seventh prove to be of little use, and least of all with a cadence-like reso- lution. Progressions like the following i iii %- d— ^ ^ i 'Sffc * c%: I "III'. VI I 98 A MANUAL OF HARMONY. are constrained and unnatural. The first inversion of this chord is, however, more manageable, as the following example shows. hy-f* ^jy — 'W l-l w^ -| — ^ i|i_ aa 1 %j i i r f - S' \ ^^^- (2 1— 1 a: I IV7 vii°7 III'y VI The opening measures of Ex. 184 {h) may be worked out as follows : i i a =g 1 (^ i :t ^J: I V III7 VI CHAPTER XII. Non-Cadenced Progressions between the Chords of the Seventh and Chords On other Degrees. §44. In all the preceding exercises and examples we have always resolved the chords of the seventh, as fundamentals or inversions, to chords situated a fourth above or a fifth below them. To this progression, the most natural one in principle, we now add freer and non-cadenced resolutions. Such progressions are called Deceptive Cadences, and can assume the most various forms : I . By combining chords of the seventh with chords be- longing' to the same key., but on different degrees from those which form the cadence-like progressions ; A MANUAL OF HARMONY. m 2. By connecting chords of the seventh in one key with chords belonging to other keys, and on different degrees. In the latter case we obtain a Modulation. A modulation is brought about by introducing into a piece a chord foreign to the key till then predominant, i. e. a chord belonging to' another key. 186. i IE » ^ C: I r ife IV V7 ^- V7 r F: V7 -^ If: I Ej -^ r 6 5 IS ■V- ^ £^^ no. VI IV7 C: I 1I7 Thus Ex. 186 passes into _^-minor in the third measure, ^-major in the fourth, and a-minor in the fifth, not returning to C-major till the seventh measure. Modulating and non-modulating deceptive cadences may be formed in three ways : a. With the regular downward progression of the sev- enth ; b. With the seventh held (or enharmonically changed fot the augmented sixth*). c. With the seventh ascending by a step. We commence our examination of the deceptive cadences with •This change of the seventh for the augmented sixth is in itself, in point of fact, •n upward progression of the seventh, because the minor seventh forms a narrower interval with the root than does the augmented sixth. 100 A MANUAL OF HAHMONY. the dominant chord of the seventh, showing the pupil some pro- gressions of this chord to triads and chords of the seventh on other degrees and in other keys ; at first with the regular downward leading of the seventh. (Comp. App. II, p. 277). T87,< N.B. C: V7 VI =J^ 7 -19- j -.g=:ffg = pzg i^__^ V7 a ; V C: V, a: V7 C: V, F: V, 7 7 7l) sb 3b 7 6 S b sb b 1^ C; V7'~' - .<^ — I — l g-'~'^a; s .'-^ - f — I — a,'-^o — :l -^ -<9- 7 6 iz?z ~e> zy 7 % -TO Z>- 6 h- 7 u6 -^- I fl< g^ I &> ig 1— ^ — 91S .■ -^ C; V7 IV C;V7 1I7 C.-V^ 11 C-.N^f.l C; V7 ' — 'vg - =5i= S 4b 6b =J^ -jS #22- i C- V7 a.-vn07 C: V7 Gb: V7 C: Y^ Ff.^^ C: V7 /■ 117 -<»- 3i=lgi =«g= :sg^§^5-_: 6b t t g 7b 1^ b =1^ C- V7 j^- 1I7 C: V7 £b; V7 C- V7 d: III' C." V7 Eh: 117 102 A MANUAL OF HARMONY. , Enharmonic. N.B. ^^- P^ ^^ -^=^^- zs>s^ etc. ik: =03= C: V7 eh- ll^-j C: V7 Bh: ^^i C : V7 a: 11O7 C: Yj eb: I1O7 The last chord, marked N. B., is a new chord for the pupil ; it will be treated among the altered chords as the augmented chord of the third and fourth. Progressions between the dominant chord of the Seventh and chords on other degrees and in other keys, in which the seventh ascends : a89. i 4: ^S^. not good. — #1 — #-*«^4- =fli= Sz C; V7 ^.- viio C- V7 E: V7 C; V7 £) : I C; V7 Z»b:V7 i d: ^: etc. W?Z w ff-g- ifcg ?5= C- V7 :; lio. C: V7 C: V7 c IV7 The chords to whicli the dominant chord of the seventh progresses jn the last two measures, will also be treated of in the chapter on "The altered chords." §45 . The seventh must be led upivards, except in the rarest cases, when, upon the resolution of the chord of the seventh, another in- terval of that chord takes, in descending progression, the tone to which the seventh properly and naturally resolves. This case may occur even in the usual cadence-like resolution of the chord of the A MANUAL OF HARMONY. 103 seventh on the fifth degree to the tonic triad. Progressions like the following ^srs;; --^^t 190. < e I fg^ ^ --^-r. C: V, are strictly prohibited under all circumstances ; because the covered octaves then formed must be considered quite as incorrect in the strict style as open octaves, although the higher part progresses only a semitone. This rule holds good for all parts ; consequently, the progressions at 190, and those following at 191, should always be avoided as bad and incorrect, whether they appear as cadence-like or other resolutions of any chord of the seventh*. 191. i — °^i — ^^1 C: V, 1I7 V a : V7 VI * As one of the few and very rare exceptions to this rule we append the following progression : -§^^' fi2- '^^^ 192. a 5 I I C: V7 a: V7 Here the bass B progresses, not to the third, but to the root E of the second chord ; the covered octaves are likewise softened by the contrary motion of the tenor and the holding of the alto. 104 A MANUAL OF HARMONY. When an interval of the chord of the seventh takes, in ascending progression, the tone to which the seventh properly resolves, an up- ward progression of the seventh is also desirable in many cases ; e. g. 193 a. \ ^ !=& 6 i C.I V7 I G: I But Ex. 193 ^ cannot be approved of, because the seventh and root of the chord of the seventh lie too close together. 193 b. We must mention, finally, that the dominant seventh may also be /ed down by a skip, e. g. in the cadence-like resolution V-I. -Sr ^^ C: V, This resolution has a better effect when the fifth of the chord of the seventh is chromatically raised. (Compare §49.) I "^»^- -6t- C: V, A MANUAL OF HARMONY. 105 The same can also occur in modulatory phrases ; e. g. 193 c. i ir-TJ-^ ZS2 : J-J — 4 m sb g^ 7b -e©-^ ?^ C; I V, F:Vt C;V7 (/.-viio. I I To illustrate the rule given at the beginning of §45, we add a few non-cadenced progressions of the dominant chord of the seventh to chords in other keys and on other degrees. 104. C: y^ F:V^ C: V7 /; V11O7 C.-V^ Ah-N^ C.-Y^ *b: ii°7 not to be recommended. C: V7 ib: vn07 C: V7 Z»|,: V7 C: V7 D: V7 The progressions of the dominant chord of the seventh to other chords, as given in §§44 and 45, will give the pupil new ideas about chord-progressions at which we have merely hinted. And in the same way that new creations have been and will be continually sup- plied by gifted artists, the supply of new chord progressions will never fail. In the following exercises we shall by no means exhaust the pro- gressions of the dominant chord of the seventh explained in the 106 A MANUAL OF HARMONY. above. A change of key within an exercise will be marked, fot the present, by large Roman numerals for major and small ones for minor. In all later exercises, however, the pupil himself should note the progress of the modulation in this manner beneath the bass. (Compare also App. I, p. 254). Exercises. Sgi ^ £ 195. ? Id C:\ V7 l\EV^^C•.N^ VI 1I7 V7 a.-Vy VI C/viiO^iiiVtI :i«Et ife: 1^ B\,: I IV V7 g: V7 I B^: 1I7 v^ , " i—. 7 6 I % f a i f ^^^t'-BT^ (^ :? IS. h" j^tfi^" 1'* ffr^ ^ w ^yy. 1 1 ' HiC i "^ fli^ \ " t? [ j 1 .41,: I IV V7 IV I ^b: V7 — r ^b: I ^; I IV V7yS: V7 *; V7 g^-"^ 711 7n ES ^=^ •si- ^=- ■^ -^ fj: vii°7 I b: VI1O7 I ^.-I S el ^■553 -(2— »- 70 -Tb- 4 3 ^ ^- * a 4 8 7 - Si— (g- JS; I V7f(: V7 IZ>; V7 5 7 " tt— K^ n ^^i—s> — (=2— — 2 — ffi^_ » JK? ■ +te -'^W^ j i 1 -A T^ d:x V7 B\):Y-jg:Y-j id:Y^ Bh-.ui'V-j g:\-j \ d: vno^. At N. B. the leading-tone ct must be led downward to f B. i t 7 ''■ B f I « t" -Ci^ r^ Hr-Th 1 — —\ — ^ — -(2 — « — -5^_sl —S> 9hF si— ^^ — r — " & ^ II°7 V V7 I g: I V7 III'7 VI <:;V V7 7b , sb b 7b 4 4 « ^y=^g :^: =^-=1 =5^ 13: :^= :t: /.■ vii°7 I - 7b -i>- =Si= -i.- 9^ =S^ ipn =&»- a; I7 B\i: V7 o; I7 ,?.■ vil°7 a; I7 G; V7 VI7 =8^ =S^ iS?r etc. ^- ibgi =fl2= 3 .- I7 ^-Z 11° a; I7 d: V a; VI I7 G;viiO In modulatory progressions, however, we are also in a position to lead the seventh of the above chord downward by a step. (See Note, §42, Ch. xi). i The seventh descends a semitone. 199. 3fc-& :g.-gtg.- 7ll ^i-^^S^ iSi=Bl -ffg— gg -£- -i^ I" - •■ -s>-^ I Progressions of the chord of the seventh on the ist degree in minor can also be effected when the seventh is held. 204. i -Ml -ftg— a: I7 B: VI1O7 Ml ^= B VIlO a : I7 ■iSr i Si^g^ -Z5Z7- te^- S^ -i.- S^ « etc. a:ij (/; IV a; I7 d : ll°7 A MANUAL OF HARMONY. 113 §47. Should many of these progressions sound harsh and strange, it must not be forgotten that they are given here out of all connec- tion with any preceding or following chords. They can all be used ; their effect in each individual case will depend on how the _firsi chord is prepared and how the second progresses. After these practical illustrations of the manifold progressions which may be effected with the secondary chord of the seventh on the ist degree in minor, the least used and hardest to manage of all chords of its class, we shall close this chapter with a few remarks. Every secondary chord of the seventh may be employed either with the regular downward resolution of the seventh, or with the •ieventh held or led upwards in resolutions of a free or cadence-like character (deceptive cadences). It would far exceed the limits of this book to introduce a table of all possible resolutions of all the secondary chords of the seventh. In the following exercises the pupil will meet with a number of de- ceptive cadences. He may also try by himself to form resolutions of the remaining secondary chords of the seventh, after the pattern of those shown for the dominant chord of the seventh and for that on the ist degree in minor. To assist his judgment in regard to the correctness and usefulness of such progressions, a few suggestions follow : In general, any progression may be sanctioned in which one or two tones common to the two chords are held in the same part or parts. But even without this natural bridge of a sustained tone, the progression may be good when the several parts are led in true vocal style from the tones of the first chord to those of the second. 205.< i t= w- 7b m ^^ -f2- ■^- ^:^ g:yu°-j c:\ i I ^ IV V 1 d. C: I C: IV VI1O7 -i: -z:*- -JgrS)- S= zyg- ? -^- fe -ei- l 3 C: 117 C: VI1O7 C: V7 a; III' 114 A MANUAL OF HARMONY, g. h. t-^2- yjS.- =^ ^-- -zyg- -zyg- ^-G- 7b 7b 7l) :^ c- v. ^; V, C: viiOy /".-Vt C.-viiOt i/.-viiOt ^ -^;^^ l =7a J »J* '^ r?^^. P^^^?=fc^ -Ife^ a t>^ =^ ]^^g=^^ -t-- ^ ^.•viiO^C.-I C.-Vt I C.-Vt I C.-Vy IV C.-V^^b:! From Examples 205^, e,y, ^, h, i, k, I, m, and n the pupil will perceive, that even the free progression of separate intervals in chords of the seventh may be sanctioned. It must be borne in mind, that the entrance of the root and seventh of a chord of the seventh in parallel motion almost always has a bad effect, and should therefore be carefully avoided. The next three examples show a bad leading of the parts. 206. \ -— * igi ^^ sr "*^ T7" 9i=^;^^^=|^ r— -=- i ^m However, isolated cases are found in Examples 193 (c) and 205 {/)-, in which the entrance of root and seventh in parallel mo- tion cannot be found fault with. A MANUAL OF HARMONY. Exercises. 115 In all exercises the pupil should mark the chords by Roman numerals beneath the bass, and the course of the modulation by capital letters in major and small ones in minor, as shown in the first two exercises. (Compare also App. I, p. 255, and App. II, p. 278.) 207. EiE^ C:\ 1I7 I IV VI1O7 IV VI1O7 III VI7 V vi7 II ^ m P -zsH d: I I ^b;V7 I g: V. SO 8 7 f «- C. 3 ^ fe =S a^S: VI c: V7 I g:\ d:Y^ n°T V, ^ t « ^^ -^ - fig fg- e£ P9^^^=F B 6^ '^ a 7b go |0 ^0 « ^ p-Sg— |g- 1g— g^- ^fct^d2^=Ei=^=^ e 6 4 7 ^ eti :^: TSl- ^ =^ I^-fe i 7n 7 7 7,b eg 60 it: 3 ^ ■ a I ^ -i — 7 S-r-G>- -s^ N. B. N. B. The line under the 7 shows that the sharp (it) continues in force which is written under the 8 for the third of the dominant triad. 116 4 MANUAL OF HARMON^Y. /■ t^a J 1- ^ ^- S =r^ 1^4^ :^=#^ ' i pttE^Sg _5 " O en 7b 8 7b 3 :^ |g-B!g- ;25H -25t- E^ § 7b 7b l7 -^^ 8 i 7 I » 7 1 O' h 1 ■ 1., 17 1 \ .\> rS 1 Bf-' HP' D/r» Un ^ --' b /^ 1 1 -3 lUi^n 1 T" 1 Hf "f - O- - \} e.\ o 1 V ^ 1 1 1 \ " -fil&sL a* — ' 1 6 7 f I =9^ ^ J3^ i :;»^ -Z5l- 6, 6 SB 3 a 6 7 6 7b ^ -«> (2- P-Vs>- Eka: sziisr =tt^ N. B. N. B. At N. B. the A\i, the seventh of the second chord, must skip downwards a fourth to Ea. This leading is correct, in spite of the entrance of the root and seventh of the chord of the fifth and sixth in parallel motion. k. 7 8 n u6ll 7 i 7b 6 5 7 i D I 11 ^^ ES Ii-=t *^ 13 ^ ^ I" r i I -FF t _a 7 _7b 7 6 7 * a fl^ ^^6g- A MANUAL OF HARMONY. 117 a V 7l> 6 7b :^= SSte giS ^* i^ |g-B lg- S et] eb %\% %%^V> 6 8 . eD =p^a=5 7 7 D ^ w ^ «(— si- tf 70 1 a 7tl 7 ^ ^ ^ s i ^——s) — g^ =iJ^ /• g=J ^/ i t I ^ -F^-fg- « « 7n I 5B fi^ 6 6 5 5 I g^fffg;;r -^- m :^ ^i€: E^a ^lz^: S S <> 8 7 3 6 g 711 3 Jt °0 X, B 78 5_ % - ^& if^ HS ■^-T^ -m 7 ^ 75 6 s 6 e » a 6 SB S sa^i^ ^—Vtf2- ^ — s>- t=t 7 6 5 3 6 7 « 6 - 8 7 IB ^s :^ =F= N.B. N. B. The lines : over the quarter-note gt indicate that the figures | continue in force. Henceforward we shall frequently indicate the continuance of a figure by a line, even where the chords change j thus s i or s i calls for a chord of thff fifth and sixth followed by a chord of the third and fourth. 118 A MANUAL OF HARMONY. CHAPTER XIV. The Altered Chords. Triads with Altered Fifths. §48. We term a chord altered in which one or more tones are chromatically changed.* The chromatic alteration of a tone in a triad may change it into another triad ; e. g. 210. C: I -g-g-- d: viio ^r- ligi bV. II' -St- o c%: I a: III' The above are chromatic alterations of the triad on the ist de- gree in C-major ; these we have already met with as natural chords. We therefore do not regard them as altered chords, with the exception of the last :ffi= j gzz: . This chord appears, not only as the augmented triad on the 3rd degree in a-minor, and but also in C-major as the triad on the ist degree with altered fifth; it is employed even oftener in C-major than in a-minor. The fifth may be altered in the triads on the ist, 2nd, 4th, and 5th degrees in major, and in those on the 4th and 6th degrees in minor. 211. - , 1 ^ I ,' ^ « 1 eJ 1 I C: I IV II V I VI "7 V7 I N. B. The first 5 in this measure indicates at once the position of the sDDrano and the natural (perfect) fifth preceding the altered fifth. Any 5 occurring in the following measures which is not crossed, indicates, in any part, the natural fifth preceding the altered one. *• 3 e 6 » 7 s ^ ^1 1 ®i s e 3 6« - n 1 1 1 • 1.. / I f' ^ r -" ■^ h ^ ' i' ei f^ =» qa; ^ J. ."<, ir 1 s 6 L 6 8 7b b — g pg - -SZ_ E^E S 7 5 =E«! ^a^ S0 87 67 60 S0 5 5t| §>l :fi=^ 5 g 122 A MAtfUAL OF HARMONY. 6 B 7 6 S07 5 87 g^^g^ ^I :^zifl^ / 3 5tl 5 6 S St) 8 7 S 5tl 8 7» 7 5tl r»' h 1 1 }•. " h / ' fT) 1 •^ b h'^ * ' 1 t' P r? n \ i S- 3 # 5060753 B 6 0370 t| SQ ^^ 8 t ^ ^ s 1^^==!=^: ^ =J^=* =*P^ >i. 8 f 4 0, 3 1 3 S -RtB— zti -t J — ' -^'■*%At-^ id — fi — — 1 ei — -zi — • 1 ' —ri - ^^^ l\i ■s> zi- ±=1 ■=^^- -tt^- W- rrsz S ^13^ 1t^ 6 5 e 7*4 650 06 36 3 -zJ- P H :fe=£ zle- :tt^ i^EB ^=H=-#l=Z- eB 4= :Ct2= fi^ :Jt^ at^ SSSi ig=fe: f -Tb- ^ r; I V7 I IV7G.V I— IV7 II V, I V7 I A MANUAL OF HARMONY. 127 I eJ y &J ^~ tl^ -gig- P= -g— gg- i I p -z^ -Jt?:^- :«^ -&- -ry- i EgE I ■^Sj±. :*=: :JM= », I « 1 ^i: -<» — s^ ^E zig= ^-^ II -Jt^ =tt^ -f-ftg- :£=fig= 102= M ;t=tifz=f^bf==f: -«|- :1^ «3-- S+ — 2= Ht^ ■<= <9— M I S^=Jf.z=t PE^ ■ I 6 6 8 I^I IB =Sg- ^3g p=^g=tf5 it^- V V7 ^: V7 — I a: V7 I ^.- V7 C; 11 ^.- n°7 C; in V I Exercises. Open harmony. 8_ H 6 % S It i^=w-- 222. ^^EiBEiE^^a IEEpES Close harmony. 3 6 3 - ^ 2 I — ^ — — . 6 t 6 5 7 7 7 6 6„ 7 g B 7 5 g 5B 8 7 -8^- gE -»-=- Open harmony. 8 3 6 I" s 58 3 I" 5 StI 3 ^^^ :^=± -Z5^ «■- 128 A MANUAL OF HARMONY. 7 f :: s ar I Open harmony. 6 i X tt S r f^ V/'u 1 n . B„.*i* / k r3 f ^ ft " * ' ] ff f-b to Zt [" e "| and find, in the chord of the A MANUAL OF HARMONY. 129 aixth derived from it employed triad called the , the universally known and often Augmented Chord of the Sixth, with a root chromatically raised tion of this chord ^^ Although the fundamental posi- is occasionally employed, and also the chord of the fourth and sixth -fe-^ (even more rarely) , we shall for the present occupy ourselves solely with the augmented chord of the sixth and its resolution. From the latter the progressions of the chord in its fundamental position and as a chord of the fourth and sixth will be seen. In the resolution of the augmented chord of the sixth we shall at first hold fast to the rule, that the altered tone is to be led upwards a semitone.* While leading the root downwards by a semitone or by the skip of a fourth, we lead the dissonance of the augmented sixth either to the complete consonance of the perfect octave or to the incomplete consonance of the major or minor tenth ; we can, however, also lead the root, in certain cases, a step upwards to the incomplete consonance of the major sixth. 223. i iE -gg- E^ :^= -^z zsz 1-"^ s As the augmented sixth must always progress a semitone upwards, it can never be doubled in four-part writing. The tone best adapted for doubling in this chord is the third ; the root is also frequently doubled. A few resolutions follow, such as *For this reason we can employ the triad on the 3rd degree in .fib- major, with an altered root, neither in its fundamental position nor as an augmented chord of the sixth. The key of ^-major possesses no E; it is therefore impossible to lead the altered tone D% up to E, as the resolution of the augmented chord of the sixth requires, to another chord proper to the key of .fib-major 130 A MANUAL OF HARMONY. may be effected in the various keys according as the chord is in C major, a-minor, a?-minor, or ^-major. i 224. 5^ lii 1-g- C: II s- I ^- I -- I g 1^ 1-"^ 5-^ ^l^gg -^Eigi 3^: IV -(S>- I IV III' III' ^- VI -s- V i i^ 7b 7b 1^^ i^ =i^ I^E^ _i2_ VI viio d: I u" VI1O7 11° etc. Of all these resolutions, that leading to the dominant triad of a- minor occurs by far the oftenest. Next in frequency is the pro- gression to the tonic triad of C-major. The resolutions to the dominant chord of the seventh in >?^-major are rarer ; the rarest of all are the resolutions leading to the diminished chords of the seventh and to the triad on the 2nd degree in ^-minor. But all these reso- lutions are defensible, and occur in practice. (Compare App. I, p. 261, and App. II, p. 279.) Exercises. 225, g§ 3 g f ^ ?^ -<=- m 8 -&- 3E fe \ u =tt^ ef A MANUAL OF liARMUlyit. 131 7 a % s a 6 « 71. 3 7, 8 69 eS ■^2- f. 3 6 a 6 6 7 7 S B i '-. If ^^* 1 ^ tr3 n '^ J-1 / »■ f J 1 /^ 1 ■^ f^ r ^ b * / 1 n « -J r aJ \- 1' ; eJ -* s V-^=^ 6 7b 8 5b 7 65 8 6 2 6 fel a= liEi «— (2- ^ en 7 87 %\. Ill fA" -" 1 1 1 T*i r" (^ r J ^ r- • 1 -^ \> J, eJ " (W 1 •=■ rt? • 1 -(2- ■^ Of « 07 « - S^ E^: :^. 4N: /. I" 5 3 6b 7 .^- t" 6D 4 2 6 7b 7 eg 4 . 6 3 g 5 gj^^^^ -^-ft =0^ 6 % V- g- ^ ", 6 7 6 7 » - *-!.. U W ^ "" 1 ff / k -3 ■ -^ n w' A ^ 1 I y "^ (5* f & fii 1 Lsl— J— e 6 7 » - ^- .h_ '^M 6 7 5 i^s :^=t g t?: i 1 s M>-d=t;^.d::g-bp 7B 8 S 60 t 5 5b t -TS>- 132 A MANUAL OF HARMONY. It is best to begin the third of the above exercises as follows ; n 1 _ 1 J 1 -^'-^r-ta 1 — — ; =1 ■-S — s4 — 1 1 s» -'-^ W - ^^^^ ra — 3 — 1=2 « 3 r 6 r 6 etc 6 7 7 R^ — tIt— «> 1 1 P -J « ^:r- I IlO, M~ 1 These resolutions are based on the resolutions of the natural (not altered) chords of the seventh on the 7th degree in major and the 2nd in minor (comp. §39 and §42). 229. SE C: vu°-. -et- I -(9- a: 11O7 I The augmented chord of the third, fourth, and sixth in minor also has other, non-cadenced resolutions ; e. g. 230. i 4 (EJ*- -Wl ii:S zyg- -^^1 -s>si- M- a: 1107 I iio- I lio. III' ''zs'S'- =i?= n°7 III'. i When modulation is employed, many other resolutions of this chord are possible in major and minor, in all of which, however, we must adhere to the rule, that the altered tone — especially where preceded by the natural tone — must always be led upwards. 231. EM^ 3^ z^Si ^z 'ISL i etc. Kemark. a resolution of an altered chord of the sixth, the third, fourth, and sixth, or the fifth and sixth, effected by leading the altered tone downwards, is also possible in case the natural tone does not precede the altered one; e. g. i 232. Fg; :=g ^ ■s'-'g- iiSflz i A MANUAL OF HARMONY. 135 but in view of its constrained and unnatural character such a progression can never produce a pleasing effect. From such forced progressions the pupil will perceive how correct and natural our rule is, always to lead the altered tone upwards. It can be led downwards, or held, only when it is enharmonically changed ; — but then it ceases to be an altered tone ; e. g. i M :-d= 's^g ^ tfdz ^- ■^-r ^B^ ^5^ P^ =E=^Z3^ ■ sj-a :igz ■S-g: i y;—S>-^^ p=^ te I etc. X The resolution of the augmented chord of the third, fifth, and sixth in minor is effected, lilce that of the augmented chord of the third, fourth, and sixth, to the tonic triad : 233. i 3^ =a: C: 117 ^-s p g- I I In minor, this chord can never resolve directly to the dominant triad. But as the dominant triad is the chord to which the aug- mented chord of the fifth and sixth naturally resolves, we make use of various devices to avoid the parallel fifths arising from a direct resolution. Direct and Incorrect Resolutions. 234. Indirect Resohjtions. -gSi- S^ 5S i^ 235.^^»-^ pl^pi : -^ <2- lez^ 5gi i a : IV7 11O7 V V IV7 III' 5 4 II 1V7 IE 1V7 HI' :=^i= -Mz 136 A MANUAL OF HARMONY. By employing modulation, still further resolutions of this chord may be effected in major and minor : 236. r, 8 7 J !_ S I letc. C: iiy F: Vt a : IV7 C: 117 (/.■^lOy a : IV7 d: VI1O7 C: iiy. A : III a: IV7 We observed above, that the fundamental position and the other inversions of the augmented chords of the third and fourth, and the fifth and sixth, also occur in practice. The resolutions remain the same as those of the augmented chords of the third and fourth, and of the fifth and sixth. A few such follow here. (For Ex. 239, also comp. App. I, p. 262, and App. II, p. 281.) 237. Fundamental position. Wz 9^ d: iS= st -sJ-Ssi- si -s^^s- 7 w=m^- ^^- C: VI1O7 I a: vSi First Inversion. i ^-=1 :^ w- ■^ J^ 6 5 e 5 6 4- 6 5 _(2_ f-^- -fg-ffig- =g=fe: igrfe: C.-VII07 I o.- 11O7 V a.- I1O7 I a; 1107 ^ .• Ill V7 I Third Inversion =i g- d: J- M ai IE 6 6 4^ 9- C.-viiOt III VI1O7 I a: 11O7 II°7 III' V A MANUAL OF HARMONY Fundamental position. 137 238.<^ i 1 -^— B^l^g— ^ f a. — \-a I ffl- ■g; l! s:=3s 7 7 6 7 7 7 7 6 -|S>- _-l^ J^^^iA. ^-g^ sl- i±j^-[^|-^-p=|i^j g[ ^-f =^j^; C; II la; IV. IV7 — I IV7— III' V IV7— ^ .■ I Second Inversion. ^)*r r^ ^ [ ^a ^1^ :|5 e 6 :i^ ^ C: lit I a;iV7 III' V7 a.- IV7 aT; iiO a; IV7 /.•V7 Third Inversion. S -\ ^ I "^ 1- zi -J^ iSi ^ :^ fe =ig= -i5»- 2 a a -4Z- eO C: 117 a- 1V7 V a ; IV7 IV7 III' V7 f :Mz ^- 7b 9 ^ -^- jb 1V7 // •'•ii'>7 a; IV7 /• V7 ife: 2 a: IV7 6 d: V i i 138 A MANUAL OF HARMONY. Exercises. Open harmony. a. 3 1 eN. B. e a? 11 } 6 * 7 6 S "m -4=1- 239. Y^—e- -<2 e>- ^•sle^, aeftaSS^el J§3 2«- Z^ £»_ i ¥ ^ 'S'-z*- 1^ ^^ % "5 11" f» Eg -|iZ-|&- Si^ ^ ai^ I#2Z =5^ -S"-:- .«-: ^^ -/= «> * 50 si' SQ 1 - J - f 6 I fe ^ -(2- a 7 7 i t 7 !» I « n fa. 8 7 f ig — s>- -»-J^ N.B. 4 B 3 a -j:^-!?- a 5 t" 8 7b ig_^^^; =t=F:: z^-^-i^ SE N.B. /■ 8 5 4 8 7P S D 1 eb S D ■ ^ ^^S^^S ^ jf ^l S ^- 3 8 7„ t J, f ' !i ^ -(2— «,- 23^ i^ :|^ ^ a - S ^ 8 7tl ^^3 A MANUAL OF HARMONY. 139 S la la a" an 4q t 6 a - «E i ES ^ :^zS i; pb~rff zg N.B. »■ a S, 6 7 ^ :gn ^ f=f^'^=^ mi a 6 - J. a t a a, A 5 - J s a 7 « « g K -gn - F: I -25^ i IV E^ -e>-^ :^*2 117 V7 -ei- :g: etc. --&- A MANUAL OF HARMONY. Ut §53. For the introduction and resolution of suspensions we give the following 5 rules. I. The suspension (whether in duple or triple rhythms) usually enters on the strong (first) beat. W^- l^E^-t-f:. 246. ■«'-z;!- t^ ±^ ^ i ff i C: I IV 117 2. The suspension must be frefared in the same part in which it enters. 3. The tone of resolution (i. e. that interval of a chord whose entrance is retarded by the suspension) must be doubled in no other part excepting the bass ; when the suspension lies in the bass itself, the tone of resolution must be doubled in none of the other parts. 4. The suspension must be resolved on the tveak (second or third) beat, and in downward progression. 5. A suspension does not neutralize parallel octaves which it merely retards Remark. The few cases in which a suspension can be resolved upward will be discussed further on. Preparation (as explained in the case of the seventh) must begin on the weak (second) beat, and be of at least as long duration as the suspension itself. Suspensions may occur before the third and before the octave (of the root) in the triad, in all the parts. Suspension before the octave of the root. 247. i K l_J ±igr -s<^- =^ '^ r -z;lg- e ^ —ei- C: V 148 A MANUAL OF HARMONY. 248. i Suspension before the third. ^i lg3 C: IV ^E^SiE :J= f-f- 1 -is— h©- IV IV Remark. Between the tenor and bass there also occasionally occurs a sus- pension o£ the second before the prime (21). The explanation is simple, the range of the bass not being low enough in a vocal chorus to form the proper suspension 98. I -Si Si hi T^" -s- 2 d=dSsJ I =^: A true suspension cannot be formed before the fifth of a triad. Progressions like those below at 249 may, to be sure (as shown in Examples 243 and 245), assume the character of suspensions in the midst of a number of real suspensions, but when alone do not have the effect of suspensions. 249. < sJ-J rtf^'^rKw ^^t 5-rr I W ^^^ I^H^^ C: IV IV VI I III IV IV VI VI VI I These progressions, which — as the figures below them prove — are all complete chords with all their intervals, lack the essential feature of the suspension, the disSitnance. Before the fifth of a chord of the seventh, however, a suspension A MANUAL OF HARMONY. 149 may occur as well as before its root or third. Before the seventh a Buspension rnay occur solely in case it is preceded by a diminished octave or (as at 250 d) by an augmented one. E^ 250. d. H-J.J [ ^ 7-^- r-r *2= ,8 7 :^ i *2= E A perfect octave preceding a seventh can never form a suspension ; nevertheless, even the following progression 251. i is i I 6 I may in very exceptional cases (like that given in Ex. 245, meas. 5) assume the appearance of a suspension. Suspensions before the Octave of the Root, the Third, and the Fifth of the Chord of the Seventh. 252. < Suspension before the octave. u b. :^3l P^"^ -19- o a 7 - g 8 7 - jS_ ^ C: IV IV IV 150 253. 254. A MANUAZ. OF HARMONY. Suspension before the third. -iS- t; "gyg- -T»- ^ 7 - 4 S 7 4 3 ^t C; IV IV IV rf- n f\ ^ fn -H Xs) >3 e^ ■■ %j ^ _^ r 4 a 1 E t \ c\* ^ 1 II f)'"^ 1 ^ 1 ■' i-J- major, and dimin. seventh. J i 3^ ;«=^ r ' t^= I 4 3 7l> 6b S « :^- I Ex. 242 to 254 inclusive contain preparations of suspensions by the octave of the root, the third, and the fifth, in triads and chords of the seventh ; it is therefore unnecessary to repeat such examples here. The pupil should, however, again examine the examples in question, that he may clearly understand preparation by means of the various intervals of the triad and chord of the seventh. As the third rule to be observed in suspensions we remarked above, that the tone of resolution in a suspension must be doubled in no tone but the bass, and, in case the suspension is in the bass itself, none of the higher parts may double the tone of resolution so long as the latter is itself not resolved. All the following examples are bad. 256. C: IV vii" a: 11O7 I 1V7 VI1O7 This faulty example now follows in corrected form- 257 a. . i ^ -19- gg- 7 a - — ■ C. I a: vilOy i i 154 ^ MANUAL OF HARMONY. The chord of resolution must always be a chord of the thjftl-. fourth, and sixth. 260. Suspension in bass before root. -syg- C: V7 -z?g- F: 117 ■^S- r :^= i I Suspensions in the bass, with the tone of resolution doubled by one of the highest parts, are entirely unallowable in strict writing. All the suspensions at 261 are incorrect. 261. — -p^ — I ■ ■ " - j — — 1— I — I ' ■^ - '^ — ^1 i The pupil should observe, in studying Ex. 258, 259, and 260, how the anticipation of the tone of resolution in any of the higher parts may be avoided. In all foregoing examples in duple rhythm we have seen, that the suspension always enters on the strong beat. The same principle must also be adhered to in triple rhythm, as Ex. 246 showed ; but in triple rhythm exceptions sometimes occur, e. g. -i i :^^ I §!=fr A MANUAL OF HARMONY. 155 A suspension does not neutralize parallel octaves which are merely retarded by it , consequently Ex. 262 is wrong. 262. i ^ ^ 4: \-^ i2=t: =1 ^ — Fig -V-a- =*^?!S2 1 On the other hand, a genuine dissonant suspension completely neutralizes parallel fifths retarded by it between all parts, even between neighboring parts, in case the leading of the other parts is otherwise correct. 263. i 3!ii ^^ -::s=X^j^ '^ ••mu H - ^i: -Tsr 7 6 I = _i2 . 6 -&- I 2 , a -^ C: IV7 V7 a: VI The suspensions of retarded parallel fifths exhibited at 263 are correct, although the retarded fifths occur between neighboring parts. Similar progressions have been written by the best classic authors in strict four-part composition. Even in progressions bearing the character of suspensions, retarded parallel fifths are allowable, especially with contrary motion in the other parts, the unpleasant effect of the open fifths being completely neutralized, partly by the retardation of one part, partly by the sus- pension-like character of the chord, and in particular by the con- trary motion in other parts. good. good. good. 264. :J. '^ 'mmrSI- i -^-^^ lJ ' I*? "^^ jn I §3 ■■m-- ■m. i C: IV7 (III) V a; VI (III') V IV7 (III') V 156 A MANUAL OF HARMONY. But little is left us to say concerning the manner of marking the suspension in thorough-bass notation ; this the pupil will have learned already from the foregoing examples. The suspension is indicated above the bass note by the figure of its interval to the bass note ; e. g. we indicate the suspension of the ninth before the octave of the root by the figures 9 8. 265. i w U-4- -2^ -- -G>7S- % 1^ -glig- i si- :rt= '^ -^zx? H ^^ e This mode of noting suspensions in the bass, which was at bottom much simpler and clearer, is now but little employed. In all the following examples suspensions in the bass are indicated by the figures required for the accidental intervals above the bass, and the continuation of these tones by means of dashes over the bass note of resolution, as already shown at 269 (a) and )c) (| z, 1 1) . We shall employ the notation shown at 269 {¥) and {d) only in case the chro- matic alteration of an interval on resolution is desired ; e. g. | 5 or 1 % etc. 2 % 271. ■ i iE ^ g^l^^ '^se^ lb y> 3 » I 272. 8 7 6 el S 8 7-87 go « - I - 987 7 - c\* n <^ 11 r3 L^ 1 II In order not to confuse the pupil we shall also occasionally mark the chord of the seventh in its fundamental position with ? 3 5 f 7 7, and the chord of the fifth and sixth with | . The figure 7 before a 6 indicates, on the contrary, only the suspension of the seventh before the sixth in a chord of the sixth, as in measure 3 of Ex. 272. When working out these exercises, the pupil should write out the A MANUAL OF HARMONY. 159 degree-numbers of the chords within the key in large and small Roman numerals, and the course of the modulation in large and small capitals beneath the bass, as we shall proceed to show in Ex. 273 (working-out of bass 272) . A mere mechanical transfor- mation of figures and chromatic signs into notes is simply writing out the thorough-bass notation in notes; this alone cannot pro- mote a clear comprehension of the chords and their progressions. Throughout his work the pupil ought constantly to keep in view, in what key he is, and which chord of that key he has before him at any given moment. To further this end, the working-out of the bass at 272 now follows. The pupil should write out his exercises in precisely the same manner, but in four clefs. 273. C: I ^■^ I I7 IV N.B. i ^ — T -' r^^ ' S 8 7 - -J- vii° II a : V7 d:V VvC.-II The preparation of the suspension must always be connected with the latter by a tie '— . The figuring 9 8 7 in duple rhythm always means, that the suspension fills out the whole first beat ; for the res- olution and the succeeding seventh the second beat is left, as shown 160 A MANUAL OF HARMONY. in Ex. 273 at N. B. In triple rhythm the suspension, triad, and chord of the seventh divide the measure equally between them. 274. i Duple rhythm. =r 13^ ^- Triple rhythm. I^ -w fzzat TSf~ ^ Jt^ ^ -W' -e> — z^ i i In this case the seventh following the octave must not be given to another part, still less should it be already present in another part. In meas. 3 of Ex. 273 we have a suspension of the seventh before the chord of the seventh. The accidental chord arising from the suspension must be regarded as a suspension, and not as a chord of the seventh on the 3rd degree, because the bass is marked 7) and not \ or |, the exhibition of a chord of the seventh with all its inter- vals not being desired here. (Comp. §52 ; also App. I, p. 264, and App. II, p. 282.) Exercises. 8 8 7 §i 275. ^ ^ ■^—zi- 9 8 7 l« f i I5 b. 3 7 - 6 5 * - 1 1 "'^. 1 /i r3 F' .n <2 11/ \ ' — (V ' — & ' 1 — isi 1 \ L a, 1? a a e 6b 4 % Q 7b 4 3 ?2 t - c\- 1 1 1 1 1 »-1. ^ \ ! e) ri \ r' - • a ' ' i US' 1 ...0 I' II 1 I- i - 7 - |5 55 I9 1 1 • 1. w » n fO -^ s> 1 ■«>- e^ L U 1 1 — E «- 1 A MANUAL OF HARMONY. 161 Open harmony. '-8 4 S M N.B. 7 e 7 6 L! 6 § U «8 1 1 J \ M «- fi» ■ « to 8 e s S S 8 ^ -w- At N.B. in Ex. c, meas. 4, comp. Ex. 257 <-, meas. 4. -^•8 i 4 t 7.5 4 8 8 7 li 1 « \l r»' tt P* r^n/rJ ^ 17|^ 1^ £y ^ ' V U" q J » ■ **P ,^ • 1 U 1_J *■ 1 /§ a - 25 4 3 f 1 7 6 6 8i 7 6 6 7 4 « 4 3 n ^_ 1 T'l "/ > (^ fZ) 1 1 -/ w \ / /-> ■ 1 "^ f2 1 1 LL ! Li — &JJ L-iS — Us>-I Open harmony. 7 6 5 6 - ^•8 i == I i « 8 7 3 3 6 7 3 4 3 S « li- JV • -Lg ^^ ?^ ^ Ei 8 - 8 7 7 6 % li 4« f"*" 4 8 nil -RtSj-tIi . (^ —» m^ ~ n — s> 1 ^ ff<^ g W^ -^-\ 162 A MANUAL OF HARMONY. !_l = t 4 L S -7 4 3 7b 4, 8 - ? 52= 1 :tt^ -«>- /S. ^S E^ 4 a g le^^ 6 6 - 4 8 6 - 4 3 -19- I • s B 5 S 8 t - 7 IB A f 26 9 8 15 Is "n-tt It ^ """ — -, ' i.ft,.'' / I p* --' * I ■• /^ ej <3 ^ 1 ' k'^l-ffy ej P ft " 1 7b 6 6 — 7b 6 6 — P - * a ^E ?• 1 6 li e 1 e 6 4 3 1 L?i r»'tt fi 1 1 '"l.Bif+'ttfl (^ (^ ^ Tt a n iii rf •tt^- >j^ij I //; V7 g--^i C: V7 /•; V7 Such ninths are mostly found only on the weak beat ; a few un- prepared ninths occasionally appearing on strong beats do not justify the assumption that they are true chords of the ninth, and may easily be explained from the freer leadings allowable in figurate counterpoint. For instance, no one can well see, in Ex. 292, any- thing further than a changing-note D before the chord-note C, which D may enter freely and skip without touching C to the fifth of the chord of the seventh. 292. 4 -J J J I i i 4=k I F: IV V7 Such liberties in the leading will be fully explained to the pupil in his course in counterpoint. Besides, the true strict style oifure contrapuntal composition does not even permit such liberties in the leading of the parts as that shown in Ex. 292, for the changing-note should enter only by a step before the proper chord-note, as shown below : ^ i^ ^=* e£ 293. j~r- tE lU J Ji „j J Jj =F=p= I 172 A MANUAI. OF HARMONY. In this case, too, impartial judges can see only changing-notes preceding the chord-note, but not chords of the ninth, which must always be prepared. Here we need not discuss whether such lead- ings as those in Ex. 293 are really permissible in the strict style. All the original chords enumerated by us, whether triads or chords of the seventh, could be erected on all degrees of the major and minor scales, and used both in their fundamental positions and — as a general thing — in all their inversions. Five-tone, Six-tone, 01 even Seven-tone chords (chords of the ninth, tenth, and eleventh), occasionally appearing as accidental chord-forms in the free modern style, e. g. w J- eB cannot be regarded as original chords, whether prepared or not. Even the above accidental chord, which we conceive as a chord of the seventh formed above the double organ-point can hardly be sufficiently prepared ; still less a chord consisting of seven intervals like the following : ^E S f 9* i| Such a combination of intervals is not proper for employment in strict writing, if only for the reason that the tone of resolution of the suspended tone is found in an inner part. But even in the fol- lowing form n^ ^ :fl '■'.j_ _-4 ^ ^=^ -= ^ . nsz P jSZ- jO. I A MANUAL OF HARMONY. 173 we cannot call these accidental formations chords of the thirteenth with omitted ninth ; we must rather consider them as chords of the seventh on the 7th degree over the double organ-point of the tonic and dominant, with the prepared suspensions B or ^ before A, this A being the fourth before the third of the said chords of the seventh, the seventh of which (^E or .£1?) can enter unprepared. (Comp> App. I, p. 267, and App. II, p. 282.) Exercises. . 8 7 9 8 7 "• 6- 7 6S98 5 9 8 5 8 t % 294. ^3 -=- m d. 6 S 4 t sg 6 Ifb t i ^^^^- St—T^- ^S II 7 7l> 9 4 t g gn e e 46 bdSe 6- 4 t 1^ ?= ^=j^ S^ -<9^^ 9 8 7 7 6 6 9 8 7 „ 766 6 60 6 ,_ 48S 4-"- 48 174 A MANUAL OF HARMONY. /■ 8 — y*" ^ T~ -(=- i?=e=n ^^E ^ « ^ — F-FF^ -/5Z- r^— t -ag- 7 8 « 6 - e 7-98 53i ^ V- i - i^^S^S 9 8 AT 6 5 6 - ' ^ 87 436 - 4 8 :^=C|:^ tg-Bjg - ■^ ^ Open harmony. h. 5 9 8 7 9 8 9 8 , 76S 75 9, S7«,, i 4« g. egg l4g, !-| ^!ifci ^g^ =1^ ■g" — z^ ii± «• 3 6 6 4 ^ 8 7 g f - > r r ? ^Sg^=§ g — z^ fS" — I- 3 4 3 2 I J « « _ _ 7 7b 5 4 6 6- II ^^^"TT" 3=gE «s: ^-=#^ EB I ^ t> r') J - 9 6 6 5 i ?i £^ -(!2- Sl gEZes 60 78 8 7 9 8 7 6 4 a Sfi^ EE 3^ I- .. 6 7 ! i 1 § 3 J 30 3 f«t II ! I li A MANUAL OF HARMONY. 176 e S 7 8 V' ^m ^^ -^ -p- -i- g- g^ leg s - a 6 7 6 7 fc^ CHAPTER XVIII. Passing-notes and Passing-chords; Changing-notes ; tine Organ-point. §57. We apply the name of passing-notes or passing-tones to tones interpolated and progressing by a stef between two tones belonging to one or two chords, which passing-notes may either belong to the first of these chords, or may transiently form, in com- bination with it, a nearly- related accidental chord-form new and rich in effect. But they may also be foreign to the said first chord, and form a dissonance with it. Such a dissonant passing-note must progress stepwise to a tone belonging to the first chord or, if a second new chord enters, to one of its tones. T%e fassing-note can never enter on the strong beat. J 295. C: I T~r^ ZSZHIZHS" T^ la: rr-r- 1 i 176 A MANUAL OF HARMONY In Ex. 295 the notes D and ^marked with asterisks are passing, notes, which are foreign to the chord, and are interpolated between the tones C- S- G oi the C-major triad. m 296. < III -S- -»- i i Ex. 296 shows us the same passing-notes between two chords. 297. i -S- ^- C: I IV VIlO S ^ Ex. 297 shows us passing-notes between the chords on the ist, 4th, 7th, and 1st degrees in C-major ; they either form new acci- dental chords with the above chords, or belong to the true original chords. We might figure Ex. 297 as follows : 298. < i ^=k i ^m This is, however, unnecessary ; in future we shall mark passing- notes in the bass only by a dash over the note, whether they form or do not form an accidental chord with the bass note. 299. i ^z: f3 m. A MANUAL OF HARMONY. 177 The dash over the note shows that no true new chord is formed over the note, but that the preceding chord is to sound on in the other parts with the passing-note. Passing-notes in two or more parts may form passing chords. 300. ^^^^m 9- r r ^ Passing-notes may also be led chromatically. i 301. < P'-r-t^^- i Chromatic passing-notes must not, however, be employed too frequently. Progressions like the following in Ex. 302 are not adapted for strict composition. I 802. ^^ .,i.».r«fii, i r-^rrrfr-r|| Passing-notes and chords in the higher parts must be indicated by 178 A MANUAL OF HARMONY. the corresponding figures and signs of thorough-bass notation over the bass-note. (Compare §58 on "The Organ-point"). 303. i^ ^ ^•^ I 6 7 6 i t a -l2- -|S>- C: I Five parts. ' mr^V^-^ i I ^ ff f i tb 8 7 J J J i J J IB C: V7 rf; V7 C: V7 Changing-notes are notes foreign to the chord, falling on the strong beat and reaching the chord-note by the step of a tone or semitone, which bear the character of an unprepared suspension. They may enter from above or below, either by a step or skip before the chord-note, and without preparation. (Comp. Ex. 293, meas. 2 and 3). 304. IP I E^ JT r M d=j= °; ..^i *^^^^ U s J i In Ex. 304 the changing-notes are marked °. Passing and changing-notes can be employed only in figurate counterpoint and on the weaker beats, for the animation of the A MANUAL OF HARMONY. 179 rhythm. The former occur in practice far oftener than the latter. In our opinion the occasional employment of changing-notes is not pre- judicial to purity of style, but their over-frequent use is not to be re- commended in the strict style. In his course in counterpoint the pupil will receive detailed instructions on this point. On the Organ-point. §58. An organ-point arises when the bass, being held through- out a metrically and rhythmically well-defined portion of a piece, forms the basis for a series of chords which, after the first consonant one, are in part consonant to the bass, and in part changing chords sometimes even having no direct relation to the bass tone. An organ-point may be set at the beginning of a composition on the tonic, in its midst or towards the end on either tonic or dominant, or even on both tonic and dominant at once. Both the first and closing chord of an organ-point should be a consonant, independent chord ; though an organ-point on the dominant may begin with the dominant chord of the seventh. Over the organ-point, chords con- sonant and dissonant to the bass tone should alternate. An excess of dissonant chords, often out of all accord with the bass, has a bad effect. It is also best to form the close of the organ-point on a rhyth- mically and metrically well-defined part of the composition. An arbitrary breakmg-off of the organ-point is not to be approved of. The lowest part among those over the organ-point, i. e. in four-part writing the tenor, forms as it were an independent bass to the other parts above it. Thus when the chord of the seventh on the 7th degree appears over an organ-point on the dominant, we get the accidental chord-form called by some theoreticians the chord of the ninth (comp. §56). 305. i i s 4 7 « - I Below are a few examples, from which the pupil will perceive that the thorough-bass figuring of the true original chords and of the 180 A MANUAL OF HARMONY. passing chord-forms over the bass tone of the organ-point is a purely mechanical one. The figures exactly indicate the intervals as reck- oned from the bass. Organ-point on the Tonic 306. a 7868 6877 7 i til§3§t§tlil§l 307. Organ-point on the Dominant. te Mln F^ii/ ,.r^F^ ^^## i ^ 7|I 7 - 9b 9 7 9 i § g I 1 I g 2 S i lb » ^^ I ^ m T f *^-^ rff^ 34 6b7-28§ E 1 ^ Organ-point on tonic and dominant ; the thorough-bass figuring is reckoned from the tonic (key-note) . 4^U 308. •V A MANUAL OF HARMONY. 181 An organ-point occurring in any of the higher parts is termed an inverted organ-point. Other terms used for the organ-point are ■pedal-point, pedal harmony, or simply pedal. Organ-points in the higher parts, however, can be employed far less frequently than in the bass, and are less suited to the strict than to the free style. (Comp. also App. I, p. 269, and App. II, p. 283.) Exercises. 8 7 7 809. ^ 1 i I I § Ig l« i I % \ 7 2 Q s ^^ t^'w^l^ a - 677- 6-96 F~T-r"^ — y i^^^ ^ ^EtS l3-ell8-6-i-£ ^=f=ffi"^"rfr^^'^r^ ^y=F ic:^- OD 7b g 76768787.97 7 ,78 g^ 6 1^ i" III IS t§ till ?t§i isi'gt i ^^ =1=^ s ^- f 6 1 § fn r^~^ t i 9 8 7t| f ■■-^ (|/ «J r_| -' T . ^ r 1 182 A MANUAL OF HARMONY. 987 e-89 S 15* liil S ^ sa a 5' s e 4 $ ^ ■<=- i^ 1^ f 6 f 3 6 % 1 i» 1 £ 15 (\- " \ 1 1 p >• _P' . K) ^ \ 1 .- ! n 1 ^ 1 1 f^_ _ H*' 1 1 1 — 1 — , ... 1 Au^ \ a \ § I I i 6 6 S la 6b =P=fl^ =F^ ^ 3tz3=t:fi e ^ e 57 $654 86 2 3 J 5 4 8 3 4 3 8 3 4 lit I #^^ I CHAPTER XIX. Covered Parallel Octaves and Fifths. Cross Relation. §59. In previous chapters vsre have already touched upon the essential points concerning forbidden octaves and fifths ; we return to the subject in order, to remark, that our former observations on covered octaves and fifths were made primarily with reference to four-part writing. The case is different where more than four parts are present, a larger number of parts often so concealing the above- mentioned progressions, that their unpleasing effect in four-part composition is quite obviated. In two-part or three-part writing A MANUAL OF HARMONY. 183 increased caution is necessary, any covered incorrect progression being much more noticeable in the same. Covered octaves and fifths can arise, as the pupil already knows, only in parallel motion, when two parts progress from any two dif- ferent intervals to an octave or double octave, fifth or twelfth. i Covered octaves by a skip. Covered octaves, one part progressing by a skip, the other, by a step. -»— ^ -a- Sr— «- 'a a Covered fifths. i fi ~^F^-^ — *~- The parallel fifths arjd octaves come to light when we fill out the skips made by the parts with small notes. In four-part writing, on the other hand, an easy and natural pro- gression of the parts is impracticable without covered fifths and octaves. It must be our first care, to show the pupil what forms of covered fifths and octaves produce a bad effect in four-part writing. To this end we shall now briefly review the forms of covered fifths and octaves to be avoided by the pupil in four-part composition. But we advise him at the same time not to be over-anxious to avoid other forms of covered octaves and fifths besides those prohibited here. For by trying to avoid imaginary errors, he might easily go to the opposite extreme of a stiff" and unnatural leading of the parts. On the other hand, we desire him carefully to avoid, in every case where it is possible to do so, the progressions of fifths and octaves censured here, not only at present, but also in the most difiScult con- trapuntal forms, such as the canon, fugue, and stretto of the fugue. 184 A MANUAL OF HARMONY. Covered octaves and fifths are to be avoided, when the two parts skip to the octave or fifth (twelfth) from one chord to another chord. 310. Ih. .-i d. e ^E^^figEEf^ ^=i — uzq t A J. A ^^-T i ^ r»**TSi- j2_ ^ ( 7^ "^ |- 1— ^^* 1 \\^ -|— J— ^ 1 I ^ ^ 75 1= — ^ — 1^ ^ 1- ^^ ^ ^ I is^ ^^ ^^ ■r -j A-i Although some of these parallel octaves and fifths here entering by a skip are introduced under the most favorable circumstances imaginable — as at b, c, d^f, k, i, and k^ where everything is done, by the aid of contrary and (at ^) oblique motion in the other parts, to soften the unpleasing effect of the incorrect progressions — each and every one of them is to be condemned. A MANUAL OF HARMONY. 18& But when merely a transposition of one and the same chord is effected, parallel octaves and fifths so entering by a skip are per- mitted ; e. g. fe 311.- ^F^ ^ ^ ^ i j- ^^jsi I I FP= i« - g "aJ - :^ -i. =F e 3=^ t=^£=i--^f— fl r Covered octaves are likewise forbidden between outer parts, when one part progresses upwards by a whole tone and the other takes the octave by a skip (comp. §2i^ 312. < i - g*"^ ii^ ■g I g ■ >>i 1 ^ 1 " »ii'-gg H .^2. j5L 9i=^^;pgr=:z|E -«' — ri9- - a^ < 'g '- FS^^I ->-i1 When the higher of the two parts progresses downwards by a whole tone to the root of the chord to which the other outer part skips, the covered octaves are permitted, providing that the leading 186 A MANUAL OF HARMONY. of the parts in general is not incorrect. Consequently, Ex. 313 (a) is good, and (3) not good, because all four parts progress downwards. 313. u. good. Wf — g-?-U g— 1 b. bad. ^^ But, when the lower of the two outer parts progresses downwards by a whole tone to the root of that chord, to which the higher part skips, the parallel octaves resulting are faulty ; e. g. 314. not good. ^-» I i When one of the outer parts progresses downwards by a step to the third or fifth of the chord, and the other outer part takes the same interval by a skip, the effect is extremely unpleasant; such covered octaves are strictly forbidden. 315. i <-^»riS- ^^^ N. B. c. — «= — &■ iSi-**^- ^ must invariably be avoided. 188 A MANUAL OF HARMONY. The unpleasant effect of all these covered octaves is immediately neutralized, when the part ascending or descending by a step pro- gresses by a semitone to the root of that chord, to which the other part skips. In the case of other intervals, however, the effect remains bad, and progressions of this kind 319. ^T— zg-»*H; ■&- -g- ^^m^^^ are not allowable, despite the step of a semitone in one part. Even if one part descends to the third of the chord by a semitone, pro- gressions like the following 320. i W- 9^ £^S.- -r^g — -zp- JiSl. ^g«- -flg-^g »^ ^^^ V^^- are very harsh and unpleasing, if only by reason of the doubling of the leading-note formed thereby. On the other hand, covered octaves in which the lower part descends a semitone to the fifth of the chord, while the other part skips to the same interval, may be written. Progressions of this kind 321a. i IE " -Q- b s> — B-^*- '■^^ =^= 3«z {»:^-^ ci-- j^ etc ^_fr^- I "- I As quite isolated exceptions to this rule forbidding covered par- allel octaves from the seventh, we can mention only a few peculiar progressions between two chords of the seventh. In some such cases, the covered octaves arising may be permitted when the reso- lution is effected to the fundamental position of the chord of the seventh, because the progression does not sound badly. The pro- gressions at No. 324, for instance, are not censurable. 324. ■g^-l?^ ^-tSi-«»» SL. s ^^=^:^=^\ 6^^. jg- JSL. big- ^^ C: V7 a: V7 /.• 11O7 ^b: V7 C: V11O7 V7 c: VI1O7 V7 Even when the covered octaves are between an inner and an outer part, the progression between two chords of the seventh may have a good effect at times, and may then be permitted ; e. g. 826. l¥. ^fV m^ g3 F: V7 d: V7 ijSsg; eI^^^=I -g- J2s rf-si i A: VI1O7 V7 ^_:^ — « — ■& — s- ^^^^ ■&- ;;s;2= Itffi- ^^^ The progressions at No. 330 are not allowable, because the lower part takes the step of a whole tone. 330. ^^ ~.sr&- l^ -^^=^SS =B Q : g -^- ^ ^^^|=g^= I The above rules for, and prohibitions of, certain covered parallel octaves and fifths, are intended to indicate to the pupil what may or may not be written. It would scarcely be possible to lay down def- inite rules covering all cases in which covered octaves and fifths may occur in four-part writing. Genei'ally speaking, the leading of the parts will form the prime consideration ; in the cases in which we prohibited these progressions as incorrect, they gave rise, in fact, to a bad leading of the parts, and may be avoided by a better leading. One might therefore simply lay down the rule, that covered octaves and fifths are not permitted when a stiff and awkward leading of the parts arises from this progression ; but in other cases they may be written with the less hesitation, that through studied avoidance of any and all covered octaves and fifths in four-part writing one might easily fall into the mistake of giving up a natural and thoroughly correct leading, and selecting a worse one instead. Mature experi- ence, artistic insight, and good taste will show the advanced pupil later what is to be done in each individual case. A MANUAL OF HARMONY. 193 The Cross Relation (also called the false or inharmonic rela- tion) can occur in strict four-part writing only at a modulation.* 331. I W ri=^^^^ -x j/j ^ /^ i y C; I V F-.yn I C; V, I ^; viio. i2: I ^ eB r -i^ 51^^ -^ t I - i 194 A MANUAL OF HARMONY. The free entrance of the chronnatically changed tone in a part other than that in which the natural tone was contained in the preceding chord, has a very ill effect. The chromatic change should rather be effected within one and the same measure in the same fart. The errors in Ex. 331 may be avoided in the following way : 332. J=i -ziz f i^J J^_J_i-i r r ^p^gg 3t r etc. ^ CHAPTER XX. Employment of Chords in Accompanying a Cantus Firmus in Four-part Writing. §61. Hitherto the pupil has erected chords and effected progres- sions only over a given bass part marked with thorough-bass figuring. In so doing he has learned the principles according to which the leading of the inner parts can be effected, in four-part writing, in the most smooth and connected manner possible. For the leading of the soprano only the general rules for leading the parts have as yet been observed, no special attention having been paid to this highest part. The pupil has had no opportunity to write an original bass. Now, before proceeding to the next exercises, which form the tran- sition to contrapuntal studies, we shall set forth a few rules con- cerning the style of the vocal chorus in general, and the leading of the soprano and bass in particular. Although in strict composition each part should have a melodious leading, one part will have, in plain four-part writing, a predominant melody. We call this predominant melody the cantus Jirmus (Italian canto fermo). To it the remaining parts must subordinate themselves as an accompaniment, so far as their own free and inde- A MANUAL OF HARMONY. 195 pendent leading admits. The cantus Jirmus may be given to any part. It it lie in the bass or an inner part, we must take the highest part or soprano so far into consideration as not to treat it like a middle part, or a mere filling. Although the principal melody, the cantus ^rmus, is given to another part, the soprano must also be led in such a way as not quite to lose the character of a highest part with a leading melody. The first rule should be, not to let the soprano hold the same tone through more than three measures, and to lead it melodiously whenever possible by steps or by easy vocal intervals. We must take care, moreover, that the inner parts are not spread out too far, even in open position. The most practical plan is, never to allow a wider interval than an octave between the alto and tenor. Should a wider interval occasionally become neces- sary, it must be for as short a time as possible, and it is best to narrow the interval as soon as may be. A passage for vocal chorus like the one at 333 cannot sound well, because the inner parts are too far apart. 333. i ill » T5!«'- Tff^ J- i i Although each individual part in this example is correctly led, and the progressions between the chords are in no way constrained or unnatural, the entire example is nevertheless to be condemned because of the excessively wide interval between the inner parts. By interchanging the inner parts we make the improvement shown at 334- 334.' i w 3E ■ 7S- f=r §a j2_ I i The interval between the soprano and alto should also exceed an octave only in very exceptional cases ; the following example is 196 A MANUAL OF HARMONY. consequently to be condemned, though there is nothing amiss in the leading of the parts or the progression of the chords. 335. I l— 1 9- ZSr- V^~\ rrr-] r 1 1 r-= ^ — 11 '■ /» « a iW 1^ II ^ ^* ' II > .... II U -.gi. -gt -fii- c -^^_j«- -^- -iS>- -«- -^- -5P R • 1 ^ g a a » irj^ ^ u . /Ik KJ f? 1 ^■' s 1 &«» _g ^5^0 > \\i. n rj w^ T^n n ^^ -(9—1 II By inverting the inner parts, we obtain the improved reading Sfiven below. 336. /■ HP ^"-^ r*'n « 1 g< 1 — '' — ''^ 1 1 . i'l 1 i^ / t i^ a ' a „ \ o- H 1 ffh I .i-« « II 1 v^ ; * ~a _ -(ff- tS?- -42- -^-"^ « -^ r-a " f Q-i-j :» o w I T- / "V* ' f^' ir> \ e> 11 1 ^ I r> 11 1 . ^-^ L^ H The interval between the tenor and bass, and that of the group of the three highest parts from the lowest — the bass tone deter- mining the chord, must also not be very wide for too long a time. 337 Q f- r^ ^ o 1 — • 1 II I 7 w % ^ ij II 1 f \> (V SJ n II 1 \^ ) ^ ej ^ «5 11 U ej -^ ■&- f Ci* II 1 T-i " II 1 ^ U ffi 11 N V U — & 1 - . a b— — H A MANUAL OF HARMONY. 197 By transposing the bass into the higher octave, Ex. 337 would be made to sound better. 338. _^ ri ^j / , •^ eJ a / U 1 cy - -f^-^- -m The I chord always produces the impression of a close when it appears unprepared on the strong beat. Except at the close, it should therefore be employed only in the form of a passing-chord (comp. §57). Such is the case 1. When the fourth of the | chord is prepared ; 2. When the root of the % chord, that is, the fifth of the original chord, progresses stepwise as a passing-note between other tones. But both conditions must be fulfilled together, in order to give the I chord the character of a passing-chord ; e. g. 341. i i^ =i --Sr S=^^ ^^ ¥ --M=- The pupil should now attempt to write, to a cantus Jirmus (given melody) in the soprano, the chords marked above the melody in the three other parts, effecting the progressions of these chords accord- ing to the familiar rules for the leading of the parts. We have 200 A MANUAL OF HARMONY. marked the major triads of the key with capitals, and the minor triads with small letters ; for chords of the seventh the figure 7 is added to the letter. The following cantus Jirtnus in the soprano contains, in meas- ure I, the octave of the root of the triad on the ist degree in C- major ; in meas. 2, the fifth of the dominant triad ; in meas. 3 and 4, the third and the octave of the root of the tonic triad. In these measures the bass must neither be held, nor form a % chord in the second measure ; in such cases, only the fundamental position and the chord of the sixth can be employed. In meas. 5 the soprano takes the octave of the root of the subdominant triad ; in meas. 6, the third of the chord of the seventh on the 2nd degree ; in meas. 7, the root of the dominant chord of the seventh ; in meas. 8, the third of the tonic triad ; in meas. 9, the third of the triad on the 6th de- gree ; in meas. 10, the root of the chord of the seventh on the 2nd degree ; in meas. 11, the fifth of the dominant chord of the seventh ; in meas. 12, the octave of the root of the tonic triad ; in meas. 13, the third of the triad on the 6th degree ; in meas. 14, the seventh ol the chord of the seventh on the 2nd degree ; in meas. 15, the third of the dominant triad ; and in the last measure, the octave of the root of the tonic triad. C G C — F d*j G'j C u d'x G^ C t* d^ G C — F d-, -S>- -iS^ sg n This cantus jirmus may be worked out as follows : C G C — F d', 342. IP 1 3^ g^ _6 zsn C: I IV 1I7 i W- dt II7 Gn ■ a • —IS— 6 . f3 a^ =g= "7 i I A MANUAL OF HARMONY. 201 From the leading of the bass in No. 342 the pupil will perceive, that this part progresses in steps, or in skips of a third, fourth, fifth, or sixth, in contrast to the quieter leading of the inner parts. All kinds of skips easy to take with the voice may be written in the bass ; whereas all intervals which are difficult to take are forbidden. For instance, even a succession of two fourths in downward pro- gression is not good. -Iff- #i I This should be avoided ; the skip of a fifth followed by a fourth, or vice versd, being written instead. . — s> a. ^ I Two ascending skips of perfect fourths, like those in the last measures of Ex. 342, may be written without hesitation, as they offer no difficulty whatever to the singer. Carefully avoid, on the con- trary, two successive fifths, whether ascending or descending. ^ i Such skips may be improved by changing one of the fifths to the skip of a fourth in the opposite direction ; e. g. I The ascending skip of a minor seventh is allowable only when the seventh is added thereby to the triad ; but it should never be written between two different chords. good. 343. good. s« good. bad. bad. :2=Sl -Iff- ^^m^ I i 202 A MANUAL OF HARMONY. The descending skip of a minor seventh is not to be recommended even in the same chord. The skip of a major seventh in either direction must be sedulously avoided. Further, all augmented intervals must be avoided, to which end they should be changed into descending diminished ones. The pupil has therefore to write, instead of =J^ _*€:. JfjSZ. 344. # 345. =9 =Jta= ^W- -&»- the ascending augmented second, the descending diminished seventh ; instead of the ascending augmented fourth, the descending dimin- ished fifth ; instead of the augmented sixth, the diminished third. The only allowable augmented interval in melodic progression is the augmented prime ^" s. )( = — , The skip of a perfect octave is permitted in either direction. Below we give the working-out of the following cantus firmus in a-minor. a E a d a El a d-T -o n / <3 /? 1 V J r^ ej 1 1 lUI p* -_ 1 G D-j G a-j D-j G D G 131 Orj /?7 G P S. d. Eb Ab Eb c Ab Bb_ c^ fy Eb ft Bb Eb I? V - TB ja- A MANUAL OF HARMONY. 205 Open harmony. t. Gb Ob eb 6b eb Db DbT Gb — abv^DbTCb eb abT Dbi Gb lt>b tV_ -^ -&- < ? , a » . g- ■I©- ■&- -g- u ■g g- -g- -g- -^ -«>- ^^ /• .,4 E A Z» ^ *7 £7 A h A ^7 ^ s c ej «-■ 1 I "« / T~0 &> 1 1 If ,,M »» ' 1 tE^4Ji — ^ :-r1 E Bt E Bt E fiT Bt E A Bt E — c%t B E E-, ^ ' zy -gT'-p- f ^ e$ gt A Bt E A /ij ^7_f «7 /J7 -E y*7 ^ /S7 -^7 -£ -O- 13 ej' , 'ejr f rita: «2: «a: s 4— 5p i. .f ^7 -Eb «o ^ «o Bb' D-, S /JQ g aO ^ D-T g U Iff <7 1 ", / n ri r? .r> 1 ■ lUI ov y lt^ ^ 1 1 Open harmony. i. f C B^ 6b A\,- Ct / gO / C f - gO C^ f " ttffi. IS ■g-Fs>- »S s; ^ ftl /. * e 6 a%° 6 c%° P% G e 6 c%^ — 6 F% 6 It n ir> It* 1 t" r? HJlft ^ / n r? n /3 Wr c f c f G c G c f c Ab d° G c ^m "^ -&- -jS- -&- ;ei^ ff 206 A MANUAL OF HARMONY. §62. The task presents far greater difficulties when the cantus firmus is taken by one of the inner parts. In working out such exercises, the soprano requires very special attention ; it must never be treated like an inner part. It should always have, as far as may be, a leading melodious part side by side with the cantus Jirmus, The following cantus Jirmus would entirely rob the soprano of its peculiar character, in the working-out given at No. 350. F -ja- -&- d^j F fS Gi I m 350. i IE i_^ di G-j =i=S= ISI z^±^. I I By giving the tenor-part to the soprano, and taking the soprano as tenor, we obtain a much more favorable result than before. 351. f\ _^y-^" ■^„ • ti 1 / ej 1 1 1 1 1 -e©- -t9- s- ■&- -9- •&- -&- „ -&- 1 r»- /■^ ■ 1 ■ 1- / a II 1 ^ \ t> >^ II V IJ The following exercises can generally be worked out conveniently in open harmony, when the cantus Jirmus is given in the alto. In a single case, the exercise can be begun in close harmony. (Comp. App. I, p. 271, and App. II, p. 287.) A MANUAL OF HARMONY. 207 Cantus Firmus in the Alto. a. C d-j Gt a d G-, C G-, C F Ifi C d C G-, C 352. m. g Vo - OL i. F F gl C-j Pi B\n .? F g F c F a ■ ■» f^ n ^ 1 II 3 u /i 1 3 1 1 1 U^ . ., r 1 e. d ^7 d S eo Ai 4 g Ai Bb g At d 1^ 1 4i-l r3 n n ir> V^TD '* 1 1;^ 1 W' 1 L \ 1 1 Close harmony. d. £b F g d Eb Bb F gl '1 Pi Bb -a- 1 Luy i f^ ■ . ^ 1 r-ft t 1 a) e> fP \ 5.L_1 1 Lr_l EbBbiEbAb BbiEb fy Bb-r EbiAbid^ g-j Ab Bb EbBbEb -s>- ^ / Z>b ebi Z>b W-t^. -19- ebi Abf ib Ab Db -IS- w^ w^ c G^ Ab d° Gt e rf? b^ c d^ G. j2- JZ- 2Z Ss -In- close harmony. k- cH f% c% f% G% c% ^ ifO ct ft cS A U"^ 1 E T' f> ^ n rs -n ■n r a CHAPTER XXI. On Modulation, §63. The exercises in this text-book have made the pupil famil- iar with a variety of modulatory transitions. He knows that under the term "Modulation" a departure from the key predominant in the piece is to be understood. In case this principal key is to be for- saken entirely, and a movement in a new key follow, in which this A MANUAL OF HARMONY. 209 new key shall be predominant, the new key must be thoroughly established, unless the two keys are very closely related ; i. e. a mod- ulation to the new key must first be effected. We shall now add a few suggestions on modulating, showing the pupil 1 . Mow to reach any key from a given key ; 2. How to establish the foreign (new) key firmly, in order to bring the modulation to a definite termination, A new key is not firmly established when one has heard merely its tonic triad. The sounding of this chord alone does not fix the key. When we hear the following chords, they all impress us as belonging to C-major. 354. C: I But even in case a second chord cannot be classed as belonging to the key, its mere entrance on the weak beat will never awaken the impression that the chord is intended as the tonic triad of a new key. It impresses us, for the present, as a chord foreign to the previous key, which begins a modulation ; but not as the tonic triad of a newly established key. 355. We can establish a new key only under the two following con- ditions : I. In duple rhythm, the tonic triad must fall on the first of strong beat ; 210 A MANUAL OF HARMONY. 2. It must appear as a cadence-like resolution of the dora inant chord of the seventh. 356. li =d= =lt^ -f^ -&- d= '^-&- fib S C: I D: V7 C: I ^b: V7 i i p 3SE =i bsj^ ^- sb i ^■- -J i: -z:*- n^z C:l o.-V, C; I Bb: V7 Taking the tonic triad of any key as a starting-point, one might easily reach the dominant chord of the seventh in almost any key, the tonic triad having in nine cases either one or two (in one case as many as three) tones in common with the 1 2 dominant chords of the seventh, while in the remaining 3 cases a connection can easily be effected by self-evident progressions and with correct leadings. Most of these progressions, however, would have a more or less brusque, harsh, and inapt effect, even in the cases where one common held tone apparently forms a natural bridge between them. The rule does not invariably hold good, that any progression between two chords having one tone in common is at all times and in all cases agreeable and harmonious, when the common tone in question is held in the same part in both chords. The progressions at No. 357 cannot be considered good, in spite of the common tone held in the same part, and although the leading of the parts appears correct, because no relationship whatever subsists between the chords con- nected in this manner. 857. i#2= c: I a: I f:\a:\ a: \f%:\ /f: i b\)\ i bV- I c%: I i A MANUAL OF HARMONY. 2H It follows, that a direct progression of the tonic triad in C-major to any of the i3 dominant chords of the seventh, and their cadence- like resolution in their respective 24 major and minor keys, vsrill not suffice in most cases to establish a new key. The progressions given under 358 have, with few exceptions, a forced and constrained effect. 358. < i r^ iE^ ^-l4-^# iiB 9t ^ ^- --t^- i: i |l g3j ^ I " |^^"=f^=| a^ tei -fi? 1-(2 »- ^ J2^ ^- E| =J=fe^-[:r|i^| _JZJ~|"T =l f^ ::2= -g- •pfg- d2Sl S te =^ M? ; ^ I 212 A MANUAL OF HARMONY. $ i m- M ■M: - Wg I w fel- i gE^ -251- ^m- =fl5 Indeed, even the sudden succession of the tonic triads of like- named major and minor keys, despite the fact that they possess ttuo tones in common, has a somewhat singular effect, which is not always neutralized by the mediation of their common chord of the seventh, the intervals of which are precisely alike in both ; e. g. 359. i ^W- =1^ -&■ 2£- I We shall therefore do well to introduce the dominant chord of the seventh, belonging to the key we desire to reach, after another chord which is related both to the triad with which we begin and to the chord of the seventh in question. This we shall do in all cases where the keys to be connected by modulation are not directly re- lated. In order to modulate from C-major to a?-minor, we can take the dominant chord of the seventh in d-mmox directly after the C- major triad, and resolve it to the tonic triad in fi?-minor. This pro- gression will not have a specially harsh effect, simply because the A MANUAL OF HARMONY. 213 tonic triad of «/-minor is also found on the 2nd degree in C-major ; this forms their relationship. 360. < ^^^ » 7— p 3 i The modulation to Z?-major in like manner would be much harsher, because the triad D-Fl!,-A is not contained in the key of C-major. We shall do better to interpolate, after the C-major triad, some chord common to both keys. 361. =g= -J^- :^ ^ 32; C: I III D: V7 D: 11 C: I V D: IV V7 ^ =flfc -«<2- T^ i C; I Ilty D: 1I7 I Z»; iiv V7 I We effect the following transitions in the same way. 862. C: I /; I DV. V7 I C: I /: i DV- V7 c%: I /.- V m: III /.• V DV. Ill c%: V7 214 A MANUAL OF HARMONY. i d= J I .J J id I ?6i= =S — I — a- ^ liZSl S ifesi i -2gl C; I /; 1 EV- V7 /; V EV- n C- I /; I EV- V7 c^: I /; V £b: II eV. V7 i fe^ ^ ^1 -«r" « ^(i^^)p :i-- S'^- jJJT'"- ^^^^# -*^=n^ i C: I VI ,?; V7 E:l C: I V7 i:ivrr/r.\^ 1 The last transition from C-major to _/#- minor will have a still milder effect, if we first resolve the augmented chord of the fifth and sixth to the 3-minor triad. 363. i^i: ■i — zj -:; ^■''^^v ^(^i^y m '' — s^ :(^): =^=Jt^ C: I V7 b: IV7 I yj: V7 /(: IV -^z I I If I E^ I pe =P =i* ^ :(^): =t ^ =fl^ -g^ I c- 1 V7 b: IV7 4; I /»: V7 /J: V7 ^: I A MANUAL OF HARMONY. 215 When modulating into remote keys it is best, in any event, to em- ploy several chords, and bring about the transition gradually. 364. =i =1= ^ ^(^)^i= ^- ^ t C: I IV *b: I Ah: V7 g%: V7 b\,: V ^b: II g%-- I i p3 T^r-oA fei: S- =1^ ^^ ^E -m- f^ :^^(^E):|^ e =J^= -bzg" C; I /.-I ^b: 117 V7 /■; V^b:vi C; I V,^; iVt^.-Vt i #^i 3t ^(Eg=)^^^^^^ =3:^(^::p=): ^ I -tK- C; I V7 *; IV7 B: I §64. The last modulation shows us 1. The resemblance in sound between the dominant chord of the seventh and the augmented chord of the third, fifth, and sixth. 2. The entrance of the % chord on the strong beat. The enharmonic change of the dominant chord of the seventh for the augmented chord of the third, fifth, and sixth yields us one of our best and most natural resources of modulation. As we use both chords in major and minor, and are able to resolve the augmented chord of the fifth and sixth to the % chord derived from the tonic triad, we can easily and agreeably connect very remote keys by means of a few chords. 216 A MANUAL OF HARMONY. As remarked above, the | chord produces, when it enters on the strong beat, a very striking impression of a close. Although not absolutely indispensable in the actual closing cadence, it strengthens the latter, and materially heightens the feeling of a complete close. §65. The most universal medium for modulating easily and rap- idly from one key into another, is the diminished chord of the seventh. It may enter freely anywhere, without preparation of the seventh. It admits of very various resolutions and progressions in major and minor, and by means of the enharmonic change of one 01 several or all of its tones it can pass over to the most diverse keys. To begin with, we shall show how easily it may be introduced, as in No. 365. Here we let the diminished chords of the seventh belong- ing to c-minor, ^-minor, and 3l7-minor, on the 7th degree in these keys, follow the tonic triad of C-major directly. =fe ig= -■^- -s- 365. C: I 7b =fe VIlO, 7l> 5b C: I /•• VI1O7 C: I ^b: viio. Each of these diminished chords of the seventh may, however, be assigned to four different minor keys by enharmonically changing its intervals and their names. 366. i 7b VIIOt -fegf- ix a: VI1O7 ^ /%■■ VIIO7 * 30 d%: VIIO7 eV- VI1O7 i 7b 6b W- fb ix eb 4b an 5fri^ 367. ^ ^ggy- ^ Ffl^ % iS?- ^7^g- /: VI1O7 d: VII07 b: VI1O7 g%: VI1P7 a\,: VI1O7 368. IE — g— ^b: VI1O7 fb -b feg'- g: vn07 ^i ^.- vn07 I A MANUAL OF HARMONY. 217 As each of these fundamental positions and inversions may be resolved to the tonic triad of that minor key to which it belongs, and equally well to the tonic triad of the major key of the same name as that minor key, and also to other keys, at pleasure ; — and as any diminished chord of the seventh may follow a triad (compare Ex. 365) — it follows, that three forms of the diminished chord of the seventh afford the cue to all major and minor keys. On ex- amining but a few of the possible resolutions of the diminished chord of the seventh on the 7th degree in c-minor, we instantly per- ceive how flexible a medium of modulation we possess in the dimin- ished chords of the seventh. -a- VI1O7 *b: 11° c: viiOt Gb: V7 c : VI1O7 D\,: V7 c : VIIO7 V i 7b f 7b b 7b 7b &>; I S, r 7b w ^ -ttef iSm- 3^ Sg= V11O7 s^ c : VI1O7 d: J1O7 F: VI1O7 VI1O7 /•11O7 A\,: viio. c: VIIO7 E\>: V^ $ 7b 7b f 7b eb b 7b fe ±g: -jgg- 1=^^ t= ^ -^ w*- VIl07^b:V7 c: VI1O7 (f;iV7 sr VIIO7 ^.' II°7 r; VI1O7 /J: V7 f ; TU°j/: IV7 ^b: 1I7 218 A MANUAL OF HARMONY. 7b 7l> Eg iE E^^5S ±g" au; ^g= %€?- r^ tr ^ rg^ c: VI1O7 a; III' <: ; viio,, e\>: 11O7 <:; viiOy^b: V7 i 7b I" 7b 2 7b is;; ^ f ; VI1O7 ^.- I ^g^ «s- <:; VI1O7 g: V7 eb /j 7b sb 7b 4 7b a £■; VI1O7 g: 11° ^; VI1O7 (/; I c: VI1O7 1107 etc. By writing the chord B-D-F - A7 with the enharmonic changes of its tones exhibited in Ex. 366, its possibilities of progression to other keys are still further increased. It would lead us too far to indicate all these progressions ; we prefer leaving this to the pupil, so that he may become familiar with the manifold resolutions of the diminished chords of the seventh according as they are written. §66. A further means of modulation is found in the augmented chord of the sixth, which, as it belongs to four different keys (comp. §50), can resolve and progress to these as well as various others; e.g. 870. • g W- -ffg - C: I m ■fg- iii Wl g;^s=(i^^ (i)ip -w- /■•vi V d: I VIlO A MANUAL OF HARMONY. 219 3?z ^©1 i£= Wi iISi ^E jgfs> ^ -\ is^ "^ 1^ J— | ^=g — z v I s > g — I g 'g —l— l ^i^ I — g— !|ig- 1— g,_i4ffl_i- 1^3 =g=^ I C; II «b: I C; ii £b: I C: ii <:; III' J: i ^: V tftfe m m ^^^3— ^f^ i^^[i&^ ■i^t^ sT-=*-^ §^ ^ ^ ^^^S enharm. enharm. enharm. i ^^=jg ^^ 1;^ pE^ l*i-«» ;»! a.- VI1O7 4; I a ,.3=: =1 ^^g=F^=r^E P5^=5i: f^-^-^ss — '=F^^tl5g-t^: ■g-Hg-^.g- rr-Tp-^ 9t enharm. i enharm. P=g E^E pp^^iS^ iEb^ Is; — ^» igJ^- 4 ; V7 Z»b: I Z)b: V7 I fe ^ q.g ^ i J p3=Pf ^-n^3=f - r ' I 226 A MANUAL OF HARMONY. enharm. enharm. enharm. b: viio ifb: I c%: i fe-tW-ti» d^ OJ He i^.=icS: **^ t'^tlJ- :^ :^=§*^=5iifl We by no means desire to recommend all these forms of the close as such, still less to assert, that all chromatic alterations of the in- tervals of the triad on the 2nd degree are necessarily adapted for closing cadences. For this very reason we have omitted certain altered forms, such as lYz te: =r^ ^^ i But whenever such formations assume the form of a chord having, like the following 7^ * ii1 l§^ ' ^ sound similar to that of the % chord derived from the ^Jf-major triad, its progression to the dominant chord of the seventh in C-major can be readily effected. 379. i &=-M=^- i±S -^ i i In all these progressions of the triad on the 2nd degree, its root D takes the cadence-like skip D- G whenever it lies in the bass, whether it appears as a natural tone or as one chromatically altered. Hence it is evident, that the progression is based on the natural laws for the connection of chords, even though the effect be sometimes strange and unexpected. Whether, and to what extent, such chord- A MANUAL OF HARMONY. 227 forms can be employed in practice, depends primarily on their preparation and introduction. §69. As we know, the seventh in a chord effects the connection between two chords in a more definite and surer fashion, on account of its necessary resolution, than the triad can do in the same situ- ation ; because the latter (usually an independent chord) is by no means subject, in the same degree as the chord of the seventh, to the compulsion of further progression, which is in many cases fixed and predetermined. For this reason, too, the chord of the seventh on the 2nd degree is, even more than the triad on the same, pecu- liarly adapted for introducing the closing cadence, especially as the natural cadence-like resolution of this chord of the seventh forces it to resolve to the dominant chord ; besides, it may easily be led to the chord of the sixth, or fourth and sixth, derived from the tonic triad. Below we give the chord of the seventh on the 2nd degree in its natural and in variously altered forms, and add, to render this point clearer, a few closing cadences beginning with this chord. 380. i ^1: enharm. ^^^W ^adgi i -i. y^ itt--^ -•-|2- 4 -s>- ^t ^^m enharm. ^^d^E^P^^ J* ^ d=i flsr ^-\=W—^^->s^ -m T-f- -&- St ¥ 228 A MANUAL OF HARMONY. ^ f=l:fl=st5^ It^aJ?: tfs ' ^p - rX=Wi We take it for granted, that the pupil understands the enharmonic change in these forms, and their further progression to the cadence in C-major, and there- fore omit their notation in detail both here and in other places. enharm. i^^^P^^ 1^ i=^ ^ ±Ei I?h2- Qh*- mrC^dbzf: enharm. 53= t^-|2- tt^t enhaim. ^^^^ I A MANUAL OF HARMONY. enharm. enharm. ^^^^N^^ 229 enharm. m m ^p?^^ i 1^ Si -I a ^ -tjg^- m- 1 JflJ -Si- -s>- i>-|g-l T-f- -,»- :t=ic ^^=P= ^ ^ a ^ i :I=S Elf :1^ ^ :fl2= :«3^ :it^ r^=B? ^ «^ ^1^ sJ-a^ fi-«^ ^— fl< ? =tts: r enharm. enharm. enharm. ^^^I^^^^^i i ^^^fei^fea^ ^iE=i5==i: i '^=g-ff^ ^^=l-fr '^ n ^''' I g. *^ ^ '^s> Q i :tts= ::«^ :tl2= II 230 A MANUAL OF HARMONY. enharm. enharm. enharm. i£=dj ^^ ^ =51 i :t^ W^ 3»i ^^ ■^^- 1^2- tl #- flTg- bfZ- ^ Ifc fi*-- 1 lis: Even now we have not exhausted all the possible accidental chro- matic alterations of the chord D - P- A- C. This would lead too far — further than necessary for our present purpose. In some cases the above chromatic alterations of this chord sound harsh, in others singular. But the pupil must consider, that, if even the not-altered chord of the seventh on the 2nd degree requires preparation on account of its dissonance, its pi'eparation becomes far more neces- sary when one or more of its tones are chromatically altered. It must be properly prepared in every case ; the mode of preparation must be left to the keen creative insight of the composer. It should also be considered, how greatly the harsh sound of many progres- sions can be softened by the employment of suspensions ; e. g. 381. -g<- -%p-^-^^p- iflt -gjg- J r -^ i I The chromatic alterations of the triad on the 4th degree may be passed over. The tones of this chord are the same as the 3 highest in the chord of the seventh on the 2nd degree. We shall merely call attention, in Ex. 382, to a form very frequently met with in the A MANUAL OF HARMONY. 231 closing cadence under the name of the augmented chord of the sixth. 382. fea^^ =P=tf -Sr I ^ ^a C: IV IV V7 I §70. The chromatic alteration of the several tones of the chord of the seventh on the 4th degree will yield, with few exceptions, effects of sound with which we are already familiar (even if in othef notation) in the case of the chord of the seventh on the 2nd degree. Other chord-forms, like -g*g- I 383. I IV7 V7 I we set aside as idle speculative superfluities. In any event, however, we shall obtain, by chromatically altering the tones of this chord, an abundance of new chord-forms suitable for cadence-building. Below we give a few examples of such for- mations. 384. < a 4 --n^ a -i?- ^ C: IV7 i rJz y= ^ iC^ s -s>- ^ 4- si * 232 A MANUAL OF HARMONY. ^^^P^=^ i m «*^=fti -i^-_f-- t=p= I ^ y^ii^ We leave it to others to experiment at pleasure with further changes of this chord. With a proper preparation of its dissonance it will likewise prove adapted for introducing the dominant chord (or the triad on the ist degree as chord of the sixth or fourth and sixth, and thus for forming the close ; though its true natural (ca- dence-like) resolution leads it to the chord on the 7th degree, not to that on the 5th. But just in this fact lies the reason of its usefulness in forming the closing cadence ; for the triad on the 7th degree is simply a dominant chord of the seventh minus its root. This chord is employed often enough (e. g. in strict three-part writing) instead of the dominant chord of the seventh, especially as a chord of the sixth ; and it is perfectly well adapted to take its place whenever it may become necessary to omit the root of the dominant chord of the seventh, whether from an insufficient number of parts (as in three-part composition), or from exigencies in their leading in four- part writing ; e. g. i -jcj- -1^1 i In the foregoing examples we have by no means exhausted the possibilities of chord-building, but they suffice to prove that a great number of apparently foreign chords, which appear in the closing cadence, are derivable from the chords on the 2nd and 4th degrees of the ruling key. Improbable as it may appear, the progression below at 385 is in reality founded upon this very chord of the seventh D— F- A - C, A being omitted, and the tones D F C chromatically altered to D%,F%, and Ct>. without fifth. with fifth. 385. m^ f^T ±s^ ^ -^ :flp= Z2JI I jg- A MANUAL OF HARMONY. Forms of the cadence like the following 2S8 886. i i^^ ^ ftg Op - =ar -eh- m ^^ -^m ^- ZSIZ Wz. 131 i ■(5^ i are likewise derivable from the chromatically altered triad on the 4th degree. i k&gi -b^^^^ffl^ ^=1 The cadence frequently met with 387. =P- I2ZI -a'ommon property readily and rapidly. It is different in the case of larger and more complicated works, particularly Instrumental com- positions. These require, to be followed and grasped in and through their whole extent, a far more thoroughly trained and cultivated musical ear. But what is meant by a "musical ear," or "musical hearing?" Robert Schumann, in his " Musikalische Haus- und Lebensregeln" (Musical Maxims for Home and Life), describes the ideal heai-er as follows : "Some one has said, that a thorough mu- sician ought to be able to see an orchestral work heard for the first time, even a complicated one, as if the full score lay unrolled before him." With this "ability to see as if in full score" Schumann means, that the listener should actually hear each and every tone precisely as it is written out in the score. In order to do this he must clearly and distinctly recognize each individual tone, and all possible combina- tions of tones both in melody and harmony, even in the boldest modulations. Further, he must be able instantly and accurately to recognize the timbre of each single orchestral instrument at any pitch and in any register, as well as all possible combinations of the diverse • One such exceptional case might be that of an excellent musician when listening to E trivial piece which makes little impression on him, or altogether displeases him ; whereas the same composition may afford considerable enjoyment to a listener less qualified to judge. Or else when two listeners of equal capacity hear the piece while in quite different moods — the one healthy, fresh, and vigorous, the other wearied, suffering, and nervous — and thus, although equally matched in musical capacit)-, capable in different degrees of being stimulated to normal impression- tbieness. A MANUAL OF HARMONY. 235 instrumental tones. "That is the highest faculty imaginable", says Schumann in closing his maxim ; we say, "that is the ideal of a musical listener." Now, even if a given individual possess this capacity for hearing only in embryo, if he have but a certain gift, it can surely be cul- tivated and developed to an extremely high degree by perseverance and practice. Musical hearing does not begin, in our opinion, until this is accomplished ; and even then the most practised listener, though he be a genius, will feel, after hearing a composition for the first time, especially in the case of really notable and original works, the necessity for an oft-repeated hearing, and this the more urgently, the greater the difficulties presented for grasping the work in its entirety by the novelty and originality of its contents. If unable to hear it frequently, he will endeavor to supply any missing links by a careful and thorough study of the score, and thus at length to obtain a satisfactory impression of the work. One must not think, however, that this result can be attained, on hearing a work for the first time, by following the score with the eye during the performance. We consider the fashion recently come into vogue, of reading the score during musical performances, to be sheer nonsense as cultivated by students of music, and by certain dilettanti and musical professionals. For, when such per- sons are confronted by a new and entirely unfamiliar work, the simul- taneous activity of eye and ear will cause mutual disturbance. While the eye follows the score, the ear cannot yield itself up wholly and unreservedly to the impression of the music, nor can the eye be quite untrammeled while the hearing is engaged. For. this the routine of an able conductor is requisite, and even he would seldom enough place himself in the predicament of having to conduct /rz'/«a vista a totally unfamiliar orchestral composition. Only once contemplate these disciples of art, turning over with anxious solicitude the octavo leaflets of their orchestra-score amid the onward sweep of an allegro movement, and judge what may be the kind and degree of the impression obtained, from this first hear- ing and reading, through such musical tasking of both faculties. And even assuming that the listening reader is partially or thoroughly familiar with the composition in question, we ask : Of what assist- ance is it in enhancing the impression, to divide one's attention between the cold, dead signs of sound, the black note-heads, and the living, resounding tones.' What should we think of a man who. 236 A MANUAL OF HARMONY. during a representation of "Wallenstein" or "Egmont" in the theatre, should keep his eyes fastened on his volume of Schiller or Goethe? And considering it from the practical, instructive side, we perceive quite as little advantage in following the score. First hearing, then reading, then hearing again, is the best lesson for the pupil in instru- mentation. After the performance or, for expert readers, even before a first hearing, a careful study of the score is certainly to be recommended to every conscientious musician ; but glancing at or following the score during the performance can be of utility only to the conductor of the latter, for the purpose of setting the tempi, indi- cating the entrance of individual instruments or voices, and guiding the performance in general. Still, in this case, too, a following of the score becomes less and less necessary, the more the conductor becomes the master of the situation, and the more he grasps and assimilates the work in hand in its minutest details ; a conductor whose eye is anxiously fastened throughout on the open score, him- self bears witness to the fact that he has not fully grasped the com- position to be performed. Decidedly as we dissuade the student from reading music while listening to it, just so decidedly do we advise him to read music while not listening to it. "Reading music" means, conceiving written signs as sounding tones. This faculty will grow in like ratio with the capacity for "hearing musically." It enables one who possesses it in a highly developed degree to obtam a more or less clear insight, according to tl^e degree of his capacity and prac- tice, into musical compositions which he has no opportunity of hearing. For analysis, and the accurate recognition of all details when studying the masterworks of musical art, the attentive and intelligent perusal of familiar or unfamiliar compositions will also be of great service, either before or after hearing them. We can now touch on another point in musical hearing : Concen- tration in hearing, i. e. in following a composition of some length. We assuredly do not go too. far in asserting, that the great majority of hearers of music are actually incapable of following, in its entire extent, one of the larger and more complicated instrumental com- positions while listening to it, especially for the first time;^^of grasping it as a whole and in detail, and obtaining a correct total impression of the work. But we shall go still further with the as- sertion, that even after repeated performances of the same music the ordinary hearer seldom becomes thoroughly acquainted with it. He A MANUAL OF HARMONY. 287 h«a gtasped larger or smaller fractions of the whole, but for all that he does not yet know the work in its totality from the first tone to the last. And even when the hearer has succeeded in compre- hending the entire scope of a symphony movement, or a symphony, or an extended work of chamber-music, either by frequent and at- tentive hearing, or by studying it in the Score or by the aid of a pianoforte arrangement, it is by no means sure that he is really capable of hearing the whole in uninterrupted succession. But in this case a slight break in listening, or a brief interval of inattention, is much less likely to bring material loss, or to be of real disadvan- tage to his conception of the whole, precisely because he has already made himself familiar with the entire contents of the work. He can again quickly seize the thread of the musical narrative (if we may be allowed to use this expression for want of a better), and can supply the brief hiatus from memory, as he knows not only the " plot of the piece, " but also all its details, from previous study. We must likewise mention the manifold trifling disturbances which dis- compose, during a concert, the listening attitude of even the consci- entious auditor, because of his inability to defend his ear against other impressions while the music is performing. A sudden Cough from his neighbor, the slightest audible accident, may distract his attention, though but for an instant. Thus, in order to follow a long composition ijuite without inter- ruption, it is an essential condition that we should as far as possible put away and exclude from our consciousness all other impressions. No other mental effort requires an equally high degree of vigilant and unceasing attention, such utter self-sinking and self-forgetfulness, so complete self-abandonment to a definite conception within a given and strictly limited space of time, as that called for during the per- formance of a musical movement. For the performance itself can no more be interrupted without destroying its effect as a whole, than can the listener rest from listening, or cease to give attention, without losing the total impression of the work. A musical work never confronts the hearer all at once, in its totality ; it unrolls itself before him, and he must himself construct it out of the ever-gliding stream of atoms, and bind them together by an effort of memory, in order that the picture of the composer's fancy, gradually assuming shape by dint of the listener's unremitting endeavor, may affect him in turn. While the diligent and intelligent reader may turn over in mind the lofty thoughts of a Plato, Spinoza^ Leibnitz, Kant, or Schopenhauer 238 A MANUAL OF HARMONY. at fullest leisure and with his own mental equipment, and while it rarely or never happens that our time for studying and taking in any other work of art is limited to a comparative!}' very brief span, the hearer must take in and be affected by the composer's work within and at a given moment. Any other art-work of architecture, sculpture, or painting presents itself complete and finished to the beholder, affording him not only the advantage of a first grand total impression, but also permitting a leisurely examination of all details for the enhancement of the total impression already acquired. Poetical works afford the reader at least this last-named advantage, even if they cannot be surveyed at a glance, as a whole, from the very beginning. Only the profes- sional musician enjoys a similiar advantage in respect to the crea- tions of musical art, being able to prepare for hearing an orchestral work by previous study of the score, or to supply, by subsequent reading of the latter, whatever was not wholly grasped during the performance. We must still more strongly emphasize the distinction, that all the works of other arts borrow their ideas from life, from Nature ; they all possess a subject-matter which is either an idealized repro- duction of actual occurrences or an idealized imitation of Nature. Works of absolute instrumental music have no such subject-matter. We must characterize any attempt to foist upon or attribute to them such a subject-matter as a misconception, degradation, and ignoring of the innermost essence of music. Pure instrumental music has no. meaning but a purely musical one, and can be grasped by no faculty but that of musical impressionability and sensibility, which faculty is necessarily preceded by the capacity of "hearing musically."* Now, if absolute instrumental music is nevertheless capable of producing an effect, and in many cases even an extraordinary effect, on very many persons who are certainly incapable of "hearing" in our sense, we must carefully distinguish, whether this effect is brought about by a partial or full apprehension of the artistic inten- tion of a composition, or is produced by some ulterior cause. This *We have intentionally spoken of nothing but absolute instrumental music, be- cause in case of the co-operation of music with other arts, especially with poetry (to which we reckon not only vocal music in the opera, church-music, songs, etc., but also, in a certain sense, the so-called program-music), a wholly and undivided!/ musical impression can no longer be counted on. For in this case other factors are intended to influence the hearer in a greater or lesser degree. A MANUAL OF HARMONY. 239 latter we should term the elementary characteristic of music, its sound and rhythm. Many persons may partially grasp the inten- tion of a composition, for the reason that the prominent themes, and isolated characteristic traits of a movement, make an impression on the hearer, and isolated melodic phrases affect him hy their charm or even impress themselves on his memory, frequently enough, whereby his dim conception of the whole is illuminated, so to speak, in places. But for the musical hearer the details of a composition become the more effective, the more clearly the necessary relation of each part to the whole is recognized ; indeed, it often happens that some detail is first rendered intelligible by subsequent features, and.w'cc versd. It follows, that we can never find the essential in- tention of a composition in one single feature, even though it be styled the principal theme, or the fundamental idea. Just in our chiefest master-works, in the grandest revelations of Haydn, Mozart, Beethoven, Cherubini, and others, these principal themes are often astonishingly simple, and betray, considered by themselves, nothing- whatever of the form afterwards assumed by the whole piece. This is not at all due to the peculiar fruitful ness of these themes, as if such later development naturally and necessarily resided in them, but simply and solely to the teeming imagination which is able to build up marvelous works out of the very simplest materials. In the case of other and humbler composers we often meet, on the other hand, with beautiful, original, and charming themes, without feeling satisfied with the work or movement as a whole ; simply because the mutual relations of the details of the work are not satisfactory to us. But, apart from the indefinable charm of certain melodies, — which, however, frequently loses its spell and vanishes in the course of time — the elementary characteristics of music, as which we men- tioned sound and rhythm, will always suffice by and in themselves to produce a very marked impression. Anyone, whether a musician or not, and even some of the lower animals, can feel this most prim- itive of all musical effects, and even a single tone or a few chords, to which assuredly no musical idea can be attributed, may call forth a gpreat effect under certain conditions by inducing a mood. But every composition contains a great number of details calculated to induce moods, these details being primarily, to be sure, the material for the representation of the musical subject-matter. By and in themselves^ too, such details affect the non-musical hearer ; they af- 240 ^ MANUAL OF HARMONY. feet him each by itself, and awaken moods in him ; not seldom, indeed, they give rise in his fancy to entirely unmusical pictures and conceptions, causing his imagination to stray in fields far remote from the real musical intention and content of the composition to which he is listening ; — and he fancies that he has experienced true and deep musical emotion if he has — intentionally or otherwise — " thought" on anything during the music. Such hearers, and they unhappily form the great majority, always remain in the vestibule only of the temple of Music. Others succeed in finding their way, step by step, into its sublime interior ; few indeed are permitted to enter the holiest of holies in musical art, and, by attaining a compre- hension of the innermost essence of music, to discover all its treas- ures, and enjoy unalloyed delight in their marvelous abundance. CHAPTER XXIV. Subject-matter and Form. It was long before the fact was fully recognized, that the subject- matter, the intellectual substratum, of instrumental art-works in music has no prototype in Nature ; that music, unlike the other arts, does not borrow the ideas for its creations from Nature or life, — that it is, as it were, " a pure, unmaterial, self-subsisting spirit-world, apart from all that is of the earth earthly, and independent of the imitation or repetition of any conception derived from the things of earth." In their sonatas, quartets, and symphonies Haydn, Mozart, and Beethoven created instrumental music. Before these glorious revelations of the inmost essence of musical art, the astounded world bent in deep emotion. In these works were seen, for the first time, musical creations of a pattern and style quite emancipated from the rigid conventional types exemplified in the opera librettos and church- music texts till then in vogue, and of the grandest and most pregnant forms and development. Music was no longer the companion, the handmaid, of Poetry; she now appeared in her full majesty as an absolute and independent sovereign. No one was able to discover how it could be, that this same pure instrumental music so mightily stirred our inmost being, that we all instantly understood its language, A MANUAL OF HARMONY. 241 comprehended it so fully and perfectly, and were none the less obliged to abandon all attempts looking towards an abstract apprehension of this immediate understanding. Everyone sought the charmed word, the "open, sesame !" of the problem ; — the poetical content of the music. No one would admit that such content might be superfluous ; its denial was even held to degrade musical art. But in the course of time it was inevitable that the idea of a conceptional intent or con- tent should be given up, and that the subject-matter of a composition should be sought throughout the same only in its musical construc- tion, in its groups, periods, and successions of tones. The gifted thinker, Arthur Schopenhauer, was the first to promulgate this notion in his noble work : " Die Welt als Wille und Vorstellung," (The World as Will and Idea), Ch. 39, "Zur Metaphysik Der Musik" (On the Metaphysics of Music). But Schopenhauer's works long remained unnoticed, and not until much later was the same conclu- sion arrived at by Lazarus, in his " Leben der Seele," (Life of the Soul), and Hanslick (still later) in his essay "Vom Musikalisch- Schonen," (On the Beautiful in Music). Schopenhauer's remarks, penned in 1819, are so plain and pertinent that we cannot refrain from quoting them here. The passage in question reads : "On cast- ing a glance at pure instrumental music, a Beethoven symphony ex- hibits the utmost confusion, which is nevertheless founded on the most perfect order, — the most violent conflict, which changes in a moment to the fairest harmony ; it is rerum concordia discors, a true and complete image of the world, which rolls onward, sustaining in- numerable forms of being in an immeasurable entanglement, and sustaining itself by incessant destruction. But this symphony ex- presses, at the same time, all human passions and emotions, — joy, sadness, love, hate, fear, hope, etc., in countless nuances, yet all merely inabstracto, so to speak, and quite without individualization ; it is their mere form without substance, like a spirit-world without matter. True, we are inclined to materialize them when hearing them, to clothe them in imagination with living frames, and to fancy them in all manner of scenes proper to life and nature. On the whole, however, this promotes neither our comprehension nor our enjoyment of them, but only furnishes them with strange and arbitrary attributes ; therefore it is better to conceive them as they are, without such mediation." These remarks give, as far as mere words can do it, a most pointed and distinctive characterization of the nature of instrumental 242 A MANUAL OF HARMONY. music. That it is not an entirely exhaustive one, resides in the in- comprehensibleness and inexplicability of music itself, and likewise in the circumstance, that language does not afford words fully express- ing many of our sensations and emotions. This difficulty becomes strikingly apparent whenever we attempt to talk about a given piece- of music. We feel immediately that we are unable to describe it in words. Now, in order to give at least an approximate idea of a piece of music, the professional language of art has gradually adopted numerous terms for the designation of certain passages and parts of a composition. Thus "Subject-matter and Form" are two tech- nical terms which we continually meet with now-a-days in musical reviews. The latter use them to designate the structure of the sev- eral movements of a work, what might be called its architectonic unity, in contrast to the stimulating and exciting power exercised, in a greater or lesser degree, over the listener by the separate pass- ages, whether these passages are already contained in the themes of the composition or are built up and developed out of them. We have grown accustomed to accepting the terms "subject-matter and form " solely in this sense, and thus they serve both the teacher and the musical reporter as a makeshift in the critical analysis of a piece of music. Still, on examining the matter with closer atten- tion, the question first forces itself upon us: "Can the 'form' and the ' subject-matter ' of music really be distinguished in this manner, and can we conceive them, let us say, as something external and internal? The answer will of course be in the negative. Both naturally belong together ; for how and where can form and subject-matter be separated, — what makes the subject-matter, what is the form, — is the subject-matter not itself the form or, reversely, is the form not itself the subject-matter.? We can hardly hope to find an answer going to the root of the difficulty ; in truth, the innermost essence of music is an inscrutable mystery, and our present purpose is simply to explain, that the con- ceptions 'form' and 'subject-matter' in music must not be taken as things outside of and beside each other. On the contrary, they are so closely united that their boundary can nowhere and never be pointed out. If we seek, to begin with, for the subject-matter of a composition, we can in no case find its spiritual essence in any single detail of the whole, neither in the first or second theme of a movement, nor in any other specially prominent and markedly effec- tive passage. In proof of this assertion we adduce th» fact, that A MANUAL OF HARMONY. 243 the themes of our most eminent composers, examined quite by themselves, are in many cases by no means so precious material as is generally assumed. Take, for instance, the principal theme in the first movement of Beethoven's ^-major symphony. It begins on the auftakt in the fourth measure of the "Vivace,"' and ends with the twelfth measure. Out of these eight measui-es the entire movement is developed, which, like the whole symphony, is one of the most marvelous and perfect works of musical art. But in and by themselves, these eight measures contain nothing marvelous what- ever, or anything in the remotest degree suggesting the beauties to follow. They in no wise justify particularly high expectations, and the whole very simple melody, which does not overstep the compass of a seventh, bears the harmless, innocent character of a pastoral jdyl (especially in its instrumentation with soft wood-wind instru- ments, two horns providing a bass, and only the rhythm supported by the strings) ; it does not afford the slightest indication of the grandeur and magnificence of the coming movement. We might bring forward very many such instances ; but prefer not to become, diffuse, and can safely leave to the sound judgment of our readersi the answer to the question : Whether, in point of fact, the first theme in the Allegro of Beethoven's " Leonore " overture, or those of the Eroica and the EiO symphony, or of a very considerable number of the most glorious creations of musical art, are materially different, in respect to their intellectual content, from the themes of humbler works. We by no means ignore the fact, that in many cases the first theme, or the very first motive of a composition, may awaken- very special interest ; but we are the less able to attribute peculiar significance to this circumstance for the reason that, on the one hand, we have seen the grandest masterworks arise from the humblest beginnings, and on the other, that a fine beginning or a most charm- ing principal theme, and even many extremely interesting details, may be found in a movement, without its impressing us on the whole as a finished work of art, and without causing us to speaK of such a composition as if it were an eminent work of genius, or attributing to it peculiar depth of musical meaning on account of its beautiful details. We only need call attention to certain of Chopin's compo- sitions. No one will dispute the beauty of the themes of the open- ing movement in the ^-minor concerto ; yet scarcely one musician of even average refinement of taste could be found, who would approve of the movement as a whole. In it everything which we understand 244 A MANUAL OF HARMONY. under musical symmetry, structural development, the design, outline, architectonic unity — whatever one may choose to call it — is turned fairly upside down ; and while the entrance of the second principal theme for the first time in ^-major has a singular effect, its later re- appearance in G-major is positively distasteful, despite all the beauty of the theme itself. Hence we may conclude, that the beauty of a musical composition is not by any means invariably and under all circumstances dependent on the beauty of its themes ; but that, on the contrary, very many most valuable masterworks possess a thematic material of little inter- est. In passing we merely remind the reader of a great number of Haydn's quartets and symphonies, of the themes in Cherubini's over- tures, of certain sonatas by Beethoven, and other classical composi- tions. Further, the conclusion that there resides, in these insignifi- cant themes, an especially fruitful embryo, bearing in itself as it were the conditions of a grand development, would be quite wrong. We clearly see that such is not the case when two unequally gifted masters employ, accidentally or intentionally, one and the same motive, one and the same musical thought, as the fundamental idea of their composition. Mozart developed the Allegro of the overture to the Magic Flute from the same motive that Clementi used for the first movement of his B\) sonata. But what a contrast between Mozart's sublime palace, and Clementi's well-built, yet common- place dwelling-house ! Hummel, in the last movement of his F- minor sonata, uses the same fugal theme out of which Mozart de- velops the grand fugue of his C-major symphony. The fact is sim- ply, not that the master takes from the theme that which it contains, but that each fructifies the theme according to his individuality and the might oi his imagination. Thus the theme is by no means of such vital importance to the composition as to contain its intellectual content, so to speak, '■'•in nuce;" still less can this intellectual content be contained in any other detail. On examining in detail the most effective features of a composition, and taking them out of all connection with the rest, we nearly always find that in and by themselves they contain nothing whatever remarkable or peculiar or extraordinary. Their signifi- cance resides wholly in their evolution out of what precedes and their connection with what follows. In its proper place, therefore, any- thing and everything will have its proper effect in a work of art, and a single tone sustained by one instrument may attain to equal impor- A MANUAL OF HARMONY. 246 tance with the most complicated contrapuntal combination,— the unison during a few progressions may be fully as moving as the prolonged swell of a melody with an elaborate harmonic foundation. It follows, that we shall find the essential intellectual content of a composition neither in one not in several or many of its details ; it must be sought only in the whole. But this Whole is termed, in common parlance, the Form of the composition ; and this being so, form and subject-matter would again appear to be identical in musi- cal art. They are proved, however, to be not identical by many works with whose musical structure we can find no fault, whost symmetry satisfies us, whose organic articulation and develQpment leave nothing to be desired, and which nevertheless, despite their fault- less musical construction, neither appeal to our emotions nor satisfy our sense of the beautiful. On hearing such a piece any intelligent musican will say, that it is extremely well put together, yet surpris- ingly tedious for all that. Here we see a finished artistic musical form, while the subject-matter cannot interest us in the least, or move or attract us — the diametrical opposite to the above-mentioned Chopin concerto. But it must not be assumed, that the composition in question consists merely of form without subject-matter ; — its subject-matter is neither novel nor specially attractive to us ; all that it can say to us has been better said before by others, consequently it makes no impression on us. Besides, in view of the wonderfully rapid progress of musical art, the musical subject-matter of a work may have been very attractive when it was written, yet thirty years later its charm has vanished. The ravages of time do not spare even works of decided eminence ; only the creations of genius are for all time, and remain untouched by change. Such works are generally far in advance of contemporary understanding, being first appreciated by later generations, who must themselves learn to grasp these mighty creations by patient study of the same. All that now remains to be done is, to assume that the intellectual content of a musical composition is something unknown, the effect of which we feel, though unable to grasp it as a concrete conception. Still, we may venture to speak of an intellectual — nota bene, musi- cally intellectual — subject-matter of a composition, even if we can- not define it with words, or explain wherein it actually consists. The lasting effect of a composition on a musically educated listener is the best measure of its intellectual content. From the earliest times music has been called the language of the feelings, probably for the 246 ^ MANUAL OF HARMONY. reason that our every-day speech, however highly developed it may be, has no words to express many feelings, and precisely the most delicate feelings and emotions. We may therefore be allowed to say, that we (instinctively) feel the musical content, idea, or thoughts of a work ; but just as we are quite unable to grasp this musical content as a concrete conception, so, also, is it totally impracticable to separate this content or subject-matter from its form, to extract it from its form and development like the kernel from a nutshell. It is simply impossible to conceive the musical subject-matter in its musical form like a body in a garment, a kernel within a nut, as a first essential in something less essential, as internality and externality. Both con- front us firmly and inseparably united in essential co-development, the first arising with and from the second, issuing from it like the fragrance from the flower, like speech from the human mind, like the spiritual from the corporeal life. We feel the subject-matter in the form, we feel how the form is filled by the subject-matter, yet we cannot disunite them like wine from a glass. Nor can we say that this subject-matter takes on a peculiar form, for the nature of musical development remains in the main unchanged, in spite of numerous variations. Still less could it be said, that a subject-matter can be w^orked into a musical form. Just as any conception which :s full of meaning and true to art is a spontaneous one, in the art of music, too, subject-matter and form spontaneously coalesce, and can therefore not be disunited. They belong to each other like the body and soul of man, they can exist and find expression only when united. Impossible as it would be to say where the dividing line is, in man, between body and soul, just so impossible will it always be for any- one to point out where, in a piece of music, the line of separation may be drawn between form and subject-matter, where their limits are, where the one begins and the other ends, wherein the soul and wherein the body of the musical organism consists. But here our comparison halts ; for Nature, throwing off" wholesale products on a stupendous scale, often enough works very inartistically, and assigns a beautiful soul to a mean, ugly, or infirm body, whereas genius knows nothing of such natural accidents; in the works of our sub- lime masters we never find a beautiful subject-matter in an insufficient form, but everything combined in most complete unity and perfect harmony. APPENDIX I. The following examples, with references to the exercises con- tained in the body of this work, and worked out by the author, afford many suggestions for the solution of the exercises. It will be of great advantage to the pupil, before beginning to work out the exercises given in the several sections, to analyze carefully and in each case the examples given here bearing on the subject in hand. The thorough-bass notation, and also the degree-numbers for the chords and the course of the modulation, are to be filled in by the pupil in the space left above and below the bass staff; the examples written out in four clefs should be played through repeat- edly. By this means the pupil will soon become thoroughly at home in this work. The examples being written with special ref- erence to certain rules, they can of course lay no claim to real artistic merit; they are intended to serve only as. a practical intro- duction, and to that extent form an important addition to this text' book. Examples. To Exercises No. 137, §37. i ^s m ^ P =s^ -is) — g- rr P -zt s r f E^ I ^3 ^^ ^= ^F^: -I5> 1=- TS> S>- f-T^'- -G> (=- -eir- --g'— arf- r zsi- r r ^ ^ -(=- f2471 248 APPENDIX J. d^=^ li fe^zfe j ij. J S3I ^ ^ f-T ^-"^gr f-^ ^^» ^^^-N= ^=i fe ^^^^^ f^ i^ g I ^ To Exercises No. 145, § 39. i s iZZ^ -g e>- P^T ! ^ g - 9 -0-J-^L^p ^ ^ fe=F^^=?^^ ^^^ f r"TT ^ ^^ ^ ^^^I jgg -g f'' r|g-ite— r|g- ^ ^ APPENDIX I. 2^9 ± m i=i^ rrr^r ^ ^-^^=t^ ■r^ -^35;g g^ 1^^ Ms ^iii i i -^—\-sir "27- H- -is-^ \-z:r -F—P- f=it ^f *" sa* i ^ -a]g- ^ To Exercises No. 165, §40. T — g— .^^rsir H=l=E t^;^: 3 ^^^^— ^ pE^z= pH-;^=^ i i ZgTl - g. ■ a g^ Ei -sH :t=3: ^^^ =^= SS ^m rn^- ?E fc^ Srf E^ — ZfT ^ f ^ f--f- ■27- feyi r i r H^^ PT I - APPENDIX J. 251 i i "^ r^rrffrf^ g^T" -Si- f2- 252 APPENDIX I. ^ I iSil TY' T w- P^i To Exercises No. 185, §43. J- i^^^^ g-^-^-^ g ^ d J'-->g. g : a g g ^p »^3 P^^^ m. i fe^^ ^fc^S ^^ ^^^^^^ gj^^ r^^ ^=^ =fl^ y^g^ =t=t ^i feiE dz bg rdi 1FF=§: =S^ f- :r- r r 5HS =»^ ?^ « — 1=- :2i 12: i ^^^ it t=B= pal f-'^'t-;^ f^'t^^ -7f -s>- i^^te^EM i --=^^^=^-^ «!-!- APPENDIX I. 253 ^^p^i^^^^ 3 istes P^l Efc -z;!- =&S -a*- :^ i ^t=^^ •^ — ^ -^- -s- f- S^~~^s -» rl=^ g i_^ t= -f2 e- t-B — «■- i ^g=i^^^^^ "^i: f- r =s^ ^;^^e! ?= i P^E ^*- r-psp laa^EgE^ iEEE ? ■ts— !«• i te5= ^^P^^ a I l=a=Ei: ¥f^ =pt ^— 2^ r ^ #:: B^ -g — si- 254 APPENDIX I. To Exercises No. 195, § 45. f'^H^"ip"^ ^^ 3 «^c^ =F1^ ^ :2==£Ei.-: i i te^ [^ 2EE^[^EE2=^ iEg: ^~^i:f^~r i^ ^^^^ ^3EEI^ i SE S fl^ g nfcri^g sg=g i Ei ES 'g — gi- -si- :«^ -«— ■— 5*- ^^^^^i^te ^* r -«■- i» i^s ^^i^ ^^^^ rg dj^ i ter s—- — r*- -g^, |g P^;ff-T^^^fi^Nj=pSfj ^= «- 9y^baJb>g' ^ 1^-^ ^ - APPENDIX I. 255 i k^-L S^gj- ffi^ l£ s= :3srL"s=t:r»: ^^ p^--fp^F^i-^=i^-J S^^ ^ ;2=1N :1^ i ^^^^I^S*^^5^ ^^^^S^ :f: r r S^ Ig -yftg fg- -f=- fcijzzn d ^1^ I ■ — & zj- 9=5 -i^- f f r rr I ' ggpr^ ^^ - g i g - To Exercises No. 207, § 47. i ^- r_i._i^ g: ^ p^ :'^— ^ -g' Z 7- r ^ ?^ -(=- ^ ^^Pt^: i iAa^^ =t^- les w ^ r I T -IS" — fs: ^ ^ p ^2: 256 APPENDIX I. i ? -^ 5^ r "11: s E^ 0^ s -si- 1 I ISI i r T^p-^f^^^f ff S — — -' — I© ^=-- i-^^^SEe =tt^ S EE6^ HEEE^ y^-j-# ^[bg-&d-^4 ^^g^^- ] d--|^^H^- "f-r \>f^F^^^. r¥- §ii^ =b^- :^=Ct^ ME -£ — =)■- t=f St*'- ^ t=t=^ i^ T ^ -«^ ifi^J p yijrpf -.f^-ris^ fl^ fc»= 4 3 - $! — jgi- SSiS^ ^=p=^=^^^f=^^ ^^ 9i%j^:^:s^;i^=y-4-^3^^ APPENDIX I. 257 i -ei- %^=te -m 5& ^ rT- ■f=— ^- ^ w— :£ gi — ^ — g ^^ ^ A^aE^^ ' g xaJ - p--i--yr ■^ S ii^ Ss -Si- ^yp^-iT ^fc^fs I W^—^-j^^^ ri r r f I fl^ &15 1^ I'n*— I— i g wr^ -|g' E^ ag= To Exercises No. 217, §48. i 3t=g: %^ pr ^ -i=- V ¥ r^ §^r -gg- * ^ li?- SeS 3 L:^ :^r=|^ r~r - (g — ftg - 258 APPENDIX I. i a ^m -ssz ig:— ^ Wz tr -^ r rr ^ i» ^ i Ei §^ S •b ^ r frsl-|-g^-=jN=Fg=gg=F^ i ■X J4^ ^ S2 ii—tS-i W-'rr i!=a s^^ r -«-- r ^s s: \p\\i\. |-uj j:^ g ;fl^ -T^(© — -^ gg' —^ ^:=tc§2 2©^:^ fei S fetM^ :te= i fcr ^ i?^ i=Bi ^ ^ r ifi-- *^ ^f- ^^JUIJHjUI^ -p: APPENDIX I. 259 ^ ^^ r^' ^4 ' -g- -fed: r^ r jXf—'i frf: F=^fi=^ 'fg- Bit- -SI- j^ M -4- m ^^ ^f :&zi&=S! f^ tS 1— S! 1 (S- ^^ I ^^ ^zj^ -s*-^^ To Exercises No. 222, § 49. -f2 «>- f^-|g-^ - ^ .ai=- IS K^ Eg :l^ t tS ^ rfSi- -f2— «>- IJ^zSife^ •fe: ^^ s |> fj g^ • I ^ • If? qg : -(&-=- h-*"- =ft^ ■260 APPENDIX I. ^ -s rJ. ! # ■ ^:Sfi=S=X ?— I— j g iu - ^=S= W- ffp- i"^gr¥=F=g^^^ fej — j-^'g asfeEfe i »= sma^ »c Ma^E^ -jg— ftg- iri^— Sg: F=t Ff^— g g- i %.R — ^- ^ — ^ — sJ— ^1 -gi- -(=- -g h -« — s(- /!==« I E^ -ts) — f->s> — ;=- =i5= III 10 H yrT~^ ^1 ,g^ i APPENDIX I. 26t To Exercises No. 225, § 50. n=^ -ir^^ r^ -r p= ^K\t- "■5F=^: M±^: fe-{^— g ft =^ :i^ ^ i :m ^ fg~~ff^- 2: i?^ iF^SHra- -<2 iS'- ^ I Mf b ' ^ - tt^=© ^ ^b r — '"^ — l '^ iJ r^ [^"T ^f^^ i -f^ 'g Z5l- a< g- I ^=F g-ftg- 1» 9==^^- p=j;p=p::g=| K ^=— fi^ :^}^ s ^- IS ^=t ?= Tg-gg- i =»^ ^ J^ » £ ?^ ±= rr 15 ^ is: 262 APPENDIX I. To Exercises No. 339, § 51, -fZ- -jg- .(=—«- li ES g Og_ -<2_^- S ^ -^a-i S"- ISI SSfe^: t-:i=it I s*— ■g - h2 Si- 4-«s rni^fr ^- i lagg| ^^^°= l^ f; -|5^- E :s=tl^ i^ — g /r? =^=^ -&-\-s- -■si- rsn—g- =iS= f^^ f^= i 5EE?^^ -f g-g ^- i^ h2 k -g ;:<- ^^ iU=2 — 5^ - I r 11 1^ ^=fe eJE -(=- -f2-fe -^z- - f^ -(2—^^ wn -(=■ ^ H r 7[T— P— fz— p-^ — = r a gi ' [" ^ - ■t=^^=h EHE 131 fct les < ? f Z ^IS -^;'- -js5— ^5? 1=^ i-Si =q:^- ^ APPENDIX L 26S rF=^ -M^ 'm m -a "Zis. ^=^ 1 ^b— 9^ — ^ r,f^ ~^ ^ M ^^ M it ^ ^^ Tg-Sfg- gas fflj Tj ^J I . l i s eg ^^ £±=3t ^ B -ffl ^ai g^' ^ l|L_y I ^ ~fe r ^ i g — -iS' — p: g^ ^FJ-Sp-ffl^ ^^^^^s ^^ I F^ ^ p^ r^st •fZ SI- ^ =s^ ^ 1P= g=rf--p^y^=^ hSZ- tS>- -&- M latE ^ ^ (2- 3E lS'-i=- [g I fg ttrg- rftz- ^^ nS> — (2- 1=^ ^^ ^ «=»- 264 APPENDIX I. - ■e— i«'— L-jfi- ^lEtElE i -jsz e, -=SZ IS^ p— w - HE ~|g fl?~ hS2- ^ 1 i^^E (S ^^fc~^~~~"& g^^pr^zr tr ^ ~ sH?gl~ -(g— I g =5^^ Wt t^ -(SI— I — ^ \-- l2tE--fz -»- E :|S= :«^ -«' 1 — & 1 — s 1 — &- ^m <= G>- C fi '- -[g — zsi- ^ /'I \> -=X- II tl « ■ r * ' ^-^ ^^=^ ^= -f^— zj- -g i-iai »^ -42 (=2— (»- -fij fi -fg— s» > g •fc^ j^— t^=^ i-^-E^ -«-r-'=2- fePE if^ i 'fete -&- -e^ -&■ -'S- -iS- -&- -& r— "^^ ^Z- i ^$^ j£i -62 ^_a- ^i^l^JZz^zrp: r^ " ^r; !— ^^^Vrr- , i Tg-i-g— ZSl- E^ APPENDIX I. 267 ^ g m I H tx -19- S^ ■^!^— as- I t=P ■^ii«i- •t=f tel I Tm^ --V^ ^^W^f^' -j f F rtTTtmfy i To Exercises No. 294, §56. ^1=6= _(z_q — ffli ilCtp -1-2 — ^ St Kil +-H- m 3E Se^e — gi — 'g- ia l?E? -■g si- /|=r 7^^ — ^- ?= :fi^ ^ g — I — G> — |-ig si- n. i -^- ?^ |g — g^ i teg^ fc^ :ttt 5«- :#s: «68 APPENDIX I. EfeEEil ^^ i -Jtgi M^ -z^- ■JS ^ -> /■ s -fS- m^^ m^ /^ N -<2- -(=- -©- tS-- IHi ?= :#2-- =#sr i -(2-4-(=— iS- «*= =fi^ 1^ ■42— fS- -^—7i- -zi J s;! — 'S'- S g= n#=r=r=S^F^^ K^ :fts: ^S IS P= APPENDIX I. 269 To Exercises No. 309, §58. ^^^ :llp=l2jc: f — ^ eJ - ini S^S -•-^» -*—p- W^ =^='^Ep^pJ*Z ^Ipg l=i:e^ =^ f=^ EEb' =:lib: it^s; :l=^=^= itifz M l,t=^ ■B»Hl: ^^_tSt^tJ^_ :Sti=«=F=t ■x=±=t i^sl— ?_= Jit i^-^=t rpzizp: U =t=±t is 4bb= -•— ^ |CzBa=r=^t I gfes^ii^ai -^— •- :t=F ^=» =t=F iE^E3; irttt ^_,_ 1^=^ -l?#3f»— 1«— h =l?=f: • ^e- ■F=t=F F=f;=t tgt 1^5- :t=Ff=:=-1: ■rir-t=t— ^- =c=t MiC^=& fe •— 1«- ^ |t tS- 1^ ^2^fe3Erp:^^^E^s^^^=i 270 APPENDIX I. SEt H n — •- ■ta^ fn f=}=--F ni m^- • — $■ — •- i s m^-- :e=Pee?e ti-H- t? H Ssfe -y^ To Exercises No. 349, §61. The cantus firmus in the Soprano. C. i. c m c d° G A\> di Gi 1 " 1 — '* 1 n 1 — *" \\<^ rs 1 f , 17 / J ' W^ <5 1 J b * ' t^ ^ -^ ' J b 1 '^ H K^ / ' /^ 1 ^ p b t 1 u ^ ^ S "^N ^ ^ H >' b/^ fl'* n uf I > r\* \t ^ ^' , 'i. v)',^ /* ir> Gf 1 fl? ::^ u 1. I y ^ 1 t: d^ C7 c df c d-j ^7 c 1 II 1' t> J, ! 1 II 1 1 fr « 1 r= r^ >^ \ n ; „ I L (7 <3 '^ ' IT' 1 «? II THi — I U uf i,' . >, ^ ^ , ^ r "^ 1 r^ in 1 C U u » S' "ff'^ •^ 1 n " 1 1 1 1 J ti Tk 1 1 1 I A P b 1 r lP ^ n " ^ n \ n 1 1 ' 1/ ' - ' ' ' 1 £ ^ ' W 1 r )"i i' '* ^ 1 ^ t. V (^ P ft 1 — s, a J APPENDIX I. 271 To Exercise* No. 352, § 62. The Cantus firmus in the Alto. Izfczli X -4 M It ± 'Hi • ^^ B\,^ E\) A\) B'O'j Eb fy ^b7 Eb7 C. f. -(9- m^ -61- -IZ- W^ n -s>- sBi Bid?-7|^-77 zt^ W- n ^b-, d^ gi Ah Bb E\> c . fy Bb-i Eb ^^ ^ iS> \—>S \—6l- ^ \ o ~~ F-^ — V g p-^ — I — ^5 — 1—1^— His- ^^-lS'- i^ V F=frV -« . ^^ i r f S «7 -Ot^ ^^ fti g c g a^ Df -s^ g -.r^— t-^- l^ Bg- -fg- IS' — |~rg~ 272 APPENDIX I. ■"S — r«'' I ■G> «2 Y<9- :Se: ff «? fc fg p g p * < ♦ APPENDIX II. Suggestions for Working out the Exercises in the Manual of Harmony, with Special Reference to Self-Instruction. Repeated inquiries from persons studying witliout a teaclier con- cerning tiie most difficult exercises in this book, occasioned me to write out the following suggestions ; they contain such explanations and hints as I am in the habit of giving my pupils in harmony at the Royal Conservatory. These suggestions will tend to facilitate the teacher's task, and prove a welcome aid to the student. To §3 1 , page 43. In four-part composition the triad may also be written without a fifth, as previously shown in Ex. 67, meas. 5- Ex. 92 might therefore begin as follows : ^^^m 92. 9^ S: -!&-=- n d: I VI Indeed, a correct leading of the parts often renders this necessary (comp. Ex. 67, meas. 5) ; Ex. 92 could not contain the tonic triad with its fifth, if the bass were to begin on high £>, and the octave of the root had to appear in the soprano. 02. — ii i^S=^ =g= ^ etc. d: I VI //: I VI V, or thus : M. :Jf^ 7 etc. t ^ T-r-\ d: I VI Exercise h may begin : i^^^&j i^^^^ 8 7 etc. \ c: \ IV V7 I IV The last of these Exercises begins thus : g%\ I III' V7 I VIlO I To 538, page 74, Ex. 142, me-Jis. 6. C/) C: V, I 276 APPENDIX II. In this case the leading-note, when in an inner part, may also b«< led downwards, covered parallel fifths not arising therefrom. Ex ercise k on page 77 may therefore begin as follows : i «f# ^ ^ 332 -^I -sa- I^ ^ 3 etc. ±=t gf- III' V V7 ^^ At the resolution of the chord of the second, the fifth of the domi* nant chord of the seventh may also skip a fourth upwards, e.g. ^m C: V7 The first exercise at 145 (a) may therefore begin thus : a: ^ =5): _!2_ etc. 9^ C- I V, To Exercises 170, §41, page 89. In the case of all triads, the seventh can enter after the octave of the root without further preparation ; Exercise a may therefore begin thus : i 3 -2^ =g= Ei etc. a 3 C: I 1I7 V7 I I7 To Exercises No. 1 85, §43, page 96. In Exercises e and/", at the places marked N. B., the fifth of the diminished chord of the seventh may progress upwards, because, being set below the root, it forms a fourth with this latter. APPENDIX II. 277 W N. B. m ^^ r—f'-T,,^. p^^ iJ!^= ft- I ^=gg To §44, Ex. 187, page 100. From Ex. 187 the pupil will see, that the dominant chord of the seventh in the fundamental po- sition must always be given with all four intervals in four-part writing, when it is to be resolved to the triad on the 6th degree. In progressions between these two chords in minor, the third of the triad on the 6th degree must then always be doubled. In Major : < In Minor: "m ± r i EEE m, C;V, c: V, VI To §46, Ex. 203, page 112. Mozart, however, writes such parallel fifths, in meas. 8 of the fugue in the C-major Fantasia, even in three-part composition, which, as regards such forbidden pro- gressions, requires still greater caution than four-part composition. Compare this passage in the above work : [i^^i ^^ v^*^ ^^ I 278 APPENDIX II. in which case the effect of the parallel fifths between the soprano and bass is, by -way of exception^ an admirable one. Hence it is sufficiently evident that parallel fifths, like those exhib- ited in Ex. 20I and 202, may be sanctioned at any time. Here we must take into consideration that the augmented fifth is a wider in- terval than the minor sixth. Either interval may follow the perfect fifth in downward progression, as may be seen from the examples below. i s^ i i tefe i ^^ I ^ ^- ^^zs^ a 7 P^ ^l I §5^ ^ f: IV III' V7 I f:\\ air : IV At. iiif: vii§ i To Exercises No. 207, §47, page 1 1 5. Exercise n may be- gin as follows : <«)< i w tefc^^ ^ P i»=a-ggi5^ r-T i==t :g|zifc^=E| 1^- ■i& ^ (S- - ^ « :g-ig: ^ g: I I etc. 8 7 6 s 68 eb 5 a 8 ' I < i a * ^ ja fb ^ t i I" a I" i'biiabiVyl «b: I*b: V7,?b:ll°7 1 ll°7 lab:V7 I V7 Exercise q may begin as follows : J-r-J^- g-Ffegg- ^1 *=5^^^«^ii -Bg- xzsz tt?2. -SZ; ■^1- tB 3S=^ ex a f-#^ aB jetc. ^ a r— jg - g J I j{ a ^ 'g- fi:lb:\., I VIlO lZ);Vp^j:V7 i ^:I^:V7 APPENDIX II. 279 To Exercises No. 217, §48, page 121. Exercise b maybe •worked out as follows : i ii r=rT ■x—^- I Vi, F: I or in open harmony : i ^ -si— g - g e) ^ f T rr J. i ii J jJ^^ IB 3^=4= ^:^J^ - ^g^— g- f^ :i: e 6 t 7b I i i b-^ tf ^ fl^ 33 ■'g g;!- V7- -f—r Exercise h may begin as follows : (A) P^ d etc. or: < iffl 8 (2 ^l*:! II I IV II S M =^ i=J. f=F ^1 3 (2- etc. ^ ( l avdtT pTjTl or in open harmony : I j^ynj^ippp :& s-^t n « e ■?" e 7 s 7 , *| J * * etc. ^ =P ^b:I II I IVvi^:viiO i_/r-V7 — I^biV, I ^.- V7VI .t.-Vt To Exercises No. 239, §51, page 138. Exercise h should begin : (h)< ^ > / | t •' 3r r r r r ::J« P 1^ fei^ -g — &' y ^ (g ^^ =^ etc. ^^^ 1" o 3 S 4 a S f i" 4B 2b en 7 Sa 2n t" aa -to a. • ■ g tj &J Ih?;^ ^^ /; I IV7 I Cb; V7 ; I 1I7 1I7 V7 IV IV, To Exercises No. 294, §56, pages 173-175. Exercise c may begin as follows : -J: ^3^^ i^ r r fH^ f f 3 6 6 9 6 -6'-:-^- E^ ^ ^ etc. ti3^ ^1— h«: -(SI- E^: F: 1 IV I IV viiOvi V Irf;V7 Iy^,•IV 1I7 V Exercisey may begin as follows : ^ bai -^-^^ =»^ -2^ -«'- -z:*- -»- I^Ei =§P=P= -!= «?- ie=ifei e: I vnOv — i G: V, I ^; 11O7 V7 i ±E=± I^: =«SI =#2= ^ -s- =fi^: =^i2si- ~W^ r ^ifc -f 9f- -Mi m V,- I D: V7 viiO /J: VI1O7 b: V APPENDIX II. 283 Exercise A may begin ; ^ i^ W fet>:a i 9 t> 7 9 8 1^ -J. ^■- I ^ IV ^b: V7 J^J_^^J:^ r ^ r =#g= i5?= 9 e etc. -r VI II - ^.-iv^ g^fc J r j- To Exercises No. 309, §58, page 181. The close of Exercise b may be worked out thus ; Exercise e may be worked out as follows : w P^J= -^ — »- U=^ J- ■ ^—'5^ i=i: f^-n^rrf—rrr-Tr- f=}tS=?=qi: i±BE 7 8 6 4 5 4 2 3 6 g 6 3-i=^ ^ r r 284 APPENDIX 11. i =i ^^ ^^ §Mf=»J=3^3^h^ el) rrrf s I a 2 3 J 5 till g t ¥ESf ?=P: t=trt i "r-s-- iH *s; r To Exercises No. 349, §61, pp. 204-205. Exercise a may begin as follows : F £b P Bb C Bb C-j F g '-^ It -zg [- ISC etc. Exercise c may begin as follows : G Df G a-j w< i w^^- ^t:^= 4^ iS o 7 Z>7 ^ etc. APPENDIX IT. 285 Exercise e may be worked out as follows : Gb D\) e\) b\) N.B.fb D\, mj Gb oOt :3r fc N. B. Comp. Ex. 59 i and Remark, on p. 26. ^b7 Gb eb ab^ N.B. ZJb7 Gb -^e>- -TS- i f .2. i U) i s I ^ N. B. One may either let the octave precede the seventh, or let the lat- ter enter unprepared by a skip in contrary motion to the bass. Exercise g may begin as follows : E Bt E Bf E f%T Bi E tts. ^-g— f-g — f-g— l-g I g ligzl : :s= -2?- f a -is»=z- 7 g- ^ -«- ^7 £ <:J7N.B.^ ^ ^7 cj ^ IC s a -<3 i_< ^53= w ^c±?" E^iE -«- etQ ■(S>- .jfiJi 2C N. B. The Third in the chord of the seventh may be doubled, when it is not the leading-note. Comp. Remark on page 62. 286 APPENDIX II. Exercise i may begin as follows : g Z>7 Eh «07 g -r~e sl Z?7 =5221 ^ ^ i=*I M- etc. -ffl- Exercise / may begin thus : b e b a%0 ft° =«2= I _iE_ -OZ N. B. N. B. N. B. It is best to write diminished triads as chords of the sixth. on ^ G e b C%°T — • UH-. 1 / A # V 1 f \ * Tfi^ r- ^ -^ -^ -S- -g- -^^ -^ etc. 1 t 1 I rv'tt ^ ir3 r> I P J-*'if n tn \ 1 ^ If \ 1 i Exercise m might be worked out thus : c f t f G («) Efc$ -^fr -ii: 6 -S>- zsz r^- APPENDIX II. 287 / c N.B..4b rfo i ISZ 3gi -fi(- -- ;i N. B. Triad without fifth. To Exercises No. 352, §62, page 207. Exercise a may be worked out as follows : (<») fe t-^— G> — - e EE^ i jS. -&- -ffl- ^ JO. -»■ n 1 ■<= 11 1* II n II 1 '^ II 288 APPENDIX II. To Exercises No. 353, §62, page 208. Exercise d may be worked out as follows : Eb «°7 -d- g a"7 g E\, -st- g --^ s i i INDEX. iirrfAw/o/ chord-forms, 94, Ii8, i6o, 164. Accomp. of chords to a cantus firmus, 194. A itered chords, 142; in modulation, 222-232. A/to, 14; as cantus firmus, 206; alto-clef, 126. Appendix I, 247 ; II, 273. Arsis ( = strong beat ), 221. Auftakt ( fractional measure beginning a movement ), literally " up-beat " 24* Augmented chord of the sixth, 129 ; of the third, fourth and sixth, 128, 13-5; of the third, fifth and sixth, 128, 133. ■''' Authentic cadence, 23. Bass, 14, 15; leading of, 199. Cai//r««, authentic, 23 ; plagal,23; deceptive, 98 ; perfect, 66; closing, varieties ot 221. Cadence-like progression, 86-0. C-clef, 125. Cantus firmus, 194, 206-8. Changing-notes, 178. Chords, altered, 118. " classification of, 12. " independent and dependent, 12. " passing, 177. " view of, 140. " also comp. Triads, Chords of the seventh. Chord ol the augm. sixth, 129. " of the djmin. seventh, 93. " of the fourth and sixth, 46 - 56. " of the seventh, 59 ; inversions of, 70 " of the sixth, 46. Chromatic alteration, 118 ; semitone, 4. Circle of fifths, 6. Clefs, View of, 126. Close, Closing cadence, 22, 66, 221. Compass of voices, 14-15. Covered fifths, 67, 182; octaves, 26, 103, 182-192; unisons, 191. Consecutives, see Parallel fifths, octaves. Consonances, perfect and imperfect, 9. Contrary motion, 18, 54. Counterpoint, 14. Cross-relation, 193. Deceptive cadence, 98. Degrees, 2. Derivative tones, i. Diatonic scale, i ; semitone, 4. Diminished triad, 25. '• chord of the seventh, 93 ; in modulation, 216. Dissonances, 9. Dominant, 13; dom. triad, 14; dom. chord of the seventh, 59; in modulation, 21a Doubling of tones, 15, 51, 58, 62 ; of the third in the chord of the sixth, 47, 58; of the seventh, 62 ; of root, in chord of the seventh, 62 ; of leading-note, 58, 8a (289) 290 IN]>EX. Dropping of intervals, 62 - 3, 87. Eleventh, 2 ; chord of the, 172. Enharmonic change, 215, 224. Enharmonico-chromatic scale, 8. Exercises for practice ( fund, triads in major ), 24 ; ( all triads in major ), 33 ; (triads in minor), 43; ( inversions of triads), 56, S7 ! ( dominant chord of seventh ), 68 - 70 ; { inversions of ), 76 ; ( secondary chords of seventh in major ), 86 ; ( inversions of ), 89; ( interconnection of chords of seventh in major ), 89; ( secondary chords of seventh in minor, and inversions ), 96; ( non-cadenced progr. of dom. chord of the seventh), 106-8; (progressions of secondary chords of seventh with chords of other degrees and keys ), 115- 117 ; ( triads with altered fifth), 121 -2; (chords of seventh with altered fifth ), 127-8 ; ( augmented chord of the sixth ), 130 ; ( augm. chord of the fifth and sixth, and third, fourth and sixth ), 138 ; ( simple suspension ), 160-3 > ( suspension in several parts ), 173-5 ; ( passing-chords, organ-point ), 181-2; ( accomp. of a cantusfirmus in soprano ), 204- 5 ; { in the alto or tenor ), 207-8. Faise or inharmonic relation, 193. Figuring of chords, 43. Fifth, 2 ; perfect, augm., dimin., 5 ; omitted in chord of the seventh, 62, 87 ; altered ( in the triad ), 1 18 ; (in chord of the seventh ), 122. Fifth and sixth, chord of the, 71 ; augm. chord of the, 128, 133. Fifths, open or parallel, 17, 135; covered, 67 ; in contrary motion, 203; succession of perfect and dimin. fifths, 30, 31, 69; of perfect and augm., in ; Circle of fifths, 6. Form, 240. Four-part writing, 14-16, 194-8. Fourth, perfect, 2 ; augm. and dimin., 5 ; preparation of, in chord of the fourth and sixth, 199. Fourth and sixth, chord of the, 46- 56 ; employment in cadence, 199, 215, 222 ; aa passing-chord on weak beat, 199; augm. chord of the, 120. Fundamental, see Root. " chords, 140 ; triads ( in major ), 13 ; in ( minor ), 38. Half-step, see Semitone. Harmony, study of, see Preface. " close and open, 21, 124. Inner parts, 15, 49. Interconnection of chords, 17, 86, 98, loi, 108, etc. Interval he\.vieen parts, 194 — 8. Intervals, perfect, 2 ; major, 2 ; minor, augm., dimin., 5 ; View of all, 7 ; inversion of, 9; omission of, 02 — 3, 87. Inversion of chords of the seventh, 70, 90; of intervals, above and below, 10; of triads, 45. Leading-note, leading-tone, 28, 49 ; in the inner parts, 65 ; doubling of, 2^, j8. Leading oi parts, 14, 198, 201 ; of bass, 199, 201 ; of soprano, 195, 200 ; of mner partS) 195, 201. Melody of soprano, 195, 206. Middle parts, see Inner parts. Modulation, 99, 208. Motion, parallel, oblique, contrary, 18 Musical hearing, 234. Natural tones, i. Ninth, 2; major and minor, 5; chord of, 270-2 ; suspension of, 156, 170. Octave, perfect, dimin., 5, 8. Octaves, open or parallel, 17 ; covered, 26, 103, 182 - 192 ; in contrary motion. 204. INDEX. 291 Omission of intervals, 62 - 3, 87. Organ-point, 170, 179. Outtr parts, 1 5. Parallel fifths, 17, 135, 203 ; neutralized by contrary motion,ao3 ; by suspension, i eev octaves, 17, 103 ; in suspension, 155. Passing-notes, 175; passing-chords, 177. Pedal, Pedal-point, 170, 179. Perfect cadence, 66. Plagal close or cadence, 23. Position, close or open, see Harmony. Preparation of the seventh, 83-5, 87, 173; of the suspension, 147, ico. Prime, perfect, 2 ; augm., 2, 5. Primary triads, see Funijamental triads. Principal chord of the seventh, 59. Progression of parts, see Leading. Progressions, forbidden, 17, 26, 65, 69, 103, 108, 1 14, 182 - 192 j of seventh by skips, 104, 139; in unison, 191. Resolution, of dom. chord of the seventh, 59, 66 ; of secondary chords of the sev- enth ( in major ), 72 - 86 ; ( in minor ), 90 ; of augm. chord of the sixth, 129 ; of augm. chord of the third, fifth and sixth, and third, fourth and sixth, 134; of suspensions, 147, 151 -2, 153-4. Koot, 3 ; doubled in chord of the seventh, 62. Scale, major, i ; minor { harmonic and melodic ), 35. Score, 16 ; short, 16. Second, 2 ; major, minor, augm. 5 ; step of augm. second, 39. " chord of the, 71 ; freer resolution of, 104; with altered sixth, 123. Secondary (. or subordinate ) triads, in major, 24 ; in minor, 38. " chords of the seventh, in major, 78 ; in minor, 90. Semitone, greater and lesser, 4 Sequence, 33; sequence of suspensions, 152. Seventh, z; major, minor, dimin., 5; preparation of, 61, 83; doubled, 62 ; unpre- pared entrance of, 61 ; resolution by a step downwards, 61 ; by a step upwards, 102-4, 113; held or sustained, loi ; skipping, 104, 139. Seventh, chord of the, 59; dominant chord of the seventh, 59; ou 7th degree in major, 78 ; on 7th degree in minor, 92, 93; this last chord in modulation, 216 j interconnection of chords of the seventh, 86 ; with chords of other degrees, and keys, io8 ; non-cadenced progressions, 98 ; View of all, 141. Sixth, 2 ; major, minor, augm., 5. " chord of the, 46 ; augm. ( altered ) chord of the, 129 ; the latter in modula- tion, 218. Soprano, 14 ; soprano