cu HARM' Southern Branch of the University of California Los Angeles Musrc LIBRARY MT50 Form L 1 S T CUMULATIVE HARMONY BY WILLIAM J. McCOY GINN AND COMPANY BOSTON NEW YORK CHICAGO LONDON ATLANTA DALLAS COLUMBUS SAN FRANCISCO I 8 COPYRIGHT, 1916, BY WILLIAM J. McCOY ALL RIGHTS RESERVED 516.7 tgfte fltfttnatum GINN AND COMPANY PRO- PRIETORS BOSTON U.S.A. LIBRARY v\ T 5 13 c. PREFACE Inasmuch as there are already available textbooks on harmony, a title list of which would form an imposing array, and among which may be noted a number of thoroughly sound and admirably constructed works by American theorists of distinction, the question would natu- rally arise, Why add another ? The greatly deplored apathy of music students toward the study of harmony is largely due to the fact that harmony methods, in general, are prepared for mature minds, which are often too much engrossed with an already acquired proficiency in executive music to welcome readily the thorough course that is necessary in order to absorb the apparently inelastic mass of facts presented, which, they subsequently discover, requires a supplementary course to determine definitely its mission in music practice. It has been the earnest effort of recent theorists so to modify the prevailing modes of procedure that a more kindly attitude toward this subject may be encouraged. It is with this object in view that the author, through many years of experience in teaching, has evolved a course in chord practice by means of which the problem of covering thoroughly all phases of the science of harmony and at the same time creating, on the part of students, a direct interest in the subject for itself has, he believes, been success- fully solved. By means of the plan here presented, the student is led, step by step, through the process of theory and practice, and becomes himself a party to the building up of the system. The work is made continuously cumulative. As each new unit is added it enters at once into the practice of music-making, and con- tinues in homogeneous action until the entire work is absorbed. Melody-making (as a superstructure) from harmonized given bass sets, and the harmonization (as a substratum) of given melodies, are introduced almost at the outset and continued with constantly cumu- lated harmonic elements through the work. The forming of melodies from combined harmonic units is regarded by the author and those who have practiced this method as a most iv CUMULATIVE HARMONY valuable innovation ; by this means the enlistment of creative effort becomes at once a source of fascination to the student, which, as new chords are involved and his own efficiency becomes greater, increases continuously throughout the course. The author desires to direct attention to the following innovations peculiar to this work : 1. The evolving of melodies from harmonic structures. 2. A tabulated system of modulation to directly related keys, con- sidered harmonically and melodically. 3. A recognition of this principle : the fact that the positive identi- fication of a key is dependent upon an assured Dominant chord is sufficient justification for assuming that the appearance of such chord, in any circumstance, serves fully to identify a key. 4. The harmonization of melodies by the three-point mode, involv- ing the grouping of all chords into three general harmonic families, by means of which a freedom in authoritative harmonization of given melodic lines is easily acquired. 5. The use made of the secondary chords of the Subdominant, Tonic, and Dominant, regarding which the author asks only that those who may already have acquired a working knowledge of chords as based upon all degrees of the scale will give to this mode of grouping for harmonization of melodies a thorough consideration entirely disassoci- ated from and unprejudiced by the edicts of former affiliations, in order to become convinced of its simplicity and superior practicability. The author is confident that a careful contemplation of the family of augmented chords as presented in this work and verified by the ac- companying illustrations will easily disperse the " bogy " mysteries with which this chord has been persistently surrounded. The study of harmony should be pursued simultaneously with the study of instrumental and vocal music. It should be thoroughly mastered and absorbed during the receptive periods of childhood and youth, not deferred until the musical character has been already formed and new lines of thought become unwelcome. This textbook is an offering of method and material from which the instructor and the pupil are expected to develop a wide scope of musical study that will prove a true preparation for other steps toward analysis and composition. WILLIAM J. McCOY CONTENTS CHAPTER PAGE I. NOTATION i Scales i Major diatonic scale 2 Relative minor diatonic scale 3 Tonic minor scale 4 II. INTERVALS 7 General name of intervals 7 Specific name of intervals 7 Inversion of intervals 12 Consonant intervals 13 Dissonant Intervals 14 III. CHORDS 16 Triads 16 Major triad 16 Minor triad 16 Augmented triad 17 Diminished triad 17 IV. HARMONIZATION IN FOUR VOICES OVER A GIVEN BASS 19 Progression of voices 19 Similar motion 20 Contrary motion 20 Oblique motion 20 Transposition 21 Compass of voices 22 V. INVERSION OF TRIADS 24 Fundamental position 24 First inversion 24 Second inversion 24 Figured bass 25 VI. THE CONSTRUCTION OF MELODIES OVER ACCOMPANIMENTS. ... 31 Accompaniments 34 VII. PARALLEL FIFTHS AND OCTAVES 40 VIII. THE DOMINANT SEVENTH CHORD 43 Resolution of the D 7 chord 44 Table of resolutions 45 v vi CUMULATIVE HARMONY CHAPTER PAGE IX. INVERSIONS OF THE D 7 CHORD 48 First inversion 48 Second inversion 48 Third inversion 50 X. SERIAL MODULATIONS 53 Rule I. Tonic for new Dominant 54 Rule II. Supertonic for new Dominant 56 Rule III. Mediant for new Dominant 57 XI. SERIAL MODULATIONS (Continued) 59 Rule IV. Subdominant for new Dominant 59 Rule V. Submediant for new Dominant 60 Rule VI. Subtonic for new Dominant 60 XII. DIRECTLY RELATED KEYS 63 XIII. HARMONIZATION OF MELODIES 66 Rule I 66 Rule II f . . . . 69 Rule III 69 Rule IV 70 XIV. HARMONIZATION OF MELODIES (Continued) 73 Rule V 73 XV. HARMONIZATION OF MELODIES (Continued) 77 Melodies employing inversions 77 Consideration of the chord 78 The abbreviated D 7 chord D) 80 XVI. SECONDARY CHORDS ON THE SUBDOMINANT 83 Subdominant substituted 6th chord 83 Subdominant added 6th chord 84 Rule VI for harmonization of melodies 86 Dominant of the Dominant in passing modulation 88 XVII. MELODIC MODULATION 93 Rule I 94 Rule II 95 Rule III 96 Rule IV 97 Rule V 98 Rule VI 99 XVIII. EMBELLISHMENTS 103 Suspensions 103 Rule I 106 Rule II 107 Rule III 109 XIX. SUSPENSIONS (Continued) 1 10 Rule IV. no CONTENTS vn CHAPTER PAGE XX. RETARDATIONS, OR ASCENDING SUSPENSIONS 115 Rule I 115 Rule II 116 Rule III 117 Rule IV 118 XXI. PASSING NOTES 123 Successive passing notes 1 24 Consideration of the various forms of the minor scale .... 1 26 Compound passing notes 1 29 XXII. CHROMATIC PASSING NOTES 132 Germ set and motus 132 Extended passing notes 133 XXIII. AUXILIARIES 136 Successive auxiliaries 1 40 Extended auxiliaries 141 XXIV. INTRODUCTORY AUXILIARIES 148 Progressive auxiliaries 1 50 Changing notes 152 Anticipation 152 False relation 153 XXV. THE DOMINANT NINTH CHORD 162 Additional rule for harmonization of melodies 1 65 XXVI. THE ABBREVIATED DOMINANT NINTH CHORD D)) 170 Rules for treatment of D)) chord 1 70 Additional rule for melodic modulation 1 73 Diminished 7th chord 1 74 Additional rule for passing modulation 175 XXVII. IMITATION 185 Imitation in two voices 187 XXVIII. CADENCES 191 Complete cadence : igi Authentic cadence 191 Plagal cadence 194 Tierce de Picardie 195 Incomplete cadence 196 Deceptive cadence 197 Passing cadence 1 98 XXIX. EXTENDED CADENCES 199 XXX. EXTRANEOUS MODULATION 203 Indirectly related keys 204 Foreign keys 207 Transition 209 Vlll CUMULATIVE HARMONY CHAPTER XXXI. XXXII. XXXIII. XXXIV. XXXV. XXXVI. XXXVII. XXXVIII. XLI. XLII. XLIII. INDEX SECONDARY CHORDS ON THE TONIC Tonic substituted 6th chord Deceptive cadence involving the Tonic substituted 6th chord . THE TONIC ADDED SIXTH CHORD TJj Additional rule for harmonization of melodies Dominant of the supertonic in passing modulation COMPOSITION OF CHORALS CHROMATIC OR ALTERED CHORDS Augmented 6th chord French 6th chord Italian 6th chord German 6th chord Modern augmented 6th chord THE NEAPOLITAN SIXTH CHORD AUGMENTED FIFTH CHORDS Additional rule for harmonization of melodies IMITATION OVER GIVEN FUNDAMENTALS Imitation in three voices ADDITIONAL EMBELLISHMENTS Arpeggios Direct arpeggios Indirect arpeggios Chromatic scale passages Ornamental anticipations IRREGULAR RESOLUTIONS OF THE D 7 CHORD SECONDARY CHORDS ON THE DOMINANT Dominant substituted 6th chord Additional rule for harmonization of melodies Dominant substituted 6th chord with 7th included DOMINANT ADDED SIXTH CHORD CHORDS OF THE TONIC SEVENTH AND THE SUBDOMINANT SEVENTH Table of direct and tributary chords SEQUENCES Pedal Point PAGE 21 I 21 I 212 2l6 2I 9 219 223 224 224 225 227 228 229 234 242 245 247 250 250 250 250 252 255 2 5 8 264 264 264 266 271 2 7 8 282 287 290 297 CUMULATIVE HARMONY CHAPTER I NOTATION Notes are written symbols representing tones (musical sounds) to be uttered by the human voice or other medium of musical expression. The terms " steps " and " half steps " are used as a medium of reference to the difference in pitch of varying tones. By a half step is meant the distance (difference in pitch) from any one note to the nearest note in general use above or below it. step > step % ste P ste P ste P ste P : o 6^- -s> ^ -fr* ^ : *r-fc- ^ ^-tt The distance of two combined half steps constitutes a whole step (or a step). step step step step m -&- i __ i' >^ step \s TZ -ii II i/ SCALES The plans of scales used in various periods and by various peoples differ materially. For a description in detail of the many forms that have been employed, the student is advised to refer to a suitable history of music and become fully informed on this very important subject. Attention will be directed for the present to the major and minor diatonic scales. I 2 CUMULATIVE HARMONY Diatonic is the name given to music that conforms entirely to the immediate tonality or key in which it occurs, as would be indicated by the signature of that key. It also refers to a series of such notes proceeding by degree in one direction. 3 Diatonic 4 Not diatonic A scale is a series of eight tones at distances of a whole or a half step apart, as represented by corresponding notes upon contiguous degrees of the staff. / 5 II The eighth note in this series which is, in reality, a duplicate in the octave of the first not only serves as the last of the series in one scale, but may constitute at the same time the first in the next scale series above. ^^ etc. The diatonic scales are in two genders the major and the minor. THE MAJOR DIATONIC SCALE The succession of whole steps and half steps separating the eight members of the major diatonic scale is as follows : a whole step be- tween each two contiguous notes except between three-four and seven-eight, which are a half step apart. NOTATION A major diatonic scale beginning with the note C would appear in whole step and half step distances, as follows: step step step step step 1 Beginning with F and with D, similar scales would appear as fol- lows: step step step step step m=^ IB- 2 3 step 1 THE RELATIVE MINOR DIATONIC SCALE (NORMAL) This scale, with the same signature, is located two staff degrees be- low the major, and occurs in the following succession of steps and half steps: a whole step between each two contiguous notes except between two-three and five-six, which are a half step apart. A minor diatonic scale beginning on A would appear as follows, 10 step step step step step "*F~ ~~~~ j^ ^ J ^t -^ T 5 1 2 678 and similar scales beginning on D and on F#, as follows: 11 step % step step % step step \\ : > 12 step CUMULATIVE HARMONY J^ step step ) step step i 123456 78 Here follow two excellent illustrations of the employment of the Normal Minor Scale. Illustration No. 1 SCHUBERT, " Symphony B Minor" fM\'" Q 1 1 I 1 VJ-ff^t) ! So- 5:1 2 ts * ^-! 1 -^ 9 1 II -. 9 _^ -* -3- "^?' 111. No. 2 Allegro moderaio Mrs. H. H. A. BEACH, op. 45, " Concerto" ((T) * M i-^ P 8 " 1 "!*" - i 2 -^ j\ A ^ VJ-J - [ -& -0 -^ :. - -0 y - PP 1 r A *Tf Ir . 55 ^^"T^ft 1 **f * -* H ^ - ^^-ft-^ 4 ^ ^_ 's * -+ 1 ^ - . ^ H^ "0 : ^ '- ^0 \ :~ --0 ^ -0 S - This scale is subject to alterations due to certain harmonic and melodic conditions, which will be considered later. THE TONIC MINOR SCALE The form of the diatonic content of the tonic minor is identical with that of the relative minor; but, while the tonic of the relative minor is a third below the tonic of the major, that of the tonic minor is the same note as in the major. The tonic minor scale of the key of C major is as follows: 13 step step step The technical names of the various members of the diatonic scale are as follows: The first of the scale is called the Tonic; the second of the scale is called the supertonic; the third of the scale is called the mediant; the fourth of the scale is called the Subdominant; the fifth of the scale is called the Dominant; the sixth of the scale is called the NOTATION 5 submediant ; the seventh of the scale is called the sub tonic or leading tone; the eighth of the scale is called the octave or Tonic. Of these the Tonic [T], Subdominant [S], and Dominant [D] are classed as primary notes, the others as secondary. A diatonic scale may be formed with any note as the Tonic, or key- note. In order to aid the student in becoming familiar with the suc- cession of sharps and flats placed in signatures to form and indicate the various keys and scales in general use, two rules are submitted : From the key of C major with a signature of no sharps or flats, proceeding by sharps: Sharp the fourth and take the fifth for a new Tonic, or keynote. 14 % Y* n With the fourth [F] sharp and the fifth [G] as the new Tonic, or keynote, a signature of one sharp and the key of G appears. 15 From the key of G with the fourth [C] sharp and the fifth [D] as the new Tonic, or keynote, a signature of two sharps and the key of D appears. Proceeding by flats: Flat the seventh and take the fourth for a new Tonic, or keynote. 16 HE With the seventh [B] flat and the fourth [F] as the new Tonic, or keynote, we have a signature of one flat and the key of F. 17 J^ ^J^ In like manner, with the seventh flat we have the key of Bb with two flats in the signature. 6 CUMULATIVE HARMONY A thorough familiarity with the various keys, as indicated by their signatures, is a necessity at this point in the student's work, and con- siderable oral drill should be given in the manner of the following patterns: NOTE. References to the Tonic, or keynote of tonalities, will be made by symbolized capital letters for the major keys, and symbolized small letters for the minor; thus: C A A A A major, C ; A major, A ; F minor, f ; D minor, d. Give the signatures in as rapid succession as possible of the follow- A A A A A A A ing major keys: G, F, D, E, Bb, A, Eb, etc. Give the signatures of A A A * A * A the following minor keys: d, a, b, g, e, d#, g#, eb, f#, etc. Name the major keys represented by the following signatures: i flat, 3 flats, 3 sharps, 2 flats, 5 sharps, etc. Name the minor keys represented by the following signatures: i sharp, 3 flats, 4 sharps, 5 flats, 2 sharps, etc. Chromatic alteration is a term used in raising or lowering a note a half step by means of an accidental sharp, flat, or natural other than those established by the signature. Chromatic alterations may raise or lower the pitch of notes without causing a change of key, or they may aid in effecting modulations. When a note is raised by means of an accidental, it is said to be elevated; when it is lowered by the same means, it is said to be depressed. By chromatic progression (or motion) is meant the proceeding from one note to another a half step higher or lower. This may be ac- complished with or without chromatic alteration. At (a) is a chromatic progression without chromatic alteration; at (b), (c) chromatic progressions formed with the aid of chromatic alter- ations. The progression at (a) is also diatonic. The student should frequently play and have played for him the scales, both major and minor, in all keys. The same may be said of all examples and exercises throughout the course of study as they occur and are worked out. It is a matter of the utmost importance that attention be given to frequent playing, hearing played, and an- alyzing all examples and exercises as they occur and are worked out. CHAPTER II INTERVALS An interval consists of two tones (or the difference in pitch of two tones as determined by the corresponding notes on the staff) to be heard simultaneously or in succession. Intervals are computed up- ward from the lower note. The general name of an interval is determined simply by the number of staff degrees involved. 19 prime 2d 3d 5th o % * f f rt-H etc - y -^ -^- j ^5i ^ _L j 1 1 u s^ p_ i ' \ one degree two degrees three degrees five degrees Intervals greater than an octave are given the same interval names as similar ones within the octave, and the octave itself is treated as a duplicate of the lower note at a higher altitude. 2O zd 21! 4th 4th m ~&- etc. The specific name includes, also, an estimate of the number of steps and half steps the interval contains. 21 augmented prime minor 3d major 3d perfect 4th & =2= -**- etc. )^ step i^j steps 2 steps 2)^ steps Taking C for the lower note, the specific intervals obtainable with- out chromatic alteration are the perfect prime, fourth, fifth, and octave; the major second, third, sixth, and seventh. 22 prime fourth fifth octave prime Perfect CUMULATIVE HARMONY 23 2 d 6th 7 th \-\ Major From the examples above the student may learn that the two notes forming a perfect prime are similar in all respects, the one being a duplicate of the other, on the same staff degree; that the two notes forming a perfect fourth are two and a half steps, and a perfect fifth, three and a half steps apart; and that the upper note of a perfect octave may be seen to be a duplicate of the lower, in the octave. Also that a major second contains one step, a major third two steps, a major sixth four and a half steps, and a major seventh a half step less than an octave. The student will now form and write perfect fourths upon each A note of the scale of C; also upon its depression and its elevation, thus: 24 Perfect 4ths -F-te3 - etc. Form and write perfect fifths similarly. 25 Perfect 5ths i -U etc. etc. Form and write in like manner, successively, major seconds, thirds, sixths, and sevenths. 26 Major 2ds etc. etc. INTERVALS 28 Major 6ths 29 Major 7ths ^r^S etc -^^^ etc etc. etc. The distance of a minor interval is a chromatic half step less than that of the major. Form and write, successively, minor seconds, thirds, sixths, and sevenths. 30 Minor 2cls i etc. 3 etc. etc. 31 Minor 3ds i etc. etc. 32 Minor 6ths etc. etc. 33 Minor 7ths etc. etc. K etc. etc. The distance of a diminished interval is a chromatic half step less than that of the perfect or minor. Write, successively, diminished thirds, fourths, fifths, sixths, and sevenths. 10 CUMULATIVE HARMONY 34 Diminished -fl etc. etc. etc. Intervals on notes marked * are not expressible in notation and are not used in harmonic combinations. 35 Diminished 4ths 36 Diminished 5ths 37 Diminished 6ths -&- 38 Diminished 7ths ^EgdElg^ ==2=^= etc. etc. etc. etc. etc. 4 etc. The distance of an augmented interval is a chromatic half step greater than a perfect or major. Form and write augmented primes, seconds, thirds, fourths, fifths, and sixths. 39 Augmented primes TCT ' fcr IK^^t* M'-m etc. F r etc. 40 Augmented 2ds etc. etc. INTERVALS ii 41 Augmented etc. etc. 42 Augmented 4ths 43 Augmented 5ths etc. etc 44 Augmented 6ths etc. etc. The student should be required to become thoroughly familiar with the number of steps and half steps contained in the various intervals. Oral practice, such as follows, is invaluable: What note is a third from C? from E? from G, etc. What note is a sixth from D? etc. What general interval does E-C form? How many steps and half steps are contained in a major third? a perfect fifth? a minor sixth, etc. What specific interval does C-A form? Eb-A? D#-A? etc. It is a matter of the utmost importance to the student that he should take a thorough course in musical dictation or ear training in conjunction with these studies, in order to attain the power of readily 12 CUMULATIVE HARMONY distinguishing tone intervals upon hearing them sounded together or in succession. Too much consideration cannot be given to this recommendation. In the formation of an interval, care should be taken to determine the number of staff degrees involved, to conform to its general name, and then to arrange the interval, by proper use of accidentals, in such manner that it will contain the required number of steps and half steps. 4.R (a) (b) (c) (), while the number of steps and half steps is i ^ as at (a) , the number of staff degrees involved is three [C, D, and E], resulting in a specific interval of a minor third. In like manner the number of steps and half steps at (c) and (d) is the same; the number of staff degrees involved shows them to be respectively a diminished fifth and an augmented fourth. The inversion of an interval is effected by raising the lower note an octave. 46 By inversion: 47 Prime octave A prime becomes an octave. A second becomes a seventh. A third becomes a sixth. A fourth becomes a fifth. A fifth becomes a fourth. A sixth becomes a third. A seventh becomes a second. An octave becomes a prime. 2d 7th 3d 6th 4th 5th /L 2 I 5? 1 2 Ifn 1 | Saz ' i ^^ ^3 u -*f- f - -*f f f r f i INTERVALS 13 5th 4th 6th 3d 7th 2d octave prime | 1 Jr & R e& , -, \ II ^0 ^0 & Offt 1 ^"r\ .^ ^3 ^ /% I vr L/ *^ j II f" f" r T Also by inversion: A perfect interval becomes a perfect. A major interval becomes a minor. A minor interval becomes a major. An augmented interval becomes a diminished. A diminished interval becomes an augmented. 48 Perfect perfect per. per. major minor major minor minor major -, %=- minor major aug. dim. aug. dim. dim. aug. dim. aug. Therefore by inversion: A perfect fifth becomes a perfect fourth. A major sixth becomes a minor third. A minor second becomes a major seventh. An augmented prime becomes a diminished octave. A diminished seventh becomes an augmented second. 49 )& 9-*5>- J Intervals are consonant or dissonant. A consonance is an interval, which, from its nature and quality, does not suggest or require a further progression or resolution; it may be classed as an interval of repose. etc. I 4 CUMULATIVE HARMONY By playing these intervals separately (as they have no connection with each other) the student will readily recognize the effect of re- pose; that is to say, they do not seem to demand a progression or resolution to an interval of different nature and quality in order that a sense of completeness may be reached, as is the case with the inter- vals in the following example of dissonances: By playing these intervals (the unbracketed ones) the student will at once recognize a feeling of incompleteness and lack of repose, a demand for a succeeding interval of different quality (as bracketed), in order that a sense of repose and completeness may be realized. Therefore, A dissonance is an interval, which, from its nature and quality, suggests or requires a further progression or resolution, and may be classed as an interval of motion. The consonances are the perfect intervals, and the major and minor thirds and sixths. 52 The dissonances are the major and minor seconds and sevenths, and all augmented and diminished intervals, as in the following table: 53 aug. prime I mil zd i. ma 2d ) au 2d ? dim. 3d aug. 3d dir 4t n. ^ 1 1 -*& -h. u * J -b& i aug. dim. aug. dim. aug. dim. min. maj. dim. 4th 5th 5th 6th 6th 7th 7th 7th octave \f 1 i ii i \ U ft J II fn~\ u =&i= ~%r \Bi& ^ 9 & vz> fi =M 1 ^K y&. ' P -&- -&- -& -<&- -& J INTERVALS While this classification is clearly represented by the notation, certain consonances and dissonances which are enharmonically similar may be identified by the hearer only through progression to a succeeding interval. The perfect fourth was formerly considered a forbidden dissonance, and while it is now classed as a consonance, it possesses a strong element suggesting further progression. Play these exercises, and have them played. CHAPTER III CHORDS A chord is a combination of three or more tones built in a series of thirds upon a given tone called a fundamental (or root) as repre- sented by corresponding notes on the staff. A triad is a combined third and fifth. At (a) the combined third and fifth form the triad of C; at (>) the triad of E; and at (c) the triad of B. A major triad consists of a (combined) major third and perfect fifth. At (a) a combination of the major third D-F^ and a perfect fifth D-A forms the major triad of D; at (b) the major triad of Et>; at (c) the major triad of B; at (d) the major triad of Gb. Combine and write major triads on each degree of the scale of C, also its elevation and its depression. etc. A minor triad consists of a minor third and perfect fifth. 16 CHORDS 68 min. per. minor (a) 3d sth triad . (b) (c) At (a) the combination of a minor third, C-Eb, and a perfect fifth, C-G, forms a minor triad on C; at (b) the minor triad on E; at (c) the minor triad on A; and at (d) the minor triad on Bb. A Form and write minor triads on each degree of the scale of C, also on its elevation and its depression. 59 etc. etc. etc. An augmented triad consists of a major third and an augmented fifth. 60 maj. aug. aug. (a) 3d 5th triad (b) At (a) the major third, C-E, and augmented fifth, C-G#, com- bined, form the augmented triad on C; at (6) the augmented triad on E; and at (c) and (d) the augmented triads on At? and Bb re- spectively. A Form and write augmented triads on each note of the scale of C, also on its elevation and its depression. 61 etc. etc. The augmented triad on B# cannot be expressed, and is not used in harmonic combination. A diminislied triad consists of a minor third and diminished fifth. i8 CUMULATIVE HARMONY 62 min. dim. dim. (a) 3d 5th triad At (a) the minor third, C-Eb, and the diminished fifth, C-Gb, form the diminished triad on C; at (b), (c), and (d) are examples of dimin- ished triads on E, F#, and A# respectively. Form and write diminished triads on each degree of the scale of A C, also on its elevation and its depression. 63 ~~ etc. etc. CHAPTER IV HARMONIZATION IN FOUR VOICES OVER A GIVEN BASS As a triad contains but three notes, one of them must be dupli- cated in four-part writing. This is called doubling. The funda- mental is considered the most suitable for doubling, the fifth may be freely doubled, but for the present the student should avoid doubling the third. 64 (*) /r-9 r , idb TK ^ 1 ff^ :. - ES E9 1 ^ * ^v **? ^i*X* ^^ -^ B^2S 3^ ^ X ^X 82 At (a) the fundamental, C, is doubled; that is to say, it occurs in two different voice parts. At (b) the fifth, G, is doubled; at (c) the fundamental, F, is doubled; while at (d) the doubled note is the fifth, A. In four-part writing the voices are known by the names given them in vocal music; from highest to lowest they are called, respectively, soprano, alto, tenor, and bass. SOPRANO ALTO TENOR BASS 65 n c \ / ^ <2 cszzzz x 3 9 . \J 7-^ 1 - -e- Z5 -G>- 4 \- EEEd - ~~7Z ^bi &* ^.^ PROGRESSION OF VOICES When a voice moves from one note to another a scale degree above or below, it is said to progress by degree (or diatonically) ; when it moves more than one scale degree, it is said to progress by skip- when it moves in a succession of half steps by means of chromatically altered notes, it is said to progress chromatically. 19 20 CUMULATIVE HARMONY 66 ; f * -9 ' 2^ - 1 In this example each note proceeds to the next scale degree above or below, therefore progressing by degree (or diatonically) . /L i im _ 1 ^i , j J Here, on the contrary, each note proceeds to another at a distance of a third or more, thus progressing by skip. 68 In this example most of the notes proceed a half step, by means of chromatic alterations, to the next, producing chromatic progres- sions. Two voices moving in the same direction are said to progress in similar motion. 69 'V ) 2 & g ^ 1 5- Z>> _2 i-9 When they move in opposite directions they are said to progress in contrary motion. 70 - ^ Z5- 1 When one voice remains stationary and the other ascends or de- scends, they are said to progress in oblique, motion. 71 Notes common to two chords to be connected should be retained in the same voice, the other voices proceeding to the nearest available positions. HARMONIZATION IN FOUR VOICES 21 This is particularly applicable to the inner voices the alto and the tenor; the soprano frequently requires considerable freedom of movement in order to obtain good melodic results; the bass often moves in succession of skips to good effect. Similar motion in all four voices should be avoided, care being exercised toward effecting contrary motion, or a common tone sustained in the same voice. 72 00 (b \ -Jt 5; & <- (2 2. VT^ $ <& {3 IS 1 a S> 9- - >WA .^ ^. jt/ i ^ - ^ At (a) the note common to the first and second, and the second and third as well, is G, which occurs in the alto in the first voice, and should be retained in the alto in the second and third chords. At (b) the note common is C, which is retained in the tenor. 73 m^r-ir ^~ gJ, ^ E^n g g =fe^= ^ ^~ es ^* S- 5!: 1 * f<* ''4- & UP ^'4 ^ 32 ^ 1 ~ ^M^ -25^ s p \-at- Transposition is a change of key by means of a corresponding change of notation and signature or the sounding of tones represented. A Exercise 73, transposed to Eb, appears as follows: 74 i-jf-Jt < =^= -0- -* u " - ^ etc. ^ ^ W^j, |Z_ ^^ c> -f- 1 5 <& Taking the model (Exercise 73) as a pattern, the student should form triads on the following bass sets, in accordance with the instruc- tions given above. CUMULATIVE HARMONY =| , |+ g _ | | , | |-qn 76 I* LS m= The student may use the ist, 3d, or 5th for the initial note in the soprano; this presents three modes of working out each exercise. Transpose these examples as in Exercise 74 to several keys, and work out as before. The difference of altitude in the various voice parts does not affect their interval relation with the bass. Hence all the following are major triads of C, with the funda- mental as the actual bass. 78 & & & o _^_ -(*?- -&- -&- -*- ^ ^^J ?? 25 *^^ * ^v ^^ ^^ fls f^ (^ ^y The usual compass of the various voices in vocal music is given in the following model, the open notes indicating the preferred compass, the filled notes including a possible extension. HARMONIZATION IN FOUR VOICES 79 SOPRANO ALTO TENOR K-= BASS It is desired that the four voices be kept as nearly equidistant as possible, the upper three voices, as a rule, occurring within an octave of each other. The soprano and alto at times may exceed this distance, while the bass part is frequently written without regard to its distance from the tenor. These exercises should be worked out in both close and open position. Play these exercises, and have them played. CHAPTER V INVERSION OF TRIADS By inversion of a chord is meant the placing of one of its notes, other than the fundamental, in the bass. When the fundamental of the chord is used as the bass, the chord is in. fundamental position. 80 ^ In the above model the triads of C, F, and G are given with the fundamentals C, F, and G in the bass part, and are therefore in funda- mental position. In the inversions, avoid doubling the bass except in the chord of f . When the third is used as the bass, it is in the first inversion. 81 /f d ^ VT7 ^ d Si &- 29 S33 1 [<> <5 V_x ^J In this example the same chords are given, with the thirds E, A, and B in the bass; they are, therefore, in the first inversion. When the fifth is in the bass, the chord is in the second inversion. 82 2 4 INVERSION OF TRIADS 25 The same chords, with the fifth from the fundamental in the bass, are in the second inversion. Figured bass is the employment of figures placed above or below the bass notes, to indicate the intervals represented in the various chords. Intervals are computed upward from the lowest note (the bass). 83 y XL ^ i^> ^> /^ ^2 f(T\ ^2 ^^ ^2 We have here given an example of figuring the triad of C, which, g complete, is |. For the sake of abbreviation, the figure 8 is rarely used; 3, 5, or both, are used only when the particular interval repre- sented is to be affected by an accidental sharp, flat, or natural; also, for abbreviation, the figure 3, when affected by an accidental, is omitted, the sharp, flat, or natural alone representing the third so altered; thus: 84 (b) (c) l*i At (a) the b alone indicates the triad with the third flat C, Eb, G. At (b) the b5 represents the triad with the fifth flat Eb, G, Bb; and at (c] the # and #5 represent the triad with the third and fifth sharp B, D#, and F#. In the first inversion of the triad the third from the fundamental is assigned to the bass, forming the intervals of a third (3d) and sixth (6th) from that note. Figured, | or 6. 26 CUMULATIVE HARMONY 85 A & > o E5 ' ^^ |(T\ ^-j ^ .u 532 b ^Z2 J -&- -*y- 6 6 3 -TS 1 - 6 if 2 P-ZT- t>6 b ~GT 6 | fj^\* w v -r* H i 1- . E 6< 5? ~f -+ d- - -^ i- 89 6 { 4 t 6 6 6 4 -fi 6 >. & 6 4 1 f^\* | it/-/ j ^ ffl. ^ 1 2S ^5 J -j 1 1 ]_^*i\_^. ^ -fi* ^ Hie ^ _ -O. 1.| 90 6 4 6 6 4 6 6 4 6 6 6 4 . ) i im\* ^j J 1 1 II it/-/ 4 J ly- - ^ =^^ 1*25 S =-54 ti2~" O ""*" ^~ " & ~ etc. >^\ f P'*/ * J (j) J l" ^> ^ ^ ^"^' ^ ^- 1 -i r 1 ^ ^ ^~t"~~ 6 4 6 6 i 4 6 #6 4 4 i 66 4 When a combination of notes forming a chord is arranged in such manner as to appear in a series of thirds, the lowest note (when the chord is complete) is the fundamental. 06 (a) m (r) (rf) (^) 1 1 L i f**> 1 /n\ /rJ ^^ C' ^^ li 53 V^l^ '"' "^ lSlr^3 JT ^ 1 -&- ^ - 5 j ^-1 ^ rt? L J I pj. r 5 4 hi "tf ^9 ** 4 1 9 L 1 At (a) the chord E, G, C, when rearranged to appear in a series of thirds, is seen to have C for its fundamental; at (6) G appears as the fundamental; at (c),Db; and at (J), B. At (e) the bass note, A, is the fundamental as it stands. CUMULATIVE HARMONY The following examples should be worked out as above, in both close and open positions, and transposed to other keys for similar treatment. 97 p 6 6 4 J: 1 ^;- 86 4 98 -^TJ^ 5 ' J J 22 ^ 1* -*--^ V^Ul , w 9 -^ a-- 1 e? v 1 1 6 6 4 66 6 J} 4 4 I i 6 6 \ /m\* **^ "St. ^ l\^/ ** -^ r CUMULATIVE HARMONY It may be noticed at (a)-(b) care has been taken to avoid using the E of the bass in the attending melody, as it would be a faulty doubling with the three upper voices, and consequently not allowed in the melody during the life of that chord. At (c)-(d)-(e)-(f), etc., the third is freely duplicated without the effect of faulty doubling of the third from the fundamental. The soprano, alto, and tenor should be placed at an altitude quite near the bass, in order that a more sonorous sound body may be obtained for the accompaniment, and a clearer field for occupation by the melody. At (a) in the following exercise the D 6 ascends to the T 5 , in order to provide four different notes for various forms of accompaniment. At the fourth, eighth, twelfth, and sixteenth measures, the melody rhythms consist of notes longer than the prevailing ones; this is done in order, through the effect of rhythmic repose thus obtained, to aid in dividing the melody into phrases. 101 THE CONSTRUCTION OF MELODIES 33 -s>- I I ry -*- ^ r The positions of the various voice parts may be changed from one note of a chord to another, provided it is done without altering the tonal content of the chord. The most frequent mode of accomplish- ing this is by exchanging notes assigned to various voices, one with another, during the life of the chord; this may affect one, two, or three notes, or the entire chord. 34 CUMULATIVE HARMONY 102 If 1 ] 1 -v,l | .1 J j J J x; * *- ^W _ B J--^ *- ^J. r r r : v * r rr-r ^j ^_j r r j J j PJ * _m ^ ^ K . 1 ^to*-' 1^^ ^* 2 ^^ \ r ^ TJTJ i 6 4 6 " r i 6 4 An additional exercise for similar treatment follows. 1O3 1 1 *" * 1 1 I J V i J V JT ^ J j J ^T JP 1 J p vCT) ^ ^ r^ f^ J- - : F t -^- i 1 -<>- -^- c j. ^ J: ; F | etc. S^\* ~ [^^/ 5J <** ^ Lf __ ^^^ /^ (5 s Jr 3 ^-^ 6 6 4 6 ^ 6^5 4 tf :^^ 6 6 66 4 ACCOMPANIMENTS We will now pass on to the consideration of ^accompaniments in various forms prepared for piano performance by amplification of exercises in four-part writing. Accompaniments are formed in a diversity of ways, such as the use of the various notes of a chord in repetition, in alternation, as after- beats, by the formation of melodic figures from arpeggios, and even in imitation and other contrapuntal forms. A number of examples of the more common accompaniment figures are here given. 1O4 r u c c-T" THE CONSTRUCTION OF MELODIES 35 (M) ' 1 i i i i r I r^^"i ~ j -o 1 n^p ^ -j._ -j.--*'-^--.*-^.- A ' F'* j ^- ^ \~s Ks KJ & f 4 6 4 i^5 - d ! i h j i r 1 " i 1 J V ~9- * -J- ' 1 1 J ^ ^ ^ m -p l^7~ (pi-5 -f * L 5 ^ 6 4 It will be seen that the harmonic content in each of these amplified examples is the same as that in the first measure of Exercise 95, with the understanding that each note of the chord (which may occur in repetition) represents a half-note duration, as in the former exercise. It is, in fact, harmonic accompaniment expressed in arpeggio figures or broken chords. By amplifying the accompaniment as submitted in the second figure of Exercise 104, the melody and accompaniment in Exercise 95 would appear as follows: CUMULATIVE HARMONY 1O5 V- etc. This should also be prepared for performance of the combined melody and accompaniment as a piano solo, with the four voices of the harmony on the bass staff. 106 Jr r ' ' ~^i m I x ^ 4 * i 1 etc. ^ 9 9 pi ^ E &f- f 1 1O7 =3 *- .^. r f- SPH :i^ The harmonic content of the accompaniment at (a) is illustrated by the same chords at (b), as they appear before being amplified. The above given basses, as well as those that follow, should be transposed to various keys, harmonized in various accompaniment forms, and new melodies constructed upon them in accordance with the given directions. THE CONSTRUCTION OF MELODIES 37 When preparing them for piano solo performance, the three upper voices should generally be kept quite within the following compass. 108 SEE Si F- j 1 J etc. : ^ i -fi ^ -*L S (L : i2fi> , P (5- , & b *> T^B ^ 17 1? =r ^ r r Two illustrations of melody formation from a harmonic structure are submitted 111. No. 3 MACBETH, " Gavotte for Strings " ^ 5 f ^ ^. - * * The C is a passing note which will be considered later. m. No. 4 SCHUBERT, " Wohin ? " iE^ ^ r CUMULATIVE HARMONY etc. The pedal note (a) will be discussed later; the bass represented is D. A An application of Exercise 95 transposed to A b is here given. 100 etc. 11O A h u 1 "- rtv * i & 3 fir \ ) c ^- jP ^ -^, ^^ -^ uJ -o ^ ^ - ^ -& etc. (<*)! b"fe^ | _, 1 1 52Et ~ <^ ^^ Gs 73 Also other examples for similar treatment. THE CONSTRUCTION OF MELODIES 39 112 ("ftHri 1 ^ S> i i v_^\ j ~& ^ c- -*" -! 1 T ^~ 1 6 6 4 6 6 5 4 itr 4 B ' 6 4 113 *J yj =5? 6 6 4 666 4 114 Ezap J 1 r ^ **i? .g to X^ 1! l / ^-*^ ^. _r4 1 ' ^^ 5^ ^^ z ' & ^*^ O_ S 1 1 6,6 66 t}6 4 4 6 66 6 4 44 icy* [" ^ S3 -^i /V z r ^^ ^ I? \ SJ2I Ii^^ ^ 1 ~r K) ** F> 1 \ \ 1 \ \ II 6 6 ^6 6 4 ^6 6 66 6 ' 4 44 115 d42 :^ 66 65 4 4 66 65 6 4 4 #6 4 #6 6 4 6 5 4 116 1 6 6 4 #6 6 # 4 j-J a> J ^ 66 4 66 4 6 5 4 Play all these exercises and examples, and have them played. CHAPTER VII PARALLEL FIFTHS AND OCTAVES In the examples for chord connection given thus far, one or more notes are common in each two chords to be connected. In such cir- cumstances good binding of contiguous chords is easily obtained, the notes common to both being given to the same voice, and the other voices moving naturally from their positions in one chord to positions lying nearest in the succeeding one. In cases where two chords to be connected have no note in common the various voices should move to the nearest available position in the next chord, in such manner that there will appear no faulty parallel (consecutive) 5ths or 8vs. Faulty parallels occur when two voices moving in similar direction progress chromatically or by degree in perfect 5ths or 8 vs. 117 bad bad bad not bad not bad Parallel perfect 5ths or 8vs progressing by skip are generally dis- agreeable in the outer voices. 118 A diminished 5th followed by a perfect 5th is objectionable in the outer voices. 119 40 PARALLEL FIFTHS AND OCTAVES The faulty parallels referred to above, while forbidden by the laws of harmony and generally offensive to the cultivated ear, are often used by modern composers for dramatic and other effects, the justi- fication for which may not be readily understood by the immature student; he is therefore cautioned against their employment in any circumstances until his work is sufficiently mature to warrant him in assuming an authoritative judgment in their use. 120 (*) r-B J 1 1 ^ - * ^ ^, ffiy^ i ;. o ^s -* ^1 ^, '^&- j^ . p>- ^-^- S ^ v)> g o J5 ^ i j- ^^ g> i W=iL;_^ ^ <5> 23 '^ 1 -J^-^sr & 6 4 6 6 6 6 S6 4 It At (a) may be seen parallel 8vs between the soprano and tenor, and parallel 5ths between the alto and tenor. At (6) are parallel 5ths between soprano and tenor, and 8vs be- tween tenor and bass. At (c) are parallel 8vs between alto and bass and 5ths between tenor and bass. In the soprano is, also, a bad pro- gression of an augmented 2d from F to G#, which should be avoided, particularly in the outer voices. At (d) there are parallel 8vs between soprano and bass, and 5ths between alto and bass. 121 '^ 666 66 6 # % r_ $*--*' f r ^^ *;,':* The same bass with the upper three voices added in such manner that there appear no faulty parallels. This is accomplished by caus- ing the offending voices to move in contrary motion; these pro- gressions frequently prevent the tones common to two chords from being placed in the same voice. 42 CUMULATIVE HARMONY Additional exercises to be worked out as above, in various keys, follow. 122 \FJ-n _, ^n ^^ (^ 1 ^^ ^^ -^ ^ \^H & " ^. c* e o ^* & f^ *~^ I I ^ 123 # It * 5 6 6 f^\* I j <*5 ^5 v^-J*l 4 ^. P^ X^ ^~ p^ TW'' \ / ^^ 5 g J * <5? ^ ^s 1 124 6 # T^ - _^-, *^ 2 H \Ls( I' 5 (? ^ , ^ 2S t-&2 2. It is suggested to the instructor that the foregoing exercises be thoroughly worked out in simple harmonization of the basses in the given key, transposed to many other keys and worked out similarly before attempting to construct melodies thereon. A good writing technique in chord connection is an absolute necessity through all the preliminary stages of the work. Play all these exercises and examples, and have them played CHAPTER VIII THE DOMINANT SEVENTH CHORD Discords are chords containing dissonant intervals. First and most important of these is the D 7 chord. This chord is formed by adding a minor yth to the D triad (which should always be major) and must contain the intervals of a major 3d, a perfect 5th, and a minor yth; figured y. This is applicable alike to major and minor keys. 125 CFDA ad bf# The D 7 chord is of peculiar value in that it determines absolutely the key or tonality; so that, regardless of the initial signature, any combination of notes that consists of a major triad and minor yth, or an inversion of the same, is a D 7 chord, the fundamental of which is the Dominant of a key whose Tonic is a perfect 5th below. 126 (a) (b) r s> -frrs; feft r ^ <^ *" _ b* /^\* ^ TtXD ff lU*3 ^j ^j Vr * ^& 4r^ lUf^^ ^^ l)^7 6^O Ar TT^I I/O* 1/&' 1 1 1 ^ b? 86 it b? T At (a) the chord Bb, E, G, C, when arranged in its fundamental position C, E, G, Bb, is seen to contain the intervals of a major 3d, perfect 5th, and minor yth, and is therefore an inverted D 7 chord, whose fundamental, during the life of that chord at least, is the A A Dominant of the key of F or f. 43 44 CUMULATIVE HARMONY At (b) the chord, when arranged in its fundamental position, in- A A dicates B as a Dominant, and is consequently in the key of E or e. At (c) the rearrangement of the chord indicates a Dominant Db, therefore a Tonic Gb, and this occurs with a signature indicating the 1 f /A A key of C or a. RESOLUTION OF THE D 7 CHORD The D 7 chord is generally followed by the T triad, to which it re- solves. The combination of T triad preceded by the D chord forms the authentic cadence, which will be considered at length under the head of cadences. By resolution is meant the progression of the various voice parts from a dissonant chord, or chord of motion, to a consonant chord, or one of repose. A note dissonant with its fundamental may not, as a rule, be doubled. Its dissonant character gives it exceptional prominence, in addition to which, notes with compulsory resolution would if doubled be likely to cause faulty parallels. 127 (<*) L/ ^ > ? ^ & ^r G> ^ & G> (3) ^ fi? c> 133 T 8 D 5 T 8 D 5 T 3 D 5 T 5 D 5 T 8 D T 5 Ss - s "^ ~ "J ^ o- In all forms of chords of the yth, the yth itself has a natural tend- ency to progress downward one degree; this is notably u true of the D 7 , which inclines persistently to the T 3 in its resolution (a). The D 3 , by reason of its proximity to the T 8 and its isolation from the T 5 , is almost as strong in its tendency upward one degree to the T 8 ; for this reason it is known as the leading tone (6). Because of the urgency in the progression of these two members of the D 7 chord, known as the sensitive tones, they are said to have compulsory resolution, and may not be doubled, as, in additi' their distinctive prominence in the chord, faulty parallel? probably result. THE DOMINANT SEVENTH CHORD 45 With the tendency of all members of the D chord toward finality, the D 5 inclines distinctly to the T 8 , which may be said to be its note of resolution; for melodic purposes, however, it very frequently proceeds to the T 3 , in which case the D 7 should be omitted, in order to prevent a doubling of the T 3 in the succeeding chord. It may also proceed to the T 5 for melodic purposes, or to aid in forming accompani- ment figures. For these reasons the D 5 is said to have optional reso- lution (c). While the D 7 is occasionally retained with this progression of the D 5 , and the T 3 doubled in the resolution, the student is cautioned against such modes of procedure as will result in a doubled 3d, in any case for the present, and until it may be done advisedly. Following the rule applied to chord connection in the triads, the D 8 , being a tone common to both chords, is retained in the same voice, becoming the T 5 (d). From the above details we form the following table of resolutions of the D 7 chord to the triad of the Tonic: The D 7 resolves to the T 3 . The D 3 resolves to the T 8 . The D 5 resolves to the T 8 or T 3 . The D 8 is retained as a tone common to both chords and becomes the T 5 . In the fundamental position of this chord the student, for the present, should omit the D f) and double the D fundamental, in order to obtain a complete triad in the resolution. At (a) the complete D 7 chord, consisting of four different notes, when strictly resolved, leads to an incomplete triad of the Tonic "Li fining but two different notes, C and E, thus resulting in an un- lance of the harmonic content of the two chords. The follow- Domina , ( , T the present, preferred: CUMULATIVE HARMONY 129 Here, it will be observed, the Dominant and Tonic chords each contain three different notes, resulting in a better balance between the two chords. The D 7 chord may at times retain its four notes complete, the 5th ascending to the 5th of the Tonic for resolution. The D 7 is classed as an intensifying chord. By intensification is meant the use of chords with compulsory resolution. This subject will receive more extended comment in another chapter. It may be stated in this connection that while with certain con- ditions (to be made clear in a subsequent chapter) the yth may be doubled, it is absolutely forbidden to double the leading tone in any circumstances, except when necessary in order to preserve a harmonic or melodic figure in sequence. Work out the following exercises in various keys as before. In the D 7 chords omit the 5th and double the fundamental. 131 Hcf* 5) & <^- ' | ?v i -o * 1 6 4 6 6 4 7 6 8 6 4 6 4 7 8 1 /A^* ^^ ii 1 V^f * f f3 s^> ^> ^^ ~ H **2 5 ^ " . ' -f ^ H 1 & ' 7 7 8 6 4 7 6 \ *6 4 1 h ! * f 7 THE DOMINANT SEVENTH CHORD 47 132 -&)'.(* ? <5? 5 ^-^\ ^ i r * i 5x> S yl - 55. 6 ( 4 [ ( r, 4 b 6 4 b7 7 >WA ^

" W^J jj-fcy-j m^ ^ ^~^tj h * ^ 7 McCov, " Dance of the Fireflies " Cave Man i * () jzr*ff-|S uj J |J_ -* * ^ ! * -*=:;_ ^_ BHi ^==v- S * -= g- f 7 V V ^-ff-^4 ^~ =t= -4 1 ^ 1 1 -1 ^ The harmonic scheme is shown at (a). CHAPTER IX INVERSIONS OF THE D 7 CHORD The D 7 chord, containing four different notes, is susceptible to three inversions. The first inversion places the third from the fundamental in the bass, the other members of the chord forming the intervals of a $d, 5th, and 6th; figured f , the figure 3 being omitted for the sake of brevity. As the D 3 has a compulsory resolution to the T 8 , this position is to be followed by the Tonic triad in fundamental position. 133 (d) / ^ i /v -t&^ ^ ^1 ^r i ~s5 "& 1 1>5! sS^ tt^ r>^ ^ f^ K . ^ ff^^ *K^ I K2; i #_.. ^ tti' - b^ ^t* r 5 i ( i *- ?6 [>5 6 # 5 At (a) is an example of the first inversion of the D 7 chord, the fundamental of which is G, with B as the bass, and is followed by the Tonic triad on C. At (b) is the first inversion of the D 7 chord on A, with C# as the bass. At (c) the first inversion of the D 7 chord on Eb requires a chromatic alteration of each of the interval figures; and at (cf) the 3d from the actual bass, F#, is indicated by the sharp alone. In each case the chord is resolved into its Tonic triad. The second inversion places the D 5 in the bass, the other members of the chord forming the intervals of a 3d, 4th, and 6th; figured |. As the D 5 has optional resolution, this position of the chord may be followed by the T triad in fundamental position, observing the given rules for resolution of the D 7 chord; or it may be followed by the first inversion of the T triad, in which case the D 7 should be omitted (in order to prevent faulty doubling of the T 3 ), and the chord of used instead of 3. 4 8 INVERSIONS OF THE D' CHORD 49 134 V *y J : ' g b" /r? ^ 4 ' ,'^ i.o 1 *"\ ^ ^ ^ 7z o | & Wp X-*' ^ * 3^. , GS ^ Eta ' 1 6 f . *6 4 r, I ' G ;>4 1 1 >6 ^6 6 4 At (a) is the second inversion of the D 7 chord on G, with D as the bass; the other members of the chord forming the intervals of a 3d, 4th, and 6th; figured 3. At (b) is the second inversion of the D 7 chord on A, with E as the bass, and the rest of the chord represented Jk by the figures 4. At (c) is the second inversion of the chord of Eb 3 and at (d} the second inversion of the chord of B, each of which is fol- lowed by its corresponding T triad. At (e), (/), (g), (h), the second inversions of the same D chords are given, with the D 7 omitted in order to avoid doubling the 3d in the resolution to the T chord. The following exceptional resolution may be noted, which may be occasionally employed to good effect: When the second inversion of the D 7 chord is followed by the first inversion of the T chord, the D 7 may resolve by degree upward to theT 5 . 135 ^ fi ^r ^ & & j f f J J 1 1 V /d & if^ -^"5 , I/ o & ^- (fo ^ i ffig -te 9- ^ \)S>f? _ -^ 22 2 )' ^ -<&- 1 1 f ^A^* f*is I ^^ ^ 1 ^"^ fl^^ pj- -^ ^ p P r \ ^-^ p ^ z . f4 6 2 ^4 6 2 b- ^>6 be 4 b b2 S6 6 #4 2 Here we have the third inversion of the four D 7 chords given in the preceding example, with the D 7 in the bass resolving to the T 3 , and with the T chord in its first inversion. 111. No. 7 *5^ WEBER, " Euryanthe " * ^ ferJ: The student should transpose the following exercises to many different keys, and work out in all the different forms that have been given. 137 /K(* g g &r- -^ ,5 t t*> i S- & ' ]^H &>G P= ^ ^ ^K ^ J ^' "*' C*' 'rzr ^? ~ ^ ^ ^^ ^.' -- ^x 11^^ Jj" & O -dS i ;tc. [(*)./ > ^J -75 *f-^ -35 r 1 77 .^ ^-" V^-l , B2 & 4 F ^ M g, Co 6 4 6 4 2 I 3 S6 4 3 5 4 6 6 5 7 1 INVERSIONS OF THE D 7 CHORD 51 6 6 6 4 6 #6 5 424 3 -&- 6 4 6 2 138 -IE? 7b Zj ^ ^f .j , I 1 i 1?^ -7^ ^ -H h- 1 r -^ 6 464 4 6 "4 ^ -<^ ^ "7 5 2 3 2 b rjirj] *

a ^ S's -. ^> ^ j gj =S ,*- ^/ GS 4 Il_q 6 5 IJ4 6 t]6 2 4 ' ^^ ?5 464 2 3 1 i 6 4 7 141 & <9- 6 #6 66 45 46 \fj' 1 1- N -b* sfc = ^ U 6 b #6 5 * 66 6 6 554 4647 2 3 142 CUMULATIVE HARMONY 143 6 b5 #6 4 3 4 6 3 EC Li & -& i i VTx , /*^ ^^ JK2 ^X f^j j M ^ ^ 5_ ^_ o 6 5 5 6 5 6 &c ^7 ^ *^i 4 6 4 7 42 4 b EZ-: fi i ^^P4- c5 -m i ! ^> 6 i r^ 3 ^- # e - 7 ^ ^- * ^-^db-^ -i I jr 1 b6 6 4 4 6 2 T ' -f *"** T 4 4 Additional attention will be directed to the D 7 chord in a subsequent chapter. Play all these exercises and examples, and have them played. A modulation is a change of key without a change of signature, and is generally transitory. Modulation is effected, melodically , by chromatic elevation or de- pression of one or more members of the diatonic scale based upon one Tonic, in such manner as to form a correct diatonic series based upon a different Tonic. 144 () ^ m 22 ==t (0 :- ^TP^= $+*- At (a) is given the accepted form of the diatonic major scale based upon the Tonic C. At (b) the diatonic succession is archi- tecturally identical, with half-step successions between 3-4 and 7-8, based upon the Tonic G. This involves the chromatic elevation of F to Ffc In like manner, at (c), by chromatic depression of B, a major dia- tonic scale is formed with F as the Tonic. At (d), (e), and (/) are examples, in similar manner, of the scale of A ^ a and the modulated scales to the directly related keys, e and d. Modulation is effected harmonically through the introduction of the D chord of a foreign key. 53 54 145 CUMULATIVE HARMONY (6) 2T 3 ^~ /> h-V, s j (M) 1 ? ?5| is reached. CUMULATIVE HARMONY By making the enharmonic change to d# and continuing as before, we finally return to the initial key of a, thus completing the circle, proceeding from minor to minor. 111. No. 9 MOSCHELES " Study in C# Minor " From c# to f#. RULE II. Take the supertonic for a new Dominant, proceeding from major to major, and from minor to minor. 148 Beginning with the key of C, taking the supertonic D for a new A Dominant, we modulate to G, thus resolving to a major triad in con- formity to the requirements of the rule. As the supertonic in the A key of G is A, this note in turn is selected for the next Dominant, A effecting a modulation to the key of D, etc. 111. No. 1O SCHUMANN, op. 21, No. i Novellette From F to C SERIAL MODULATIONS 57 Also by Rule II from minor to minor we commence with the key of a and modulate to e, thence to b, etc. 14O $' etc #5 RULE III. Take the mediant for a new Dominant, proceeding from major to minor, and from minor to major. 150 , / <,, / C H^^^i *^ f \ -. ^J^" ^^ 17 ^ / inir -^ V ^ etc. p ^ /5 1 Vfc ^ & f^j 2 7 tf b7 Beginning as before with the key of C, and selecting the mediant E for a new Dominant, we effect a modulation to a, conforming to the requirements of this rule in proceeding from major to minor; as the mediant in the key of a is C, that note is selected for a new Domi- A nant, with a modulation to F. Continuing after this plan until the A key of Gb is reached, the enharmonic change is made, followed by the A return to C. As the minor keys obtainable by this rule are included in the above, the student will not be required to use a as an initial key. 58 CUMULATIVE HARMONY 111. No. 11 SCHUBERT, " Unfinished Symphony in B Minor" X Qf> K , 1 I (TV H3 1 J SI2 =E ] J J , 1 3 J / ^ - v^ ^ x_ -J * ^ ^* I^X"*LLf J ># N* _ ^^^ ^^M / A A From b to G. Play all these exercises and examples and have them played. CHAPTER XI SERIAL MODULATIONS. (CONTINUED) RULE IV. Take the Subdominant for a new Dominant; major to major (a), and minor to minor (6), also singly, minor to major (c). 151 A A A A I'..- a g not serially XI & u ^ Cf *^i <=> '* ^ 1 B -r & i ft" & . (a) 1 etc. (6) HtZ & \ etc. & (c 1 & ) S5I r ^ s f)^ 6> =. & The student should also commence with the keys of F and d, by this rule, to reach a number of keys not included in the circle when A . the initial key is C or a. 152 A A A A F Eb d c ( ( ( 111. No. n 1 ^h> z 5P5 ^ ^ <= 19^ & ~^ P^ fi$^ '- ^ $2 . etc. J etc. ^}-: - u (^ \\^. i 5> %) f 12 b7 b5 7 b CHOPIN, " Mazurka," op. 56, No. 2 ^r * 1 | N L In fiW ik i jf 1 1 V rt n m ^j^lK f^~ yi. ^ ** *S^\ ^D ' ' ~ ^2 ^~j ffl\ ^ ' ' ^*^^? k*O -^ VsL/ ^? ~r etc. 1 ^s 1 ^ ^fc**' ^ ^^ 7 # 7 $ With C as the initial key, we select the subtonic B for the new Dominant, modulating to e. As the signature of e is one sharp, the subtonic in that key is D, which is the note to select for a new Domi- nant. 111. No. 14 SERIAL MODULATIONS 61 CHOPIN, " Nocturne," op. 15, No. 3 S,vi\ M * " >y ' lf\ 4 ^ t "1 r V-/ ** 1 i. f li." -.-} * s I <: ^ Uo'u^" X ?- i *- V I ^f 6 5 A A Yrom g to Bb. Let the student clearly understand that it is woJ the 3d in the D 7 chord (the subtonic elevated to serve as a leading tone) that is indicated as the note for selection by this rule for the new Dominant. The yth of the scale in the minor mode is required to be raised chromatically when it forms a part of the D 7 chord in order that the 3d in that chord shall be major, but this fact in no wise affects its scale existence for serial modulation, which must conform absolutely to its signature indication. Chromatic alterations of the yth and 6th of the scale for melodic u\es will be discussed later. For the purpose of acquiring a thorough familiarity with the various inversions of the D 7 chord and their resolutions to the Tonic, the student should review the preceding modulations (or at least a con- siderable part of them), using the D 7 chord with its resolution not only in its fundamental position, but in all its inversions. In order that they will appear in the most agreeable succession, the third inversion may be used first, to be followed by the second and first. Care should be taken to resolve each member of the chord in accordance with the rules. 155 RULE I A c A F D I) I) I) ^k ^~ tT & te' ^ b i^ b**^ ^ B^ ~^ 5$ ~ $ &~^ "^ ^ * ft fen & 1- 1 f-i ,0 j^j ff? c^- 1 7 464 6 2 b b5 62 CUMULATIVE HARMONY 2t j ~ijl ^ b~^ ^ fc^l ^r~ ^g (0} S s> g & S ^ ;d ^ etc. rVV .^, i u lit |5J- P** , 1 V{3 ^ J , \ r%L^-i j l/Gx i l/i-*' ^^ b7 4 b6 4 6 2 b b5 By Rule I taking the Tonic for a new Dominant the modu- lation with the D chord in fundamental position, as already used, ap- pears first; following this the third inversion of the same chord with the D 7 , Bb, in the bass, resolving to the T 3 in the succeeding chord; next the 2d inversion of the same chord resolving to fundamental position, and, finally, the first inversion similarly resolved. This com- pletes one modulation. A By this rule the succeeding key is Bb, in which the same plan should be followed. The student is advised to do this work by several of the rules, and in both major and minor genders. CHAPTER XII DIRECTLY RELATED KEYS The directly related keys to any given key are those that may be represented by the same signature, or by one sharp or one flat more or less; also the Tonic minor of a major key and the Tonic major of a minor key. A Hence, the directly related keys to C, with the corresponding rules for modulation through which they may be reached, are as follows: A A A By the same signature, a; by one sharp more, G and e; by one A A f A flat more, F and d and the Tonic minor, c. As a signature of one A sharp or one flat less than that of C is obviously impossible, they are not considered. A F, modulation bv Rule I; A G, modulation by Rule II; a, modulation by Rule III; A d, modulation by Rule V; e, modulation by Rule VI; and the Tonic minor key of c with the same Dominant. In like manner, those directly related to the key of a are: A A By the same signature, C; by one sharp more, G and e; by one A A flat more, F and d and the Tonic major, A. One sharp or one flat less are, of course, not considered. A d, modulation by Rule I; e, modulation by Rule II; A F, modulation by Rule III; A G, modulation by Rule IV: A C, modulation by Rule VI; A and the Tonic major key of A with the same Dominant. 63 64 CUMULATIVE HARMONY The ones most closely allied among indirect modulations are those by Rule IV from major to major, and Rule V from minor to major. A A Thus from C and a, by these two rules the indirect modulation to A Bb is attained in both cases. Indirect modulations are frequently effected by combinations of two or more different rules. A . In order to modulate from the key of C to g, Rules I and V may be used in combination, thus: 156 A A To modulate from G to F, Rules V and III are employed, thus: 157 in \ \\ *L 3 S >^-. E ^s^> & Yf' Saz 3 ifg g \j & fm\'^ , BSSS i | ! , SC25 | 22 &. -^" " IP tt Modulations are frequently effected through a repetition of the same rule. 158 ii ir -ft 75J & ^ t(\\ A ii l |j ^j^I? 1^^^ luESJ ^^ 1 1 ^ ft { f- TSSi ffiZ! -P-J -.. i-s & f ~^ ^-^ > 7 ft ft DIRECTLY RELATED KEYS 65 A A Here, by repetition of Rule II, a modulation from C to D is ac- complished. By what rules or combination of rules would the following modu- lations be accomplished: A AA AA AA A A AA A A A A A C to Bb, C to F, C to G, G to e, G to F, F to g, F to a, C to e, A AA A A AA A A AA A G to b, D to a, d to C, F to e, Bb to Ab, A to b? The instructor should add many other modulations by combination of two or three rules, all of which should be thoroughly expounded, both orally and by writing. The following oral practice should accompany the above: A Modulating from C by Rule I, what key would be reached? By Rule II? III? IV? V? VI? Modulating from A by Rules I and II? Ill and IV? V and VI? CHAPTER XIII HARMONIZATION OF MELODIES From this point the practice of harmony will continue under given melodies. The entire scheme of harmonization of melodies will be conducted through the use of the three primary notes, the Tonic [T], Sub- dominant [S], and Dominant [D], and their chords in various forms; and it may be stated here that the scope of this three-point mode of harmonization will include the employment (as tributaries of these chords) of all harmonies to be found in the works of the standard composers, together with their progressions and general treatment. The student will, for a time at least, place the primary initials T, S, D, in capitals above the notes of melody, to aid in selecting de- sirable basses, and to assist in subsequent analysis. RULE I. Harmonize the first, third, or fifth of the scale with the Tonic [T] (a), the fourth or sixth with the Subdominant [S] (b), and the second or seventh with the Dominant [D] (c) , 159 D D 7T z;H ~ a p ^h <& ^B f i f ^ f- p- J r o P :h -*- \ (a) 1 (a) T" (*) -i- (*) r (O p (O i ^_^ j 1 1 The yth should be used in the Dominant chord when it is followed by the Tonic, unless its use causes a doubling of the T 3 in the reso- lution, in which case the yth should be omitted. 66 HARMONIZATION OF MELODIES 16O I (*) I ^ Sf At (o) the given melody moves from the second of the scale to the third, that is, from the D 5 to the T 3 ; as the D 7 [F] has a compulsory resolution it must, of necessity, resolve to the T 3 [E], causing an un- desirable doubling of that note. At (b) the D 7 has been omitted, the complete triad of the Dominant progressing regularly to the triad of the Tonic, without the offending doubled 3d. An example of a melody harmonized as directed above, using fundamental basses only, and adding the yth to the Dominant triad when it can be done without doubling the 3d in the resolution to the succeeding Tonic triad, is here given. 161 ( *T ) (* ) \ (c T ~ ) (^) D ! T S f S 4 J (A T E ) > J~ 2 i^^ ^*1 i i 3 ^~ J & i \MJ ' $ ?5 ^"^ gj -j s}- as ^ tJ & J -x^J- -^- ^< y^, -fiJ- 7 7 [i*7I7T 1 j ! j5> ^^* ' ^ ^ ^f ^ 1 & D T D T D D T i I) 1) T I) n /c , J 1 -^ " S C^ d H( ffh~~ ^ 13. ^ * 1 vy a -^ -zS 7 -* ^ ^ 7 ^ ^ 7 : -&- r *\* ^ (^ c/ ^^ ^ v ^ & 68 CUMULATIVE HARMONY At (a) the first of the scale, C, is harmonized with the Tonic, C, the triad of which is C, E, and G, with C in the soprano, and G and E assigned to the alto and tenor in a position as near the soprano as is possible. We have thus properly harmonized the initial note. At (b) the seventh of the scale is harmonized with the Dominant, G. As the D 7 chord is G, B, D, and F, it follows that with the D 5 omitted and the B already in the soprano, the doubled G and the F would be available for the alto and tenor. As the G is the note com- mon to this and the preceding chord, it should be retained in the same voice (the alto), thus leaving the seventh, F, for the tenor. At (c) the common note G is retained in the alto, and the D 7 re- solved to the T 3 in the tenor. As the melody note at (d) proceeds to the T 3 at (e), it is obvious that if the yth should appear in the Dominant chord at (d), it would demand a resolution to the T 3 at (e), thus doubling that member in the latter chord. To obviate this, the 7th is omitted, and the D triad used instead. As the note common to the two chords, G, is in the alto, the re- maining note B is assigned to the tenor, thus placing the chord in open (or dispersed) position, as are, by natural progression, the next six chords. At (/) the fourth of the scale is harmonized with the Subdominant, the note common, C, being retained in the tenor. At (g) the fifth of the scale is harmonized with the Tonic; in order to retain the note common in the tenor, the alto descends a 4th to E, a distance of more than an octave between it and the soprano note, G. This distance is lessened in the next chord. At (ti) are applications of the following rule: When the second of the scale is followed by the first, the D 3 in the fundamental position of the D 7 chord may be omitted and the funda- mental doubled, thus assuring a complete triad in the resolution. The omission of the 3d from the Dominant is always of a passing or temporary character, and should never occur in the penultimate chord, the following solution being preferred: When the D 7 chord is in fundamental position, the D 3 , if it occurs in the alto or tenor, may descend to the T 5 , resulting in a complete triad as the chord of resolution. The bass, in this case, should move in contrary motion. HARMONIZATION OF MELODIES 162 69 T D T D nil L__J y a 4O dL- x ^^ ^^ l-.\ ^ <- v t/ 5 X ^ x' 1 | i '* * ""^ ^ t- ^ r 7 This resolution of the 36 of the Dominant is, at times, quite effective, particularly when the second of the scale, followed by the first, appears in the given melody. RULE II. When the first of the scale is repeated, it may be har- monized with the Subdominant. 163 T S T (g : <5 RULE III. When the fourth of the scale is followed by the third, the fourth may be harmonized with the Dominant. 164 i) / 1 \ -_ -_ V y ^^ *^ ^S ^ u 1 1 1 J I (^ /Sr 5> (C* L!W'* ^^ ^ O As may be readily seen, the fourth of the scale with this harmoni- zation is the yth in the D 7 chord, duly resolved to the T 3 . It is not to be assumed that this rule applies to all cases, as the fourth followed by the third, notably in the cadence, is frequently harmonized with the Subdominant. Harmonize the following melody, conforming to the above three rules; transpose to several different keys and harmonize. 165 CUMULATIVE HARMONY TSTD TSDTDTSDTST (a) (b) ({:) (^N '-; ^ ^^ P ^ o gg f. (?>( v -* j ff Sj ^2 x^ ^> s^s CS ^ ^. n 7 7 \ r 7 y r, -^ ^? ^_ " X ^2 /^. "jl ^J ^v f. irh ^* *_ At (a) the first of the scale C, repeated, is harmonized with the Sub- dominant. At (6) the same note, again repeated, is given the T harmony. At (c) the positions in the chord of the alto and tenor notes are changed to improve the voice leading and bring the various voice parts to better relative distances from each other. At (d) the fourth of the scale is given the S chord; while at (e) the fourth, being followed by the third, has the D harmony. At (/) the D 3 descends to the T 5 , giving better relative positions to the voice parts than would have otherwise been the case. At (g) the positions of the alto and tenor have again been changed within the chord to get better subsequent voice leading, such as avoidance of parallel octaves and of all voices moving in similar direction. RULE IV. The fifth of the scale may, at times, be harmonized with the Dominant; when it occurs several times in succession, it should be harmonized alternately with the Tonic and Dominant, generally selecting the Tonic for the first harmonization. 166 T D T S T D T yr irh o .. /O K -^. ^~ - V- J g r^ f> ^^ *r ^ - ., r ^ ^ J 1 ^ ^^\ ^^ [22j 3* ^^ & ' * w ^ ^ W4 * 2 *- ! *o ' P =F=r -&-. r r r r r r r, J^ J j . J J J ^ /wyo ^^s*-} f f ^ P * i* 3EZJ 1 2 1 1 Q '6 66 66 744 4 Jff -f & -* -* - 1 1 1 1 i ^K * * -& F * F ^ -^ J "EK \r \ \ G p "~n Jf \ p f* m f 3 \\ lev) J & & 168 mrJOto "*J~ m * I* P" r " /o xf p/ * (2 p p ^ p ^ -t -^ ^ * ~"^&~^~* Z= 1 1 1 1 1 , 1 \j m & i a i J[ n /^ M Fri^'Pi* i* \(Tj ^& P r ' r i i ' L I i ' i 1 i 1 M M ~H --$&-- * * & d wh-+*- f -d d- i 51 1 |S ' <5 1 1 111. No. 15 T LOWELL MASON, "Hebron" T T S T S D T / JU 2 ^ t 1 _ 1 1 (fh^U j~ d * ^ V- J 2! ^ J d g 8 , s V & 1 & 1* 1* (^ (? p ( P^U^ 1 1 . \ ^^t? ^j (5> 0~ -+ rff 9 -iSf 6 ^ 4 CUMULATIVE HARMONY These exercises should be transposed to various minor keys and harmonized in accordance with given directions. As the 3d from the fundamental in all D chords is required to be major, and as that note, according to the key signature, is minor, it must necessarily be elevated in order properly to form such chord. The subtonic thus becomes a leading tone with a tendency to re- solve upward to the Tonic. This necessitates, therefore, the elevation of the seventh degree of the scale in such transposition. Exercise 167 transposed to a would appear as follows: 169 2C3 J 11 j i J ^ ^ ^ f f J r f r ,j j i r r r j ' etc. uJ J /W\ * ' 7 tt j j * [^/f j * * ^E i' ^t 5 A ' -- r * Z -* n 6 J ' J ' 6 _ S6 6 ?f6 4 5 4 7 1 CHAPTER XIV HARMONIZATION OF MELODIES. (CONTINUED) RULE V. When a primary note or fundamental is followed by another a fourth higher, a D 7 chord may be formed upon it, effect- ing a passing modulation. This frequently occurs when the T chord is followed by the S chord, the T chord becoming a passing Dominant to the key of the Subdominant as by Rule I of Serial Modulations. The Tonic chord thus becomes temporarily a Dominant of the Subdominant [DS]. 170 T (a) i At (a) is the usual harmonization of the first of the scale with the Tonic, and repeated with the Subdominant. At (b) the minor yth Bb is added to form a D 7 chord and a passing modulation, as by Rule I of Serial Modulations. 111. No. 16 CHWATAL, " Lovely Night " * 1 1 ^/ * o "~ i j J XT p rj f * 1 01 J JF -J j? \ff) '^"4 : $* ~jm r ^. r i fS ff^^~t7"H : fe -^ ^5 V CZfijkZ 1 1_ * ^ *Passing modulation as a Dominant of the Subdominant. The following exercise involves the application of the preceding five rules, and should be worked out in several keys. 73 74 CUMULATIVE HARMONY 171 (a) 1 1 - (- ^) 1 1 ,0(< (* ) 1 1 :/ ) jf f I - 72 1 '^ i^ ^ f) <-* [-?5> m\\ V *' i - /^ -^ -2 \Vj J i*""? ^ ^ "> ^ ^ * x 1 ^/ rJ 1 <; J-: J 1 -^. . J. -&- & J <; etc. /w\ g o ^x J^I? 1^ is^ \^J / i -2 ^*---\^. <=2 -'-^ f 2 f 12 ' ~^ K LT 1 u 7 7 ', n f-. f3 si f' 7 1 *"* *^ \-}'> ** -^ Sj| f'f 1 1 J * J , | | etc. /*^*~) 22 * ^_ 2?J t^^/*? j ^^ -^ ^ ^ ^ k f^t f2 ^ fp 25 i j 1 r i j^T /V ^"^ *^X *^ ^7 ^r? ^^ v-> ^ 1 1 -J ....... ... II 7 6 CUMULATIVE HARMONY 173 \ A / v ^ -^ 1 : (5 s ' ^ ^^ f^ ft\\ ^ \:\) o (2? ^ .V ^"^ ^^ f? r J gg 1 1 jf "^ ^y ^? ^i ^y ^ 1 2 II f(T\ -^" || \^\J 174 L/ (? E: e -*22 ^*^ j^ / s /^ ^^, & -^ /*} & _. {3 ?T\\ ^ Tin f 1 r ' ^Mr 1 i L/ ^ ,v f-^ ^^ X^L 5 s? *? ^^ P ^ ^2 & --^ II /Vy\ l z I 1 siz 1 1 175 i L/ a? ^ a S[J X? /" i ^/ 2 ^y ^^ & ^~. {3 //T\ \ r f \ \>L/ . 1 P ^ y fi- V ^ ^-i ^*^ ^5 e? ^ S3 ^-. irh 1 -. Transpose these exercises to many keys and harmonize similarly. Transpose to minor keys and harmonize similarly. As the T chord in the minor mode is a minor triad, the ^d must be elevated in forming a DS chord. 176 n j 1 J 1 1 1 \J i J E <5 f^ ^ ^ I * xJ & SI ^ /^T\\ y f^S ^^ TTj^? K n \Jv.l/ - ^-J ^~ (2 Tr^ fj ^ X"^ J J J_ J 1 Ju d^' >^A 5 ^2 "* -** L"T */ ^ ^^ ^* k^-x'^ / &. S^J 6 6 7 tf 5- 7 7 1 At (a) the second quarter appears as a DS chord, the T 3 having been elevated as required. Progressions of voice parts by augmented interval should generally be avoided. This applies particularly to augmented 2ds and 4ths ascending. Augmented 2ds are, however, sometimes unavoidable at present in given melodies transposed to minor keys. CHAPTER XV HARMONIZATION OF MELODIES. (CONTINUED) EMPLOYING INVERSIONS The following exercises should be harmonized in accordance with the preceding rules, the student employing the inversions of the various chords in such manner as to form diatonic passages of greater or less length, with a view to making the bass part as melodious as possible. These exercises should be worked out in both close and open position. 177 (a) (6) (c\ (d) (e) n 1 | | Jfi\ & ^ _j '* ^ **" "* z ^ <3 <5i f ' 3r- ^ ~ ^ h= id -* ~& ^ <* -Si -* b W- i^ f^\* -*"l | WJ'l j E ^2 ^^, -_ ^^ \-s\^ v 19 '^ A ^^, * ^ fZ* -^ J -^ & i^ ^* 4 2 6 4 3 6 4 2 6 6 5 6 6 4 b5 ' J J- -, fS ^ , | <^ pj- , \~s a? ** x^. ^y t^ 565 567 343 343 ) the 4 chord is preceded and followed by the triad same bass note, C. At (6) the f chord is preceded by a triad and followed by a D 7 chord on the same note, G. II. When it occurs between two bass notes a diatonic degree above and below its bass. 180 (a) >p - - ^ S3 at &> S3 <3> fi s - & t) 2 3. ^- ZZQ & f 2 rl*> PJ- -5 S3 66 566 4 34 At (a) the \ chord occurs between the bass notes E and C. At (b) it occurs between the bass notes F and A. In both instances it acts as a passing chord between two different positions of another chord. III. When it is preceded or followed by other positions of the same chord. 181 1/r >n ^^ 2g -_ 5i -^ Ifl) ^ 2 OJI Z IT & i > <* - ICy 2 ^ r? *^ ^ .g ^ 65 6 43 4 IV. When it is followed by a triad or seventh chord on the same bass for the formation of a cadence (to be considered later), or when as the second inversion of the T chord it is followed by the third in- version (or the first inversion) of a D chord. 8o 182 (*) CUMULATIVE HARMONY (d) A 1 | _, ,-j J 13, o (frr^ V S3 f^3 f2 i<2 ^ 1 j ^ _i ^ _j 1 -^-H 75; ^ jrj ' ' ^- t -^' jr ^*^ 6 4 5 6 7 4 646 66 42 45 6 4 6 At (a) the 4 chord is followed by a triad; at (), by a D 7 chord, both of which in turn are followed by a triad on the Tonic. At (c) the \ chord is followed by the third inversion of the D 7 chord on G, figured 2, which is resolved to the first inversion of the Tonic, C. At (d) and (e) it is followed, respectively, by the first inversion of the D 7 chord and of the D triad. The bass in this chord is generally doubled. The initial, final, and penultimate notes of the bass part should be in fundamental position. The S chord should not, for the present, follow the D chord. The student should carefully avoid overlapping the voice parts, particularly the bass, which must not appear above the tenor. THE ABBREVIATED D 7 CHORD D) With the fundamental omitted from the D 7 chord, the three re- maining notes present a series of thirds forming a triad on the sub- tonic, as a leading tone. The subtonic is here considered its nominal fundamental, its real fundamental being the Dominant. Symbol, D). This chord is at its best in its first inversion (D 5 in the bass), and with the D 3 in the soprano; it is, in fact, otherwise not very satis- factory, and is rarely employed. In this position the D 5 is doubled when the chord is followed by the first inversion of the T triad (a) ; when it is followed by the T triad in fundamental position, the yth is doubled, one resolving to the T 3 and the other ascending to the T 5 (6). The second inversion (D 7 in the bass) is acceptable only with the D 5 doubled (c). HARMONIZATION OF MELODIES 183 8l vCl) & 2; & o 1 L j /^~\t /O ^ jif? l?> rs (* So ^^ "^ ^5* '6) The chord is rarely used in its fundamental position, and the student would do well to avoid it. This chord was much fancied by the old masters, who generally omitted the fundamental in the second inversion of the D 7 chord. m. NO. is HAENDEL, " Belshazzar " ' 111. No. 19 MOZART, " Fantasia in C Minor" fi w ^- : ^^ d x $ Ji IS H r 3 U i f O ^ ^ k * L ' * j j i rtv" 1 A '" ^ V- . ^ 1 -^ 9 -F- J r rP fe tr ^ ^. ' = s p- "U L -g-^^ __^^_^_^^ - s m^m f / a V KH 1 -A * ^- * fv. ^p -f^ t\ ^- ffi^^ * =* - a^- r- * J ** K 184 1 i 3 4 6 J 6 ) 3 T-J 6* 6 xkf( i- b ^ 5 ^ 6 ~|~ j * " \ ^j ^ -^- (^ (^ -5t- ,5 -d etc. 6 ) 1 ,r, t 5 6\ 6 IB) 1 4l 6 82 CUMULATIVE HARMONY EZ- _| i 1 (? N^ bi> \ 6\ 6\ 6 1 6 | [>7 #6 6) b/ 4J b5 4 1 -^ ^j ^^^ M X_x I ^^ o \ \ ^- II 6 66 4 5 6\ #6) 185 E^Z* fP -, j : __ ^^^ ^s ^ Jr^' (^ -^ - tr 66) 6 j:6) 6 5 E2 2 J ;5/ ,-5 i .1 j 2 N_^ ^ 'C' "JT 1 G' ^^ 1 1 11 #6) 'ft '6\ 6 6 6) #47 5 -^ -HS- 6 #6) Z!- li: a CHAPTER XVI SECONDARY CHORDS ON THE SUBDOMINANT In the Subdominant chord, the 6th may be substituted for the 5th, to form the Subdominant substituted 6th chord. Symbol, |_S_. This chord is an application of the triad of the supertonic (which is its fundamental) to Subdominant harmonization, and will be directly considered only in connection with and as a member of the family of S chords. It has the greater local significance as a primary chord when it appears in its primary position with the Subdominant as the bass, although in both its fundamental and \ position the Subdominant character is always present, excepting when in its fundamental position it is preceded by such dissonant chord as would tend to localize it as a point of destination or partial repose. As in the triad, it is the S 3 that is not suitable for doubling. This is particularly true, as to its application, in the major mode. It may be understood that the minor 3d from the fundamental of any chord is not as objectionable for doubling as is the major 3d. This chord may be freely used in all inversions, as exemplified with symbolized figuring in the following: 186 () (6) (c) (d) |_5_or [3 |_6_ At (a) is the triad of the Subdominant, F, in the key of C. At (6) the 6th is substituted for the 5th. At (c), (d), and (e) are given the chord in its various positions, with symbolized figuring. 83 8 4 CUMULATIVE HARMONY The secondary Subdominant symbol l_ is used in connection with this chord for purposes of immediate identification, and as an aid in subsequent analysis. 111. No. 2O Andante BEETHOVEN, " Sonata," op. 14, No. 2 * Lf j > jf " 1 "1 *i M IS 1 P *i fe=*: S 1 r J r F* r J * . J P -5F -3- -*- J :g: :gz -* - J ^ - -g- ^4 *j h _ i i - f Or- == =fc= \ ~ ' J!_ J 1 -M LI 111. No. 21 F. GIARDINI, " Italian Hymn" * / yft i / XL '* i m j \ l(n A J i ^ **" \ JOT T- 9 J 3 * 01 '^ i j 00 L_ . f- - & m 3 /^ylfo p 0) | r F L m V^ tt A * * In the Subdominant chord the 6th may be added to the triad to form the Subdominant added 6th chord. Symbol, ||S_. This chord, in like manner, is an application of the supertonic yth chord for Subdominant harmonization, and will be classed directly as another member of the family of S chords. It may be freely used in all positions, the figuring for which should have the special symbol ( []_) attached. 187 (a) (b) (c) (d) (e) (/) 1 7T i j^^ r^ i*J ^ tt ^ *i J^ ^ g- f<^; S 1 (9 --? ^ ^^' 17 I 6 I 4 l| 4 ]5 l_ I* At (a) is the S triad in the key of C. At (b) the 6th is added to the triad. At (c), (d), (e), and (/) the various positions of the chord, with symbolized figuring, are given. SECONDARY CHORDS ON THE SUBDOMINANT m. No. 22 b" J MENDELSSOHN, "Part Song" * 1 ., K I _ | ptv V (H y < chord in fundamental position. As the primary note is the Subdominant, F, the preceding primary note, C, being followed by another a fourth higher, is converted to a temporary Dominant by addition of the yth. The simple existence of the D 7 chord on C involves a temporary modulation to the Subdominant, and is resolved equally well to all forms of the S chord. 192 (a) ( * * S b U- -^ -j- -5- -* * ~* ~*~ /^"\ ^ fit 1 Ls-r */ * 2 ^ i a SZO s i T ^ r*s 466 2 4 (0 D ^ J r i . j/ g> _i i i j 0i 4 * /?k a * TCTT P ^- * J*~ J '* J^ S < i-^ J f f - * 9 1A "' * 9* 9* P* r J -^ tr- W- j 9* r \>9^~ ^-: ^ ||6 4 6 4 4646-76 ||5 2 3 2 [|S 4 4 7 At (a) the primary note, C, being followed by the primary note, F, is converted into a temporary Dominant by addition of the yth, Bb. At (b) the depressed $d is used in the first inversion of the S triad. At (c) the second of the scale is harmonized with the [S chord in fundamental position. The primary note, C, at (d) is con- verted to a temporary Dominant moving to the primary note, F, with the [S chord. At (/), (g) the harmonization of the second of the scale is divided between the [|S and the D 7 chords. At (//) the fourth of the scale is harmonized with the Subdominant, and at (i) the second of the scale is given the [|S_ chord with depressed 3d. The following example's should be worked out with application of the given forms of the S chord, alternately, for practice. CUMULATIVE HARMONY 193 XI / S^j m VL. 1* | (T3 -^ f i r VMJ 1 1 1 J 1 1 \J _ 1 > - 2 -r ll J\ A p 1 ^ ^ II BE 1 i II 332 1 1 1 1 194 t If . o it * i ^ /kb f2 1 r 1 * 1 1 v^ly *T 1 1 n 1 , i i* r X (7 j ^ i* J J J x- j - 1 n K 1 DOMINANT OF THE DOMINANT [DD], PASSING MODULATION The admission of the [[S_ to the list of those available for harmoni- zation invites in turn a second application of the rule for passing modulation as given on page 73. The one already in use occurs when the Tonic as a primary note is followed by the Subdominant as another primary note, a fourth higher. When the |[S_ chord, whose fundamental is the super tonic, is fol- lowed by a D chord, the fundamental of which is a 4th higher, a D 7 chord may be formed upon it, effecting a passing modulation as a Dominant of the Dominant [DD]. As the given melody may not be altered, the necessary chromatic alteration must be made in the lower voices. 195 ) *) <0 d) I J /L / & ^ B fr\\ + ^~. ^^ SS2 /^ S3 -^ r i J J -* 1 1 1 -&- -&- 1 (&- ^ r 1 /VA gg E f*3 t*^} ii^/*/ * '**' r^x \^^ i , ^f ^ n<*"3 ?. f^ r t/o^ ^^ *i ^^^ i 6 i 4 2 6 6 ' 6 4 2 6 i g 6 5 SECONDARY CHORDS ON THE SUBDOMINANT 89 J J J f ^ "" P *^- I* P* . h, (--> '' '* & ** ' & __. j , '<> ^"\ ^/ (? [^/ 1 f? ^ f- *s y i^ i i 6 5 4 2 r 14 113 4 3 * b 6 5 5 5 b e r 4 7 At (a), in order to prevent the soprano and alto from being too far apart, the inner voices have been exchanged. At (b) the second of the scale, harmonized with the [S chord, is followed, at (c), by the third inversion of the D 7 chord, Y serving as the bass in both chords. At (d) the first of the scale, C, repeated, receives the ||S harmonization, with a supertonic fundamental, which, being followed by a funda- mental (G) a fourth higher, is altered to become a D 7 chord [DD]; this has been done in the last half of the note, thus effecting a passing modulation (as DD) agreeing with Rule II of the Serial Modula- tions. A similar case is at (e), where the chromatically altered note ap- pears in the alto. This may be accomplished also by chromatically altering the 3d (F) immediately upon reaching the fundamental located a fourth higher, leaving the [jS form of the chord to be implied; but the student is advised to do so but rarely, until its meaning is thoroughly absorbed, in order that the original idea in the harmoni- zation should not be lost. 9 o 196 CUMULATIVE HARMONY () (-5) (*) ( 1* v 1 ^ ^ \ \- 5 6 #6 5 4 3 At (a) the first inversion of the D 7 chord is resolved to the T triad, upon the last half of which at (&) a DS chord is formed leading to the (|S chord; this in turn is altered at [c] to become a DD chord suc- ceeded at (d] by the triad and yth chord on the normal Dominant. In the following example the same harmonizations are given with the intermediate normal progressions omitted, although implied, and the passing modulatory progressions approached directly. ' - DD D DS D yr > * - *l ^^ f^S J cs L.. , . ii L*^*^ vL> g! c^ *5^ fT^i U'^' -^J /^~\ ]j' *^s & /o K/*v ^5 Cr^ \S** 6 4 & JJ7 524 As will be seen from the above, D 7 chords may follow one another in immediate succession, thus effecting a series of passing modulations by successive D chords. 111. No. 24 CHOPIN, " Waltz in C# Minor, " op. 64, No. 2 *The D 7 chord on DS followed by the D 7 chord on Gft. SECONDARY CHORDS ON THE SUBDOMINANT 91 111. No. 25 MENDELSSOHN, " St. Paul " V Tf/t s 9 * 1 -* i JH J , ^ - -+ 1 ft*)3* i* I* 1 m c2^( ! ta * ' f- -F ^ u> 86) 6 5 4 *The D 7 chord on A, followed by the D chord on D, with an interpolated chord. The application of D 7 chords in this manner may be regarded in general as an effort toward intensifying the harmonic progression toward the cadential Dominant, which, with its resolution, is the real point of destination. This intensification is enlisted primarily by the substitution of dis- sonant chords, as chords of motion, for those of resolution which create an impression of partial or complete repose, thus deferring the effect of finality until the concluding Tonic harmony through its Dominant has been reached. Work out the following exercises in both major and transposed minor keys, introducing passing modulations through the DS and DD chords, opportunities for which occur with the following harmonic successions: T to S chord and [[S_to D chord. 198 wm * ii ^ 199 ' * 20O CHAPTER XVII MELODIC MODULATION We have learned from a previous chapter that modulation is effected melodically by establishing a correct diatonic scale series based upon a Tonic other than the prevailing one. It is not necessary, however, that a complete new scale series should appear in order to bring about such modulation. A section of one key, consisting, possibly, of no more than two or three notes, may be assumed to be in a foreign key, and when harmonized ac- cordingly may be positively identified as belonging to that tonality. 201 (a) (b) (c) n J \J iy ^r ! \}r~" es i> ^ B fy slEEjE ji^ 1 ^ J *9- i i - L i & fe*"- r? * & ' i*^ (- P ^ f^> 6 l>5 ~T $6 L_ r 7 $ !EE ^ F '^ ^ J r r *s . ^* ' A /m\* ^y f PR^ * ^ ' f 3 f 3 ^J 4 3 At (a) we may assume that the two notes G and (which are the A fifth and fourth of the scale in the key of C) are the second and first A of the scale in the key of F, and by harmonizing them accordingly, they become positively identified with that tonality. 93 94 CUMULATIVE HARMONY At (b) the D may be assumed to be the fifth of the scale in the key A of G, which becomes positive by harmonizing it accordingly. At (c) the C and B may be assumed to be the fourth of the scale fol- A lowed by the third in the key of G. At (d) the depressed B, which A is not a part of the diatonic scale of C, may be readily assumed to be A the fourth of the scale in the key of F, and at (e) the elevated F may A be taken as the seventh of the scale in the key of G. All of which is substantiated by corresponding harmonizations. Here follows a series of rules for melodic modulation, at indicated notes, to directly related keys. As modulation is effected harmoni- cally through the Dominant of the new key, the indicated notes must necessarily receive Dominant harmonization. In each modulation the new key will be retained until the next indicated note is reached. RULE I. When the indicated (+) note of modulation descends, a half step, it goes to the third of the scale in the new key. 202 I 1 | 1 i & i 1 /TT-T"^ & -_. -'* t> -51 t "^ H : s> f(T)\ J " i^) -O 1 9 tl^ 2 & ., 2 ^* "^ -, ^y j*5 5^ O' ^ /y PJ *^ -^ r ^ /^ -j J r \ r i i i I 1 1 1 ! & & \ r - J r i 5 J /WA r^ o* D* ^^ ^ l^rf'*/ * ^ ^_ 22 _ V X\ y x^ fl^^ O^5 n< ^^ '^ n 1/-X r i i i 84 2 6 4 2 IB f 4 7 At (a) the note of modulation, E, ascends a half step to the first of the new scale, F. As the E is the seventh of the scale in the key A of F, it is harmonized with the Dominant, C, thus definitely effecting a modulation to that tonality. At (6) the E again moves upward to F, but, as the key of F is already in force, a modulation cannot be made to that key ; therefore the E A moves to the third of the scale in the key of d. Since the T 3 occurs in the soprano, the yth may not appear in the preceding D chord, as its use would cause a faulty doubling in the res- olution. In the second measure a chord with C in the tenor is succeeded by one with C# in the bass, which is the employment of a note in one voice part, immediately followed by its chromatic alteration in another. This is known as a false relation, which, while usually for- bidden, is allowed when the fundamentals of the two chords involved are a 3d apart. As F and A, the fundamentals of these chords, fulfill these requirements, the objection does not apply. 9 6 CUMULATIVE HARMONY At (c) the indicated note, F#, ascends a half step to G. As G is A not directly related to F, the modulation would be to g, which being A represented by one flat more than the key of F, is a directly related key. At (d~) the F# again ascends a half step to G and may invite a modu- A lation only to the tonic major key of G. At (e) the modulation back to C is obvious. At (/) the note of modulation, C#, ascends to D. A A As the key of D is not directly related to the key of C, the modula- tion must be to d. At (g) the modulation returns to the initial key A of C. 111. No. 27 MICHAEL PRAETORIUS, 1610, "Choral" XT 5Z ? | G- s l/n\ I/ ^ y & VMV <^ J ^ ^ < :2 ~ -&- T" / j P C*' > ^> t-** ny*ri -* ^ I?T\ \ ^ r, V fj ^^ ^"^ 22 p ^? i x> SEE ^^ r>i _-J ^ S{ -_ 1 j , r 1 r 1 i - *-^ Lt^* ^ * |* * L ^ '^ k^^-/ -, J |^ r GS T$r 5 6 4 7 RULE IV. When the indicated (+) note of modulation ascends a step, it goes to the third of the scale in the new key. 206 >iit I tit JT I V ^ - ^ & I(T) J '^ ; - X- ?y iy fy fy -<2 f {2 r i I J -&- - J J J J 1 -J-J c^\* *' - ^ -^ ^ r fr S"{ {3 f^ \^/*f ii - / i^j (^ ^ V ^\ j *"* ^ *- {? ^ i r c 5 6 6 6 1 4 7 It will be noticed that the modulations by this rule are effected without the use of the 7th in the D chord, the resolution of which would cause a doubling of the 3d in the succeeding T chord. 111. No. 29 AHLE, 1664, " Choral " /\ ^r-^rr f- (fl) ^ J ^, s ^ V- ^ ^r- -5>- 1 P * 1 r r ^j. r fl*l"* f^ & ** ^ 2 ^^t^~ p. r^ J*^ f^ 6 86 4 6 6 s^ CUMULATIVE HARMONY The student will work out the following examples after Rules III and IV from several initial keys. 2O7 n "*" + + 4- + -&- r^ ^ \f fy H ^ - (5 <3? r 5 z fn^\ , ^ -f / 1 ^ ^s ^ u *^? 2 ^S rr\v7 f^2 -,-, ssp f f^ S^s l^ /v o rs G I J. 1 1 ~^* 1 -,&- -!- ! . -J- ] /^\ ^ ^s [^// i -** E 2 ^^*^\ / /^ (3 -^J 1 ^ x^ ^, ^2 ^> 2 ^ /^ I J a 1 4 6 1 u- 1 1 1 6 4 b 6 |17 6 The application of Rule V will be readily understood by the student without special comment. 111. No. 3O SCHUMANN, "Nachtstiick" MELODIC MODULATION 99 The following examples, including the application of all the five rules for modulation, should be worked out from various initial keys. 210 [~/Kr > C, -^ r - p^ ST~ 5=1 3 --&=& t* " a_^,_- > _tt^- ^T" -1 ^ h ? + -^ fl I >^ 1 jf "> Si ^ (^ -p -*3 fij "s 7^ ~^~~^~^\ Cu ?- H S 211 f JJ H ~ ^ + + L ^ /y ~_ < a t fy f 's - e-*? -/vK( -* \ a h ?~ V ' \ \ + + \ V ^ ' /p ^. /r ^, ^ <^ 1 ^j S^J Is* fe * *n\ Vf^f RULE VI. When the indicated (+) note of modulation ascends a fourth or descends a fifth, it goes to the first of the scale in the new key. 212 A + \ J J -X L. . i /n> - 1 r i .I (^\* * s T IC^* t* ^ f s t E . U ^ S f -^ f 3 ^ a -^ r"^ I I 86 4 2 + m 84 82 i ^ >- ioo CUMULATIVE HARMONY 111. No. 31 NEANDER, 1680, " Choral " J -5 ^ ^n *. Tr ^ & f^s ^ JJ ^ f*3 1*3 fT- J^J fD Li ->S [ fix . -<% ** 1 r^-r /W"\ HP "" ^^ ^^ cs [^/*y i xy ", ^s ^^- / * ' (2 -F-J Work out the following exercises for application of the six rules, from various initial keys. 213 ^ ^fr if^^'hrH^T^ i If 5 ^^ /L frj "3P ^ ^ ^ & ill irh \ II 214 n + + + + tt 1 _^ffl__JL*__+ x^> <^> r^ rn ^y n i r\ ( 4 f b^? 5* i fir L <> ^> 3 1 i I Two examples follow in which the student will be expected to select and indicate suitable notes of modulation, endeavoring to apply all of the six rules. Care should be taken toward effecting modulations only . to directly related keys. The instructor may utilize the preceding examples with the indicatory symbols eliminated for the same purpose. 215 MELODIC MODULATION 101 216 ^o w jf Fl^" i I ^" 2 /O ^5* ""> K II |/t\ A> TI 1, *^ I "** Double indications (+ +) will be in frequent use in this work. The second symbol determines the modulation, which goes into effect at the first. 217 n t J J ^r -y- 32 79 1" ^ ^ fe^ ffrv li^X ^~ ^* $Jz f /^ rl^^ ^1 ^S ^^ T i 1 ^ -- c( ! 1 1 , J- J- -19- f^' ^ ^^ ^^ S ^-, ^^rf' ^^ S3 n/*D ^2 ^^ ^^ ^^i 111. No. 32 7 UI * j^j J 1 m f 1 4 * 1 u 1 6 4 BARNBY, " 29 Bethlehem" M r-f- f - ^^ J I !* < ft* i 1- J i j' fc\-*'. ^ - M - 4 ESp ^ # gj *l * >5 ff ', 2 i i 5 1 r* 1 * tf t 2 ^6 ff ^6 TT^ 4 4 5 6 3 3 5 HI 1 I 4 7 i Additional examples follow: 218 i ' * -~^^: + + + 6 102 219 CUMULATIVE HARMONY E^NT^ 22O ffif^ r s ir 221 t, A In example 218 the following modulations occur: C to G, e, D, d, A A A F, a, and C. CHAPTER XVIII EMBELLISHMENTS An embellishment is a note used in connection with a chord of which it does not form a part. (It may also be a deviation from a given melody.) The list of embellishments includes: suspensions, retardations, passing notes and auxiliaries of various species, arpeggios, etc., which will be marked for identification by the diagonal stroke through the body of the note. Symbol, J ^. SUSPENSIONS A suspension is a note, which, having occurred as a note of harmony in one chord, is sustained or repeated in the same voice through a portion of the time of the succeeding chord, of which it does not form a part. 222 8 4 3 A. m g Ifn StZ m \J m (a) J (9 (*) (O J (' p 1 A suspension is said to be prepared when it occurs as a member of the chord of preparation, as at (a) ; suspended when it is sustained as a dissonance in the succeeding chord, as at (6) ; and resolved when it descends one degree to a harmony note in the same chord, as at (c). At (d) is given the two chords as they appear without the sus- pension. The classification figures 8-4-3, tna ^ * s > preparation 8, suspension 4, resolution 3, indicate a suspension of the fourth, prepared by the octave, and resolved to the third. 103 IO4 CUMULATIVE HARMONY Such classification figures, representing the preparation, suspension, and resolution, placed above the notes so represented, may be used with excellent results to impress upon the mind the functions of the various notes and to serve as a medium of identification and reference. In the classification of suspensions it must be understood that the various species are distinguished by the interval distances of the various notes involved from the primary note, and not from the actual bass notes as in the case of symbolized figuring. 223 3 6 5 5 9 8 7 4 3 yr 3 ^ g f(T\ a j^, 1 SY r (a) =J= ( ; .) ( 1 (O ^^ [ 9^ e & rj l^y f^S ^ E2 _^~ w %^^ f^ r ^^ ^ _j | | ^^ -"^ 1 1 1 I\ 8 6 b5 N 8 'e 4 K6 7 6 K4 4 3 N The primary note G is followed at (a) by the primary note C, which is a fourth higher, granting a suspension of the Qth prepared by the 5th and resolved to the 8va. This is illustrated by the classi- fication figures 5-9-8, indicating a suspension of the Qth prepared by the 5th and resolved to the 8va; the notes and the symbolized figuring t\8 indicating a suspension of the note above; that is, the gth, D, re- solved to the 8va, C. At (b) the primary note C is followed a fourth higher by the primary note F, with a suspension of the pth, prepared by the 5th and resolved to the 8va, occurring in the alto. At (c) is an example of the same suspension, with the chord of preparation in the second inversion and the chord of suspension and resolution in the first inversion. At (d] the chord of suspension and resolution appears, in the second inver- sion. At (e) the suspension occurs in the bass with the symbolized figuring as described above. EMBELLISHMENTS 107 The symbolized figuring will be readily understood by the student without further comment. 111. No. 33 ARTHUR SULLIVAN 11 St. Edmund " 5 g g RULE II. When a primary note is followed by another a fifth higher, we may suspend the 4th, prepared by the 8va and resolved to the 3d. 227 8 4 3 8 4 3 -4 3 -4 3 \\ ^ & ^ '^ -^ &. \ 7 ^ ^> ^ J r r (a) 1 (*) 1 o 1 (^ ft*^ - ^ 2 & 5e ^ \^ o -jp ^ ^1 35 M ": ^ C ! i N3 r N 3 K6 4 3 ^ '1 6 N At (a) the primary note is followed by another primary note a fifth higher, inviting the suspension of the 4th, prepared by the 8va and resolved to the 3d. At (b) the primary note is followed by another a fifth higher, with the suspension of the 4th in the alto. At (c) is shown the same suspension with the second inversion of the chord and the attendant figuring. At (d) the suspension appears in the bass. The following exercises should be worked out employing the sus- pensions admitted by Rules I and II, transposed to other keys for similar working out. io8 CUMULATIVE HARMONY 228 -9 8 5 9 8 +5 9 8 itv~^ * 3~ 5* 3 * sar' o O f 5 * ' . i N - * r 1 1 etc. J J e 1 -si -&- (^).p- & k * > t . Sj1^ ^ 2 ^s )t-f*S ^-i^^i ? fM\'^ ti,, 5 r 1 T f J J & J r "" r cs L^-^ 'fti^ 1 ^ 1 i ff / * ^^ 5 ^r~. 22 ^s T*^ U i*** ^ 2 *-^ i^ TS 111. No. 35 K3 BEETHOVEN " Symphony II " op. 36 8 4 3 S8== 5t :J: EMBELLISHMENTS 109 RULE III. When a primary note is followed by another a fourth higher, we may suspend the 4th, prepared by the yth and resolved to the 3d. 230 I i I * * /K ^ ^ s 75 to ' 1 J ( ' } - J r 2 " f* i v 'i r j j j ( "U JSSi 3 &* <^ ^ 4v ^, * S 1 - ~i ^f T- J ^^\ * [^ < J [^/* / * ^ 1 \^ ^ tjl j ! ^X 1 3 3 ^^ -*- t\3 (\3 CHAPTER XIX SUSPENSIONS. (CONTINUED) RULE IV. When a primary note is followed by another a fifth higher, we may suspend the 6th, prepared by the 3d and resolved to the 5th. 231 3 6 5 3- 6 5 3 6 5 3 6 5 3 6-5 n ^-^. J ' s 1 k ** i_ u & * * s^s ^ fl s ^ ^X ^> IfTV rt j -^ ^~, -. \A) & -^ ^ w ^ ^ J 1 -& c: \~ & \ (b >i 1 -&- r,v ^ i \ \ \ /^\ f-j -^ s r^ ^ o l^^Jf \ * x^ V ^ \^-s x^3 \ ^2 i^j 1 x*^ I ^ ^^ ^ 5J ^- ^^ 1 l\5 6 4 N6 4 2 r 6 \3 \ h s5 6 6 4 N At (a) the primary note C is followed by another a fifth higher, with a suspension of the 6th, prepared by the 3d and resolved to the 5th. At (b) the chord of preparation is in the second inversion, and the chord of suspension and resolution in the third inversion. At (d) the suspension occurs in the alto, and at (e) in the bass. The following exercises should be worked out by Rules III and IV, observing closely the restrictions given above. 232 3 6- 59 i | i * ^ >*f W/ ^ ^..j w ^ 9 Tl'S' CM) '' * .* l^ 1 "^ ^-'' 11 J- J- i ^ L ^ I r c> ^s>- ' i etc. &t (^ p}* / > & ^W^hv ' ^ ^ s^s -., r " i i \ r ^ "\ r*^-^ ~P~ 4 3 N N3 N3 *: 3 l\ SUSPENSIONS in -^ <9- (S \ , 1 I \ H 233 *' Jfrg =F-[ J g -gJ g* ^=6?=^ ^ 111. No. 37 L. M. GOTTSCHALK, "Last Hope" 3 6 5 z ^ ^ h-3- % When a suspended note is affected by an accidental, a similar sign should be placed before the symbol of suspension in the bass figuring, thus: 234 -4 3 3 < -6 5 , " J J =S5^ At (a) the note of resolution (the D 3d,) is preceded by a suspension of the depressed note above, Eb. At (6) the note of resolution (C#, figured #6) is preceded by a suspension of the note above, which is not chromatically altered. At (c) the note of suspension is indicated 112 CUMULATIVE HARMONY as a 4th affected by a sharp (C#). At (d) the suspension occurs in the bass, where, with a chord of 4, the actual bass F#, as the resolution 3 of a suspension, is preceded by a suspension a degree higher, which is affected by an accidental sharp (G#). The relative position of mem- bers of a chord may be changed to provide a preparation for a suspension. 235 *" "** I ' \J 1 . ^ h j U VT &0~ * * ps ^ T" / /**J ^? ^^ J * 1 1 J J (W* ^, P*' l* J > ^ N s <^ r N. ,A f. 5 - i N o bN3 5-4 bG Two examples are here given of the primary note ascending a fourth, inviting a passing modulation in which the addition of the 7th pro- vides a preparation for a suspension of the 4th in the second chord. Occasionally the bass note changes to another note of the chord simultaneously with the entrance of the resolution of the suspension. 236 i K8 4 6 2 4 N6 4 111. No. 38 GLUCK, " Orpheus " ^^ ^ . ^-. * 9 *b -0 -- ij' X c r cto i ^ Sa2r J M ^ m -5- _ T B : d 9 fo*\* < 9 n ^ 4P ^ t ^^, * ># ^ ~"' i ^ K6 4 3 K6 4 3 r SUSPENSIONS Double suspensions are formed by combining Rules I and III, or II and IV. Other suspensions of this species will be given later. 237 5 9 8 3- 7 4 3 8 -6 5 -4 3 fi - ~ ' x- vi M <*Lt^ ia & S ^^ ~ * f(T\ * * S j ^_ y & ^r r j \ Ix -&- V J 1 (5V s? (? L^' \ s-2 =* (3 1 K5 7 ^ 111. No. 39 W. H. NIEDLINGER, " The Bumblebee " 5 9 8 7 4 3 B: f=f =fe The following exercises are appended, to be worked out with sus- pensions according to the four rules given above. 238 + 240 * =p: --" tt CUMULATIVE HARMONY a^m^pn^r c cjr r p 1 if u> ^^ 1*"'""^ ^ Add the three upper voices to the following bass sets, employing suspensions of the various species (with classification figuring). Transpose to numerous keys for similar treatment. 242 S3 13=? 646 2 ||4 7 |]3 6 6 |5 7 4 5 1 b 6 243 A Key of e 4 6 2 Ul 6 7 CZ-SD ' , -n__2z__i__a 5^53 J ^ /-D -j /^ r __3j & ^ 1 -&- lie 'e |4 fte 3 1667 i 4 * Pff BxG i fr ^ ^^ /*!> --, ^ ., j^l/ ^^ ^^ fO ^^ ^x &' i ^? ^ ^ _^^-, 6 ||6 6 17 6 ! 6 6 7 1* Ik 14 fc ik * -Ac^t? 2^ 1 ' ~i H ^n ^-\ i H 1 6 117 -6 1 117 , 244 5 ^m ^ |J76|_6_ b5 6b7 5 \ --^-=\ . _ i M -^b-fr* ttw I -^, L_ ^' | n 6 5 |6 6 5 4 ^ . ^ - "* A 1 7 " t 2 6 6 ^ 4 7 CHAPTER XX RETARDATIONS, OR ASCENDING SUSPENSIONS Retardations are similar to suspensions, except that they resolve by ascending one staff degree to the note of resolution, instead of de- scending, as in the case of the latter. The resolution may be heard in the bass during the life of the sus- pension, at a distance of a yth or more. Retardations are, in general, much less agreeable to the ear than are normal suspensions, and of less frequent occurrence. Disso- nances, as a rule, are acceptable only when they progress downward one staff degree to a consonance. Normal dissonances of suspension are agreeable for this reason, and because during their existence the hearer experiences the anticipation of a well-defined resolution. Among retardations, those that progress by a minor second to the note of resolution are the most acceptable, those progressing by a major second rarely serving to enhance the beauty of the harmony. Of the progressions by a minor second, the seventh of the scale resolving to the octave is the most popular, although the third of the scale to the fourth in the major keys and the second to the third and the fifth to the sixth in the minor are often used, particularly in combination with normal suspensions. The uninviting progression of a major second in the resolution of a retardation has led composers to modify the harshness and relieve the uncertainty of the anticipation by chromatically elevating the note of suspension. By this means the anticipation of the resolution becomes more intensified and quite definite through the preferred progression of a minor second. Examples of this form will follow. The symbol for retardations is the radical (i/) inclined upward, indicating that the note on the diatonic degree below has been retarded. RULE I. When a primary note ascends a fourth, we may retard the yth, prepared by the 3d and resolved to the 8va. "5 n6 CUMULATIVE HARMONY 245 i i 1 Lr 1 ^*~ -^ ^~ Vi -J" V ^** lfi\ ^^ , -,-, ^>\s f^J *P ^ () 1 i (d) 1 2S* ^-* ^ fZ* S [E25 ^^/ 2 ^ 1/8 At (a) the 3d, as a preparation, is sustained at (b) as a retardation of the yth, resolving at (c) to the 8va; the classification figures above indicate a retardation of the yth, prepared by the 3d and resolved to the 8va, with the symbolized figuring below showing a retardation below the 8va. At (d) is an example of the retardation of the yth in the bass, figured as a retardation below the actual bass. 111. No. 40 HAENDEL, " Messiah " * 3B! r^ 111. No. 41 JAMES H. ROGERS, " Rubaiyat of Omar Khayyam " 3 7 8 5z*z RULE II. When a primary note is followed by another a fifth higher, we may retard the 6th, prepared by the 3d and resolved to the yth. RETARDATIONS, OR ASCENDING SUSPENSIONS 117 246 ZI ty ^. ^^ ^^ vy & ^ w ^ i I i > ^* 1 -&- a 1 f^\* ^s 5^ f^ I^y* v^^ ^ 2 i/7 4 1/3 At (a) is an example of the retardation of the 6th, prepared by the 3d and resolved to the yth; at (6), the same, with the chord in its second inversion and the retardation in the alto. 111. No. 42 BEETHOVEN, " Symphony II " Larghetto 3 6 7 ^ J^" "X _ 1 7f*fy$+ ^ ^=* 1 f ..s *- c fi\ ' W ' - ^" S r fl^B " v^iy (^ tJ i i * """ "^"4" ~*~ ^ ^^Aalp Cii ^^*ff^ tJ ^E Jfl ** n ^ ^^^^^^^ , . i | * RULE III. When a primary note is followed by another a fourth higher, we may retard the 2d, prepared by the 5th and resolved to the 3d. 247 3Z & -^ ^ fc ^ tf p 1 & i() -&- z> i ^ - ^ ^ /J ^ < ' s */ J , !^* etc. X J * J y ; t *s ^^/( fr} gj ^ 5^ (^ ^^ ' ^ U 6 1/3 4 3 1 s5 ffi f - ^ f # (^ '^ ^ > X # 03 v> _P &? ^ + 1 1 1 if p< ^r fi >f ^^ /^ i^ ^ r im ' | . II Double and triple suspensions, or reta suspensions and retardations, are fully suj may seem to demand, providing they ar prescribed limitations. 25O e Q___B S A rdati< table e use -5 3 Dns :fo :d ^ | ? i , or combinations of r use as the occasion with due regard for in Q 1 A A 7 fl 1 CB /i M ^ <9 <9 9 < () /ET ^ " J _l ^ ^^ s 5i ^ 1 ^ ' r? (? fy ... 22 ~^ t N3 5 K3 3T O O 7 1/8 t/3 5Q S 7 jl 1 f 4 Q i -3 J 37 fl o i I '' sj e ^ t ""if i 1 &\ ^*" ^ 1 * ^2 K ^ 2 ~j I r | x s ;() j 1 e. ^_ J -r r wy{ ^ -~L ^^ <^ (!> s^> ' ~Ps N6 f 3 - A l\8 K3 1/8 I2O CUMULATIVE HARMONY At (a) we have an example of a double suspension of the 4th and gth; at (&), a double suspension of the 4th and 6th; at (c), a double retardation of the 2d and yth; at (d), a combined suspension and retardation of the 4th and yth; at (e), a combined suspension and retardation of the 4th and 6th; at (/),' a combined double suspen- sion and retardation of the 4th, yth, and gth. 111. No. 45 MENDELSSOHN, " Quartette in A Minor," op. 13 35g | ^J f(l) 4- j J 2 JIM m ' m 8* * fl Jp .^ *_s * ^ * * J J (W* ^ dxU I ^ >* * # Chord suspensions are also to be found occasionally when all voices are included. 251 B 1 rh i^- Ss SOT ** *! 5 h I [^/* ^ a Sha"^ 5 jjH 4 1/8 3 N3 [\ Retardations by Rules III and IV, in the major mode, and II and IV, in the minor, which resolve by whole steps, may be chromatically elevated above their respective preparations, in order to intensify their progressions to the notes of resolution. 252 5- Q Ix ~^. 1 1 ^~ -s 1 1 /* -N -^ i [y r^ W ^ , J LJ . z? ^ S' 's 'I * s^> ', liv, J f^\ ^2 ., /lx flj^ * V^ y S ^ 2 ^ A t \ a) ( *) ( : ) ( ^) /w\ ^^K ^S ^> [^/* v ^ /'^ ^ j. "^ fV xy 8^3 - \S X \/Z \ # I/ 7 flj 6 5 ttl/3 RETARDATIONS, OR ASCENDING SUSPENSIONS 121 4- -6- X" > w & ** M 11 (CD '? ^ ~ i m ^j ~f>~^ 1 / ^^ ! ^-^ J ^T i i ^_ (g\ /WA ^^ e? -^ . E5 ** /^ %^>" ^ & .^j 9 6 1/5 6 #1X5 1/8 At (a) is an elevated retardation of the 2d; at (b), of the 4th; at (c), of the 6th, in a; at (d), of the 4th, in a; at (e), a double retardation of the 2d, elevated, and the yth; at (/), of the 4th, elevated, and the 6th; and at (g), a double retardation of the 6th, elevated, and 4th, elevated, in e. 111. No. 46 Andante con moto 3 - 6 7 8 - 4 - 5 MOZART, " Quartette in 5 --- 2 - 3 3 - 7 - 8 *=5 ^^ P- yafc-n: -,s 111. No. 47 BEETHOVEN, " Symphony II " Work out the following exercise, employing the elevated retarda- tions in various keys. 122 CUMULATIVE HARMONY 8 4 3 3 -6 5 -2 3 3- -7 8 5 2- -4 5 -25- f J etc. ^=*= K8 6 4 6 5 N -f^ (2- &- II Work out the exercises given in the chapter on suspensions, as accompanied melodies, using retardations in like manner. CHAPTER XXI PASSING NOTES A passing note is a diatonic embellishment used in passing melodi- cally from one harmony note to another a third above or below it. 254 ^ , 3 ' (a) 6 6 f- 6~~ |[7_ At (a) the passing note D occurs between the two harmony notes C and E. At (6) the passing note B occurs between two harmony notes of different chords. At (c) the passing note occurs in the bass, and at (d) in the tenor. 111. No. 48 BEETHOVEN, " Sonata," op. 22 Adagio con mo I to espressione y, P-9 =F= -f gP^H- TT ^ .1 r-n * J fef', t^~9 lliail 1 J m Jll 2 2 B! -P P *-'&4>H 1 I 9-*9 Si v 9 * V ^ 9 111. No. r- . 49 P- >- X. SCHARWENK * ' \, " Minuet," op. 18 . r~ j ( ( ( I/ , !/! * J P ' | r^^ 1 -i I* + *-- E 1 P- v^p "=! ^ ^ p - J~3 , J i 1 ^=~^- ~ ^pd^E -f 5 ^^9-4" ^fc - \- 124 CUMULATIVE HARMONY Passing notes may be accented (a), or unaccented (&). 255 (a) (a) 1 II 1 1 i ' 1 1 2t * * J * * i ) * ^B .] , ff _ ^ V v ' / A y ^ ^ ^ 1 -J- ! /Y 4 i 9 ^5 [M i=f SCHUMANN, "Album," op. =t *An example of successive passing notes. What is said of passing notes occurring in the accented or un- accented parts of the bar or beat is true of all succeeding species of embellishments. In the minor mode, in order to escape the disagreeable ascending augmented second, the sixth of the scale, as well as the seventh, is generally elevated, thus effecting what is frequently termed the melodic form of the ascending minor scale. PASSING NOTES 257 o (a) (*) () -yf - j 1 i i 1 t" ' f'\ m & 1 i I frW '^ UiiJ ffla <=> i 9 * M K f*^^ J Glf S^ 1 | 9 -*- J 1 -% -& \ , ! (PT* "^ 5* ^ 1 (Z> 1 75 ?B (ff fie At (a) is an example of successive passing notes between the fifth of the normal scale and the octave in the key of a. The normal sub- tonic, G, through its isolation of a whole step from the Tonic, lacks in ascending tendency; it consequently fails in the capacity of a leading tone, which is an important melodic function of this degree of the scale. The elevation of the subtonic gives it a leading-tone quality, strongly inviting an ascending progression to the Tonic (b). Here again, however, the melodic tendency upward of this passage is interrupted by the normal sixth of the scale, F, which, because of its proximity to the fifth, E, has a tendency downward; this fact, com- bined with the unmelodious ascending progression of an augmented second, makes the elevation of the sixth of the scale (c), as well as the seventh, in a passage from the fifth of the minor scale to the octave, practically a melodic necessity. This is true more particularly in vocal music; in instrumental music, the elevation of the seventh only is frequently practiced. The successive passing notes descending between the octave and the fifth of the scale may be employed without elevation of the sixth and seventh, or with elevation of the seventh only, the progression of the augmented second descending being melodically quite satisfactory, as well as serving to aid in identifying the minor mode. 258 y r | ~i = n n (n) * Jf ^ J ^ i^ ^ J /*N. ^ ISr * ^r 22 '^ ^p; ^3 X^ 126 111. No. 51 CUMULATIVE HARMONY HAENDEL, Overture, " Messiah" 0** 1 -m ' ^^ 1 ^ ~M~~ - IS * ^ ^ " -. ^ n B #* "T * ] i "^ C^\*^ ^-*^ &- [EziS t< \^ ' ^ ^ 4 2 6 i 6 4 ? An extended consideration of the various forms of minor scales would seem to be quite in place at this time. 259 n () ^ ^. () ^ -19- .r /*^? ^^ ^-i ^^ '"^ T I ^ J^l i*^" ^^ _,_ <-2 ^ 5 1 / T\ ^^ '^ ~ ^ r r^s v^ y L 1 I. The first reference was to the normal minor scale, consisting of whole steps except between two-three and five-six, that is, as indi- cated by its signature (a). II. With the introduction of the D chord, the seventh of the scale is necessarily elevated from the signature indication, in order that the third from the fundamental of that chord may be major (6), thus causing the sub tonic to serve as a leading tone. This forms what is commonly known as the harmonic minor scale, although it may be considered merely as a table of the notes em- ployed harmonically in that key. III. With the introduction of passing notes the melodic element enters freely, and by their aid we are enabled to construct the ascend- ing melodic scale with the sixth and seventh elevated and the half steps between two-three and seven-eight (c). While this form is generally employed with the T and D chords, it is impracticable with the S chord, as the normal sixth of the scale is an essential mem- ber of that chord and is not subject to alteration. The form best suited for employment with the S chord, both ascending and de- scending, is the normal scale, although the seventh is frequently elevated in both directions. 111. No. 52 Andante PASSING NOTES 127 MOZART, " Rondo in A Minor " 111. No. 53 W. W. GILCHRIST, " Home they Brought her Warrior Dead" 111. No. 54 GILCHRIST, "Dolphin Lullaby" ,? p -*- H*^ 111. No. 55 BEETHOVEN, " Sonata Appassionata," op. 57 A classification of the minor scales to be used melodically with the three primary chords is as follows: 128 CUMULATIVE HARMONY With the Tonic chord : ascending, the elevated sixth and seventh, and, occasionally, the elevation of the seventh only ; descending, the seventh elevated and the normal scale (a). (Also, conforming with certain ancient modes, ascending as a normal scale.) 26O (a) vb !* r " 1 \ ' = 1 ^ *" *~ I 1 ' 1 ' HT* ^ 2? /r i ' ' r i* m m FT\"" " i i* m m sstz ' 1 1 tj 1 1 1 ssss ic^ ?5 j j j 1 /L / (fl)* i 0- > * f- P ~ j ^ A J L-T J -F te/'ri C^l / <* + if r m M f r 2 ^ 1 1 '4 6 3 P ! r C) =S E -frS> a 5 ^K I* ^ r i* J r i i r J. J- J- (55* t^ I* 2 U^ ]|7 (jb_ it 1 4 b7 r- r r ;^nj r r i r r i r 264 r r " r r r r r r i r r r i r r r CHAPTER XXII CHROMATIC PASSING NOTES A chromatic passing note is a chromatic embellishment used in passing melodically from one harmony note to another a major second above or below it. 265 fi 1 } P" i HT^ HH 1 * >/ ei KJ J jf- m y.m 9 Jf - M * m C2 1 m U L ^ SStZ m & JJ 5 C* "J3 1 (a) J J -*- J LJl (*) ( 6 * J ) i /V * 2 , e) lJ P 2 SZZE SCZ ( r- * l i r m 1 I 6 4 2 6 ^^ 3 At (a) appears a chromatic passing note between the harmony notes C and D, followed by others in the soprano. At (b) is a chro- matic passing note in the alto, and at (c), a chromatic passing note in the bass. The following given melody, called a germ set, is to be harmonized in such manner as to present the best opportunities for the employ- ment of passing notes and chromatic passing notes tending toward the formation of a continuous eighth-note motus in alternate voices. By motus is meant the melodic change of one or more voice parts from one pitch to another ; when such changes take place in a continuous succession of eighth notes, a continuous eighth-note motus is presented. Transpose to other keys for similar exercise. 266 x v j. CHROMATIC PASSING NOTES 133 3= ^ j. etc. -&- ~ ?: 111. No. 59 MOZART, " Rondo in A Minor " An extended passing note is an embellishment used in passing melodi- cally from one harmony note to another more than a third distant, in such manner as to approach the second note by degree from the side upon which the first is located. The approach should be diatonic from above, and chromatic from below. 267 (a) (b) (c) (d) 134 CUMULATIVE HARMONY At (a) an embellishment, A, is used in passing melodically from the harmony note C to another harmony note, G. It approaches the second note, G, by diatonic degree from the upper side, the side upon which the first one is located. At (&) the extended passing note D# approaches the harmony note E chromatically from below, the side upon which the preceding harmony note is located. At (c) the ex- tended passing note F approaches the E diatonically from above, and at (cT) a similar embellishment, B, approaches the harmony note C chromatically from below. 111. No. 60 HECTOR BERLIOZ, " Faust " An extended passing note may be used between two harmony notes a third apart, providing it ascends to the second note chromati- cally altered from below, as at (a) (a). 268 (a) (a) /L * 1T^ a__3HK__r ^^ fm T _ * E_ 532 {? J * [ -J - J ftV * ^^ f=> * ^ fij 4 6 3 5 111, No. 61 SCHUMANN, " Novellette," op. 21, No. 2 i, ^ * CHROMATIC PASSING NOTES The following exercises may be worked out in several keys, using extended passing notes, after which passing notes and chromatic pass- ing notes may be added to form a continuous eighth-note motus in alternate voices. 269 J f (' M ' * 'ff -L * ^K 1 Y f ^ / J J 1 i ^ j J. J etc. [^// A i t*^ sp %^_-^v j ^* ^>^^ r ttr \ r w^ 2 II 2J nr i cj ii or~ or r ,u + "li + ^ *s t 1 m. V m V r r^ P n /L m * P m fr * p J Im 9 * 1 n %m + ^ + p + * + ^ y tr i* r r 1 r /^V j^ I ^^ \>L/ I 1 11 1 n + ' - y > i* <^? ii* 31 i* /u tt* 1 " 3H -** * L - 4 1 f 270 -f p- * r r ir J r r ir ' ' ' j r t" r r f if : r CHAPTER XXIII AUXILIARIES An auxiliary is an embellishment located a degree above or below a harmony note, which precedes and follows it. It is diatonic above and chromatic below the harmony note. (Chromatic aux- iliaries above are occasionally used by composers.) 271 (a) (b) (c) (d) A o r~4 j J J J 1 1 1 1 H M 1 * JJ-^p| ^ ' ^ fn\ f? m m ff . 1 J -J- ^ -r j j fi*\* ^^ [S25 ^^S xy -^ a ? 5 At (a) and (c) are auxiliaries above, and at (b) and (d), auxiliaries below. In each case the embellishment is preceded and followed by the harmony note upon which it depends for existence. Work out the following exercises, using auxiliaries above and below wherever practicable. Subsequently add preceding embellishments to form a continuous eighth-note motus, first, in the soprano, then in the alto, tenor, and bass in succession; this may be done also in alternating voices. AUXILIARIES 137 ' J i. etc. 15. I f. s 273 ES & ' & NOTE. When embellishments are to be employed in the soprano, three staves should be used, in order that the given germ set may, for comparison and analysis, remain unchanged. 111. No. 62 MOZART, " Variations " 5 ' (fh^ " | ^ i S32 H LnHH* r f r ad N ^ ; i i j ^ n f- f- r n -r- 3^ 1 j ; = L - 138 CUMULATIVE HARMONY The auxiliaries below the third and the seventh of the scale in the major mode, and below the second and the fifth of the scale in the minor, may be diatonic. Auxiliaries a diatonic whole step below these notes are particu- larly satisfactory when used in melodic connection with auxiliaries a diatonic half step above. The auxiliary below the seventh degree of the minor scale may be a chromatic whole step. Occasional examples are to be found of auxiliaries a diatonic whole step below the second of the scale in both major and minor modes. 274 rp ^ -E i J ^ J n J \ K i^ r "^ i T f -*- ff "* -- /^~\ ' . I^!/ * ^* ^x ^ ^ ^ r> tv sy (^ i^ t - \ \ 1 1 AUXILIARIES 141 r " 1 s *" | | ^^^-^ r LJ r J jt J 1 1 if^^ O' Kg ( -I[f2 2 H* SP 111. No. 64 HENRY HADLEY, " The Nightingale and the Rose " A llegretto grazioso ^-*ft- nr^u^J < nn ~ t=^j _J-^= ^J_ . __ ^T7 r> * 9( f * 1 f 22 - 1 111. No. 65 DAVID STANLEY SMITH, "The Dark" 3 6 -5 8 4 3 An extended auxiliary note is used in passing melodically from one harmony note to another, approaching the second note by de- gree from the side opposite that on which the first is located. The approach should be diatonic from above, and chromatic from below. 279 142 CUMULATIVE HARMONY At (a) is an extended auxiliary above the harmony note E, which it approaches from the side opposite the first harmony note, C. At (b) is an extended auxiliary, B, below the second harmony note, C; it is preceded on the opposite side, above, by the harmony note E. At (c) is an extended auxiliary, F#, below G; and at (d] an extended auxiliary, C, above B. At (e) is an extended auxiliary below the seventh (as a leading tone) of the minor scale. 111. No. 66 > Allegro BEETHOVEN, " Sonata," op. 14, No. 2 111. No. 67 CHOPIN, " L Polonaise in Eb," op. 22 The student may work out the following exercise, using extended auxiliaries in the soprano wherever possible, as indicated in the first four measures. 28O AUXILIARIES 143 ' ' ._ S : C: r /L * i* X ITU r i ^K t 1 IJ o ri r^i C3 J J + , 1 r -i >r J u 1 d * J- trjj- * * B ^32 2 jft /o ^ J J ^^ J j r j etc. rtV e/ * ' m = 1 J rir Tfh-r . . .,_,! -f 1 f ' Also, the same exercise with extended auxiliaries in alternating voices, as follows: [44 CUMULATIVE 281 HAKMUJNY V 1 W m ^ P l /K i* ^ r 1 VM/*T ! J i . ^"7" 1 1 ! J j ^ 1 Jr ' Vtu * ' 1 * u J ^ \J3^ - ~ 9- 2 9 f -^- i SEJb J etc. j z -^-- -*- fW^*/ ^ ^> ^ l^y*^ ^ 2 ^^-^ ' ^^ ^ w ^ , , Jl* w ^ 4 _T I f 5 2 6 6 From the same germ set form a continuous eighth-note motus, first in the bass, then in the tenor, alto, and soprano successively, utilizing the various embellishments thus far admitted. To the germ set, notes may be added in the soprano, only as embellishments. When such embellishments are also harmony notes, they must be given due consideration as such in the selection of harmony notes for the other voice parts. A separate staff for the germ set, when embellishments are to be employed in the soprano, is necessary. 282 iS 1 --- 1 :J: r etc. :4 4-7 3 I J | ! J *r ' j ^ ^-^ j/f" * * 9 ?T\/ _ S V^-l/ ^ a n ^ 4^ g (u) ff*-^- J^H *- s ^ Z3 /^"\j* C . . ^B V ^ ^E [^^/d* uff<* / 1 > ! ^ * ^ ^ 1* ^^^ ' M ^*^\r^ _ r ' 5 j 1 \ M ' 5 / /L ^jt~Sn J Z . F i F -f ~w f i == i _, "t_i + m +^" + : r m (P /L B 4?^ | ^ ^ irh F ~ ^ Combinations of various rhythmic figures may be formed in alter- nating voices, some examples of which are given herewith : 285 FFfF*FFFFF f ! h-T L_H ! r i I I I Also a continuous sixteenth-note motus in two voices simultane- ously. 286 3. H3H3_ iiiifci: ^ etc. rJi- -J */ X JL r . r i ii qfcE 111. No. 60 J. S. BACH, " Choral Prelude " (for organ) ^^>=^ ^33 i AUXILIARIES 147 Additional exercises for similar treatment follow. 287 m r ii r ir- r if r ir r -+ p ^E=5 e 288 ^ (2 3 CHAPTER XXIV INTRODUCTORY AUXILIARIES Auxiliaries not preceded by the harmony note upon which they de- pend occur frequently at the beginning of a composition or phrase, and for that reason are referred to as introductory auxiliaries. An introductory auxiliary may be used on the accented or unaccented part of a measure or beat; it may appear as a grace note, in which case it is termed an appoggiatura, or in combination with other notes may form a turn; or it may occur as an independent note of definite rhythmic value. 289 ^JE -&- (e) At (a) it appears as an introductory auxiliary below the harmony note G, on the unaccented part of the beat; at (b), as an auxiliary below 148 INTRODUCTORY AUXILIARIES 149 E, on the accented part of the beat; at (c), as an auxiliary above E, on the accented part of the measure; at (^Aa JP 9 9 l\rf'* \ %^^j-/ 2 ^ \ * -^- ^ "*~ IF "T" 1 1 t 1(6 |^ 4 [[5 2 H\-^- 6 64 _. _ ^-V^ ~^~" ~J" ( f -(-} * , 9 F +bm. . \+^-* *- A IX ! 1 "-ft*- 1 Mf M 1 ' 3& v 1 S i* m r m- II X * * U r * m & 'l\ CUMULATIVE HARMONY 291 /r u/ 1 \ r m m 1 X, r _i (cf) y p ^ ^ ^ dp ur \ j f i J * -J- i T etc. V^f*\ 4 ^ A ^^^ n * ' p \ ^ r r 1 : * ^r * n P < Ill 7 #6 4 3 P ^^^ 6 7 5 b 111. No. 7O 4 |4 4 116 I 7 6 7 2 {J3 b ll5 [[b5 4 MOSKOWSKI " Tarantelle," op. 27, No. 2 McCov, " Prelude to The Hamadryads " Progressive auxiliaries are of two kinds: an auxiliary above, re- turning to a harmony note a third or more below; and, conversely, an auxiliary below, returning to a harmony note a third or more above. It may return to a harmony note of the same chord, or of another. INTRODUCTORY AUXILIARIES 292 . -- , J- ' r :-=f The student will have no difficulty in comprehending this embellish- ment as exemplified in the above example. 111. No. 72 PERI, " Eurydice " VT J B fm o ^ . V-L/ A f r -s tv ?F =f (,, ^ZuffQ ^ * L^^/**^f j ^S- - 5b^ kJ 111. No. 73 MENDELSSOHN, " Quartette in A Minor " tr ^y .- ?E 152 CUMULATIVE HARMONY Accented passing notes and auxiliaries are frequently longer than the harmony notes to which they belong. 293 io J -J J r* J *t xf* fj) ^ p^ z? ___ . I I /WN ^2 } [^2* & i^y* ^^ ^ r ^ At (a) the changing notes are formed by a combination of aux- iliaries below and above; at (b), by a combination of an extended auxiliary above and an extended passing note; at (c), of a passing note and an extended auxiliary above, and at (d), by an extended auxiliary below and an extended passing note. 111. No. 74 SPOHR, " Nonet " Allegro* ^ ?f=^^ m fr :fc ^ An anticipation is the use, in the same voice, of a harmony note of one chord during the latter part of the time of the preceding chord, INTRODUCTORY AUXILIARIES 153 of which it does not form a part. It is generally short, although it may occupy a half of the time of the chord to which it is attached. It occurs in one, two, or three voices, and may, in fact, involve the entire chord. 295 A ^ & r 3 ty &. WJ /!/ -_ r- ^j f^ rm j w r j 1 $ J r j r j j (W* f^ & & a & fy p u_<2 5* <2 6 ?> 111. No. 75 n i 6 5 7 6 5 RICHARD WAGNER, " Parsifal" uVi^" v J W U/5 S3 V, ** h -^ _|^ h- rT [<) "^ -^ ^ ^' V5_ h) f -* /-^^ J-> ^t- - 1- 3 1 1 j- 'k ' s -s.=^^- P^^P F*r uJ. . S . ! *^*1?*- s J bs t L^"\ o 1 ' /**" * v IffJ' fS Ui- ^^(7 O k: *0 4?P^ W5W-* &^- -19- F* 111. No. 76 A K -t^- X } x^ " < ^' HAENDEL, "L'Allegro" < y. ?_ _ /Th /] o ^ fr> p v' ^ ^ ^ i*^ 5 &^-*^M s r~ i e) & ' J j_ -5 \ \ ^-i ^3 y^/\ u . Sf ly_y*. L'/l^ I ^ A ^ h V ~ i F ~^ The student should continue the use of all embellishments in his work. A false relation is the employment of a note in one voice part, and its chromatic alteration at the same time or immediately following in another part. False relations do not seem to be objectionable: when they are pro- duced by embellishments (a), when the fundamental of the second chord is a third above or below the first (b), and when the note and its chromatic alteration progress in opposite directions (c). 154 296 CUMULATIVE HARMONY (a) (b) (c) tfh * v s^ ^ **-i V-L/ o 10 ^^ 17 i rr --TT 1 J J J J r i r * ^ L^ * ff ^ ^^ ^^^ C^B The following exercises should now be worked out in several keys, with a continuous eighth-note motus in alternating voices, and then in individual voices, employing introductory auxiliaries, progressive auxiliaries, and changing notes. The same may be subsequently done with a continuous eighth- and a continuous sixteenth-note motus, employing all preceding em- bellishments. 297 INTRODUCTORY AUXILIARIES 155 yfL fT iT "MI i* Cx f b (^ ( ~\ 1 1 r i I V ) i i I i 1 + m + m + 1 -P- m jf & i* ( U ^p & I 1 i^* ^ X ffl* 1 * - s> i f:\ cr. 1 t - i At (a) we have an introductory auxiliary below; at (6), the chro- matic passing note C# and the extended auxiliary E, forming changing notes on the harmony note D ; at (c) , the harmony note C used as a progressive auxiliary above the Bb, for motus; at (d), the retardation E and the extended auxiliary note G forming changing notes on F; at (e), (e), progressive auxiliaries; at (/), a passing note in the tenor, for motus; at (g), the suspension D and the extended auxiliary B form- ing changing notes; at (h), a progressive auxiliary in the alto; at (i), the passing note and extended auxiliary for changing notes; at (/), (y), double changing notes in the alto and tenor, moving in sixths; and at (&), an introductory auxiliary beginning a phrase. The following germ sets should be worked out in like manner in several different keys. 293 ^rmmfe^EfeE.te 299 156 CUMULATIVE HARMONY 3OO yr "s : '*~ , m i " * - r? 4f F^ r 1 r II Double and triple embellishments in combination may be used with excellent effect in passages of thirds and sixths in similar motion, and in contrasting passages moving alternately and together in con- trary motion. When embellishments occur thus in combination, they should, as a rule, be consonant one with another. Dissonances, even extremely harsh ones, may appear singly, to be followed by a combination of more consonant intervals, but a series of extremely dissonant chords in immediate succession should be avoided. 111. No. 77 ARTHUR S. SULLIVAN, "The Mikado" 3 65 At (a) are auxiliaries above; at (b) auxiliaries below and extended passing note; at (c), retardation; at (d), changing notes, extended 157 auxiliary below and extended passing note; at (e), chromatic passing note; at (/), changing notes; and at (g), extended passing note. Occasionally an entire definite chord belonging to some related key is built up from embellishments. Special effort should be directed toward acquiring a good writing technique in this section of the work. A ready facility in four-part writing, with independently moving voices, constitutes a strong element toward future success in analysis and composition. 3O1 3O2 >>*! 8 =# - -. * r III I 158 CUMULATIVE HARMONY 3O3 The next step will be the further utilization of a germ set as a basis for the formation of a melody with piano accompaniment. In these exercises four staves should be used in score. The first or upper staff is to be occupied by the given germ set, the second by the completed melody, while the third and fourth, in brace, are to be used for the piano accompaniment. Harmonize the germ set in accordance with the rules for harmoni- zation of melodies, placing the chords in four voice parts on the two lower staves in accompaniment form as heretofore. Care should be exercised, in constructing the chords for the accompaniment, toward correct voice progressions and other established laws. In the following exercises each chord should have a duration of a half or whole bar. Embellishments are to be used wherever necessary in the construction of a plain, broad melody in song style, employing only half notes, dotted half notes, quarters, dotted quarters, eighths, and the combined dotted eighth and sixteenth notes when the exer- cise is in common time. In | or time, series of sixteenth notes are admitted. Rests may be used wherever they are considered ad- vantageous. The time value of germ notes may be shortened or lengthened when admitted by the harmonic requirements. The harmonization in the accompaniment must be so constructed that the given germ notes will consist only of duplicates in unison or octave of the notes comprising the three upper voices of the chords so employed. The harmonic content of the accompaniment thus becomes the substratum of the melody, as the melody forms a superstructure to the harmony. INTRODUCTORY AUXILIARIES 304 ^ e 159 ,) ar H*^ * irj^ J j J j J ' J j m m fe r^J J ' J J i ^ gf-f-nr r i6o 305 CUMULATIVE HARMONY tet feE : m These exercises should be worked out in similar manner, with different melody and form of accompaniment, after which they should receive new treatment for piano solo. Additional germ sets are here appended, also other suggestions for accompaniment. 3O6 P5 j^^=gES 3 3O7 INTRODUCTORY AUXILIARIES 161 308 Jit -*- m ,+ - V - 1 j f^S ffr ^ + X - ^^ 1 f ^ "^ i . _ ^^ 13) <& ^ 7 ^j S ^ W ^ j 5 * f r ~^~ "l 1 *" ' ^ J 7~Ti 7& 72 j J J- Jg. = [W^ f 5 2 -r* ^ | > ^_ y^,. ''^ I ffi^ 1 7 46 5 6 | 4 7 6 G 3 4 364 2 2 At (a) is an example of the first inversion, at (b) of the third, and at (c) of the second inversion. The harshness and ambiguity of this position of the chord, due to the omission of the yth, may be readily perceived; at (d) the gth is prepared as the 3d in the ||S chord. 111. No. 80 SULLIVAN, " St. Edmund" /k If / J J ~J J r '\ f \ K\ m H ^ ^Y 1 j j-2 W_ fl ^rj . & 9 & m r r & * **" ^ r? tf iff O / !-* / L^^'^V m ^ 1 a EB v ^ S "C \ y [^ [ f5> * i | 1 1 679 5 The Qth is most effective in the soprano. This suggests an additional rule for harmonization of melodies. When the sixth of the scale is followed by the fifth, the sixth may be harmonized with the Dominant. This will be easily recognized as the D 9 resolving to the T 5 , as at (a). The second choice for use of the gth is in the tenor. It should never appear a second above the fundamental, as its resolution would thus be anticipated; for that reason the fundamental should never appear within an octave below the 9th. 316 not good good H? n / ( 1 1 (m J J f f J J 1 f y^A ^3 <5 J5|^ & E2s ^ x f^ /^ 7 r ' 3 7 2 3 2 i66 CUMULATIVE HARMONY As in other chords, the position of the various notes of the D 9 chord may be transferred from one voice part to another during the life of the chord, the D 9 resolving to the T 5 in the part where it last appears, as at (a) (a) below; or when the D 9 progresses by skip it may pass entirely from the chord without losing its identity as a note of harmony (6). 317 /L m _i i & ifh * & 9 M 532 f^ .f--. m .^ tr -f- () J J \ (a) J t (*) J j i /W\ fy d [225 \^^s ^p ^4 "S. ^~> F r 9 9 9 The gth frequently occurs as an embellishment above the D 8 or below the D 3 in the D 7 chord, to which notes of harmony it pro- gresses before the resolution to the T chord. 318 (g> <& Of* ^, fy <^ r 1 (a) ^ '* Ci' ' /<> ts r, At (a) A is introduced as an auxiliary above the D 8 , G; and at (b) it appears as an extended auxiliary below the D 3 , B. This must not be mistaken by the student for a D 9 chord, which it temporarily re- sembles in appearance and quality. 111. No. 81 DEBUSSY, " Arabesque I " Tempo rubato THE DOMINANT NINTH CHORD 167 111. No. 82 CLAYTON JOHNS, " The Barefoot Boy " : I. -r ' '(' To aid the student in understanding the distinction between a D 7 chord with embellishments formed by the aid of the gth and the D 9 chord proper, let it be understood that: When the 9th progresses by degree, either upward or downward, thus disappearing from the D chord before the resolution to the T chord, it must be considered an embellishment and not an integral part of the harmony. If it resolves directly to the T 5 , or, progressing to a different note of the chord, it resolves from that note to the T 5 , or, in progressing by skip to another .note of the chord, it disappears entirely, leaving only a D 7 chord to. resolve to the T chord, it is an essential member of the Dominant harmony as an interval of a gth. 111. No. 83 HAYDN, " Quartette in G /L ( J m o* ^ ^& 9 \ a W- r 1 b ? i* _P ^^ ' ^ ^ _ . * . - LT i r ^ ^ f V 1 ^-^- -*, = S> H^ 111. No. 84 -n-fii ^3 MASSENET, " Elegie " i f ', ? H/ 1 . i68 CUMULATIVE HARMONY Ff f f The D 9 is occasionally ornamentally resolved by the interpolation of the D 3 (in the form of an embellishment) before its resolution to the T 5 . In such cases the quality of the D 9 as a harmony note is not lost, as it is when the succeeding D 3 is attended by its compulsory resolu- tion to the T 8 . 310 XL _i S ifh * -^ 532 i*? ^?J f f y^\ I^/* j \^^" o A chord of the D 7 may progress to a D 9 chord. 320 ^- Harmonize the following, using D 9 chords wherever practicable, in accordance with the directions given above. 321 r\ \ 1 J J it 1 1 w \ 82 f xT / c** ^ 1 1 ^J (*^ (^ ^(T)^ ^ i^ ^ & ^ & J J J J 1 - J; \ \ etc. tz> a CJ (^(-7 ^ (2. (2 ^ THE DOMINANT NINTH CHORD 169 E -&. |S f S 322 ii =d= ^ S- H *- - etc. ^ ~CT -a 66 36 676 6 4 \1 6 16 CHAPTER XXVI THE ABBREVIATED DOMINANT NINTH CHORD D)) With the omission ot the fundamental in the chord of the D 9 the four remaining notes present a series of thirds in the form of a chord of the seventh on the subtonic as a leading tone. The subtonic is here considered as the nominal fundamental, the real fundamental being, of course, the Dominant, which is also the primary note of the chord. The symbol D)) will be used with the figuring for identi- fication in analysis. 323 _9C 0_ -r ' ')> 7)) The treatment of the abbreviated form of the D 9 chord is subject to the following conditions: I. No member of the chord may be doubled or omitted. II. The D 9 may not progress to the D 8 or D 3 before the resolution of the D chord without losing its identity as a note of harmony. With such progressions the chord will be recognized as a D 7 chord with an embellishment, as heretofore described. 324 y E j fcB & ^ g $1 ^* j r I* ) & -&- r (o . j F?7i ^ ^/ 22 i ^^^ <*^ -_ a \ ^^ * E ii r\6 5 6 4 3 1 4 3 170 THE ABBREVIATED DOMINANT NINTH CHORD 171 At (a) the interval in question is shown as a form of suspension; at (6) as an auxiliary above the harmony note, G; and at (c) as an extended auxiliary below the harmony note, B. III. This chord may be freely used without preparation in all in- versions except, perhaps, the last one, in which the D 9 , in the bass, is preferably (not necessarily) prepared, as at (a) below. 325 () (O /L & f(T\ _~ V-U Q^ J r -f- -f" ~~r- 4 J J /^A p^ v "1 ^^ y* 1 L^y* 1 *^"~" * "^ r O^ ^X 52 1 1 \\ )) \\ j) This inversion, although prepared, is not as satisfactory as the others, owing particularly to the somewhat objectionable I chord which follows as the resolution (6). This unsatisfactory condition may be overcome, in a measure, by a diatonic progression downward through a succeeding chord, as at (c). The various positions of this chord may be described as follows: 326 The fundamental position (D 3 in the bass) is figured 7)) ; the first inversion (D 5 in the bass) is figured |)); the second inversion (D 7 in the bass) is figured 3)); the third inversion (D 9 in the bass) is figured The resolution of the various members of the chord is the same as when the real fundamental is included. The D 5 , except when in the bass, may resolve upward or downward to the T 5 . 172 CUMULATIVE HARMONY 327 1 (n) % ^> , Z2 [j^J TL ^ -^ /*J ^^ II ! J ^ iT 2_ ! zs ** t,7)) b 6\\ 6 #4 I 7 6 E 4 b7)) 7)) 4\\ 6 PX ^ -^ * 3 * E 1 1 r . H - . _^_u |J7 9 #4j \ 6 4\\ 6 7)) [66 7 J #2// 4 1 5 4 111. No. 85 JOHANN LUDWIG KRESS, " Bourrde," from Suite tr 7)) 6-5 4 THE ABBREVIATED DOMINANT NINTH CHORD 173 111. No. 86 MOSCHELES, " Study," op. 70, No. 4 The resolution of the D 9 to the T 5 suggests an additional rule for modulation in a given melody: When the indicated (+) note of modulation descends a step, or a half step, it may go to the fifth of the scale in the new key. The modulation must be, of course, to a directly related key. The note of modulation will here be, obviously, the D 9 (major or minor), resolv- ing to the T 5 . 33O p- i CUMULATIVE HARMONY As may be seen, the alternate notes of the melody in the exercise above should receive D)) chords. It should be transposed to other keys, and harmonized both with fundamentals present and omitted. 111. No. 87 GRIEG, " Gavotte," op. 40, No. 3 * The D 7 here resolves to the T 8 in order not to anticipate the subsequent T 3 in the melody. ill. No. 88 SCHUBERT "Grand Duo," op. 140 BJ J f * s ^j . wiy 2 jj.. ^^ if J. \ r "r I /^~\* _ - ^- 1 L^/*/ 4 !-"*" /^/ ^L< m. & 7)) 3;; The minor D)) chord, commonly known a.s the diminished jth chord, has long held an important place in the harmonic structures of all forms of composition. It contains a minor 3d, diminished 5th, and diminished 7th, and appears as a series of minor 3ds from the nominal fundamental. The four notes constituting it, therefore, stand as points dividing the octave into segments, distant a step and a half apart. Mem- bers of the chord frequently occur with enharmonically changed notation for purposes of simplification and for improved voice lead- ing. For analysis the student should mentally arrange the chord in a series of thirds and then identify the major third below the lowest note as the fundamental Dominant. Altered notation may gen- erally be corrected by consideration toward directly related keys. This chord is frequently used in the major mode. Harmonize the following exercise, using D 9 and D)) chords where feasible. THE ABBREVIATED DOMINANT NINTH CHORD 175 331 (a) () {) < u I _>^ t j V * HP b K \ n i* "i* r r r D) 6 4 1 b 7 [ 5 6 4\\ |6 ||4 6 5 - 32JJ 14. |J3 4 r-9 -f J P H (A * - r * * -^ ^ 9_ -^ w: * (> ^ ^ P- \ U f U th- ; ~1* ! ( ^- 1 - i ^ ||7 C < ; ) 6 4 3 6 9 1(7 5) (T * ^^ . P L- . ! J j j ^ J^^ ^ - r ' > ^ 4* .. M -. =3 i r " A -iU - - 1- tt + ^ V i* r ( flp - * * - t flr i* U i* r X- 1C 3z I ?r W i * Jn* * U f> V 5 =^ i 7 8 CUMULATIVE HARMONY 334 HE =at - -*= ~~i W f r r r r r r 4 j L -/^ - , J J (V)' S*- ^ B* a i^ 2k" p. Tfh- 1 ^ F ? - ft* b7I>7)) |5_ 6 6 7)) 4 P* S m f?r\" 11 ^ i* i ^ sa2 fla r ^ 2 r r i* b* r LJ ~ ttp | J - r i j 1 r t^ etc. -*- t[J ^ /^"\ * ^b 1*" ^ * .. *- 6^ = 2* !- S4 6 2 \\ JJ 4\\ 1,6 -^-s- 1 * *- tt* * ~f 1 ' ^ - r a r-* ^-^ w-^ 1 I1 i -1 1 i i i Melodies should be constructed from the following germ sets, using the D 9 and D 7 chords where they may seem most effective. They may be worked out, for solo with accompaniment, and for piano solo. THE ABBREVIATED DOMINANT NINTH CHORD 179 335 V.) q= 1 1 & m ^-f-r^-tt 336 A Key of c J - r CUMULATIVE HARMONY Beginning with the harmonization of melodies, the work of the student has been conducted, generally, under a given melody or germ set. From this practice, the. ability to develop good melodies, it is confidently hoped, has been assiduously cultivated. The forma- tion of melodies with full knowledge of, and due consideration for, their germ content is of the utmost importance toward the attain- ment of success in melodic composition within the bounds of such limitations as circumstances may demand, as well as to a better ap- preciation of the same in the work of others. The plan of harmonization and melody formation over a given bass set, must, however, be considered of equal importance, and should be diligently pursued throughout the work. While, heretofore, melodies have been evolved over a given bass set, using duplications from the upper three voice parts of the harmonic structure, the student may now enlist the employment of embellish- ments upon the harmony notes as may be desired in such melody construction. In the following exercise the student should fill out the three upper voice parts, as indicated by the symbolized figuring of the given bass, in the same manner as heretofore. THE ABBREVIATED DOMINANT NINTH CHORD 181 338 A J \ j-|3 J tJ- ^ 4m ^p ( ^Q 2 10)4 * -^ r p r J r ^ *" bJ J 1 /WA ^ L^r*^" * u p * P* ^^^* ( fp SP r r b7)) 11 5 x: " km & 9 J j i S^ J J J J. etc. j^^5 ^^ m it A U m pf ijipT Cpf [ IT" 1" i fi " - ff4-4\\ 6-6 IJ6 7 N4 2 3JJ J}5 6 2 5 4 65 4 6 W)) 6\\ b5Jj ME^-J ^ I 1 L -\- ( ! J ' ~J tf^ ^ ff^ j 1 J J &* ^ 4T ' 6 b7 4 4 2 b5 9 [6_ 6 4 7)) ft6\\ 6 7)) 6 7\\ 5JJ 4 *)) ^ ^E5 6 7 4 ft 4 Also work out the above exercise with an eighth-note motus in the soprano, the alto, and the tenor, in turn and alternately. In like manner work out a sixteenth-note motus and various other rhythmic figures. 182 CUMULATIVE HARMONY 339 ^ J- etc -F- ) 111 34O ~jK~~"Ti /I i- ^ /k ft i 2 W a c b *fc ~m \\) ^ ' F- *t B*- "JF- f *- J 1 , 1 i Jetc. - y^\li ft '?*ir^ & 5 - Harmonize the same bass set for accompaniments, in various forms, from which melodies are to be constructed, employing harmony notes from the three upper voices and their embellishments. 341 b7)) K J 6 II 4 ^ -^ An additional exercise is appended for similar treatment. THE ABBREVIATED DOMINANT NINTH CHORD 183 342 JT U7 \ ' pi J |0 A lUl ' ^ jjj /L nf l 1 * 1 -a 1 h = 1 ^~ IV* m m * VU K 5 tr .J. .J. t?.|}- jj. +- -+- * * /^A P/'. / W-W / J)) S^ LC/" M^ ^^b *^s *-^ 22 i #.H ^ T\ J- ^ ^, '^ ^^ z 675 46 b7)) 7)) 4 fa 2 ~t S3 3J) Js 4 6 H? 2 6 6 5 4 b BACH-GOUNOD, " Ave Maria" ^ _ ^ W ^_ 1 84 CUMULATIVE HARMONY f- CHAPTER XXVII IMITATION With the introduction of embellishments the student has been brought directly to the practice of certain phases of counterpoint. Counterpoint is the art of combining separate melodies in such manner as to conform to the laws of harmony. By separate melodies is meant two or more sets of single-note successions that differ melodically or rhythmically from each other. If in placing these melodies in immediate association (to be sounded at the same time) the laws of harmony have been complied with, the parts will necessarily appear in satisfactory harmonic agreement; ideal contrapuntal results are not obtained, however, without due consideration for individual melodic succession in each part. In the following example a single-note succession of five notes, called a subject or motive, is presented at different locations in the scale; as the rhythmic and melodic figure in each case is identical, they are to be considered as melodic duplications. 343 ^^ W-J *-- I If we were to combine the first statement of the subject with either of the others in immediate association, the result would be harmoni- cally satisfactory. 344 n J 1 ! j ! 1 ! J 1 * *- j lm ^~ -55 I \ -* m- * m ^ * h^ H 1 ^^L' i m m 19 * ^ J i r r r i The effect of such combination is the delivery of the subject in the soprano with a duplicate of the subject serving as a harmonic support in a second voice, but the element of rhythmic or melodic independence is entirely lacking. 1 86 CUMULATIVE HARMONY If, however, the melodic succession of the contrasting melody is distinctly at variance with the subject, its individuality directly be- comes apparent. 345 V * r Here the two tone successions are melodically at variance, and the independent melodic effect is evident. Now cause the contrasting melody to appear in a different rhythmic succession, thus: 346 Si rr rT and the effect of independence becomes at once more pronounced. As will be perceived, rhythmic variance is a most effective medium toward independence and individuality of voice parts. The same medium is equally necessary in three or more parts. 347 1 J ~y ~ x * GS & n * * * * 1* CCT) tt * : 1 ^- (9 J 1 If 1 ^ 1 * 1 /W\ 1 i d 2| pg k^ I P- 3 f ',. One of the most important divisions of contrapuntal writing is that of Imitation. Imitation is a musical device consisting of the announcement of a phrase in one voice part and its immediate recurrence in another. An imitation may be a repetition of a complete subject or frag- ments of its stronger sections. In the imitation the rhythmic figure is required to be an exact reproduction of the rhythmic figure in the subject. The melodic form must agree with the following conditions : IMITATION 187 The melodic figure in the imitation ascends and descends as in the subject. Where the progression is by degree in the subject, it should proceed similarly in the imitation. Where it progresses by skip in the subject, it must also proceed by skip in the imitation, but the skip may be greater or less than in the subject when made necessary by harmonic limitations. It may be understood that chromatic exactitude in the imitation is not required ; where in the subject a progression of a major interval occurs, a minor may occur in the imitation; for a diatonic progression a chromatic may be used, and so on. A skip of a third in the subject may not be made a degree less in the imitation, as it would thereby become a progression by degree. It is at all times desirable that the melodic figure in the imitation appear as nearly like that in the subject as the harmonic limitations will permit. IMITATION IN Two VOICES Using the notes of the given germ set and such embellishments as may be desired, form a melodious subject in the first measure of the following exercise. This is to be succeeded in the second measure by an imitation of the subject in the second voice, formed from such harmony notes and attendant embellishments as may be necessary for its construction. At the third measure, form a new subject, to be imitated as before in the fourth measure. This process is to be continued in each succeeding two measures to the end. In selecting notes for the imitation, choose such as will, in con- junction with the germ notes, best represent the chord of which they form a part, care being exercised toward the use of harmony notes other than those contained in the germ set. These are preferably the ones forming intervals of major and minor 3ds or 6ths, aug- mented 2ds or 4ths, and diminished 5ths or yths. Perfect intervals and minor yths are also admissible, although they do not form as satisfactory combinations in two-voice writing as do the others. Attendant embellishments should be added in such manner as to result in the least possible harmonic friction, one with another; rhythmic discrimination should be observed toward the employment of successive shorter notes in one voice simultaneously with longer ones in the other, thus giving to each an independence and indi- viduality especially desirable in contrapuntal composition. i88 CUMULATIVE HARMONY Limited successions of 3 2E -*-^- f + . - f 351 ' 190 111. No. 91 CUMULATIVE HARMONY BACH, " Two-part Invention," No. i 1 I Meno mosso _L r\ u * - J. P^ -^ i , ^ ^ Jr u ^ - . 1 ' J -tf- J' " t|J ( X :f: 5at 111. No. 93 BACH, " Two-part Invention," No. 15 ^^ CHAPTER XXVIII CADENCES The cadence (or close) is a harmonic device consisting of the final and penultimate chords of a composition or phrase, which serve the purpose of effecting a more or less complete finality. Cadences are divided into three general classes: the complete, the incomplete, and the deceptive. The complete cadence consists of a final Tonic preceded by a penul- timate Dominant or Subdominant chord. Of these the authentic cadence (Tonic preceded by the Dominant) is the most common, as well as the most complete and effective. It appears to advantage at the end of a composition or phrase, and is practically a necessity in effecting modulation. While the identification of all forms of cadence may be readily determined by the last two chords, in most instances, one or more additional chords are included immediately preceding the penultimate Dominant which have an important bearing on the progress toward complete or temporary finality, and tend to confirm the real tonality. Of these preparatory harmonies, classed as pre-Dominant chords, the one in most common use, and which seems to be most effectual, is the pre-Dominant | chord, or second inversion of the T triad, with the Dominant in the bass. This chord generally appears, as does the final T chord, on the accented part of the measure, in double or quadruple time. Next in importance for this purpose is the S chord, which is used in all its various forms and positions as pre-Dominant harmony. The chords of the DS (Dominant of the Subdominant), followed by the Subdominant, and of the DD (Dominant of the Dominant), preceding the penultimate Dominant, seem effectually to prepare the ear for that chord as the real dominating factor in key identification. Here follow a few examples of authentic cadences extended by pre-Dominant chords in various plans; these chords are so enlisted for the purpose of intensifying the harmonic progress toward the penultimate Dominant. 191 352 1) CUMULATIVE HARMONY TDT VT ^~> ^> & & ^> L. ^> & d -^ (^ I(T\ _ 22*3 ^ 55 ^~ L^^^ y*^? " ^ ^_ ^ ^^^^ ^r -gL ^. L^^ j*^ * z r o ly g r b ^> x s. I /^ 1 ' a * -1 * ^ 1 V ^^^ & 3: -' 1 ^ . -?^W27 _ > _^ \ i ^- 4 2 6 7 II : 6 5 6 4 7 ^; ) 5 7 The student should form cadences in the manner indicated above, employing three, four, or five of the S, DS, D [S, and DD chords in their several species, including those of the D) and the D)). This should be done in various patterns and in many keys. 111. No. 94 HARVEY WORTHINGTON LOOMIS, Song, " At Midnight " fili ? P-s- t: -t^ Twelve DD D))D pet - als T g^i^ waft J~ ed H 3^ ,U-: CADENCES 193 fcss ^ down. *5 Here is shown a DD with interpolated T, the |S^and [[S chords, and a S de- ceptive cadence, followed by the D)) as a confirming chord. The pedal notes (described in a subsequent chapter) A in the third and fourth measures and D in the fifth measure should not be considered as members of the attending chords. 111. No. 95 BEETHOVEN, " Sonata," op. 14, No. 2 J, _*_ _^_ ij. Here may be seen the DS to the S chord, and the DD to the D with interpo- lated T chord. 111. No. 96 CARL BUSCH, Song, " Crossing the Bar" DD 3 6 5 /K w * * r * *_ ^ tir * ! 1 * J J J r" i i u, >.> j ^] ? * I I r j ^ ** * * ^"^ 4 * ^^ ^ pf^ fl I *> I i r- j, fe). d tH- & p I I I 194 CUMULATIVE HARMONY The plagal cadence is essentially a final T chord preceded by a S chord. This cadence in its simple form has long been in common use in church music. It has, however, at times attained prominent positions and become an important factor in the works of the master composers. 353 ^ j \ & f\ ^^ ^y L/y ^ 31 ^j ?T"\ ^^ j V*^ \) TT n > D'R Su ft ^&' *^& ' 3j -j-^^ -^r jj^ fl ^ V \>jy +i n ^2 ^x_?' Z^S*** jl|i i <) ^^ 1 ^? ' j*^ 1 * 1 ^/ lf U'i *f 1 fjS * ] ^ ^^ ^P gP ~"~ ff it"^ f 2 ^" ^^X ; >-: CADENCES 195 Many of the earlier composers, as well as some of the modern ones, have made effective use of the Tierce de Picardie, or final major T triad in compositions of the minor mode. 354 f C J ? \\ f-' * i^ 28 tFt lr^. "*" i i j ^- fe 1 '&- ~n ^ F i 111. No. 99 BACH, " Prelude IV in C# Minor" ntt 8,, L- P 1 ^ Vftrb - /r 5 IT" ^ * 1* J ri & | ( f r ^ *F^ * fTY ff j. 1* * ^ 1 *^ p* ^- v y 4- ^ r + * * *''!. .9 * 9^* i E 4r^ i* ^ -^ 9 22 g^OV i ^HII i _j_ f ^ . & * . T 1 a 111. No. 100 n K ARTHUR WHITING, " Blow, Blo\ rail. v, Thou Winter 1 Wind " /^s ^rfi% 3 fcs: i (fK o ^~ ^"~* "^ ! ~"jj ^1 ' \*\) n s o^ "Jl 9 ^^ jj^'i * ^n G^ f^: ^- "^ ^- * ^ ~^ 196 CUMULATIVE HARMONY 111. No. 101 BACH, " Organ Fantasia in G Minor' te $F=\ The incomplete cadence (half cadence, or imperfect cadence) may be viewed as an authentic cadence, incomplete because of the omission of the final T chord. Its most familiar form is a reversal of the complete cadence from Dominant - Tonic to Tonic - Dominant, the T chord appearing in its second inversion as a pre-Dominant 4 chord; any directly related chord, however, may precede the Dominant in this form of cadence. 355 /r " & ^ 2? 2 L^ ' --^ ' -- f(\\ ^ *-' >-- , ^ :^g^=^ ;; 3 P ARTHUR BERGH, "The Raven" &!lfcj=e==td rj^ -^ P^4P _L- This illustration supplies an example of the incomplete cadence, Subdominant- Dominant, establishing a point of partial repose. 111. No. 1O3 CADENCES WAGNER, " Tannhaueser " 197 :;,*- , . g 3 The deceptive cadence (false^ cadence, or interrupted cadence) con- sists of the D chord followed by a chord other than the T triad, gener- ally by the submediant chord of a major key or of its tonic minor, or by a form of the Subdominant chord. 356 far fil ss. ^4 ^, &. KB *r- ~^- ^ ' *z> fe^ c) e? -$>- z? -$- 7 1 * f^\* L * l 1 l^^7 k_ 357 xi zi (^ 2 ^? V ' ^ ' g ^ ^> ^ 7 7 >^Aa ^^ _- " ^j V V / -^ L * c ^^^' II 111. No. 1O4 W. J. BALTZELL, "Thistle-Down" l>) n s 3a=^=d aE?E* 198 CUMULATIVE HARMONY ill. No. 1O5 N. CLIFFORD PAGE " A Thing of Beauty " 111. No. 1O6 EDWARD ELGAR, " My Love dwelt in a Northern Land " i SEE ^ ^r A A An interesting example of the D 7 chord of C to the T chord of A. It also A presents a form of plagal cadence in a, intensified by an interpolated D 7 chord of A A C, and ending as a Tierce de Picardie in A. FIELD, " Nocturne, E Minor " -t- ^ This subject is extensively considered in a subsequent chapter. These chord combinations are of frequent occurrence at points other than at the end of a phrase or of a composition, with the chords in their various positions, and are termed passing cadences. The D 9 is rarely used in the penultimate chord at the end of a com- position as a part of the final cadence; in other parts of a composi- tion, however, where only temporary finality is sought, it is used quite frequently. CHAPTER XXIX EXTENDED CADENCES An extended cadence consists of an authentic cadence (described in the previous chapter) preceded by a succession of chords directly related to the key of destination, that serve to intensify the harmonic progress toward the penultimate Dominant. The effect of the employment of such successions of chords is to create an increased atmosphere of expectation and suspense, sub- sequently to be gratified by the arrival at a definite point of destina- tion formed by the authentic D and T chords of finality and repose. . Extended cadences may be employed at the close of a composition or at the end of a division; in the latter case serving in the pre- vailing key of the work or aiding to effect an important modulation. The chords admissible for the formation of extended cadences are as follows: the chords of the T, S, D, the DS, and the DD. These are acceptable in all positions excepting the primary positions of the D and T chords, which are to be reserved as the penultimate and final positions in the authentic cadence. 358 DS S DD DS S DD I) y ~\ f i -1 1 d d h- r 'Z -f^ ^ * - & & ^<*-# b a) (b ) Hr (c ) ( b d) & & J 1 (/) I (*0 *: -*L _ ^. w~\*ci 5 *~~ ,, "* ^f - *_. - ) P iy Hj^ Pfi 3 %t - ^ 1 \~ r -* " " "-T - ^^ I t> 6\\ IS 4 " ' ' )) > s 7)) 6 4 In the above example the problem set forth is to proceed by as- cending chromatic progressions in the bass from the Tonic toward the Dominant, to which note the chord of the \ is given, followed by the penultimate D 7 and final Tonic chords. 199 2OO CUMULATIVE HARMONY It will be readily perceived that there is no point of distinct repose until the final T chord, preceded by the D chord, is reached. The direct point of destination is the Dominant, which is, of course, followed by the Tonic as the true goal. At (a) appears the third inversion of the D)) chord as a DS. This is followed at (b) by the supertonic as the fundamental of the |S chord. At (c) is the third inversion of the D)) on the DD; at (d), the first inversion of the DS; at (e), the S chord; at (/), the fundamental position of the D)) as a DD, leading to the pre-Dominant | of the authentic cadence. 359 TDDS S DTDT ill 1 r\ \ & J * V- ^ -* M ~ & r -^ \_ n -.-, CCi) f 3 f 2 *-^ 2 r fy -&- j. * \ J J \ J -*- -G>- (m\' ~3 u . ^j [1*J. & (? i^ ^~> n^^i *-^ V^xft f^ 1 (5* 6 4 1 1 1 . .\ \ 11=111 i)) : 7 Here the bass progressions are downward from the Tonic, F, in similar manner. Form extended cadences in various keys, proceeding from the Tonic to the Dominant, both ascending and descending, as directed. The student may now form extended cadences, modulating to the following keys in the given succession, using the final Tonic in each key as a note of departure from which the basses should proceed chromatically to the penultimate Dominant of the succeeding key. The bass progressions are to ascend or descend (as the case may be) in the direction of the greatest distance from the note of departure to the note of destination, for the sake of practice in acquiring harmonic technique. The chords available for this purpose include those of the [S, [|S, and S depressed 3d, and the D)) in the D, DS, and DD chords. A A A A C-a-e-G-b -A-f S-D-d-F-g-d-B b-F-a-C EXTENDED CADENCES 201 36O (C) n ( (a)E a) i DS DS 1 1 i 1 D s DD S 2 1 I - -^ * 3 tf j - . ^ r U f r j j j l?tf *= if x 3 Wi Si. y- ^ /5 #~ fe u r \ #6 4 3 8 :)) l T 6 T . J) ) f tt6 4 3 ill DD XT i5/ ^> fm SL f^ ^r ^ J -&- etc. f'5x~~~ ffj^ Tl^ 5^2 b k ^a A Starting with the initial key of C, the first modulation is to a, whose Dominant, E, is the point of destination. As its greater dis- tance is downward, the progressions, for the sake of practice, are made in that direction and continued as in the previous examples, to the Dominant (E), upon which the preparatory \ chord is followed by the penultimate Dominant leading to the final Tonic. It must be understood that the harmonic successions from (a) to (b) inclu- sive act as intensifying chords in the key of a. As the Dominant in A the next key of modulation, d, is reached at a greater distance by ascending, the progression should be made in that direction, and so on through the given series of modulations. This mode of procedure is not to be considered as the best means of reaching a new key by modulation, but rather as a means of gain- ing a familiarity with the various harmonies at one's disposal for such purpose through an intensified close, the student ultimately selecting, in composition, such as may seem most desirable for the purposes in 202 CUMULATIVE HARMONY view. It must also be borne in mind that the enlistment of these chords serves to create an atmosphere of homogeneous harmonic variety, and always tends toward confirmation of the ultimate Tonic. The harmonic schemes evolved from this process may be formed into accompaniments, over which melodies may be constructed as in previous exercises. In each key the duration of chords may be re- duced or extended as may be necessary in order to make the entire length of eight, sixteen, or thirty-two measures. CHAPTER XXX EXTRANEOUS MODULATION Extraneous keys are either indirectly related or foreign. Modulation has been practiced thus far only to directly related keys, a passing reference, only, having been made to the exceptions in serial modulations by Rule IV (in both genders) and by Rule V (from minor to major), in which cases the modulations effected are not to keys that are directly related. 361 Bb -9 1 k 7K s> sh- t=_ <5> <5 L 2^ HZS - ^ i> .._ L InN ^ . ^ f -*' ^ -~< /^ f -^ v- \J ^ \y ^s -. fl^' ^ g f^ -- HJ*^ f^ b7 7 b "7 -* t7 P/^ - ^ s & 2 At (a), following Rule IV, by taking the Subdominant for a new A Dominant a modulation occurs to Bb, which being represented by A a signature of two flats more than the key of departure, C, is not a directly related key. At (b), following the same rule but proceed- ing from minor to minor, the key of modulation, g, is indirectly related. At (c), proceeding from major to minor, by Rule V, the A A key of d, having one flat more than C, is directly related. At (d),on the other hand, proceeding by the same rule but from minor to A major, we reach the key of Bb, which is not directly related. A modulation may be immediate or deferred. It is immediate when it is accomplished through the use of the D chord of the key of destination only. A modulation is deferred when two or more D chords are utilized in order to reach the key of destination. 203 2O4 CUMULATIVE HARMONY It may be seen that by the rules governing serial modulations the note for a new Dominant is, in each case, selected from the diatonic content of the key of departure (the key from which the modulation is to occur). By following this plan modulations may be accom- plished to keys which, by reason of their gender, do not bear as inti- mate relationship to the key of departure as is borne by directly related keys, but are sufficiently close to invite immediate modulation to them without impairing the general harmonic homogeneity. Such modulations are to indirectly related keys. INDIRECTLY RELATED KEYS Included in this class are the following: (i) Those reached by the rules for serial modulation proceeding from major to major and minor to minor, when they proceed, instead, from major to minor and minor to major, as illustrated in the following example. 362 A A A C (I) f a (I) D 1 A A c (ii) g 1 A a (II) E V J j J X ^ frgfe 4?~S^ - fc liS 1 S""EL^ ^g AJ JJI $&- S-jt^^ \My -^J J tJi^X TL*^ 5^ * .7 b 7 ft ft 7 ft [7 }; -7 h G> J <3 ^J %^^ ^X ^^ 2? S s ^^ 111. No. 108 BEETHOVEN, " Sonata," op. no /Ajfe > tzzz: 1 2 i ' c "M - H * H U 4 d < / i ! 1* P ' * 1-^H- 1 fm\* H i " ^ p 'i I CfcfcE lEfig 3 I _ L i ^2 _ F MF G ) t. 3 T~ ))5)) Modulation from f to C instead of to c. (2) Those reached by the rules proceeding from major to minor and minor to major when they proceed, instead, from major to major and minor to minor, as in the following example. EXTRANEOUS MODULATION 205 363 C (III) A a (III) f C (V) D C (VI) a (VI) c +\ 1 - ~*ii>-- r-J 1 1 ts ^ h i& ^ tV ? r ^, ~~&~$j& & - 5 1 ^i ^ $ -,> hff^r- fit}' - -* <5 & & >> 4E ^ 111. No. 1O9 DVORAK, " Walzer," op. 54, No. i ea >~2o~ |^ X 3=3 " 4- > ^J- ; : I fe -&>- A A A A Modulation from A to F instead of from A to fit. (3) As exceptions in the above two classes, those reached by Rule IV when proceeding from major to major and minor to minor, and by Rule V when proceeding from minor to major. 364 A A A A A A C (IV) Bb a (IV) g a (V) Bb ~f A & ^p B ^ 5 t ^ 5< I \ *-* ^ - -^ ^ ^ ~^3 \c * nCc 89 -. fl'S' -^ /^" rT/^" es JLT - 77 1 B b b7 Cs (T- ^-^ <5 tlxv ^ D^C (4) Those that proceed from major to minor when proceeding, instead, from a major key as though from its Tonic minor. 365 206 CUMULATIVE HARMONY A At (a), by taking the mediant of c instead of C we reach the key of Ab instead of a; at (b), by taking the submediant of c instead of C A ^ A we reach the key of Db instead of d; and at (c) the sub tonic of c leads to Eb instead of to e. in. NO. no CHOPIN " Nocturne," op. 37, No. 2 ^f^ 3& h A A A A Proceeding from G to Bt> instead of from G to b. 111. No. ill ETHELBERT NEVIN, " In the Night " 111. No. 112 CARL DEIS, " Waiting" A A A A Proceeding from C to Ab instead of from C to a. For additional reference see 111. No. 102. EXTRANEOUS MODULATION 207 A A table of the indirectly related keys to C would be as follows: A A AAA A AAA (i) f g, (2) A D E, (3) Bb, (4) Ab Db Eb; and of the indirectly related keys to a, as follows: (i)DE, ( 2 )fc\ ( 3 )Bbg. It is not to be understood that modulations are to be effected solely from the T chord of the key of departure; they are fully as satis- factory when proceeding from the S chord or the D chord. see 15 Foreign keys are those extraneous keys not included among the indirectly related keys. Modulations of this class are rarely satisfactory, except when ac- complished by the enlistment of two or more Dominant chords, in- volving one or more passing modulations before the key of destination is reached. 367 A C ^n ^> 11 1 3*5 5 |(TV ^ iij ^r 2 ffjK ^ T! .Ly Ullg ! 1 H*T: | ^-^ fit ^i /^J x fy 4 3 ^* 5 M tf Among the foreign keys to the key of C are the following: c#, f#, A AAA Gb, B, b, d#, etc. 208 CUMULATIVE HARMONY Modulation may be satisfactorily effected through the medium of the D 7 chord, confirmed by the T chord of the key of destination; or by means of other forms of the family of D harmonies, such as the chords of the gth, augmented 6th, and of the S group such as the Neapolitan 6th, etc.; or it may be accomplished through the aid of ambiguous chords, that is, those belonging to both keys; or by the various intensifying chords of the extended cadence, involving, per- haps, passing modulations, all of which may serve more fully to con- firm the harmonic change, and thereby tend to increase the beauty of its general tonal effect. 111. No. 113 WAGNER, " Lohengrin " -fr- 111. No. 114 Poco andantino FRANCK, " L'Organiste " EXTRANEOUS MODULATION 209 The student would do well to evolve and classify all available modes of modulation, and through practice become expert in applying them in problems such as the following: modulate, and indicate by what A A A AA A A AA AA A A rules, from C to Ab, d to f, A to C, g to C, F to bb, Ab to eb, B to A A A C, A to F, etc. Transition consists of passing into a new key without the process of modulation through the use of a new Dominant. Transition is generally to the major or minor mediant or submediant, to the Tonic major of a minor key, or the Tonic minor of a major key. 368 , -fcy /K ~&^i. P<5 -yg^ ^k^ ~ ?-> V.LJ * U f J5J gj t* ^ TT b g vb b etc. fm\ h-r ]J' cs 25E \-s & 22 r -5 h m ^ 5 i- ~ * J -*- -^ 2 - 5 ^- ._^H 5 * T- /A\*^O r? Hi ! v j| - . _ I^/ *f f 1 1 i n 1 u ^"^ 'A. f 3 f* V P * J i ntt K 1*2 ( ^ _^_ 1* h* hi Hi h 1* JrfLi* P.. 2 , ~ r w* u+ , PM C* X up-, ^ . f(t\ "Eg X i Z r ^!r V ') F r F r wP bU K^B D0i 1^ >^ ^; r ^ ^ r -*- 1 | b-^- ?-r 1 1 b-0- U.0 "fc~ ^4 hi ___. *^ kT. jg/'ff. 5S-_. IP pz^^ p T Pp B_ I* ^r- _Bi =RI EE 2IO CUMULATIVE HARMONY 111. No. 116 CHARLES WAKEFIELD CADMAN " Sonata in A Major " t-Jir CHAPTER XXXI SECONDARY CHORDS ON THE TONIC In the chord of the Tonic the 6th may be substituted for the 5th to form the Tonic substituted 6th chord. Symbol Tj . This is an application of the submediant triad for Tonic harmoni- zation, and will be utilized and analyzed as a tributary member of the family of T chords. It is most frequently used in fundamental and primary positions, although it is occasionally employed in its second inversion as a \\ chord. 369 TJ ~dj e^ cJ eJ ' z=l 7$ ^j ;H -^ I i V ^j ^ *3\ (~ty \ * Q & :. \-40f * ^ ^ ( ^' C^\ m ]ff_J* (2) / Tta^ ^ H *^ \ ^^ r 22 />* > & ^ 6 5| 6) 6| 6J 61 ll The Tonic substituted 6th chord has a more positive local signifi- cance as a primary chord in the major mode than in the minor, and the Tonic quality is most in evidence when the chord is in its primary position, with the 6th in the soprano, and preceded by the D chord in one of its various forms. When the D 7 chord is followed by the primary position of the T| chord, the D 8 resolves to the T 6 . 37O D TJ D TJ D TJ < J * 2 1 1 & J.. W-. ^ -& . Z5 -& & -<^>- *= & ^ i i 7 A 6 5 6 ' 4 6 3 J 4 61 2 4 212 CUMULATIVE HARMONY When the D 9 chord is followed by the primary position of the Tj, the gth is retained as a common tone and becomes the T 6 . 371 D TJ D)) TJ D TJ 1 ^ 1 f"T\ 5" o. <^X s ^X ^r \-\) & 2 & J ^^ /*^? g .5 -i/ ^ 1 ^ -5<- - e ft " I ^ In the fundamental position, on the contrary, it has a bold individual character, although suggestive of further important progression (6). When the Dominant chord resolves to the fundamental position of the TJ chord it constitutes one form of the deceptive (false or inter- rupted) cadence. SECONDARY CHORDS ON THE TONIC 213 In this form of resolution the D fundamental is not doubled, as parallel octaves would result, the D 3 resolving to the T 6 or T 8 in the major mode and to the T 8 in the minor, the restriction in the lat- ter case being a precaution against augmented progression. 373 A C D TJ I) II A a D u 1] s <* -, / \ ( \ 2 W III -* Cs **/*" '^ ^^ ^"'f* V-y * 2 I / *Zs ** -^ ** J ^* i D & '-^ 2 "*" (tiy ^ t^ 1 ^ ^J The deceptive cadence of the tonic minor mode may be used in major keys. To prevent the unsatisfactory progression of an aug- mented second, the D 3 should resolve to the T 8 . 374 ^ A A In the above example the D 7 chord resolves to the TJ of c instead of to C. The student should give considerable attention to the analysis of chorals, hymns, and other forms of composition, marking the various chords with symbolized figuring. 111. No. 117 LWOFF, 1833, " Choral " b&l ^ . B 1 1 1 ^ j ^ ^* 1 1 *-' f + f $ ^'&4 ~~* p f- | | u ^~ 6 f. U 6 214 CUMULATIVE HARMONY ^^ % -Shr ^ 667 5 4 # 7 6 4 #6 4 3 =& -?2- ^ ^ =: zg^JtLjLfc it=E^3=^=: *=t 66 7 4 S 11 6 7 Notice the double 3d in change of position. 111. No. 118 N. CLIFFORD PAGE, " A Thing of Beauty " 3 L* ^ ^ ^F==^^=^ , 7)) In c with a deceptive cadence, followed by a modulation to f through the diminished yth chord. 111. No. 119 OSCAR WEIL, " Just You and I," op. 31, No. i XL" 1 B 1 * A 1 _ 1 ' ^ ^ - 1 ^ ^ m r- ^ rk tf/i -i s. * i^3 ^ & V]J 4- ' ^ jj f_ 9 ^r [^/^JJ. I T ^ S^ /*7? >-^ C,-i. J ** 2_ U SECONDARY CHORDS ON THE TONIC 111. No. 120 E. R. KROEGER, Suite, " Lalla Rookh" Lento 215 T and j_[S chords alternating over the Tonic acting as a pedal, and an auxiliary above, depressed to prevent the progression of an augmented 2d. 111. No. 121 ALEXANDER EWING, " Choral' 4 * -&-: f= n CHAPTER XXXII THE TONIC ADDED SIXTH CHORD T[| In the Tonic chord the 6th may be added to the triad to form the Tonic added 6th chord. Symbol T|| . This is an application of the submediant yth chord to Tonic har- monization, and as such is classed as a tributary member of the family of T chords. 375 Til /T" 1 |iT\ >> ^, &.S2 & 532 ^ ^J Lg t^ i^ll & &< ^^ fZs f^s 5SJ2 3S ^? & f. f 3 G J j i r \ \ ! f^ ^ , tz rf^ ^-^ fy -^ &- & -* (2 ' :i 6 6 5 | 4 3 5 9 HI 216 THE TONIC ADDED SIXTH CHORD _T[j 217 $> 2 ^ ^5 g 22 ^> ^x \y <* *> i i f f a i T i e> ^ ^ ^^ ^ f3 {& ^ I li 4 4 3 3 2 [\ 5 ^ H J)) J| The Tj chord preceded by the chord of the D 9 is much more satis- factory in primary position when written in five voices, particularly when the D 9 chord is in fundamental position. 377 yr ds f ^ '^> < o^, vy *^s f ^A **s (^ f 3 [^25 f. %^ S -* ^ fP r 9 5 5 i ill As the notes contained in the 6j and |ij chords are the same as those forming certain S chords in other keys, a positive identification may, at times, be obtained only through the succeeding chords, which may indicate a modulation to the key of the Dominant or of its relative minor, in which case the chord in question becomes an intensifying factor in approaching the cadence to the new tonality. 378 >c |m f. . P ml X" ii W * * flr i^ i^jr^' ^^ J 1 1 fT - -*^ ^*~i ^ 5 tr -y ^^ L^ *> s _^. ff ~ 5_ ^^ 6l 17 7 it. X^ ^ i ,. 6 #5 7x x Nt6 *)) 6 ^ II ||6 l LL5 il 11 ^fil 11 Transpose the above bass sets to several keys for new treatment. The enlistment of this new branch of the family of T chords suggests an additional rule for harmonization of melodies. The sixth of the scale may, at times, be harmonized with the Tonic. This is applied to best advantage when the sixth of the major scale, preceded by the fifth or sixth with D harmony, occurs on the accented part of the measure. 382 VT a v * b - /L |(Tv ^ ^ ^s S f /^ V 7 ^ ^ ^2 1 J 1 tr J 1 1 f+Y * j. ^^ /V /'v <5^ ^*J*\ * e: WSJ. _ \^_ ^ 6 ^ \^> * fj ^ j 4 3 c, 9 4 3 \ 6|| The Tji chord as an additional factor in harmonic material admits the third application of the rule for passing modulations, those pre- viously noted being the DS and the DD. When the T added 6th chord, whose fundamental is the submedi- ant, is followed by the S substituted 6th chord, the fundamental of 22O CUMULATIVE HARMONY which is a fourth higher, the _T| chord may be altered to form a D chord, effecting a passing modulation as the Dominant of the super- tonic, symbol D[S. 383 T TJ [S T DjS |S \J jj\^ /T\ -- ^Sl/ ^~ ^^ & T T ,^) ff_x'5- ff & s m \- & **' c3 CB** \^^s rj fi f3 S3 5 |5 7Al I At (a) appears the T|j chord followed by the [S chord, inviting a passing modulation as at (6). All forms of the D chord are admitted in passing modulations. 384 D[S |S DD D 1 /L E D* E frv n saz ff^ tf * k ^ gM J \ Jb^ i ^ 1 1 /^A gg U A 2^t A ^ ' ^^ 5* 2 1 ^s p 6 5 '- i) 4 7 The pre-Dominant | chord is frequently interpolated between the chord of the DD and the succeeding D chord. 385 DD D n ' 1 ^ (S* ^3 I(T\ ^^ i - ^-^ _ ^ j S3Z h 2 ^J^-^ 53 Cf * 0*7; * *J* ^ j ^^^ | 52 ^. 16 b7)) 6 _[5 4 7 386 THE TONIC ADDED SIXTH CHORD Tjj 221 DS DS DD , mm 4 4 6 $4 ,~ ff" 6 9 61 t>7)) 2 2 |,7)) 4 DD DD ' P^. =*=3=t3 4 #6U \*_ $* 6 ^J 7 ^-^ 4 2 bSJj 2 fas S 61 [6_ 7)) 6 DD DS DD 4\\ |> "^ ^\ 6 ~*1 "" LL- 6\\ 5JJ 4 6 5 7)) 4 4 6 | 7 2 4 It was noted in a previous chapter that the DS may be succeeded by the [S or 1|S chord. Extended cadences, as given in a preceding chapter, should now be formed to include the Tj , Tjj , and D [S chords. 111. No. 122 WM. J. McCov, " The Only Voice " XUr^" ^ ^ vj ~~1 # = v^r/ ^> ^ ^^ O^ J 2 W^TI-J? ^ fe ^ M ' 1 1 ^-'(7 u ~~ fy i 1 u vl * 1 1 1 ' 1 ' I 1 ' 6 6 ,, 6 5) 4 5 9 !-U nr, Harmonize the following germ set, applying the new harmonic material as given above. 387 ^ s i CHAPTER XXXIII COMPOSITION OF CHORALS The student will now select several chorals from a standard hymnal or choral book, to be used as rhythmic patterns for original melodic and harmonic treatment. The harmonic structure should consist of chords belonging to the tonality that may be selected for the composition, with certain specified modulations in the form of authentic cadences at the end of each section. The hymn is to be divided, at points suggested by the divisions in the original, into four sections, the conclusion of each of which should be in the form of an authentic cadence to a directly related key, preceded by a few preparatory or intensifying chords selected from those available in extended cadences. As examples of such chord extensions the following plans are submitted : T 6 , [S 6 , Tt D 7 , and T; S, DD|, T|, D 7 , and T; DS|, S 6 , ^DDJi)), TJ, D 7 , and T; T, DT_]J, T|, ^ D 7 , and T. These chords refer to sectional keys of modulation. A plan of modulations for a choral is here suggested: The first section modulating to key of mediant, the second section modulating to key of Dominant, the third section modulating to key of Subdominant, and the conclusion in the initial key. Two other plans follow: Modulations to Dominant, supertonic, submediant, and the initial key. Modulations to mediant, Subdominant, Dominant, and the initial key. Other plans may be selected and modulations indicated by the student. Modulations should be to directly related keys. For model see 111. No. 117. 223 CHAPTER XXXIV CHROMATIC OR ALTERED CHORDS Chromatic or altered chords are those in which one or more harmony notes are chromatically elevated or depressed from the diatonic con- tent of the immediate key without necessarily causing a positive or passing modulation. This chromatic alteration generally affects the D 5 , which, by reason of its having an optional resolution, readily invites an elevation or depression to determine definitely the direction of its course and to aid in intensifying its progression. Chronologically, this was at first accomplished progressively, by the aid of chromatic passing notes (a) (a), but subsequently the chro- matically altered notes were engrafted as essential members of the chords (b), and the chords classified accordingly. 388 n ( a ) sy (a) (*J r^ \J , 2 \ C J /fl\ ^ <^ % ^ ^ s i" 4 3 6 4 3 4 3 4 3 f^\* [^y ! w ^y <* "** s^ ^^ Til flp pJ5! ^ 1 1 ^ An augmented 6lh chord consists of a D 7 or D 9 chord with the fundamental 5th depressed. Symbol (c) \> ^ * ^ ? S! & * J-3 176 5 4 7 4 7 DD I) DS I) DS D fa -r> o ^ U ^~ -$S 3 SE ^ ^ && i5< S 2 -* (^ 7^r^-P- M ^ -6?- -^ . ^- r " i >g '< 2? fcz ty i^ /y J r f W 2 (.4 - A -&- G*\' , & . f 3 (* ESE fs 75 1 [_ Jr*) 6 7 4 II. The second inversion (from the D fundamental) of the D) chord, with the bass (D 5 ) depressed and the D 7 doubled, is known as the Italian 6th chord. Symbol 5 6

^ ~ fl ^ *y ^"^ 5 ^^ ^ l -&- 1 ~^t~ ^2 ~** f> &- ^_ (+\' 1 i^/ ^f -^ ^2 ^^ .(2 ^^ f J fe e ^} S2J h c E vh ^/ y 22 1 ^ Q t ' / / J-'D) 6 7 4 I 6 5 *6 5 6 7 4 230 CUMULATIVE HARMONY For the purpose of identification the fourth form will be known as the modern augmented 6th chord. While all species of this chord are best in the original position (second inversion from D fundamental), they appear also in the fundamental position and all inversions, to greater or less advantage. Resolutions of the augmented 6th chord to the various species of the Tj chord present many very novel, as well as charming, harmonic effects, that are much practiced by modern composers. The student should practice in framing original harmonic plans from which bass sets may be arranged for development, as heretofore. The following table presents some examples of such combinations. The student would do well to experiment with these chords, as he may be assured that a mine of harmonic resources will be opened to him. 393 D T D D T D & ^ ffh \) ' K. ^ i*2 in ^ i^j J r T" b-^ J. Vp -&- J J r ? **- J. Z3s *%? _ [rJ- U-2 i" f? \_^ W p /-2 *2 2S ** ^-! r * IT a . l\ I k a u 5 (ft) & ^ ^ /5 ^ si <& 25 z? z? L_ ^^O .-^ f? ^"} tf? ^j b ^ ^j T f ^ J f - J i r etc. J J /^A ^-, . ^ i^/* f*J_ ^^ fo/^j 1 n^v bi*^ k^^ r^ I/ 5^ ^^ 'S' i '^ fu __ ^^ : i S 5 i i 1.,; ^- ill Lx-g\ 1 6 I! 5 tt) :n Work out extended cadences, effecting modulations to the follow- ing succession of keys as before prescribed, utilizing the Tj and w '^ ^~ f 3 ./ ^J_ f^ _bj _ 1 fm\' & W? IS' *^ yfj' *\ ^~ ^^_^ * \ ' f^ ib sn 6 4 7 Fill out the remaining three voices from the following figured bass set, working out various forms of motus in the individual and alter- nate voices. This may be done in several keys. 395 J^E ^ 6 Ib5 4\\ 6 6 6 b? S 5 6j 4 6 ||6 - 7 bSJ |t}6\\H6 4 4 - (5 1 fi \-\) (? _-, 32 /*5 ffJ*D -j ^^ -&- A j^_ 1 V r 1 f^\ + !^/ ^-~ ^ *^M^ r^ S' s^ i f? 6 4 7 S 1 Jb6 6 7 4 tf I 234 THE NEAPOLITAN SIXTH CHORD 235 (c) -* & S ' ^ "h **j ' 2 ^? C'v b <2J 5 >^, ^i ES fl ,- &* D 'j^ ) J -!> * fcfi > ^^ ^ ^ f5t 1 5? S ^ jr ( f?> g ^ ' . r ^ jf 'x '^ ^^ ip ^ L * ^ STJu /-If - ^ ^, P/ .-^ -^ -*,. s^s ~* ^ f^ ^ ^/ j fls ^- tt ; 7 ^ i>6 tj b 6 5 II 6 7 4 (^ J > 6 At (a) the chromatic passing note is between the diatonic S 6 and the T 8 ; at (ft) and (c) the Bi? is an integral part of the Neapolitan 6th chord, which is followed by the pre-D f chord; at (d) and (e) it takes the place of a pre-D chord followed by the D chord ; at (/) and (g) it is fol- lowed by the chord of the DD, the two serving as intensifying pre-D chords; at (h) the Neapolitan 6th chord on the S of the relative minor is enlisted to form a species of plagal cadence. Work out extended cadences using this chord. While in modern music it is employed in all positions, care should always be exercised toward preventing disallowed progressions. 111. No. 131 CHOPIN, "Waltz," op. 34, No. 2 While this chord progresses more frequently to the T| chord, the progression to the D 7 chord, as seen above, is not uncommon and is very effective. 236 111. No. 132 CUMULATIVE HARMONY LOEWE, " Ballad of Edward " /foWs^H- r* i ^d d ^ 1 1C) " E 8 J ^* "1 J "htll 1 S S~ l?'* 9 ~ -d J ^ fl"* * * -- -- /W"\ r /"4 ft ft 9 [^x* [/ r* Wl) vIK ! m ^ "'t? U l { W -T ^ &- 1 4 4 b2 b2 111. No. 133 EUGENE BLANCHARD. " The Sea Gipsy," op. 5, No. 2 I ^J , . d. fg^- ^H 1 :?5*v5r -=Hft- * An example of the Neapolitan 6th chord on the |S of the relative minor, borrowed for use in the major mode. Fill out the following figured bass sets in four voices with varied motus, after which the same harmonic structure should be formed into accompaniments, with melodies constructed thereon in different forms, as heretofore. 4O1 K2* " Z_E_ i* ^ n A ^-'htl i ^ j * ! ^ D) J |}6 6 '5 4 6 4| &\\ |"b6' 5 aj| &)) U 4- ^ 6 7 _5J 7)) 6 4 if 5^ i ^E \\ )) // THE NEAPOLITAN SIXTH CHORD 237 The student may also write a melody from the following germ set, which is to be harmonized in four voice parts, using various species of motus; also prepare as solo with accompaniment, and for piano alone, applying the new harmonies given above. 4O2 ggtftfv I 5* i 3 1 & J [ * -1- S> - Jf 3 5J) * 7 Itj6 6 #4 '' ^r- 4 2 _5| 6J 3 ^ 1 * #4 2 |#6 6 6|| 4 i|j CHAPTER XXXVI AUGMENTED FIFTH CHORDS An augmented 5th chord consists primarily of a major or minor triad with the 5th elevated. Symbol j?. It is the outcome of the practice among early composers of intensifying the progression of voice parts that move a whole step from one chord to another, by means of chromatic passing notes. They occur in the T, S, and D chords of major keys and in the S chord of minor keys. As the diatonic degree above the T 5 and D 5 in the minor mode is only a half step, the opportunity for chromatic intensification by elevation is not available in those chords. 4O3 At (a), (c), and (e) are given examples of intensification of pro- A gression by chromatic passing notes in the primary chords of C, and at (g) the same in the S chord of a. At (b), (J), (/), and (h) the chromatic passing notes are enlisted as integral parts of the chords; at (i) and (y) the T 5 and D 5 in a pro- ceed upward a half step, forbidding the entrance of a chromatic passing note and, for the same reason, the formation of an aug- mented 5th chord. A table of augmented triads available for use in immediate succes- sion is given in a subsequent chapter. 238 AUGMENTED FIFTH CHORDS 239 111. No. 134 All" ritmico ARTHUR FOOTE, " Flying Cloud," op. 73, No. 4 The harmonic plan of the above is as follows: 111. No. 135 = The S augmented 5th chord (^S) of the relative minor mode is used in the major, and, conversely, that of the relative major is used in the minor; the progression to the following chord in both cases being governed by the prevailing gender. 4O4 (a} At (a) the -fS of a is used in the key of C, to the D triad of which A the chord progresses. At (7>) the S augmented 5th chord of C is used in the key of a, the progression being to the D 7 chord of the latter key. Augmented 5th chords may appear in any of the various positions, those with the major 3d being most satisfactory for inversion. The -PS chord in the minor mode occurs less frequently as a chord of 6 or \ . In the chords of the D 7 , the D 9 , and the D)), the augmented 5th is frequently used with most satisfactory results, particularly in the D 7 chord. In the resolution of this chord the T 3 is usually doubled, although the D 7 frequently resolves upward to the T 5 . 240 HARMONY 4O5 If **, ^ ._ ^ +{^5, es ff ~ W ~r s< . \sly > -Q ^^^ ^^ _ 5J ~j \J * -Or -&- (^\* ^^ -^ " LV*'* fl/ +*^-, f^S \^^S (^ fZs f* >& 5 > ^6 6 ^^^ 4 | 5// 2 m OLEY SPEAKS, "The Lassie I loved Best " The demands in resolution of the ^PD chord frequently overshadow those of the resolution of the D 7 to the T 3 , as may be seen below. 111. No. 137 WM. R. CHAPMAN, " This would I Do " I m 9 ^\^ 1 1 ^ ^ J= 111 *- 7 AUGMENTED FIFTH CHORDS 241 The chord and symbol at (a) will be described in a subsequent chapter. 111. No. 138 WILSON G. SMITH, " Fulfillment " ^ * >Kfo L j:l'/ X "1 & ,3 fD ^-* d * 5"* tf *i 2 iS 8 *i * * ^ ix ^T w^ ^^ /rT * ^ . ^^"\ i ^^ PJ !/ U / > ^^rt K i \ ^ * 111. No. 139 GEORGE W. CHADWICK " A Ballad of Trees and the Master " 3: fcfc=: Clean for - spent In - to the woods * Q^- m i m 7 }} b6 \\ b6 \\ f^ 6 \\ 5Jj 4 ) 4 4) 2// 2/7 377 The harmonic plan, without the embellishments, follows. Note the D 7 resolv- ing to the T 8 in the bass, as may be found in the works of Haendel end his contemporaries. 111. No. 140 242 CUMULATIVE HARMONY Other chords of the yth with augmented 5th will be referred to in another chapter. Additional rule for harmonization of melodies: When the elevated 5th of the Tonic, Subdominant, or Dominant is followed by the next diatonic degree a half step above, it may be harmonized with the augmented 5th chord (^5). The following bass set is submitted for various modes of treatment, without and with embellishments: 4O6 xLa s __ j ^-^ * W ~^ fi *r^ & S' * 11 j j J T r r r r j T ,,J r r i IT | J_ ft*)' ,^j ^| f * *?* "^ 5* ^^( o m m P^ \ 1* * 1 ^ > rl r ~ i i s ^ f C C>U7 O xj V # j#5 ^ 5 4 2 4|| 6 3J 4 fU e |S 6\\ J>6 sjj a I 2 ^ ^ |b_5 || 7 I #6 b ||b5 4 >3 e b5 S-: ;. 7 7 5 # 6 6 b I #6 4 >b5 -^:- -j P --: f | -5 ^ * ^""^ i 1 1 p m. ft* 6 J>6 4 5 U ' >7 b? 6 6 5 MS 1 - >7 6 Jl 7 )) 66 7 5 4 . Here also is given a germ set to be harmonized in various forms without and with embellishments. 4O7 il j*-H*-f-^ AUGMENTED FIFTH CHORDS 243 In recent compositions the D 5 is occasionally elevated and de- pressed simultaneously, the elevation resolving to the T 3 and the depression to the T 8 . The D 7 here frequently resolves to the T 5 . This double chromatic alteration of the D 5 is employed in the D 7 , D 9 , and D)) chords as well as in the D triad. 4O8 **t --S*- r -&- I [a\ 1*1 X 6J f'\ 2? 72 1^- 1 2 ,9 (^ H?s* (> ^ If | P- T~ i J i ^ ^ t? (5* ^ (5? " b^ ^L <*: - 7 .' (^ ^p 3 ^ f r\\ 6 I- xMjSVV 6 ' 6 5J| [ 6)5 ^ <^ 5/7

J%? * Jfc* i* J * x*~ ^ J J i r T J , J T' i ^j J ^ lm\' Z&> Vs? > ,,& ^J TT ^ ttP pj. n S3 n_ &9 u ? f ^w-' & D2 Tfi J>fi J>fi 'I J>6 "I # 1 4 ^>ft5 < J 1 4 1 TT T DD T DD T DD J>6 f ( -F# 5 T J 1 ^ DSD ; f 1 H f tt ' S D S f -J -.-, ,^- M wJ fes " W d tr C* 8_ ^ H^ IlT\ W So To^ 1 ^ " SSE ^ Jtr^ tr^ tTi o Jtr^ i (5? f? f? 1 1 1 , 1 Ji 1 -J- ^ .rJ- li^- Lfc j u/^? LL if u '^ 1 i nr J J \ J ^-J ^-tt^ *f^ s f* -y u lf-2 P fl>^ *fT\ ^ II- TT 1 J>J+C J>R [>C [>C j^fi c 'I P 3 *n O 'i 'i -n TT ^ 5 T T* T# 1 * T ^ ^5 I ? < f 1 * r>6 -n'^ ^1 TT" ; f 4 ^ CHAPTER XXXVII IMITATION OVER GIVEN FUNDAMENTALS The student may now undertake the writing of two voice parts contrapuntally, over a given fundamental set, with specific effort toward imitation. The subject or motive may be chosen, which is to be uttered (fre- quently alone) in the first measure either by the first or second voice and imitated in the succeeding measure by the other voice. During the progress of the imitation the voice part announcing the subject in the first measure should continue in different melodic and rhythmic succession, as heretofore practiced. In the third measure the same subject, accompanied by a con- trasting melodic succession, may again occur, to be imitated, as be- fore, in the fourth measure, and so on throughout, always with due consideration for the harmony as indicated by the fundamental set. Effort should be continuously enlisted toward the evolving of tuneful melody lines in both the subject and the contrasting voice part. The parts should be so prepared that disagreeable successions of dissonant intervals may be avoided and that the general effect may be musical. 411 Subj. 246 CUMULATIVE HARMONY The subject is announced by the upper voice in the first measure, imitated in the second, reannounced in the third, and imitated again in the fourth, to agree with the foregoing directions. The student should seek to individualize the various voice parts by the application of distinctly different rhythmic and melodic figures. Invent new subjects for similar treatment in different keys. Two exercises follow for further practice. 412 t 3=g izti: IMITATION OVER GIVEN FUNDAMENTALS 247 etc. -: J _H w *-: ^/T *-T- * m *-v- ~m~* *~ t H 413 (<) b r-* ' tf H m & P GS , m Imitation in three voices is developed in similar manner, with the subject appearing in a selected voice part at the initial measure and imitated by the other two voices in succession. The subject may be announced in the first measure and imitated by the other two voices in the two succeeding measures, the fourth measure being occupied by fragments of the subject or by other contrasting melodic suc- cessions in the various voice parts. At the fifth measure the subject may be taken up as before. 414 ()*' ~* 5 'i* ' *- ' "" = brC C. = ^^ /^\ ^^^_ ["'/ ^J ^^^ \^\ ^~ ^^^ j f(*J./ 1 >j ^^^\ y ^* 248 CUMULATIVE HARMONY VZJ' ^ ^^ -S^ u & ^ 1= The student may utilize the bass sets given for imitation in two voices, for similar practice in three and four voices. 111. No. 142 BACH, " Prelude VII," Preludes and Fugues, Book I gy*=j ^fc IMITATION OVER GIVEN FUNDAMENTALS 249 111. No. 143 BACH, " Symphony in C Major " -LJ7* J-- * . , ,J- = gEEi CHAPTER XXXVIII ADDITIONAL EMBELLISHMENTS An arpeggio is a melodic deviation from a note of the germ set to another harmony note of the same chord. A direct arpeggio returns to the germ note from which it deviates, before the succeeding germ note is reached. 415 -*?- j iT^. J 4 An indirect arpeggio is one of two or more arpeggios occurring in succession before returning to the germ set; it may return to a germ note other than the one from which it deviated. 416 P T -J L Other embellishments may be applied to arpeggio notes. 250 ADDITIONAL EMBELLISHMENTS 251 417 J i J Form various figures of motus in the soprano from the germ set in ercise emloin combined areios and other em- Form various figures of motus in the soprano from the germ set i the following exercise, employing combined arpeggios and other em bellishments. The same may be done in the alto and in the tenor, ca taken to prevent unnecessary overlapping of the voice parts. 418 M*^ ^ f 6 4 -al- j. ^^ ^ ^ r H :" ^2 - t ^1H Utilize the following germ set as a basis for sprightly melody to be constructed with the aid of arpeggios and attendant embellishments. 252 CUMULATIVE HARMONY 419 /L "R J i II irh ff II Chromatic passing notes may be used between harmony notes and diatonic passing notes to form chromatic scale passages. 42O ^ i f J- t*= 111. No. 144 CHOPIN, Etude, op. 10, No. 2 -4 W ADDITIONAL EMBELLISHMENTS 253 s n Pfi ;. rcp " J ^ f O: % - - =T P s EE .- 3f * : yi: Harmonize the following exercise and apply chromatic passing notes to form a sixteenth-note motus, first in the bass, then in the tenor, alto, and soprano in turn, and finally in alternating voices. Other rhythmic figures may be employed in like manner. The customary orthography of the chromatic scale is by elevations of diatonic notes in ascending passages, and by depressions in de- sceading. The following exceptions to the above may be noted: in ascending passages the depressed seventh of the scale is occasionally used in- stead of the elevated sixth, and in descending, the elevated fourth should be used instead of the depressed fifth. (In chromatic no- tation, it must be admitted, composers of the past have been very uncertain.) 421 ( . J- S: Jfc 254 CUMULATIVE HARMONY ^ m i 111. No- 145 MOZART, " Symphony in D Major" 111. No. 146 BEETHOVEN, " Sonata for Violin and Piano," op. 96 q*-*- ^ Sf-rHf=ji If- An ornamental anticipation occurs when one or more harmony notes of one chord are interpolated between the anticipation and the anticipated note of the succeeding chord. Embellishments or combined embellishments and harmony notes may be employed in the same manner. 422 , J J a r 111. No. 147 ADAM, " Cantique de Noel " im^'b Ul ; _^t _-LJ^Lf ^^ F . 4 ---t 4 -4 /LiV U . ^-J J ^ ^ "^ 9 rv- o ^ / g *^ ^ ^ V_xh uf I j ^t ^ ^ t p P [j a (S *^~ 9 f r ADDITIONAL EMBELLISHMENTS 255 Anticipations of passing notes are occasionally employed with ex- cellent effect. 423 r -, -J- , r ^ i Suspensions are frequently resolved ornamentally by the inter- polation of other notes of the chord or of embellishments on the suspended note. 424 5 9- (O J 6 5 rf~ T!^= -, E? = V p^ J j H-[ ^h NjJ ''[. n J a & .^ * i * ^* 1 ^ ^, 22 ^ E 6 5 5 5 i 5 256 CUMULATIVE HARMONY Example 424 shows a suspension ornamentally resolved in various forms, such as: at (a), (6), and (c) the 5th of the chord above and below interposed; at (d) the 3d of the chord interposed; at (e) the 3d and 5th alternating with the suspended note; at (/) changing notes on the suspended note; at (g) combined auxiliaries and har- mony notes; and at (ti) combined anticipation and auxiliary. 111. No. 148 BEETHOVEN, " Sonata in C Minor," op. 10 1 1 1 , ^1 1 * I/ [/ o H * 9 V9 l J xf p Ufl *" x J ^ _ V47 4 *S> 1 ^ (9 -&- kL ~tr. "i: (\* K Q 1 r*~ 1 ^p-b4 1 In addition to the suspensions already given, others may be added; in fact, modern composers admit and practice the suspension or re- tardation of any note of one chord that progresses a diatonic degree to its position as a harmony note in the next. 425 3 9 ? -65 -6 5 3E E 3 ^ t / K ^ ~si IP -^ " -t fm (3 **X^3 V P / f5 ^n ,-, m 4 I-'O' Saz - s > 'u^ ^ 3,"" _, ; J 1 1 etc> 1 1 *" pj ^s ^^ 1 j ! , etc. f*\' ?~ -^ VL>- ^-S 2 ^^ ^^ ^ r*-^i r p^ ?.*> Kg E =j ^J-=4=^F t- -| H u 4 < i> 4 ^= =^ ^- - " l * j - j .. b s ^- tfJ - Q S3 us F* j* {? Bzl ? f S >j & Bi* r i ^ 'b KA * l "i 1 y P'fr 1 1 ' K3 N 6 1/8 ADDITIONAL EMBELLISHMENTS 257 Extended passing notes are frequently inverted, the embellish- ment departing by degree from the first harmony note, instead of approaching the second one by degree. The departure is generally diatonic above and chromatic below. They are classed as extended passing notes inverted. 426 J ' 1 1 J J y * ** \ 9 r / ** 9 m f * CD ^ ^-, J i ^ ,. a ^2 ' i i / "^- J j r j ^ ' .* <> 8J2* ^^ ^ a. . a a. r f a 111. No. 150 BEETHOVEN, " Sonata," op. 109 9 6 5 CHAPTER XXXIX IRREGULAR RESOLUTIONS OF THE D 7 CHORD Reference to the transference of the D 7 from one voice part to an- other has already appeared in this work. The yth is also subject to ornamental resolution, effected by deferring its progress to the T 3 through the interpolation of other notes of the chord, of embellish- ments, or of combinations of harmony notes and embellishments. In all circumstances the yth must finally resolve to the T 3 in the same voice and at the same altitude as that in which the yth appears. 427 (a) (0 d) j j j J 1 r-^-d 1-1 1 m * aH 1-1 y?T ^i -^ i?T\ -^^ ^j - -,_, ., *IZ ^~ 533! ^ ^ 5[J ^-** 5j_ ^ ^ \ J 1 1 J -s>- \ \ B^25 5I^x fO ^^ ^2 *^i ^^, ^-> ^~. ^^ 7 7 r 7 1 | 1 7 (r) X '** ^/ ^> r^\ "^ ~ ^~ ^_ -^ -^ ^ -^ * r \ J J 1 & i -5. _ ^"V 2 ^ l^y ^ /^r /^ ^^^ s^ I i 1^,1 . 4 6 6 7 2 4 2 At (a) and (6) the D 8 above and below is interpolated; at (c) the 5th is interpolated; at (d) the 5th and 8va alternate with the yth; at (e) appear the changing notes E and G; at (/) the 5th and 8va, and at (g) the 8va above and below, occur in conjunction with the yth. In the chapter on cadences the deceptive cadence was mentioned with special reference to the D 7 chord followed by the Tj chord of a major or minor key or of the tonic minor of a major key. IRREGULAR RESOLUTIONS OF THE D 7 CHORD 259 The cfTective device of deferring the resolution of the D to the T chord by interpolation of one or more of the several species of the Subdominant family is considerably practiced. The interpolated chord, which may appear in any of its various positions, should, when thus followed by the T chord, be considered as a form of plagal cadence. 428 JT ^ ^s ^ -, 3 , _ ^ * & ( \ ^ ' f "J * 4 ^f * & 1 m V _s ^** ^ ^/ *^s -^ * & 9 & fj ^ V^, -* ' s5 ^ ^ i 9 ^ 7 6 4 7 t 6 14 4 |]2 5 i 2 7 1 1 7 In other parts of a composition the progression of the D funda- mental bass is to the S chord in fundamental or inverted position, which may be succeeded by the D chord in one of its various positions. 429 DSD 1 ' T DSD T i 1 1 Jf ~~^ JF ^^ * * } ^ * 3 * 7 % \ "* ^Z 52iz ^2 81 i^ __ ^ 1^ P "~2 x v 31 tf (--*- 1 1 1 ^ -* ^L J J j ^' * ^T> (^ - ^j L S^j ^ SL tf^ -, ^/ ^s i ^ . ': ' '! T ' * 6 7 454 2 2 6 i I 111. No. 151 W. J. McCOY, " Egypt," Act III 260 CUMULATIVE HARMONY When the resolution of a D 7 chord is to be followed by a D 7 chord representing a different tonality, the chord of resolution is frequently omitted, the D 7 chords following each other in immediate succession. (See DS and DD chords.) At (a) the D 7 chord on D is resolved to the corresponding T triad on G, which in turn is succeeded by the D 7 chord on G duly resolved to the T triad on C. At (b) the resolution of the D 7 chord on D is eliminated, the D 7 chord on G following in immediate succession. At (c) and (d) the same process is carried out, the successive D 7 chords on G and D appearing in the same manner. This process may be carried out in sequence through a considera- ble number of tonalities, each succeeding D 7 chord representing an implied resolution, as well as a positive declaration of a new key. 431 ( c .2 (^) -X- i u . ^ u_ & b . f[ ~ ich" - LL *j rr r-j W - u ^^ s^s y>* Cj if 53 \ r 1 1 J J -* b^ bfi A _& -G>- -e> A " ^\* f^ u 22 \^J* * 238 _, & T^-,/ f? kss f ^ b7 b? IRREGULAR RESOLUTIONS OF THE D 7 CHORD 261 The passing modulations with resolutions at (a) and (b) are re- peated with the resolutions eliminated, leaving only the successive D 7 chords in sequence. 111. No. 152 CHOPIN, " Mazurka in G Minor," op. 67, No. 2 ^f^^^^^^^=^^^f^^^^^ \ TT H I I I I \ I 1 , ft t &*- * b? b7 Each of the D 7 chords above is understood simultaneously to resolve to its corresponding T chond and progress to a D 7 chord for a succeeding modulation. See 111. 153- 111. No. 153 /L b 5 SEES ^ ~ *^^- ITr *r \ i p r **" etc. r "T 1 * -*- >W\ jfl Cl L^x* I/ , i " Successive D 7 chords frequently appear with an interpolated f as a pre-Dominant chord to the D 7 chord on the same note immediately following it. 432 ^^ *"^" cy c^ s f^ EB f/GX V- i> r(* ,-^1 ^4 i* J \ \ f^t ^ ~r i i | & ^ K -X -_ /^ ^^ i -^ " i I* ^ ~~ ^ J 6 >* i , 5 4 b/ 262 111. No. 154 CUMULATIVE HARMONY BEETHOVEN, " Sonata," op. 13 When the D 7 progresses melodically one degree upward to the T 5 in one voice, the yth may be doubled in another voice for resolution to the T 3 . This resolution of the D 7 to the T 3 may not occur in the bass part. 433 /T S3 _ ^x Li\y.i 13 ^* ^ SEE JL ^^ (<^ ^^ * ij i 1. /^A , i ^^ [v^y t ^^^ Hii /^^ f^* p _25 <** ! t~ r 6 6 5 4 7 In the minor mode when the bass part descends by degree from the Tonic to the Dominant, involving successively the chords of the Tonic, Dominant, Subdominant, and Dominant, the normal yth of the scale, as the minor 3d of the Dominant, is sometimes used, to avoid the descending progression of an augmented second. This is known as the Phrygian cadence, 'and is found occasionally in modern works, as well as in those of the older masters. 434 6 [6_ IRREGULAR RESOLUTIONS OF THE D 7 CHORD 263 111. No. 155 MENDELSSOHN, " Scotch Symphony" 1= ^=% * . CHAPTER XL SECONDARY CHORDS ON THE DOMINANT In the Dominant chord the 6th may be substituted for the 5th to form the Dominant substituted 6th chord. Symbol IT). This is an application of the triad of the mediant to Dominant harmonization, in which general capacity it will be considered in this work, both for harmonizing melodies and for analysis. As in the cases of the [S and the T^ , this chord has the greater local significance as a primary chord when in the primary position. It may be used, however, in all its various positions to greater or less advantage. In the resolution to the T chord the D 6 may remain as a tone com- mon to both chords and becomes the T 3 , or it may ascend to the T 5 or descend to the T 8 . The D 6 appears to best advantage in the soprano. The 3d of the scale may at times be harmonized with the Dominant. Discrimination must be used in this chord similar to that in the D 9 and the D)) chords. If the D 6 ascends or descends one degree before the resolution of the chord, it is not an essential member of the chord and must be classed as an embellishment. 435 /r ~ & 532 i S^j -- 1 A J. 1 225 ) ^ * ,^ 2_ ^ -"*' ,^-' -^ ^, -^ . - ^ -^ 1 1 J_ r f ! i 1 r f S^\ ^f ' -* ^ ^ ^ -*z- k."^* ^ Sj ^> ^- ^ ^ ^ ^ ^ v^ x ^. r^ ^ ^^ f* ^ r | i . i (T 6 15 6 56 [5 The student should work out serial modulations by several rules, using the secondary chords on the Tonic and Dominant. Following are some examples of various resolutions to the T| chord. 437 3t~ J3 . ^ g & * <5 ^ >2 ^ f Jl | "3 1 ^ 1 | ( ! 1 g:--^ h^ *c ?5 " ^ W Si . ty 1 [6 1 * i [6 |S 1 , 1 ^J is- ^ 1 6 5j 4 266 CUMULATIVE HARMONY /T E ^ & <*" f 2 * " - 1 1 c- 1 1 fv ^ ^ ^X &/ "* *^ vfj' /^> X^, x^ _^^- ' x,/ x^ X5 "6" 5] 4 T _5j 4 f* 5 1 A ^ . The student should, at this point, select numerous rhythmic figures from standard hymns, as before, for application of the additional harmonies here given to original harmonic and melodic combinations. Analysis of all forms of composition should be unremittingly pursued. It is hoped that diligence in playing these examples and exercises and hearing them played has not been relaxed. The value of the practice of mental analysis cannot be overestimated. With the inclusion of the yth, the D chord attains an additionally distinctive Dominant quality. (Expressed, Dominant substituted 6th chord with yth included.) Symbol fD^. In the ID 7 chord the 6th resolves preferably to the T 5 or T 8 ; the presence of the D 7 , which has a compulsory resolution to the T 3 , causes a doubling of the 3d when the D 6 is retained in the same voice, which is generally not as satisfactory in four voices as in five or more. The D 3 resolves to the T 8 or descends to T 5 . When the resolution is to the Tj chord, the D 3 may descend to the T 6 ]. A few examples of various positions of this chord and their reso- lutions to the chords of the T and Tj are here given. 438 j ^ L/ ^> , *? ^ rj V^ ^^ ^, > fT\ ^ I i ^? ~^*~ 'S- T 1 ~& 1 /i*\ ^g & ^~ Gs ^ tf^ ^^ l^x 2 ^ r^ ^*/ r^ a s^ x^ X3 ffl SECONDARY CHORDS ON THE DOMINANT 267 H^ ! I 1 ! 1 1 5* 4? / i z? /^ f > < '* 9 |9 ^ >2 f2 '' ! i I J I J- ~p -&- \ \ <. CS 9 s. y "^ ^ ^ <9 &- J 1 1 The sixth is rarely good below the seventh. Such arrangements of the chord with progressions as are given in Exercise 439 are uninvit- ing or altogether inadmissible. 439 S r ^ ___ q Im "* -' j* , ^ ^. & Cr ' f r /^\ ''^ LT<; * *^s f^ ^J %^_X y". -'y ^/ s* 7 6 r 4 i i: 4 Add the three upper voices to the following given bass in accord- ance with the figured indications; transpose to other keys and work out as before. The student should then take the harmonic structure thus formed as a basis for an accompaniment, from the upper three voices of which a melody should be constructed as before. 440 i -> j (S' =^- ! , 14 ill - fflp*=t := ^ [TV-run^ ^ ^, M cs> ^5 ^ u j g I J 1 ^1 /j^\fO ^ ^ L^^'TT^r | r* Ip u ^^X y| ~ A & ti= 6- "5 [6 6 5 4 i ^ =(== -" 1 442 Germ Set Solo Piano Ace. A- =^:S? = -z*- etc. - -*- E^E .:: 4 3 443 Germ Set Pft f2~- Piano Solo =P=Pc SECONDARY CHORDS ON THE DOMINANT 269 tff. P*E Jfc S^ i i 41: ll etc. 270 CUMULATIVE HARMONY -9-. + 1 111. No. 156 EDGAR S. KELLEY, Lady picking Mulberries Z_5^^I =t -e* $4 '- :^ 111. No. 157 McCov, " Song of the Flint "Cave Man 111. No. 158 WILSON G. SMITH, " Fulfillment" - **n -U ^- J * ^> ~~r5 . ^-^ ^"s i? 5'drs jg S- r [ l 2 ^^ ^* [ x f^ z ^^^r i f* (2 ^ c -^ ^ -&- 7 \i 16 In Illustrations 157 and 158 occurs the [D chord with D 7 included. CHAPTER XLI DOMINANT ADDED SIXTH CHORD To the D triad the 6th may be added to form the Dominant added 6th chord. Symbol ilD. This is an application of the mediant yth chord to Dominant harmonization, and is included in the family of D chords. As with other secondary chords, its primary significance is most pronounced in its primary position, with the 6th in the soprano. The resolution to the T chord is much the same as that of the D chord. The D 3 and D 5 resolve as in the D 7 chord. The D 6 has three resolutions: it may remain as a common tone and become the T 3 ; it may ascend to the T 5 ; or it may descend to the T 8 . 446 /r ^ ||(T\ ^ jr _ I\MJ ^ J - I - A : \ f 1 - 1/iV icj. O {? ^s * -, & IS /L ^ -. ^^ f(TV ^. r , ^.-. S? /*!? ^ _ SS2 ^ r ^ *J_ ^ re: ^-^ 5^ 3 o r J - j r r j ' ^ i n^/ ^x f> ^ U Hi \ 5 16 6 5 5 f(T\ j-^ ^ v /*^ ^^ 21 [^> " ^s ^s ^^^ /TI? f^ /*^ ^* /*" y^> *I? ^^ *? p^ f-^ *^ -^ (0 II ^ ]j ^ P S la ^ I 3 H 4 5 3 - r J4 _6j 7^~^~ <5 f*-: '^ 4'^ ^ ^ z *> ' 1 f 3 X^- \ i lifts At (a) occurs the fundamental position of the llD chord followed by /\ the T_| chord in C, with the fundamental ascending a 4th; at (6), with the same fundamentals, the flD chord is altered to become a D 7 chord as the Dominant of the submediant [D Tjj, effecting a passing modulation. At (V) occurs the fTD chord followed by the Tj chord in a: at (d] the TT) chord is altered to become a D 7 as a D Tj, form- ing a passing modulation. 276 CUMULATIVE HARMONY 453 -V -* K * PI ex j -& ^ ttU [J *' 's c\ \ _ 9 It 7 t^y* i ' ^-\ i i SZ. m CM m n ^ i i ^x 6 [_5^ 6\\ 6 5 ~" bS/j 4 4\\ 4 8 s ^ r ^5 75!- b7)) Utilize the following germ set for composition in various forms, applying the chords recently submitted. 454 * *P" F E Extended cadences with chromatic bass progressions from Tonic to Dominant in selected keys and from final Tonic to the succeeding penultimate Dominant through a series of other keys, as in other successions, may now be worked out, to involve applications of the T| , Tjj , ID, flD, and D Tj chords. DOMINANT ADDED SIXTH CHORD 277 There are to be found in the works of recent composers (and older composers as well) occasional examples of the D 4 substituted for the D 3 . This unit (otherwise known as the Dominant nth) is, with very rare exceptions, an embellishment over the D 3 or under the D% to one of which it progresses during the life of the D chord. If, therefore, it progresses upward or downward one degree before the resolution of the chord, it is to be classed as an embellishment and not an actual member of the chord. The D 7 here often resolves to the T 5 . It occurs also in conjunction with the substituted 6th to form the D substituted 6th and 4th chord. Symbol ||. It may be employed with the D 7 or D 9 . 111. No. 161 * SCHUMANN, Novelette, No. 8 I * ... 'I jtSssi - ! i f X* ' : JH S f l\ '1 j A 5l ^ * V^ly *J- i 1 -- m m m J * * -4 "4 4 T -2- i J 9 ^S-fJ-^ s 2 ^ -^ 9 -+ N* \^_ * i ^ A _ *^ " it 9 5 ^ : 1 " "T" ^ f" ^" ' F 111. No. 162 HENRY HOLDEN Huss, "Crossing the Bar " ^ * ?.a ^ ^SE S b * _5j 6 CHORDS OF THE TONIC SEVENTH AND SUB DOMINANT SEVENTH By adding a diatonic yth to the triad of the Tonic or of the Sub- dominant, the chord of the Tonic seventh [T 7 ] or the Subdominant seventh [S 7 ] may be formed. In the major mode these chords con- sist of a major triad and major yth. In the minor mode the T 7 chord consists of a minor triad and major yth, and the S 7 of a minor triad and minor yth. 455 T S' T S" si JF * 3; ff\\ 2 (#}*a The fundamentals of all chords of the 7th are naturally inclined toward other fundamentals located a perfect fourth higher. As may be seen in Exercise 456, the fundamental of the D 7 chord followed by that of the T triad (a), of the supertonic jth [ j_Sj followed by the D triad (6), of the mediant yth [ID] followed by the submediant triad [Tj] (c], and the submediant yth [Tj;] followed by the triad of the supertonic [ \_^\ (d) are examples of this tendency. 456 (a)D T () ,|S D (O^D T (^)T[| [S (e) T S ^ ^- ^ & ^ '~i a - .r- f\\ * ^ J* ^ "2 m ' 532 ^ i .^> ~*. ~^~ ^ "^ ^* ^ ^. ^ -& z^ K* es ^ -- -- teV (? *~ j E? * ^t ^ , zJ - e ] ** I I I c * e | I - 5 -r^ 7 || I 5 This is equally true of the fundamental of the T 7 chord, which is best succeeded by the S chord, as seen at (e) in the example above. TONIC SEVENTH AND SUBDOMINANT SEVENTH 279 The progression of the fundamentals in each case, as may be seen, describes an ascending interval of a perfect fourth, which is recognized as being the most satisfactory fundamental progression toward tem- porary or permanent repose. m. No. 163 EDGAR S. KEL.LEY, op. 8. No. 2, - ISRAFEL" ^^.A-;-g-i- n_._S5_l- m. No. 164 CLEMENTI, " Gradus ad Parnassum " 111. No. 165 VICTOR HERBERT, "Natoma," Act II - 280 111. No. 166 CUMULATIVE HARMONY SCHUMANN, "Novelette," op. 21, No. 2 ^dr ^- 7 - D) The fundamental of the S 7 chord is, however, denied this natural progression, owing, first, to the fact that the diatonic fourth above the Subdominant (which, harmonically, is the leading tone) is not a real fundamental, assuming as it does the position of a nominal fundamental to the D) chord. In addition, this ascending progression is that of an augmented fourth, which is not considered available; the descending progression of a diminished 5th is but little better, involving as it does a doub- ling of the leading tone and an absolute failure to contribute an impression of resolution. 457 S 7 r-fl- J- D) S D) S 7 D) j , ^--, ZT ' ^n 5^ ] 9^ VT\ ^ 2J ^x ^ \^- J ^s s _.' ^> ^c^ ^^ GL (**\* t^-) ^r [\^y C*' i y %^__ x 1 ^J - 7 5) 7 5) 7 5) It is for these reasons that the most acceptable progression of the fundamental of the S 7 chord is to the real fundamental of the triad on the leading tone, which is the Dominant. 458 S D | T S D T L/ ^x --i j I XfL - 1 ^^ s 32 /Vr\ ^* -*j ^.-j **f -r J ^X \My ^^ ^^ , ^S *Txii -&- -a*- N*^ ^ ^ ^ ^ ^^^ '^ f- 7 7 7 =: TONIC SEVENTH AND SUBDOMINANT SEVENTH 281 In modern music, chord progressions from the S 7 chord to the D)) chord are, however, occasionally employed. 459 S D)) S D)) I I , 7 7 *?)) These chords may be used in all inversions, no member being omitted and none doubled; in the fundamental position, however, the 5th omitted and the fundamental doubled, with the yth in the soprano (Ex. 456), is quite satisfactory. Harmonize the following bass sets in accordance with the figuring, and construct melodies, as before. 46O I "I *4/ r*r '>' ** S2 (** 4J^ -^ ^J f^ ^- \ 6 74 5 2 5 bs)) 7 *J)) 6 CZ; \^> -J , ^J Ef - } *r c? ^ 7 7 i;6\ v 6 it^ i6\\ 6 fi ii*X ^ 11 IT H I ^fQ y&=i ^ Tl J 1 ^ ^ ! ^ ?6 6 # 7 4 T-. 5| 4 t}5 2 b S 7 9 611 ill 461 &h^ ' e 4 _6j 2 :^:: J tf l r TLU Lf ii: ) 6 b6 b 7 4|| 7 it ill i ii 282 CUMULATIVE HARMONY In addition to the chords tabulated above, modern compositions contain many effective examples of the chord of the Qth on the Tonic, the Subdominant (see 111. No. 165), and the supertonic. This subject, as well as the more extended utilization of material drawn from the overtonal system, such as the so-called whole-tone scale, successions of augmented fifths, etc., will be treated at length in a subsequent volume. The exercises offered in this chapter may, as heretofore, be utilized as the basis for accompaniments upon which melodies are to be con- structed. Extended cadences may also be worked out in the usual manner, involving the recent chords contributed. A table of the direct and tributary chords included in the three primary families Tonic, Subdominant and Dominant is here A given in C. THE TONIC GROUP 462 1 2 T Triad (Also occasionally with depressed 3d in major keys) T 7 chord Ffe T substituted 6th chord [Submediant triad} (Occasionally with depressed 3d) T augmented 5th chord T added 6th chord [Submediant 7th chord] (Occasionally with depressed 3d) T 9 chord TONIC SEVENTH AND SUBDOMINANT SEVENTH 283 ;R< * THE SUBDOMINANT GROUP 2 S triad (Also with depressed 3d in major keys) S substituted 6th chord [Supertonic triad] (Also with depressed 3d in major keys) S augmented 5th chord S 7 chord S added 6th chord [Supertonic 7th chord] (Also with depressed 3d in major keys) Neapolitan 6th chord Neapolitan 6th chord A in a * J. S 9 chord (Also with depressed 3d in major keys) THE DOMINANT GROUP 2 D triad D 7 chord 284 )-: - CUMULATIVE HARMONY 4 r\ Abbreviated D 7 chord [Leading-tone triad] D 9 chord 5 vp/<- Abbreviated D 9 chord [Leading-tone 7th chord] 7)) Italian 6th chord French 6th chord German 6th chord ;-0-S>- Modern augmented 6th chord )) 11 D substituted 6th chord D augmented 5th chord D added 6th chord TONIC SEVENTH AND SUBDOMINANT SEVENTH 285 13 , D substituted 6th chord with 7th included D added 6th chord with 7th included (In five voices) 15 16 D substituted 6th chord with 7th and gth included (In five voices) D 9 chord complete (In five voices) D augmented 5th chord with 7th included D augmented 5th chord with 7th and gth included 19 French 6th chord with D added 6th 20 French 6th chord with elevated D 5 2 86 CUMULATIVE HARMONY Italian 6th chord with elevated D 5 Modern 6th chord with fundamen- tal included (In five voices) 22 b-6>- \J '^ German 6th chord with Xj y*D /VIA "^ 532 elevated L) jj^L ^=^= '. ^P#8 6 ^b5 24 / f \ ^2 ^2 Lv-VJ. 1 fm -& %' 4th, and sub- \ V^L/ ^^ & - f? ( stituted 6th and 4th chords j /WS i^? 1^2 j^ 1 L^^* i ^^-^ ' IT 6 6 4 4 CHAPTER XLIII SEQUENCES A sequence is the repeated occurrence of a melodic or rhythmic figure upon different degrees of the staff 463 etc. 464 XL t* '^ ^~\ f2 ^J PM > a e fat *-^ saz r J I 1 4 1 -^- -&- \ | f^\* ^^ ^j _ HZp S .j ^> ^ C^l , f-> F 1 1 ! U A sequence is tonal or real. The tonal sequence is confined to the diatonic limits of the key, and is subject to the following conditions: I. It is the general name of the intervals (as 3d, 5th, 6th, etc.), not the specific name (as major, minor, etc.), that is to be considered. II. Augmented intervals may freely occur in any part. III. The leading tone may be doubled. IV. The diminished triad may be used in any position. The above privileges (II, III, IV) are allowed only in the repetitions of the sequence, not in the original figure. The final repetition also must be free from disallowed progressions. V. The second inversion of the triad is usually considered un- available. VI. The original figure may consist of two or more chords, with embellishments if desired, and may be repeated upon higher or lower degrees of the staff. 287 2 88 CUMULATIVE HARMONY 465 J 1 J 1 ! gj 1 d -&- 1 ->- V o 2 < C **' ^~ ! -*^ "-^ /r f > (5> 2 jj p f^ I* 5 1 |2 ^ ^ ^ - ' i The rea/ sequence is of a different character, in that the intervals employed melodically and harmonically in the repetitions must be identical in quality, that is, they must be of the same specific distance (as major 2d, perfect 4th, diminished yth, etc.). This generally necessitates a passing modulation at each repetition. 467 This form of sequence is not as satisfactory as is the tonal sequence; a compromise of a much more agreeable character is frequently formed of modulations alternating to major and minor keys. SEQUENCES 289 468 A C ^ ?=F ^ ' et fr 5 37 CL 1 r J *' 111. No. 167 BACH, " Organ Fugue in G " .' ;e .' 1* !*. fr* ^ E * *- 111. No. 168 BACH, "Organ Prelude in E Minor" ntt * J U -x I, ^ l/^ *j J| S C v ^i ^ ^, IT | ^ 1 . ^ ^ J. J ^L /W"\M* * J L^^'"^/ * 2 ^ >v_ \ j 1 ^ ^ ^ I r 2 go CUMULATIVE HARMONY 111. No. 169 GOUNOD, " Redemption " tr '=$? or />eaW, is the use of a note sustained continuously through a definite portion of a com- position while a succession of alternating consonant and dissonant chords are being sounded in the other three voices. The pedal point, in most cases the Tonic or Dominant, is placed generally in the bass, although it is used with excellent effect in any of the other three voices. When occurring in a voice other than the bass it is termed inverted pedal point. The first and last chords should be in accord with the pedal note, that is, they should be chords of which the pedal is a note of harmony. The harmonies in general use as passing chords are the primary chords of the prevailing key and of the directly related keys. In the works of modern composers, however, no restrictions seem to be considered in the employment of harmonies formed by combinations of diatonic and chromatic embellishments. The student is advised against the use of any chords excepting those drawn from directly related keys until his work has reached a mature stage in its progress. In the following example of the Dominant pedal point the chords are all of the prevailing key. The embellishments are marked. 469 An example of pedal point on the Tonic is also given. SEQUENCES 291 47O ^ ^EE^ -Br~ J-L^ L-J :iM?*^ In the following examples chords from directly related keys are included. 471 S H * W b* 4 A 1* 1* A ^ ^ ^ .- ^ ~j ~C ^" 1 J n 4tJ l^J |^ r"""! ^' "^ ^ ^5j fl 4P ^F fl ; \L*f *"" IT 1 T^r^ rf ^ 22 fiL- ^-^fnin 9 - ^=r V + ^ f =E F=r=^ 1,1 ' J fr* bJ- -J- 472 T DS S T DD D T DD D . -^ ^ ->4 * J. i J. 2Q2 CUMULATIVE HARMONY . ^ Double pedal point is frequently used to excellent effect, particu- larly in compositions of a pastoral character. The combined Tonic and Dominant are most generally used for this purpose, the lower note being the Tonic. 473 \J ** ^^^_ B^sSi xT ' / \ ^^^^\ _ m(\\ \ i . ^^ M ^HZ . *( * * * * ^X 1 ^^ V ^*" " 1^" n 1 I ^> V7 a i Illustrations of various species of pedal point are appended. 111. No.lVO W. J. McCov, "The Hamadryads" SEQUENCES 293 - * " 111. No. 172 CHERUBIM, "Quartette in C Major" -g-ygj-ynr--- b< ^e =-> *- An excellent illustration of Tonic pedal with embellishments. 294 CUMULATIVE HARMONY 111. No. 173 WALLACE A. SABIN Prelude to " St. Patrick of Tara " J: Jr ^L/ j*" ivfliJ' t~> \ > x. .*- j V 1 -' / *T A p i* ' * ^ x -?- f- r r i i "^^r "fe" i *-. i i I J 1 1 i ^~ 3 /w^\^ ^ t> i _l CslfSLySl ^5 > ^^Q .#>! S J *< *^ M N J* ^r "* HF J ^ ^ 111. No. 174 PURCELL, " Service in Bb " J -. 111. No. 175 HELLER, " Dans les Bois," op. 128 111. No. 176 SEQUENCES 295 E. A. MACDOWELL, "Shadow Dance" ~2-*S*-> (g) tf 4-*f -*. = = f i ; -<&- /^\** f I? o [^ / -^ _^^S ^^^ 5 /i ^^ ^> ^ T" ! p -.r- r-v J I ^ J ^ J ^ J ^ ,"^ t-ff : In five-part harmony avoid doubling such members of the chords as have compulsory resolution. Those best suited for doubling are: (i) in the D 7 chord, the D 5 and D 8 ; (2) in the D)) chord, the D 5 and D 7 . Crossing of the parts should generally be avoided. INDEX Abbreviated Dominant ninth chord, 170 Abbreviated Dominant seventh chord, So Abbreviated minor ninth chord, 174 Accompaniments, 34 construction of melodies over, 31 Added sixth chord, on the Dominant, 271 on the Subdominant, 84 on the Tonic, 216 Altered chords, 224 Anticipation, 1 52 of passing notes, 255 ornamental. 254 Appoggiatura, 146 Arpeggio, definition of, 250 direct, 250 Arpeggio notes with embellishments, 250 Augmented fifth chord, 238 Augmented sixth chord, 224 resolution of, 225 Augmented triad. 17 Authentic cadence, 44, 191 Auxiliaries, definition of, 136 below the third and seventh in major keys, 138 belo%v the second and fifth in minor keys, 138 below the seventh in minor keys, 138 extended, 141 introductory, 148 progressive, 150 successive, 140 Cadence, definition of, 191 authentic, 44, 191 complete, 191 deceptive, 197 extended, 199 incomplete, 196 passing, 198 Phrygian, 262 plagal, 194 Tierce de I'icardie, 195 Changing notes, 152 Chord, definition of, 16 of the sixth, 25 of the sixth and fourth, 26 of the sixth and fourth, Rules I, II, III, IV, 78, 79 of the sixth and fourth. Rule IV, 191 of the sixth and fourth, bass doubled, 24, 80 of the sixth and fourth between Domi- nants, 91, 193 of the Subdominant seventh, 278 of the Tonic seventh, 278 Chromatic alteration, definition of, 6 Chromatic chords, 224 Chromatic passing notes, 132 Chromatic progression, 6 Chromatic scale, orthography of, 253 Chromatically altered notes, how indi- cated, 25 Compass, of voices, 22 for accompaniment, 37 Compound passing notes, 129 Compulsory resolution, 44 Consonance, definition of, 13 Contrary motion, definition of, 20 to avoid faulty parallels, 41 Counterpoint, definition of, 185 Deceptive cadence, 212 Deferred modulation, 203 Diatonic, definition of, 2 Diminished intervals, definition of, 9 Diminished seventh chord, 174 Diminished triad, 17 Directly related keys, 63 Discords, definition of, 43 Dissonance, definition of, 14 Dominant, definition of, 4 Dominant, of the Subdominant, 73 of the submediant, 275 of the supertonic, 220 Dominant added sixth chord, 271 Dominant ninth chord, 162 abbreviated, Rules I, II, III, 170, 171 best use of ninth, 165 inversions of, 164 ninth as embellishment, 166 ninth ornamentally resolved, 168 not used as penultimate chord, resolution of, 163 with augmented fifth. 239 Dominant seventh chord, 43 abbreviated. So as intensifying chord, 46 deferred resolution of, 259 determines tonality, 43, 75 exceptional resolution of the third, 68 exceptional resolution of the fifth, 32. 46 exceptional resolution of the seventh, 49, 243, 277 298 fifth omitted, 45 first inversion of, 48 fundamental position of, 45 irregular resolutions of, 258 ornamental resolution of the seventh, 258 resolution of the third in successive Dominants, 74 second inversion of, 48, 81 successive Dominants, 74, 90 table of resolutions of, 45 third inversion of, 50 third and seventh not doubled, 44 third omitted, 68 with augmented fifth, 239 with depressed fifth, 224 Dominant substituted sixth chord, 264 with seventh included, 266 Doubling, definition of, 19 in five-part harmony, 295 of the bass, 24 of the leading tone, 46 of a note dissonant with its fundamental, 44 of the seventh, 46, 80, 295 of the third, 19, 45, 83 Embellishments, definition of, 103 applied to arpeggio notes, 250 double and triple, 156 list of, 103 on accented or unaccented part of bar, 124 symbol of, 103 Enharmonic change, definition of, 54 Exceptional resolution, of the Dominant seventh, 49, 227, 243, 276 of the Dominant third, 68, 213, 216 Extended cadences, 199 with chromatic bass progressions, 276 Extended passing notes, 133 inverted, 257 Extraneous keys, 203 Extraneous modulation, 203 False relation, definition of, 153 when not objectionable, 153 Faulty doubling, of the bass, 24 of a note dissonant with its funda- mental, 44 of the third, 19 Faulty parallels, 40, 105, 129 Figured bass, 25 First inversions, 24 of triads, 24 of Dominant seventh chords, 48 Foreign keys, 207 French sixth chord, 225 resolution of, 225 Fundamental, definition of, 16, 29 most suitable for doubling, 19 nominal, So, 170 progressing upward a fourth, 73 real, So, 170 Fundamental position of chords, 24 Germ set, definition of, 132 for melody with accompaniment, 158 German sixth chord, 228 Harmonic modulation, 53 Rule I, Tonic for new Dominant, 54 Rule II, Supertonic for newDominant,56 Rule III, mediant for new Dominant, 57 Rule IV, Subdominant for new Domi- nant, 59 Rule V, submediant for new Dominant, 60 Rule VI, subtonic for new Dominant, 60 Harmonization of melodies, Rule I, 66 Rule II, first of the scale repeated, 69 Rule III, fourth of the scale followed by the third, 69 Rule IV, fifth of the scale, 70 Rule V, primary note followed by an- other a fourth higher, 73 Rule VI, second of the scale with sec- ondary Subdominant chords, 86 additional rules, 165, 175, 219, 242 by three primary chords, 66 Dominant not to be followed by Sub- dominant, 80 employing inversions, with diatonic bass passages, 77 initial, final, and penultimate chords in fundamental position, 80 Imitation, definition of, 186 in two voices, 187 in three voices, 247 over given fundamentals, 245 Immediate modulation, 203 Incomplete cadence, 191 Indirectly related keys, 204 Intervals, definition of, 7 augmented, 10, 76 computed upward, 7 consonant, 13 diminished, 9 dissonant, 14 general name of, 7 greater than the octave, 7 inversion of, 12 major, 7 minor, 9 perfect, 7 specific name of, 7 Inversion of chords, 24 Irregular resolution of the Dominant seventh chord, 258 Keys, directly related, 63, 65 extraneous, 203 INDEX 299 foreign, 207 indirectly related, 204 Leading tone, definition of, 5 Major diatonic scales, 2 Major intervals, 7 Major triad, 16 Mediant, definition of, 4 Mediant seventh chord, 271 Melodic modulation, 59, 93 six rules, 94-99 additional rule, 173 Melody over indicated bass, 31, 180 Minor scale, definition of, 3 harmonic, 126 melodic, 126 normal, 4, 126 relative, 3 Tonic, 4 Minor triad, 16 Modern augmented sixth chord, 229 Modulation, definition of, 53 deferred, 203 extraneous, 203 harmonic, 53, 63 immediate, 203 passing, 73,88, 175, 275 serial, 53-62 Modulation scheme for chorals, 223 Motion, contrary, 20 contrary, to avoid faulty parallels, 41 oblique, 20 similar, 20 Motus, definition of, 132 Neapolitan sixth chord, 234 Nominal fundamental, 80, 170 Normal minor scale, 4, 126 Notes, definition of, i auxiliary, 136 changing, j 52 common to two chords, 20 passing, 123 primary, 5 secondary, 5 suitable for doubling, 19 Oblique motion, 20 Open (or dispersed) position, 28 Optional resolution, 45 Organ point, 290 Ornamental anticipation, 254 Ornamental resolution, of the ninth, 168 of the seventh, 258 of suspensions, 255 Parallel fifths and octaves, 40 as used by modern composers, 41 progressing by skip, 40 Passing cadence, 198 Passing modulation, 73, 88, 175, 219, 275 Passing notes, definition of, 123 chromatic, 132 compound, 129 extended, 133 repeated, 130 successive, 124 Pedal point, 290 double, 292 inverted, 290 Phrygian cadence, 262 Plagal cadence, 194 Primary notes, 5 Progression, chromatic, 6 faulty, 40, 105, 129 Progression of voices, 19 by augmented interval, 76 by degree, 19 by skip, 19 chromatic, 19 Real fundamental, So, 170 Real sequence, 287 Relative minor scale, 3 Resolution, definition of, 44 compulsory, 44 of Dominant added sixth chord to Tonic, 271 of Dominant added sixth chord to Tonic added sixth chord, 271 of Dominant chords to Tonic substituted sixth chord, 21 1 of Dominant chords to Tonic added sixth chord, 216 of Dominant fifth, 45, 46, 162, 171, 172 of Dominant seventh, 49, 227, 239, 243, -77 of Dominant third, 44, 68, 213, 216 of Dominant third in successive Dom- inants, 74 optional, 45 Scale, definition of, 2 harmpnic minor, 126 major diatonic, 2 melodic minor, 126 minor, for use with Tonic, Subdominant, and Dominant chords, 128 normal minor, 4, 126 relative minor, 3 rule for formation of signatures, 5 technical names of scale members, 4 Tonic minor, 4 Second inversion of triads, 26 Secondary chords, on the Dominant, 264 on the Subdominant, 83 on the Tonic, 21 1 Secondary notes. 5 Sensitive tones, 44 Sequences, definition of, 287 real, 287 300 CUMULATIVE HARMONY tonal, 287 rules for tonal, 287 Serial modulations, 53 Signatures, 5 Similar motion, 20 Step and half step, definition of, I Subdominant, definition of, 4 Subdominant added sixth chord, 84 Subdominant ninth chord, 282 Subdominant seventh chord, 278 Subdominant substituted sixth chord, 83 Subject for imitation, 185 Submediant, definition of, 4 Submediant seventh chord, 216 Submediant triad, 211 Substituted sixth chord, on the Dominant, 264 on the Subdominant, 83 on the Tonic, 21 1 Subtonic, definition of, 5 Subtonic triad (abbreviated Dominant), 80 Successive Dominants, 74, 90 Supertonic, definition of, 4 Supertonic seventh chord, 84 Supertonic triad, 83 Suspensions, definition of, 103 double, 1 13 of chords, 120 on accented part of bar, 105 ornamentally resolved, 255 prepared, sustained, resolved, 103 resolution not doubled, 105 Rules I, II, III, IV, 106-110 Table of chords included in the three pri- mary families, 282 Tierce de Picardie, 195 Tonal sequence, definition of, 287 rules for, 287 Tones common to two chords, 20 Tonic added sixth chord, 216 Tonic minor scale, 4 Tonic ninth chord, 282 Tonic seventh chord, 278 Tonic substituted sixth chord, 211 Transition, definition of, 209 Transposition, definition of, 21 Triad, definition of, 16 augmented, 17 diminished, 17 major, 16 minor, 16 Voices, change of position of, 33 compass of, 22 difference in altitude of, 22 names of, 19 not to be overlapped, 80 progression of, 19 progression by augmented intervals to be avoided, 76 ANNOUNCEMENTS MUSICAL ART SERIES Under the editorial supervision of RALPH L. BALDWIN, Supervisor of School Music, Hartford, Conn., and E. W. NEWTON THE MUSICAL ART SERIES is unique in school music. It offers authoritative versions of standard, appealing music of every class, in a form at once convenient, economical, practical, and artistic. The teacher is now enabled to select for his classes just the sort of songs that he wants, without putting into their hands a comparatively bulky and expensive songbook which contains much that he does not want. The smaller books of the series are uniform in size, binding, and price. They are so arranged that they may be used with either a four-part or three-part chorus without loss of harmonic content. Christmas Carols Standard College Songs Familiar Operatic Classics Standard Familiar Songs Familiar Song Classics Standard Folk Songs Fifty Standard Hymns Standard Patriotic Songs Songs of Peace and Patriotism Standard Popular Songs Each volume 4to, paper, 32 pages, 10 cents STANDARD SONG CLASSICS 4to, cloth, 176 pages, 60 cents FORTY-ONE selections, none of which is commonly found in collections for high-school use. Each selection, however, is a masterpiece which every high-school pupil ought to know. Together they offer great variety in every phase of mood, form, verse, and music. We can now furnish orchestrations for any of the selections in this book. i?ob THE STUDENTS' HYMNAL Edited by CHARLES H. LEVERMORE, Recently President of Adelphi College Brooklyn, N.Y. 8vo, cloth, 218 pages, 50 cents ^ I ^HE two hundred and fifty hymns admitted to this collec- tion have been carefully chosen for the dignity, strength, and musical beaut}' of their tunes and the depth of feeling and poetic merit of their words. Here are the best hymns of the Wesleys, Isaac Watts, Reginald Heber, and James Montgomery, Caswall's and Neale's translations of historic medieval hymns, and, of the later writers, the work of Frederick W. Faber, Horatius Bonar, Washington Gladden, and Phillips Brooks, of Frederick L. Hosmer, John G. Whittier, Oliver \Vendell Holmes, and Samuel Longfellow. The collection is rich in morning and evening songs, in pro- cessional music, and in hymns appropriate to the festivals of the Christian year. The music throughout has been arranged with reference to the needs of the average singing voice. The Hymnal includes also selections of Scripture readings, drawn from the Established, the Revised, and the Douay ver- sions, comprising those passages .especially marked by poetic form and majesty of thought. i8oa GINN AND COMPANY PUBLISHERS MT-. UNIVERSITY OF CALIFORNIA LIBRARY Los Angeles This book is DUE on the last date stamped below. JULO 1963)^ Sfeml-Ann. loan /HQV-ir&HKl -OELA ? fltfi/^- ^*M^p^^ ) RtC U WUS-bll m M J/L NOV23 19* 1 B n r ' % SEP S 1967 fiflTD MUS-L w?m M/lVffJ^ft m^ 7 2 '"n / n li ftflMj ^ / Q/5f Jj^f^ jy* -^ Form L9-rt6m-8,'62(D1237s8)444