MODULATION 
 
 AND 
 
 LATED HARMONIC QUESTIONS 
 
 ARTHUR FOOTE 
 
 difornia 
 
 ional 
 
 ility
 
 MODULATION 
 
 AND RELATED HARMONIC 
 QUESTIONS 
 
 THE ARTHUR P. SCHMIDT CO., 
 
 BOSTON NEW YORK 
 
 120 BOYLSTON STREET 8 WEST 40TH STREET 
 
 Copyright, 1919, by THI AUTHOR P. SCHMIDT Co. 
 International Copyright Secured
 
 Jht fttruumt of 
 JOHN KNOWLES PAINE
 
 PKEFACE 
 
 THE author has endeavored to set forth a statement of the various 
 means of modulation found in music from Bach to the present time; such 
 problems as are offered by certain composers of the past few years, however, 
 have not been dealt with, for in their works tonality is of set purpose made 
 increasingly negligible, the question of modulation per se (as it has always 
 been conceived) not being of importance. Illustrations from composers of 
 all periods show the practical application of principles. 
 
 Harmonic questions are discussed at length in so far as they are con- 
 cerned with the matter in hand, not having been entered into purely for 
 their own sake; in the first chapter detailed explanation is also given of 
 some fundamental, though often imperfectly understood, points with regard 
 to scales and key-relationship (since comprehension of and ability in modu- 
 lation presuppose thorough knowledge with regard to these matters). Chap- 
 ters X and XI touch directly but little upon real modulation, though cover- 
 ing subjects that are extremely important as aids thereto. 
 
 Exercises, to be both written, and played at sight, are added to the 
 
 fi+ 6+ 
 
 chapters on V 7 , vii 07 , and 6+, " ' and 4+, while a collection of modulations 
 
 3 
 
 made from a given major and minor key to all others will be found at the end 
 of the book; in these it has been intended to avoid the purely mechanical, 
 however correct it might be, and to offer only such productions as are rea- 
 sonably musical. 
 
 BROOKLINE, MASSACHUSETTS, May, 1918.
 
 CONTENTS 
 
 CHAPTER PAOB 
 
 I. Scales and key-relationship The different forms of the minor 
 
 scale Circle of 5ths 1 
 
 II. Modulation in general Transient modulation Progressions 
 
 that are not properly to be considered as real modulations ... 7 
 
 III. Change of keys or chords without modulation Third-relationship 11 
 
 IV. Change of key by moving to a new tonic a 3d above or below A 
 
 table of such changes 15 
 
 V. Modulation (continued). Diatonic, chromatic and enharmonic 
 Modulation without any chromatic alterations of notes Bridge 
 chords Misunderstandings 'through chromatic alterations ... 19 
 VI. Modulation by means of V and V 7 Fifth-relationship (leading- 
 tone) Modal ending Successions of dominant 7ths and of 
 other 7th chords Chromatic alteration of various notes of V 7 
 Modulation to the dominant of the dominant, and to the sub- 
 dominant of th " sub-dominant Exercises 22 
 
 VII. Modulation by means of the diminished 7th chord This an am- 
 biguous one Very large range for possible modulation Ex- 
 ercises 41 
 
 VIII. Modulations introduced by chromatic alterations in the 3ds or 5ths 
 
 of triads 54 
 
 IX. Modulations made or introduced by chords of the augmented sixth 
 
 6+ 6+ > 6+ 
 (6+, c , 4+ 4++). Various derivations of these chords Prob- 
 
 3 3 
 
 able derivation in many cases Their resolutions Identity 
 
 fv4~ 
 
 in sound of r and V 7 Neapolitan 6th Exercises 55 
 
 X. Harmonic changes (sometimes with modulation), resulting from the 
 symmetrical movement of individual voices, chiefly by steps and 
 
 half-steps 67 
 
 XI. Harmonic changes resulting from the elision of chords 75 
 
 XII. A table of modulations 79 
 
 Index .... 99
 
 MODULATION 
 
 CHAPTER I 
 
 SCALES AND KEY RELATIONSHIP 
 
 1. Without an exact and thorough knowledge of scales and of key 
 relationship it is impossible to understand modulation. 
 
 The major scale, being unvarying in all keys as to steps and half-steps, 
 offers no difficulty (4, the Circle of Fifths). The different forms of the 
 minor scale, however, often produce misunderstanding; without going into 
 the question as to how and when these variations came to exist, the follow- 
 ing shows the facts as they are today. 
 
 I 
 
 2. (a) and (d) correspond with the ^Eolian mode (thus being a survival 
 from the old modal scheme, in which there was neither leading-tone, key 
 relationship nor modulation). The introduction of the leading-tone resulted 
 in (6) and (e), while the smoother and more singable form of (c) arose 
 through the raising of the 6th degree a half step, the descending scale (/) 
 corresponding to (c) being also used freely at one time, (a) and (d), though 
 without the distinctive character of a minor scale which is furnished by the 
 leading-tone, being indeed identical with the scale of C starting with the 
 note a (note below), are much used melodically and in scale passages; in 
 such cases the key will probably be defined by the underlying chords (either 
 expressed or inferred). 
 
 NOTE. Large capital letters indicate major keys and scales, small letters in 
 italics being used for minor ones, while small letters not in italics mean individual notes 
 (e.g. C, a, b). Large figures indicate major triads and other chords having a major 
 3d (IV, V 7 ), small figures meaning chords with a minor 3d (n 7 , vn 7 ), and the dimin- 
 ished 7th chord being marked vii 07 ; the usual figured bass indications are used, aug- 
 mented intervals being marked by a + /* + \ and doubly augmented ones by ++ 
 6+ \ ^ 5 ' 
 
 / A. P. 8. 11864
 
 2 MODULATION 
 
 The scales (6) and (e) leave us in no doubt as to the key, nor do they need 
 for that any assistance from chords; (c), as an easy and singable form, is 
 more used than (6), while also leaving no doubt as to the tonality, but the 
 descending form (/) is almost obsolete, though in common use at the Bach- 
 Handel period, (c) and (d) combined result in the so-called melodic scale, 
 (6) and (e) the harmonic. 
 
 3. As an example of the way in which (c) and (e) may occur in the 
 same passage as well as of the employment of (6) the following extract 
 from Haydn's Rondo all' Ongarese will serve. 
 
 =Ffc=*==* 
 
 S 
 
 5 
 
 : 
 
 r- 
 
 In the Bach Chromatic Fantasie there is an excellent illustration of various ways 
 in which the minor scale appears, the descending scale (/) being shown at the end.
 
 MODULATION 
 
 m^ 
 
 -?-+- 
 
 In the following (Schumann: Paganini Caprice, No. 1), we have a curious example. 
 3. 
 
 -f-9- 
 
 f0- 
 
 f(fr> 
 
 P-S- 
 
 In the next illustrations different forms of the minor scale are used simultane- 
 ously, (1) being taken in a harmonic sense and (2) melodically. 
 
 BACH: "Well Tempered Clavichord," Prelude and Fugue, No. 4 
 
 
 "^ L i C i L 
 
 0) 
 
 (2) 
 
 i 
 
 (1) 
 
 ^ 

 
 MODULATION 
 
 4. Inasmuch as the leading-tone is our main factor in modulation, as 
 well as for determining keys and their relationship, the Circle of Fifths of 
 major keys is of great use; e.g. by introducing f#, the leading-tone of G, 
 we can begin a modulation to that key from C (G being the 5th above C 
 and the first ascending 5th shown in the circle below) ; this process of rising 
 by 5ths can be carried through until the complete circle is made, C being 
 reached again at the termination. 
 
 .. J J ,- 
 
 ' * eJ . 
 
 
 
 JS2. 
 
 A 
 
 ^z 
 
 i
 
 MODULATION 
 
 
 In the following are given instances of how scales actually occur; time 
 will be well spent that is taken for finding their keys: (e.g. in the first one 
 we have d# and a#, but not e#, i.e. either the key of B or g%, deciding that 
 the key is B and not g%, because there is an f# and not an f x ). As will be 
 seen later, confusion may result from chromatically changed non-harmonic 
 notes, especially in figuration and passage work (19), in which case it is 
 necessary to disentangle the harmonic notes and to construct the scale 
 from them, it being often also the case that there is a chord to help as an 
 indication. In what keys are the following scales ? 
 
 =f
 
 MODULATION 
 
 6. It will be worth while to ascertain in what keys each of the follow- 
 ing chords can be found, remembering that while, e.g. the triad c-e-g is found 
 in the keys of C, e, F, f and G, (in other words in five different keys), the 
 V 7 g-b-d-f can belong to but two, while the dominant 9th points definitely 
 to one key. The following chords are grouped according to the number of 
 possible keys in which they may be found (the harmonic form of the minor 
 scale being the only one considered). 
 
 6 keys 
 
 4 keys
 
 MODULATION 
 
 CHAPTER II 
 
 MODULATION IN GENERAL 
 
 7. This term means that a progression of some kind is made from one 
 key to another by means of certain devices; it is decisive and final only if 
 fixing the new tonality to such a degree that leaving the new key would 
 necessitate another distinct modulation. 
 
 8. As will be seen later (Chapter V, seq.), there are various means em- 
 ployed in the production of a clearcut modulation (e.g. a cadence with V 7 ). 
 Theorists formerly held that every change of key brought about in such a 
 way was to be considered a modulation, without regard to the length of the 
 progression, and whatever its effect. A broader view is this, that one 
 which is confirmed by a stay in the new key for a satisfactory length of time 
 is to be regarded as definite and conclusive (e.g. No. 43), but in cases such 
 as those shown in Nos. 8, 33, while the modulation may be made in the same 
 manner as is the case with the former, changes of key succeed each other 
 so rapidly as to justify a different classification, these being appropriately 
 termed Transient Modulations. The presence of V 7 presumably indicates 
 a definite key in most instances, but (a) its resolution may not be the chord 
 expected but into another key, or (6) the V 7 may be an apparent one, e.g. 
 really a supertonic 7th chord with an altered 3d, as in the following, in 
 which latter case there is no modulation. 
 
 The resolution o/ such a chord will settle the matter. 
 
 A passage of sequential character has thereby a strong feeling of modu- 
 lation (No. 7). 
 
 On the other hand, there is a kind of progression in which chromatic 
 and enharmonic alterations result in passing chords foreign to the main key, 
 which should be regarded purely as such, but not as causing changes of key. 
 In Benjamin Cutter's Harmonic Analysis will be found an excellent state- 
 ment of this point of view : "There is ground for belief that from the time of
 
 s 
 
 MODULATION 
 
 Haydn, perhaps from that of Bach, composers have thought it possible to 
 raise and to lower certain scale steps, and to obtain thus non-modulating 
 chromatic harmonies which sound like modulations but do not leave the 
 key. In a piece in C major, for instance, we may find the dominant or 
 diminished seventh of d minor, with its resolution, and this followed by C 
 major chords ... A real modulation is made only when the modulatory 
 process is confirmed by a stay in its evident key; these seeming modulations 
 are only intensifications of triads of the key other than the primary tonic, 
 generally the subordinate triads, accomplished by use of their seventh 
 chords; and these chords or progressions in question are only altered chords, 
 or progressions in the primary key." " In other words, judge a chord by 
 what it does." (36.) 
 
 In the following passage the chords marked x do not at all affect the 
 main key, although some theorists might wrongly explain them in the 
 manner indicated below. 
 
 GRIEG: Ballade, Op. 24 
 X 
 
 C: c: 
 
 r~ i n ' 
 
 ~3 U ~~* 
 
 J J J 1 
 
 ] i ; i 
 
 1 ~i 11 
 
 " ^ 
 
 
 y=h=^ 
 
 *- ba 
 
 1 I s fat* 
 
 ^ ^ #J fl 
 
 i 
 j j 
 
 
 G: F: 6 + 
 4+ 
 3 
 
 F: 
 
 
 Among the illustrative excerpts quoted later from various composers, 
 there are many of transient modulation, as well as of successions of chords 
 which do not constitute real modulation, tonality not being fixed by them 
 (e.g. No. 77). Nos. 7 and 8 are to be considered as transient modulations; 
 while in No. 9 there is simply a succession of V 7 , that causes a rapidly shifting 
 series of harmonies which carry us from C to Ab (25), the result of such a 
 series being always an inevitable modulation which is finally effected by 
 the last V 7 .
 
 MODULATION 
 
 7. 
 
 i 
 
 BEETHOVEN: Sonata, Op. 14, No. 2 
 
 -P-^ 
 
 i 
 
 ^ 
 
 C: 
 
 d: 
 
 -S \ . \ 
 
 
 -V ! 5 1 
 
 H 
 
 1 r 1 
 _ j . 
 
 
 *^- F 1 
 
 ^E * 
 
 f* - 1 EE =3 - 
 
 Observe that the fleeting changes are in this one succeeded by a definite final 
 modulation. 
 
 8. 
 
 CHOPIN: Nocturne, Op. 9, No. 1 
 
 /: V 
 
 9. 
 
 ftfrsTn 1 
 
 CHADWICK: .Sohi-rzino 
 h
 
 10 
 
 MODULATION 
 
 tefe '''i j h- ^ J JiJ =^=3 
 
 -r E-^ 
 
 1:1 
 
 1 1 
 
 v 
 
 V 7 
 
 9. Since some chromatically altered chords are deceptive, seeming, how- 
 ever, at first sight to denote a change of key, care must be taken to dis- 
 tinguish them from such as really produce modulation; they frequently 
 take the form of an apparent V 7 , vn 7 , or vn 7 , in a new key. 
 
 PT rn 
 
 &- 
 
 ^^ 
 
 ^^4=^- 
 
 1 
 
 ^^ i l^Cr "|| 
 
 10. The act of modulation implies a progression, which nearly always 
 shows alteration of some note or notes belonging to the key which is being 
 left (though not invariably, e.g.) ; 
 
 
 
 
 i 
 
 
 
 I 
 
 rr 
 
 i i
 
 MODULATION 
 
 11 
 
 and, on the other hand, it must not be inferred that simply going from the 
 tonic of one key to that of another (even though some note or notes may 
 be chromatically changed in the process), comes under that head. The 
 term does not include this. Modulation may be compared to crossing from 
 one side of a street to the other, to accomplish which the space between 
 must be traversed. 
 
 CHAPTER III 
 
 CHANGE OF KEYS (OR CHORDS) WITHOUT MODULATION. THIRD- 
 RELATIONSHIP 
 
 11. Having briefly touched upon the general subject of modulation, 
 it is well to take up the point referred to in 10, before going further. In 
 substance the matter may be summed up as follows : 
 
 A mere succession of keys, especially when the chords are mainly triads 
 or their inversions, does not of itself constitute modulation. It is sometimes 
 hard to draw the line, but a few illustrations will demonstrate this point. 
 
 SCHUMANN: Concerto
 
 12 
 
 MODULATION 
 
 11. 
 
 WAONER: "Parsifal 1 
 
 IEE= 
 
 r^ i- 
 
 - ^ i ^ ^ ^ ^ i 
 -- +-^j * ^ * *_k 
 
 
 
 5^i 1 ,9 K 1 0-f-J 
 
 
 r~v * j i* 
 
 "-^^ . 
 
 i ^ 
 
 p ; 
 
 r * T n\I V 
 
 M . 
 
 
 
 d^' <* - 
 
 
 ^^_L,^I = ^ = * t. 
 
 1 
 
 At,: 
 
 12. In the preceding there are examples of third-relationship, which is 
 almost as strong as that by fifths. We find that the familiar statement as 
 to keys nearest related to a tonic major or minor shows this point conclu- 
 sively; e.g. besides G (the 5th above) and F (the 5th below) we have, as 
 nearly related to C, a (the 3d below C), e (the 3d below G), and d (the 
 3d below F) ; as nearest related to a, besides E and e (the 5th above) and 
 d (the 5th below), we have C (the 3d above a), G (the 3d above e) and F 
 (the 3d above d).
 
 MODULATION 
 
 13 
 
 Of these illustrations there are in the one from Schumann's Concerto 
 the keys of C, e and G, and in that from "Parsifal" those of Ab, Cb and D 
 ( =E bb),the change being by thirds. This same principle of inter-relation- 
 ship by 3ds has also been sometimes carried out in the choice of keys for 
 symphonic movements; e.g., in Raff's "Lenore" symphony, in which the 
 keys are E, Ab (G#), C and e. 
 
 This matter of change of key and of simple successions of chords without 
 modulation comes up for further discussion in Chapters X and XL 
 
 DEBUSSY: Nocturne
 
 14 
 
 MODULATION 
 
 8va 
 
 r J u j=* r r I JLJP ? t 
 
 In this last illustration there are simple changes of keys (or rather of chords), 
 except that at measures 4-5 there is a progression in which the voices move about 
 by steps and half steps (36), in such a way as to make what may be fairly con- 
 sidered a modulation, while at measure 8 there is a decided one brought about by 
 
 VII 07 . 
 
 13. Change of key may occur by means of so-called "pivot" notes; i.e. 
 notes common to two chords, the change taking place at the appearance of 
 the second chord.
 
 MODULATION 
 
 15 
 
 SCHUBERT: Fantaaie Sonata, Op. 78 
 
 
 CHADWICK : Pianoforte Quintet 
 
 
 In No. 15 compare the succession of chords (Bb, feb, Dt>) with examples given 
 later (38), in which there are elisions of certain factors; in this illustration from 
 Chadwick a result like that in No. 77 would be obtained by omitting the chord of 
 6b. Both methods give valuable and fresh ways of working outside of the conven- 
 tional system. 
 
 CHAPTER IV 
 
 CHANGE OF KEY BY MOVING TO A NEW TONIC A 3D ABOVE OR BELOW 
 
 14. This, while coining under the same general head as that covered by 
 Chapter III, is of sufficient importance to warrant separate discussion, 
 which is best introduced by a consideration of the following table based 
 on relationship by thirds.
 
 16 
 
 MODULATION 
 
 
 8. 
 
 10. 
 
 11. 
 
 12. 
 
 g 
 
 II TT FT " 
 
 j J. j J. bj -gi i>J 
 
 i^=ti^ 
 
 &" tr& > p'- 
 
 J- bJ 
 
 
 ^2- 
 
 Some of these (Nos. 1, 2, 5, 7, 8, 11), are entirely commonplace, but the 
 others, in varying degree, are striking in their effect. Illustrations of No. 3 
 are given in examples 16 and 17; in Nos. 3, 4, 6, 9, 10 and 12 there are 
 elisions of chords; i.e. in No. 3 we jump from C to Ab (eliding c), in No. 4 
 from C to ab (eliding c and Ab), in No. 6 from c to ab (eliding Ab), in No. 9 
 from C to Eb (eliding c), in No. 10 from C to eb (eliding c and Eb) and in 
 No. 12 from c to eb (eliding Eb). Nos. 4, 6, 10 and 12 are of comparatively 
 recent development (38). 
 
 BRAHMS: Rhapsodie, Op. 79 
 
 t 
 
 f
 
 17. 
 
 MODULATION 17 
 
 MOZART: Fantasia and Sonata in c 
 
 
 N Pv 
 
 ^? 
 
 I 
 
 Ftf 
 
 18. 
 
 BRAHMS: Symphony in C minor 
 
 H 
 
 fct* 
 
 i bU- 
 
 -X ft 
 
 m 
 
 
 -gL' -? ? -$? 
 
 <*:? 
 
 XXX XXX 
 
 xx x 
 
 F: 
 
 19. 
 
 LISZT: " Les Preludes ' 
 
 -ft- 
 
 1^ 
 
 T * , s, m i-MH-i 
 
 
 
 
 ^ 
 
 ;', -
 
 18 
 
 MODULATION 
 
 JnJlJ J 
 
 PI iH jlj 
 
 jji FT"* j m 
 
 -g-gj^-^- H -^- -g- -^- H -a- 
 y y 
 
 q q 
 
 i F r 
 
 ^^ 
 
 VofC: 
 
 d-*Oj 
 
 7 - 
 
 ^.-. 
 
 -W5>- 
 
 -* 5 
 
 ^ 
 
 w^l 
 
 ^S: 
 
 
 
 
 :f=it 
 
 V of El.
 
 CHOPIN: Etude, 3 Etudes, No. 2 
 
 CHAPTER V 
 MODULATION (continued) 
 
 15. A modulation is nearly always effected by the introduction of one 
 or more notes foreign to the key which is being left but belonging to that 
 towards which the progression is made; the number of chords, and of note- 
 alterations through accidentals (when the latter are necessary) varying 
 greatly, e.g. a modulation from C to G, F, or a, requiring few chords and 
 but one accidental, while that from C to 6[? should be more gradual. In 
 writing or playing it is desirable that the first key shall be clearly established ; 
 in the following, e.g. the first chord does not do this strongly, sounding 
 almost like IV of G, 
 
 
 rf^g 
 
 -rr 
 
 -& 
 
 g 
 
 while 
 
 ^asf 
 
 II 
 
 
 J. 
 
 is satisfactory. 
 
 16. Modulations may be classified as Diatonic, Chromatic and Enhar- 
 monic; of these the first is the most frequent (in the older music even more 
 so than in that of to-day), while there has been much development of late 
 years in the enharmonic variety, which now possesses greater freshness and 
 Interest than do the other two. 
 
 In the following examples it will be seen that with the diatonic modula- 
 tion of (a) the notes b and a affected by accidentals are in each case in the 
 scale of the new key, and in the chromatic one (6) the accidental f# (not 
 being in the scale of either key) results in a chromatically altered chord, 
 while in (c) the first chord (x) is enharmonically changed at measure 2.
 
 20 
 
 MODULATION 
 
 J 
 
 BEETHOVEN. Sonata, Op. 7 
 
 J -^ . : ?>- 
 
 BEETHOVEN: Sonata, Op. 31, No. 3
 
 MODULATION 
 
 21 
 
 17. While some alteration of notes is usually found in diatonic modula- 
 tion, that being generally brought about, at least in part, by a change of 
 leading-tone, it is possible to modulate satisfactorily without this means, 
 the result being accomplished by the aid of chords common to both keys, 
 which may for convenience be called Bridge Chords. In the first example 
 given in 10, e.g. the third chord, being an inversion of the second triad of 
 C and of the fourth triad of a, and thus common to both keys, serves as a 
 bridge by which we can pass from one key to the other, while the feeling of 
 the key of a is so clearly emphasized by what follows that the leading-tone 
 is not needed to secure a clear modulation. This method is not so common 
 as e.g. that of having V or V 7 of the new key mark a definite close, but proves 
 an attractive and often useful alternative. 
 
 18. In enharmonic modulations there are chromatic alterations of notes 
 made in such a way as to secure changes of key that are always interesting 
 and often surprising; the device is piquant and subtle, affording oppor- 
 tunity for originality of treatment. Parry defines it as "the translation of 
 intervals which according to the fixed distribution of notes in the modern 
 system" (e.g. on the piano keyboard) "are identical, into terms which rep- 
 resent different harmonic relations." Here is a typical illustration, in 
 
 /> i 
 
 which use is made of the similarity hi sound of V 7 and ^ . 
 
 19. While in the majority of cases the key will be evident, especially 
 where V 7 is a factor, passages often occur where there is possible misunder- 
 standing, on account of the number and kind of chromatic alterations; we 
 must then disentangle notes belonging to the key from those foreign to it. 
 Examples will illustrate this, notes not belonging to the key being marked 
 with x. 
 
 24. 
 
 BACH: Well Tempered Clavichord, Fugue XII 
 
 
 ^^ - - - 
 
 ^K 
 
 1 
 
 BrU' 
 
 
 
 r'r 
 
 tf^rn 
 
 , 1 
 
 r^ 1 ^ j
 
 22 
 
 MODULATION 
 
 
 
 nn 
 
 I 
 
 HN>^- 
 
 -* 
 
 f>\ 
 
 
 CHOPIN, Op. 10, No. 6 
 
 
 In the second of these the et} in measure 1 is so written for convenience, 
 being the enharmonic of fb; in measure 2 gjj is harmonic, but not so in 
 measure 3. 
 
 CHAPTER VI 
 
 MODULATION BY MEANS OP V OR V 7 
 
 20. This, the plainest and most common form of modulation, is especially 
 used when strength and decision are desired rather than subtlety or fresh- 
 ness. In the modulatory scheme ascending by fifths, when the progression 
 is from one major key to the next (C-G, Gb-Db), or from one minor key to
 
 MODULATION 
 
 23 
 
 the next (a-e, eb-&b), the beginning is usually made through the entrance of 
 a new leading-tone, that being indicated by an accidental (#, * or t}) ; this 
 means is also used when a progression occurs from a major key to a minor 
 one (C-a, B-g%, Gb-eb), there being also other accidentals present in some 
 cases (e.g. C-g). In modulating from a minor key to a major one it is gener- 
 ally the case that the leading-tone of the former will, as the first step, be 
 cancelled by a tj, #, or b (a-C, </#-B, eb-Gb). While an authentic cadence 
 in the new key forms the strongest ending in all these cases, it will be ob- 
 
 /> 
 
 served in (a), (6) and (c) of the following examples that there is no 4, V or 
 V 7 , the modulation not thereby losing in definiteness. 
 
 (Leading-tones in parentheses.) 
 
 a: e: (d#) 
 
 ^ 
 
 
 Gb= eb: (d)})
 
 24 
 
 MODULATION 
 
 o: C: 
 
 B: 
 
 r 
 
 (a). 
 
 > t>4 \j- 
 
 r*rn 
 
 ^- <y fp 
 
 
 i 
 
 S 
 
 rfrrpf _ 
 
 i j j ft 
 
 i i i i 
 
 ^ 
 
 ,*5tKqc 
 
 2ii 
 
 ff 
 
 eb: 
 
 ,.( c > 
 
 3M 
 
 Jafcfc 
 
 rrrtrr 
 '^' 
 
 1 
 
 j 
 
 4 - 
 
 04. f 
 
 g.p p ^ qz 
 
 ^r-rr^ 
 
 21. When the modulation is downward by a 5th, into a key having 
 more flats or fewer sharps, the first step usually taken is to cancel the leading- 
 tone of the first key by a if, b, or #, at which moment another note will auto- 
 matically appear as the new leading-tone; e.g. in the first example following 
 (C-F), the leading-tone (b) of C is cancelled by bb, the e in the same chord 
 appearing as leading-tone of the new key, F. 
 
 *fc 
 
 II 
 
 5^ <g- 
 
 :J: 
 
 UlirJ J-J J 
 
 I 
 
 4 P 
 
 r^r 
 
 C: F: 
 
 ~r 
 
 *-& 
 
 i '*
 
 MODULATION 
 
 25 
 
 22. While the actual process of modulation can be completed by means 
 
 / 6+ 6+ 
 of diminished 7th chords, augmented chords of the 6th 1 6+, K , 
 
 4+ ) , 
 3/ 
 
 etc.. 
 
 without the aid of V, V 7 or I*, these latter are often useful as additions in 
 such cases if it is desired to strengthen the progression, even though the 
 latter be already effected. 
 
 As has been pointed out (10), it is also possible to modulate without 
 any of the above factors, and even without the employment of accidentals. 
 
 23. In the case of minor keys a beautiful result can be obtained by a 
 modal ending (e.g. v-i), inasmuch as one form of the minor scale is identical 
 with the ^Eolian mode (2). 
 
 ?5; 
 
 *T 
 
 ^-^^ 
 
 I 
 
 26. 
 
 Song, " Hame, hame, hame ! " (From " Seventy Scottish songs,' 
 edited by HELEN HOPEKIRK.) 
 
 28 en
 
 26 
 
 MODULATION 
 
 Here is another interesting ending without | or V, and, in character, like the 
 preceding. 
 
 27. 
 
 ELGAR: ' 
 
 ' Coronation Ode " 
 
 L/ I/ 
 
 k S 
 
 1 ll 
 
 rfn f7 h/ * 
 
 P ' 
 
 m & 
 
 (Cl) 4 
 
 J- f * 
 
 H 
 
 C/ 
 
 I 
 
 t 
 
 > * i 
 
 ^ I/ 1 
 
 | -J- ^ - 
 
 I 
 
 ^~)~* t? / t 
 
 
 ~ ~ H 
 
 -^ h h\ / < 
 
 i _ 
 
 
 24. ii 7 , vii 7 and vn 7 are interesting factors as adjuncts to modulations 
 by V or V, sometimes, indeed, also forming the sole means for concluding 
 a progression, as in (a) and (6). 
 
 & 
 
 g-lsL-kJ:fe 
 
 g 
 
 T-^T 
 
 m 
 
 ^^r 
 
 r-^r 
 
 ^^- 
 
 f=f 
 
 1 
 
 (a) 
 
 r 
 
 i 
 
 H
 
 MODULATION 
 
 27 
 
 26. Two well-known chord-successions consist of a series of dominant 
 7ths (or inversions), and of a series of secondary 7ths, the device, how- 
 ever, being one that must not be carried out at too great length, as it easily 
 becomes tedious. For purposes of modulation the availability of the sec- 
 ond series lies in the fact that at any point a chord can be altered by an 
 accidental, the resulting 7th chord consequently being in a new key; with 
 the dominant seventh series it is obvious that a new key can be chosen at 
 any point in the progression.
 
 28 
 
 MODULATION 
 
 ^fc 
 
 ^ 
 
 5=^ 
 
 i 
 
 I s IN etc - 
 
 V 
 
 t 
 
 M^Hi 
 
 i 
 
 m-r 
 
 f= 
 
 / 
 
 9^8 
 
 9+- 
 
 H 
 
 Chopin avails himself of this progression in the Etude op. 10, No. 1, measures 
 37-44. 
 
 Similar modulations through note-alterations could be made in No. 29. 
 
 29. 
 
 GRIEG: Gavotte, " Aus Holberg'a Zeit" 
 
 Jf ^ 
 
 irKy 
 
 2 
 
 * * & 
 ~r r r r~ 
 
 
 P i* P 
 
 SgZS 
 
 J 
 
 A 
 
 ^ F- 
 
 -4 F F i 
 
 L r F F f 3 
 
 ^r-4 1 1 
 
 1 4 
 
 ~\ f\* 1 
 
 fl).4 J g- 
 
 =r=-J J 4 1 
 
 -J 4 * S3 
 
 1 ! H^ 
 
 w 
 
 S^T r 
 
 Another point of interest and one useful in modulation is that the chord 
 V can not only be changed to vii 07 by raising the bottom note, 
 
 i 
 
 but can also resolve in the following ways: 
 
 V 7 vn 7
 
 MODULATION 
 
 29 
 
 
 p^p 
 
 I r 
 
 by simultaneously raising the bottom note and lowering any one of the other 
 three a half-step; the opportunities offered are obvious (37). 
 
 In the following illustrations (30-41) are seen typical ways of employing 
 V 7 for modulation. 
 
 30. 
 
 CLAYTON JOHNS: Canzone 
 
 tt 
 
 i{=5j: 
 
 j. j. 
 
 
 & 
 
 ^ 
 
 31. 
 
 TSCHAIKOWSKI: "October," Op. 37, No. 10
 
 30 
 
 MODULATION 
 
 32. 
 
 CHOPIN: Etude, Op. 10, No. 12 
 
 -
 
 MODULATION 31 
 
 WAGNER: "DieWalkure" 
 
 *-=*- 
 
 :r 
 
 
 , 9-0-- -0- -0- 
 
 ^MfTJ 
 
 1 
 
 8: 
 
 
 m 
 
 m 
 
 (HP 
 
 4^- 
 
 V 7 
 
 1 
 
 -^- -fK_ J_ _^_ 
 
 f|LJUL_|l^ 
 
 ^ 
 
 ^S 
 
 IT- 8f * 
 
 ^ 
 
 =: 
 
 v 
 
 36. 
 
 
 STOJOWSKI: Prelude, Op. 1, No. 2 
 
 ^^ 
 
 A 
 
 V 7
 
 32 
 
 MODULATION 
 
 36. 
 
 WAGNER: "Lohengrin" 
 
 ida^^tM^^ I]* .*| trfrW^fJTd 
 
 )>'!! fe&frfcP^EZ ^j^ [_^ ^f^f^ 
 
 F 
 
 u 
 
 1 
 
 n 
 
 37. 
 
 V 7 
 
 ROSSINI: " Stabat Mater ' 
 
 /r 
 
 ^4 g =f- 
 
 n 
 
 
 
 ri 
 
 tr 
 
 'V 7 
 
 gfc^ 
 
 38. 
 
 HENSCHEL: Song, "Resurrection" 
 
 V 7
 
 MODULATION 
 
 33 
 
 
 ^B 
 
 v 7 
 
 The preceding shows successive chords of V 7 , rising step by step; in the 
 right place, as here, an effective progression, as well as one often helpful in 
 modulation. 
 
 In the extract from Faur6 observe the voice-leading (36). 
 
 FAUBE: Impromptu, Op. 31 
 
 26. It is sometimes the case with the modulation by V or V 7 that the 
 composer carries it not only to the new tonic, but beyond, to the dominant 
 of that tonic, then turning back again definitely to the new tonic; or it may 
 even happen that the progression is made to the dominant of the dominant of 
 the first key, without an intermediate step. In the first of the following 
 examples we see a modulation effected from G to D, with a further one
 
 34 
 
 MODULATION 
 
 to A, the dominant of D, to which latter key (D), an immediate and final 
 return is made; while in the second one a modulation from E to F# is pro- 
 duced by vn 7 , after which the key of B finally enters. 
 
 40. 
 
 BEETHOVEN: Sonata, Op. 14, No 2 
 
 ; 
 
 *F 
 
 ^S 
 
 LUMIH 
 
 A: V 7 
 
 j q-f ^=f= ;. f f r f r-f 
 
 i~> Ui_^. 
 
 :i? 
 
 i 
 
 ffc^ 
 
 is 
 
 . 
 
 *-* I- 
 
 fc^E 
 
 ill 
 
 -=f *- 
 
 O .i 
 
 BEETHOVEN: Sonata, Op. 14, No. 1
 
 MODULATION 
 
 35 
 
 B: V 7 
 
 27. In a similar manner a very satisfactory modulation can be effected 
 in the progression I-IV, after the key desired has been reached, by going 
 one step beyond it to its sub-dominant, and then returning to it, thus 
 closing the modulation definitely; e.g. from Eb to Ab, then a passing pro- 
 gression to Db and a final return to At?. 
 
 J ! J ,UJ 
 g ^ i <& , -.si 
 
 ^ 
 
 r 
 
 Eb: 
 
 Db: 
 
 Ab: V 7 
 
 EXERCISES 
 
 In which it is expected that all varieties of chords shall be used, and modulations 
 made by V, V 7 or an inversion; basses not marked indicate triads, and slurs passing- 
 tones, while a figure 8, 5 or 3 over the first note means that the soprano begins on 
 that interval; a discreet use of appoggiaturas, passing tones, suspensions, etc., is 
 advised. The modulations are mainly transient, being sometimes even less than a 
 measure in length. The exercises should be played at sight as well as written. 
 
 1. 
 
 3 
 
 J 
 
 f^^ 
 
 6 6 
 
 1 6 6 
 
 2 5 
 
 ^ 6:62 666 7 
 2 4 
 
 2. 
 
 6 7 6 i 
 3$ 4 2
 
 36 
 
 MODULATION 
 
 
 7t 6 
 6b 5 
 
 626 
 
 767 
 5b 4 
 
 - - 
 
 
 6 6 
 6 
 
 266 
 4 
 
 
 76 
 6
 
 MODULATION 
 
 37 
 
 7. 
 
 
 j 7 46646 
 4 3 4 4 2 5[> 
 
 3 
 
 6657 
 
 8. 
 
 
 r j 
 
 
 - * 
 
 J 
 
 
 
 1 
 
 I/ 
 
 Q 25 
 
 e 
 
 
 26 7ft 6 6 6 
 42 5 
 
 
 9. (Chant) 
 3 
 
 risZicLgzn > 
 
 _ 
 
 
 
 
 -," 
 
 
 * r" 
 
 
 IZfSI WE 
 
 ^~ 
 
 
 1 
 
 ^"^ ^/ 
 
 
 
 
 4 675^ 
 
 2 4 
 
 r?=xri*-^t &~^ f~r^-- ' <^ *~< s ' ' 
 
 
 (2 r- 
 
 zBifjiffg 
 
 -P* 75 
 
 ^= 1 
 
 -i 
 
 75 ' 
 
 : :=i 
 
 
 22 I] 
 
 _^_!^J 1_ 
 
 
 1 
 
 
 
 
 
 
 
 2 6 7t{ 2 
 
 6 
 
 5 
 4 
 
 10. Open- 
 3 
 
 close 
 
 
 c , .; , :,:, t; , 5b (>. 6 5{l 
 -' 3b 3[> r, , 3b 4j7 
 
 -Open 
 
 6 6 
 
 ^67 65 7 
 2 44 
 
 11. (Chant) 
 I 
 
 /9 &> 
 
 6 6 ft 6 
 
 5 5fa 
 
 P : ^ b * 1 
 
 ^rrH^ 
 
 '' 1 * 
 
 - 
 
 (2 
 
 <S> 
 
 hf f 
 
 ^i=fl 
 
 7b 6 ft i a 5 ft 
 
 52 4
 
 38 
 
 MODULATION 
 
 In the following exercises the bass is not figured, and chords of the 6th, 7th, etc. 
 are often required: modulations by V, V 7 or an inversion are marked by a X. 
 
 12. 
 
 
 
 1 ^ 
 
 XXX 
 
 ~t 1 1 1 1 
 
 i h 
 
 
 "vLbb" 
 
 3 
 
 m 
 
 -f9 
 
 < 
 
 J 1- 
 
 
 
 
 
 m 
 
 * ?^ 
 
 -*n 
 
 t-*-i 
 
 
 ^-H 
 
 13. 
 
 14. 
 
 ^ 
 
 PJ- 
 
 f -s> & 
 
 F 
 
 
 16. 
 
 II 
 
 17. 
 
 IT 
 
 & 
 
 18. (Chant) 
 8 
 
 
 5 
 
 -g 1 Hg I J
 
 MODULATION 
 
 39 
 
 19. 
 
 
 5 
 
 S^ 
 
 
 20. (Chant) 
 3 
 
 ^E 
 
 6 
 
 21. 
 
 
 
 Soprano melodies; modulations with V or V 7 are marked with X. 
 22. (Chant) 
 
 g -p 
 
 r I T 
 
 
 23. (Hymn-tune) 
 
 -T^- 
 
 ^4 
 
 ^ 
 
 =F= 
 
 ^^=f= 
 
 r'ir J i^ || 
 
 24. 
 
 = 

 
 40 
 
 MODULATION 
 
 
 25. 
 
 26. (Hymn-tune) 
 
 
 
 v-r 
 
 II 
 
 27. 
 
 fcfcn 
 
 28. 
 
 ^^ 
 
 X X 
 
 r r r J 
 
 29.
 
 MODULATION 
 
 41 
 
 
 30. 
 
 InB. 
 
 x 
 
 nttri 
 
 
 J r . 
 
 I j_i i J |q 
 
 
 J 
 
 6+ 
 4 
 3 
 
 
 - BH - * - H 
 
 CHAPTER VII 
 
 MODULATION BY MEANS OP THE DIMINISHED 7TH 
 
 28. This is frequent, being also much used in quickly passing modu- 
 lations. 
 
 It is often employed in a modulation that is later concluded by V, being 
 especially attractive when the progression is from a major to a minor key, 
 
 #J L_4 
 
 
 i 
 
 r^rrr 
 i 
 
 r 
 
 r
 
 42 
 
 MODULATION 
 
 as well as when from one minor key to another. 
 
 *f=* 
 
 ^ 
 
 ~#. 
 
 ; up 
 
 ^F^ 
 
 '~ L T 
 
 V f-^ 
 
 II 
 
 29. Being an exceedingly ambiguous one, the diminished 7th chord 
 furnishes a natural path for modulation in various directions; so easily, 
 indeed, as to have been employed with too great frequency, with the result 
 that it has lost in freshness. But an illustration such as that below from 
 the quartet of Franck (No. 49) shows it to be still a useful tool. The reader 
 is reminded that its flexibility arises from the fact that what are practically 
 the same sounds can be expressed by various notations, indicating different 
 keys, e.g. 
 
 It 
 
 #* 
 
 I 
 
 And as, besides the usual resolution in these keys, there are dther irregular 
 ones, the range of modulation is very large indeed. 
 
 
 etc. 
 
 m 
 
 0+ 
 5 
 
 C vir vii 07 
 o 
 
 7 
 
 Various opportunities for modulation are also given by the changes in 
 tonality that result from lowering any one of the four notes of vn 7 ; in the 
 following, the second chord in each instance but one allows us to proceed in 
 a new key. 
 
 
 ^: == = ( } *--* =- = 
 
 t= 
 
 

 
 MODULATION 
 
 43 
 
 CHOPIN: Polonaise, Op. 26, No. 1 
 
 :i 
 
 67: VII 07 
 
 c: vn 7 
 
 43. 
 
 MOZART: Sonata in F major 
 
 - 
 
 fr"ffr p- 
 
 VII 07 
 
 e^f 
 
 i 1 
 
 In 43 there is a decisive modulation at X
 
 44 
 
 MODULATION 
 
 MENDELSSOHN: Phantasie, Op. 28 
 
 vn<>7 
 
 : 
 
 at 
 
 * 
 
 etc. 
 
 t 
 
 =? 
 
 ^ .
 
 MODULATION 
 
 45 
 
 SCHUMANN: Roman ze, Op. 28, No. 2 
 
 VII 07 VII 07 
 
 VII 07 
 
 VII 07 
 
 1 
 
 WfT ^ 
 
 
 
 V1I 07 
 
 46. 
 
 8va, 
 
 =te 
 
 WAGNER: " Tannhftuser " Overture 
 
 e 
 
 8va. 
 
 &-9 
 
 ** G : 
 
 vn7 
 
 > 
 
 : vii 07
 
 46 
 
 MODULATION 
 
 te- 
 
 
 Zoco 
 
 In No. 46 observe the enharmonic variations 
 
 and at (a) the changes of key by tonics moving a F^Q) g- 
 
 3d upward (14). 
 
 47. 
 
 LISZT: Song; "Comment disaient-ils ?" 
 
 ft _ f f- 
 
 F-ff - - - -^ > 
 
 -P - 
 
 -t^ru 
 
 i 
 
 -(G-. 
 
 4=- 
 
 ^ 
 
 B: 
 
 
 
 ^ 
 
 ffS: 
 
 .VIlOT. 
 
 Observe that the first vir 37 is written, not with the expected fx, but with gj, as re- 
 ferring to the following key of B.
 
 MODULATION 
 
 47 
 
 In the illustration from " Les Preludes" there is a fresh and interesting change 
 from successive vn 7 to a modulation into e at the 8th measure. 
 
 LISZT: " Les Preludes " 
 
 VI1 07 
 
 J-J- 
 
 r 
 
 r 
 
 *l T 
 
 Ftp 
 
 FT! 
 
 ^i= 
 
 VI1 07 
 
 49. 
 
 CESAR FRANCE: String Quartet 
 
 
 VI ,07
 
 48 
 
 MODULATION 
 
 STANFORD: " Phaudrig Crohoore" 
 
 
 51. 
 
 ZC-3EJ 
 
 
 
 ^ 
 
 
 F 
 
 M 
 
 ft-* II 
 
 fm A L^ . 
 
 
 
 
 
 
 ^* 
 
 1 ^ Li II 
 
 IUJ 4- ?* 
 
 
 
 
 
 
 jZ 
 
 1 GZ; II 
 
 I) 
 
 
 
 
 
 
 1 
 
 
 r-v *ff O | 
 
 
 
 
 
 _iJ 
 
 
 1" ^-j 1 | 
 
 1 * if j j ', 
 
 
 
 
 
 7m - 
 
 
 I \ 3 ^^ 
 
 ^ W 
 
 
 
 
 
 
 1 
 
 \/ ii 
 
 R. STRAUSS: Song, "Traum dutch die Dammerung" 
 
 Ju 
 
 C: 
 
 J] 
 
 
 i^tJ 
 
 6+ -t E:6
 
 MODULATION 
 
 49 
 
 In this last notice that a# in the second vii 07 seems to point to b, but is 
 really enharmonic for bt>, referring to the following D. 
 
 In the next two examples there are changes (at x) from V 7 to vii 07 
 according to a familiar procedure, the modulation in No. 53 being a con- 
 clusive one (in the latter vn 7 becomes a chord of the 9th). 
 
 MOZART: Sonata in F 
 
 
 HOPEKIRK: Prelude 
 
 
 It 
 
 -It 
 
 *: 
 
 f 
 
 -* 
 
 V VI1 7
 
 50 
 
 MODULATION 
 
 EXERCISES 
 
 in which modulations (mostly transient) are to be made with diminished 7th chords; 
 to be played as^well as written. 
 
 1. 
 
 -^Ja* g) 
 
 P <s 
 
 _t^2 E 
 
 H 
 
 -& EF 
 
 bbW 
 
 __| 
 
 r^ 1 
 
 
 ^ 
 
 fc * 6 7b 64 '7b 
 2 6b 3b 
 
 I ^ z Se : 
 
 ~t ' 
 
 
 x> & 
 
 F 
 
 
 H 
 
 is 
 
 -^-N> 
 
 ~y& ^ 
 
 
 1 
 
 H 
 
 
 -1 1 
 
 - H 
 
 9 '76 '6 6 4 6 ft ft 
 5 534 
 
 f 2 F- 
 
 
 667 
 4 
 
 7tj 
 
 3i} 
 
 ^ 4 
 5 3 
 
 6 6 
 
 J * 
 
 3. 
 
 
 6 5 
 4 
 
 I 
 
 6 I 
 4 2 
 
 6 7 
 
 5 
 4 
 
 4. 
 
 T'ffl* YD 
 
 "r* ' 
 
 3 
 
 
 (^ ^> 
 
 
 
 
 
 
 j 
 
 
 
 -^ r ' 
 
 B* 
 
 i c 
 
 
 i 
 
 ,! u _ 
 
 & 
 
 
 J 
 
 \\ 
 
 1 
 
 t 
 
 
 
 
 1 
 
 a <<L& 
 
 
 ^3 
 
 II 
 
 06 7 
 
 5(J 5 
 
 ? 4 67 4 
 
 34 3b 
 
 5. 
 
 M^ 
 
 ^ 
 
 I i 6464 
 3 3 4 3b 3b
 
 MODULATION 
 
 51 
 
 II 
 
 6006 
 3 3 
 
 6. 
 
 
 6 7 
 
 6 7 
 
 fir 
 
 6 * 
 4 2 
 
 6 6 
 5 
 
 7. 
 
 4 3 
 
 7 7 
 
 7 6 
 3 6 
 3 
 6 
 
 Unfigured basses; chords of 6, 4, 7, etc., often required; modulations, marked 
 with x for vii 07 , or an inversion, are mainly transient. 
 
 8. (Chant) 
 5 
 
 
 
 II 
 
 9. 
 
 x 
 
 
 $=^ 
 
 10. 
 
 m 
 
 fefi: 
 
 H 
 
 ^ 
 
 
 
 --i- 
 
 1 
 
 J 
 
 5! 
 
 II 
 
 -gy 

 
 52 
 
 MODULATION 
 
 X 
 
 12. 
 
 a, P , 
 
 
 13. 
 
 
 1 r 
 
 Soprano melodies; notes marked with X are to be harmonized with vii 07 , a modula- 
 tion being caused in each case. 
 
 14. 
 
 ' 
 
 ftFf- 
 
 =f-- 
 
 
 15. 
 
 r r f 
 
 -m * M 
 
 -F 
 
 = 3 * 
 
 /5/ M 
 
 
 j w 
 
 _- U 
 
 *-W F ^- L H 66" 
 4 4
 
 MODULATION 
 
 53 
 
 
 17. 
 
 Hfc 
 
 
 yi x , x x 
 
 1 
 
 18. 
 
 ^ 
 
 ss 
 
 19. 
 
 EB- 
 
 20. 
 
 
 
 
 6+ 
 
 4 
 
 8
 
 54 
 
 MODULATION 
 
 CHAPTER VIII 
 
 MODULATIONS INTRODUCED BY CHROMATIC ALTERATIONS OF THE 3D OR 
 5TH OF TRIADS 
 
 30. These chromatic alterations are of two kinds, of the 3d and of the 
 5th (in which latter case there is often a 7th present). The alteration of 
 the 3rd, which is usually from major to minor, is very serviceable, as will 
 be seen in the following (altered 3ds being marked x). 
 
 ^-=i 
 
 g>^ 
 
 E 
 
 ^-_ fei- 
 
 bJ 
 
 -L 
 
 1 
 
 TfrjT 1: 
 
 f 
 
 J \\J ?^:frj ,_ H=bgn 
 
 r^L^i r~ r- frp -*- *^<g 
 1 N - X| r r 5 f r 
 
 The alteration in the 3d, as well as that in the 5th, results in chords 
 that constitute rather an adjunct than a necessary factor in modulation, 
 while also frequently offering the best and most attractive solution of the 
 problem. 
 
 31. The 5th is augmented by raising its upper note, and, while the 
 resulting chord is much employed harmonically, it is seldom a real element 
 in modulation, being equally efficient in its original form without alteration, 
 as is shown in the following.
 
 MODULATION 
 
 55 
 
 r- 
 
 J 
 
 r 
 
 r 
 
 W- 
 
 f 
 
 .J J.J.i.J J 
 
 CHAPTER IX 
 
 MODULATIONS MADE OR INTRODUCED BY CHORDS OF THE AUGMENTED 
 
 (6+, 6+, 6+, 6+ 
 5 4+ 4++ 
 3 3 
 
 32. These chords are of great use, often affording the best way of 
 obtaining a desired result, as well as one that is quick without seeming abrupt. 
 Their flexibility comes chiefly from the fact that any of them can be derived 
 from a number of different keys, although the context usually shows the one 
 to which it is actually to be referred ( 33) ; chromatic or enharmonic changes 
 will of course occur, all such chords being altered ones. In the following is 
 shown how such a chord can be obtained through changes in one or more 
 notes; observe that the lowest note is lowered, or the top one raised, and 
 that even both of these things may happen. 
 
 i^ I-* 
 
 tof *\ih 
 
 .11 

 
 56 
 
 MODULATION 
 
 \ 
 
 -1 h 
 
 \~ '' \ 
 
 ] 
 
 . J , 
 
 1 1 1 
 
 Xf kti eJ 
 
 EDEEZ 
 
 X 
 
 -&-i ^ 
 
 '- 
 
 ^ - _J_ 
 
 
 i 
 
 _ j. 
 
 az ^ I 
 
 J J 
 
 - ^| 
 
 Ix v 1 
 
 > a 
 
 
 ,. J 1 
 
 J. J. 
 
 ^i fi i^- 
 
 ** r 
 
 ^r^F 
 
 
 b^ . ^ 
 
 ->-r 
 
 ^ Mt ^' 
 
 \ 
 
 
 
 
 
 ,^_ U 
 
 F 
 
 
 6+ 
 
 ft 
 
 
 I 
 
 R 
 
 
 :i 
 
 --5- 
 
 ^ 
 
 6+ 
 
 6: 
 
 ( enharmonic ) 
 
 
 F 1 ^- 1 ^ 
 
 -> 
 
 =1 
 
 -^!- 
 
 /: 
 
 6+ 
 5 
 
 - P-HT= 
 
 tiH^V 
 
 ( enharmonic ) 
 
 /* i 
 
 It is seen that the same 2 chord is in these examples derived in various 
 o 
 
 ways (in two of them by enharmonic change) after passages occurring in 
 the keys of d, Bt>, F, 6 and/. 
 
 33. But while such is the case with regard to this and the other aug- 
 mented chords of the 6th, it is nevertheless well to remember in modulating 
 that a 6+ chord may often properly be assumed to result from the first 
 inversion of the fourth triad of the minor scale (which is of course the second 
 
 6+ 
 triad of the relative major scale), a 4+ from the second chord of the seventh 
 
 3 
 
 * i 
 
 and a from the fourth chord of the seventh of the minor scale; the 
 o 
 
 context will show whether this is the case.
 
 MODULATION 
 
 J i J i J 
 
 For e.g 
 
 ^P^ 
 
 
 _ , L , 
 
 natural resolution will be 
 
 i 
 
 J. 
 
 57 
 
 are probably derived 
 
 
 i 
 
 while the 
 
 Iflfe I fl 
 
 or or 
 
 It is seen 
 
 JOL. 
 
 from 
 
 / 
 
 4 
 
 fe 
 
 
 
 T r r 
 j i . i 
 
 how 
 
 ?= T^ 
 
 I 
 
 quickly and easily a modulation can be made. 
 
 Or, to illustrate further, if we are in the key of e and wish to modulate 
 
 6+ 
 to D or to 6 the 4+ chord used below may logically be regarded as derived 
 
 3 
 
 from the second chord of the 7th in the scale of 6 (the seventh chord of the 
 7th in D). 
 
 
 *' 
 
 
 p 
 
 r 
 
 ~^s 
 
 f- 
 
 4 
 
 r 
 
 r~r 
 
 r 
 
 3 
 
 4* 
 8
 
 58 
 
 MODULATION 
 
 34. There are two points of importance which add to the availability of 
 these chords; 
 
 (1) that they all resolve with equal naturalness to a major key, and to 
 its relative minor, 
 
 iLJ J 
 
 and (2) that one of them ( the ^ + J is in sound practically (in the case of the 
 organ and piano absolutely) identical with V 7 . 
 
 In the following example we have both of these points shown, at (a) 
 and (6) the different resolutions and at (c) the identity in sound. 
 
 (a) 
 
 (6) 
 
 (c) 
 
 te 
 
 9 
 
 j-^g -i 
 
 mi 
 
 =e 
 
 rr 
 
 .; 
 
 H 
 
 U I I , I I , I I , J 
 
 -- -g- -^ J_uJ |g j -^^g* '-^ r ^ 
 
 j. 
 
 V^jytf -4- 
 
 ^sh 
 
 I! 
 
 C: 6+ 
 5 
 
 35. Attention should be called to the fact that, for convenience in 
 
 /* i 
 
 writing, the _ chord may be noted as one with a doubly augmented 4th 
 /6+ \ 
 
 (H 
 
 l-l in which case we shall probably find the res- 
 
 zzzH
 
 MODULATION 
 
 t* 
 
 olution to be to a major ? chord. 
 
 m 
 
 64. 
 
 _1 
 
 ROBERT FRANZ, (Song) 
 
 
 
 = 
 
 4-H- 
 
 3 
 
 56. 
 
 BRAHMS: Intermezzo, Op. 117, No. 2 
 
 
 =*= 
 
 I F 
 
 i j : 
 
 ^ 
 
 - 
 
 . 
 4^ 
 
 i 
 
 -T^-y^-rfr^r-^S F au 
 
 -tz __ 5^=3 I *" I 
 
 1 i j- ' I I ^P I != P ^-U 

 
 60 
 
 MODULATION 
 
 56. 
 
 SCHUBERT: Symphony in B minor 
 
 & 
 
 i^ 
 
 a? 
 
 - a*- 
 
 Iftt F 
 
 ^j t Ig-^ 
 
 :H 
 
 t-y> v 
 
 57. 
 
 ftg: it 
 
 PARRY: "L 1 Allegro ed II Pensieroso" 
 
 N 
 
 
 
 58. 
 
 6+ 
 5 
 
 CONVERSE: "The Pipe of Desire" 
 
 t
 
 59. 
 
 MODULATION 61 
 
 PARKER: "Morven and the Grail" 
 
 
 ^^==5r? 
 
 m 
 
 rr 
 
 6+ 
 In measure 3, Elf. V = A: g (enharmonic) . 
 
 60. 
 
 BRAHMS: Symphony in c 
 
 PAINE: "Oedipus Tyrannus" 
 
 *^?F=fa&* 
 
 m 
 
 -**&- 
 
 -9r 
 
 ^^ =J~UJ tj* 
 
 ^^ 
 
 Wi 
 
 1 
 
 6+ 
 5
 
 62 
 
 MODULATION 
 
 ii^i 
 
 ^ 
 
 
 >- 
 
 -- -(2. 
 
 i^J 
 
 T~ 
 
 CESAR FRANCK: Sonata for Violin and Piano 
 
 In No. 62 the chord at (a) is written as a V 7 because of the feeling that there is at 
 
 s* 
 
 this point of the key of G or g; with the vn 7 , which follows, the resolution is to a ^ 
 
 of the chord of Et>, but after its reappearance it is (at b) succeeded by an apparent 
 
 stt 
 
 V 7 , this latter, however, being so written (instead of as a 5 ) for convenience. Observe 
 the regular melodic progression of soprano and bass (36). 
 
 .^.v.l-^-^A) $+ 
 
 
 
 This is a suitable place for referring to the Neapolitan 6th as a real fac- 
 tor in modulation (cf. the first movement of Beethoven, Op. 27, No. 2). 
 
 A. WHITING: Humoreske 

 
 MODULATION 
 
 63 
 
 i 
 
 
 
 
 EXERCISES 
 
 6+ 
 
 in which modulations are chiefly made with 6+, - . 4+ (or an inversion), being 
 
 3 
 
 mainly of a transient character; to be played at sight, as well as written. 
 1. 
 
 5 
 
 ES3E:S 
 
 4+ 
 3 
 
 m 
 
 2. 
 
 646 
 4 2 
 
 7 J * 
 
 |:4 
 
 6+ 6+ 
 4+ 5 
 3 
 
 3. (Chant) 
 5 
 
 6+ 6+ ft 
 5 4+ 
 3 
 
 6 5 | 
 4 
 
 6 6+ 2675
 
 64 
 
 MODULATION 
 
 6. 
 
 h^iSS * * 
 h^-*^ ' h 
 
 :=^= =P 1 
 
 f- 5 r 
 
 t- 4- ' i- 
 6 
 
 6+ g * 6 s * 
 
 4+2 2 
 3 
 
 i 1 m f 3 
 
 P i j 
 
 6 fty 
 
 4 
 2 
 
 (~Vjf J 
 
 1 #J f P P F 
 
 ^TT H 
 
 : ^ * r ^ 4 
 
 _j j & 1 
 
 _K fp i ! g 
 
 2EEJ 
 
 6 6 
 
 3 * 
 
 1 1 1 
 
 6+66 6 5 # 
 545 4 
 
 
 6. 
 
 : 
 
 
 6t| 6 
 
 46 6+ 
 
 2 4+ 
 
 3 
 
 e 
 
 
 6 
 5b 
 
 6+ 6^665 fa 
 5 42 64 
 
 7. 
 
 i 
 
 =E^J J^ 
 
 ^ 
 
 6+ 
 5 
 
 6+ 
 5 
 
 y^.. J - I i i -I F-g . i u * w vw H^ fg> f i n 
 
 ^ I ^^4^=ib=^^^^^f = f = f = Fg^^^H 
 
 6 6+66 5 
 4 #" 4+4 4 
 
 Unfigured basses: augumented chords of the 6th, (or an inversion), are marked with 
 X, which in each case signifies a modulation. 
 8. 
 
 8 x 
 
 
 jzp~^TJ~j^^^3 
 
 m 
 
 
 4 6 
 
 3 5b 
 
 
 *=&=& 
 
 i^i^ i i i i i i i ,-, 
 
 ^J^O^LjEEfl
 
 9. 
 
 MODULATION 
 
 65 
 
 n f --f- f , ^-^L 
 
 m 
 
 f~nnnf. 
 
 *>- 
 
 10. 
 
 
 -y-f ' P , , |- 
 
 
 1 f 5 ^"! 
 
 r-p i 
 
 
 7^ II 
 
 -^ i i r r r 
 
 i 
 
 1 
 
 1 i 1 I 
 
 r SEEH 
 
 11. 
 
 X 
 
 r r 
 
 J ^ J 
 
 II 
 
 12. 
 
 
 13. 
 
 14. 
 
 
 Soprano melodies. Notes marked with X indicate modulations to be made with 
 etc., or an inversion. 
 15. (Hymn-tune) 
 
 r r i-i [
 
 66 
 
 MODULATION 
 x x 
 
 17. 
 
 
 mm 
 
 JUJ L. 
 
 S 
 
 18. 
 
 -^= 
 
 ^ 
 
 F=*^ 
 
 - 
 
 19. 
 
 XXX 
 
 
 x xx 
 
 
 20. 
 
 
 -* k 
 =^=1 
 
 InF
 
 MODULATION 67 
 
 CHAPTER X 
 
 HARMONIC CHANGES (SOMETIMES WITH MODULATION), RESULTING FROM THE 
 SYMMETRICAL MOVEMENT OF INDIVIDUAL VOICES, CHIEFLY BY STEPS AND 
 
 HALF-STEPS 
 
 36. THE progression in the illustration from Franck's Violin Sonata 
 (No. 62) is aided by melodious movement of the soprano and bass, which 
 latter proceed mainly by steps and half-steps; this idea, as systematically 
 applied to the leading of two or more voice-parts, has been developed in 
 recent years, Wagner being largely responsible for the attention paid to it. 
 It results in an efficient, subtle and flexible instrument not only for producing 
 quick and interesting harmonic changes, but also sometimes for introducing 
 or causing a modulation (e.g., Nos. 72, 73). As a rule, however, the opera- 
 tion of this device comes under the classification of Change of Keys or 
 Chords without Modulation (Chapter III), the value of the scheme lying 
 mainly on its harmonic side. The question is definitely summed up by Parry 
 in his article on Harmony in Grove's Dictionary of Music, in which he calls 
 attention to the fact that polyphony is the root of the matter: "The essential 
 fundamental chords are but few, and must remain so, but the combinations 
 which can be made to represent them on the polyphonic principle are almost 
 infinite. By the use of chromatic passing and preliminary tones, by retarda- 
 tions, and by simple chromatic alterations of the notes of chords according 
 to their melodic significance" (i.e., of the separate voices) "combinations 
 are arrived at that puzzled and do puzzle theorists who regard harmony as 
 so many unchangeable lumps of chords which cannot be admitted in music 
 unless a fundamental bass can be found for them." 
 
 37. The first suggestion of the idea appears in the following wellknown 
 scheme, which is made further available by the frequent chance afforded for 
 enharmonic changes, 
 
 for any one of these chords can be taken as the point of departure into a 
 new key, e.g. (the entrance of the definite key being marked by an x).
 
 68 
 
 MODULATION 
 
 ^ 
 
 ': 
 
 ^ 
 
 
 n 
 
 ^ 
 
 
 PfnOr 'H^f^g^W 
 
 9 
 
 A number of examples of such chord-successions are given below, as well 
 as illustrations from various composers, in all of which the individual move- 
 ment of voices, up or down, is shown by the lines / and \ ; in some cases there 
 is real modulation. 
 
 1. 
 
 ^ri 
 
 J ^ 
 
 fi^. . 
 
 14 p=" 
 
 i 
 
 -fiL 1-^- N -J-. |-J- 
 
 _ Uf * ^ f+ - U-_ 
 
 ^ 
 
 frf^ 
 
 3^ 
 
 ^r^'U 
 &:^ 
 
 5=r 
 
 :^
 
 MODULATION 
 
 >'M ,' 
 
 .UUJ- J . J #J. J, 
 
 ,5? 
 
 6. 
 
 IB 
 
 
 I J I 
 
 1 ' uj 
 
 -, 1 
 
 \ . 
 
 | 
 
 
 | 
 
 i i 
 
 2: z| 
 
 t2 " 
 
 i 
 
 7 
 
 
 
 b- 
 
 & -j 
 
 F^ J ^ J H 
 
 /L r 
 
 1 
 
 
 
 1 
 
 
 r I (^ " 
 
 1 f i 
 
 r- H 
 
 @ J ^ 
 
 1=1 i 
 
 
 
 1 
 
 i 
 
 ^E 
 
 d d -J H 
 
 
 7. 
 
 ^ 
 
 Bij: 
 
 f=f=T 
 
 :ll
 
 70 
 
 MODULATION 
 
 8. 
 
 tJ 
 
 J aJ 
 
 ^^B ^ 
 
 9. 
 
 t -_k^- 
 
 rr~fr'f g Si 51 " 
 
 m 
 
 * 
 
 i 
 
 - 
 
 1:1 
 
 
 as 
 
 ts< 
 
 ^i= 
 
 Ez=>b:^ti=i 
 
 ra- 
 
 -5, 
 
 FT 
 
 10. 
 
 1 
 
 11. 
 
 12. 
 
 :4ir^ 
 
 ^"^: 
 
 II 
 
 13. 
 
 14. 
 
 tr- gJ^- J-^J=^= H&Bf^^^ 
 
 /.-=u!= ^ * 7 ^&=H^A 4*-5^ =a>. 
 
 
 1:1 
 
 I ^ I. I i ~"^~ ~ l/ ~ Uf3 
 
 ^^^p^^Tv7^r(|)i^ 
 
 - 1 ]L-
 
 15. 
 
 MODULATION 
 16. 
 
 71 
 
 S 
 
 I 
 
 vtt 
 
 } J- 
 
 J 
 
 i 
 
 :: 
 
 -&- 
 I 
 
 17. 
 
 18. 
 
 
 , i u i 
 
 (2- 
 
 l" 
 
 -- 
 
 ^:<FT-T^ 
 
 ^2^ 
 
 =s 
 
 64. RAFF: "LaFileuse" 
 
 (Chords only.) 
 
 65. 
 
 WAONER: "DieWalkOre 1 
 
 : =- 
 
 k ) : e 
 
 -w- 
 
 
 ^ j. ^.
 
 72 
 
 MODULATION 
 
 FRANCK : Chorale in a for organ 
 
 In these measures of Franck's Chorale the change is effected as follows, 
 
 / 
 
 LCD 
 
 
 while here are examples of a few of the modulations that could be brought about 
 with these two chords by the device shown in 37. 
 
 jfc/Trg jfra-ltt/Tr? \rr^ I ftg^ \<*~~?~$? %? II 
 
 r~. _i. 'h ~1 h-_h- J'h-^-h l-^-j 2 - _l- M Jh~^ == H 
 
 4k 
 
 
 1 
 
 a E 
 
 67. 
 
 PIEBNE: " The Children's Crusade ' 
 
 Ja l^ l^uJ JiJ X I I '^ I I I 
 ^^i^^gjI^^^^^Ul J' *V " j 
 
 
 i 
 
 6+ 
 
 4+ 
 3 
 
 6+ 
 5
 
 MODULATION 
 
 73 
 
 68. 
 
 MASSENET: Song, " Pofime du Souvenir" 
 
 to* 
 
 i 
 
 i a - 
 
 J=t 
 
 A 
 
 T 
 
 tr mr t 
 
 "111 ii 
 ^ ^ 
 
 C (or c) 
 
 69. 
 
 DEBUSSY: Nocturne 
 
 J 
 
 ^B^M=^=i==M^ 
 
 
 
 
 S 
 
 
 
 II 
 
 70. 
 
 STILLMAN KELLEY: "The Pilgrim's Progress " 
 
 8 
 
 
 *1'y- ^ * *- 
 =^'(t ^^^ 
 
 J 
 
 r, *, 4. *, 4 9
 
 74 
 
 MODULATION 
 
 
 71. 
 
 BIZET: "Carmen 
 
 m 
 
 m 
 
 m 
 
 2C 
 
 :i?s: 
 
 72. 
 
 M-fi^ 
 
 w& 
 
 I ' ' I l tf-F 
 
 PALMGREN: "The Swan" 
 
 -O- 
 
 m. 
 
 jte ~~"%- ~?l 
 
 73. 
 
 LOEPFLER: Song, " The Hosting of the Sidhe 
 
 feg 
 
 * 
 
 *= 
 
 ^ 
 
 ^r a - 1 g^ 
 
 ^ 
 
 :V~u: 
 
 '^^ 
 
 r^ 
 
 *f
 
 MODULATION 
 
 75 
 
 CHAPTER XI 
 
 HARMONIC CHANGES RESULTING FROM THE ELISION OF CHORDS 
 
 38. A striking and suggestive development in harmony has resulted 
 from this device of omitting one or more links in a succession of chords which 
 touch various keys that superficially do not seem near to each other; if the 
 omitted steps are supplied the progression becomes commonplace, though 
 logical enough, the really close relationship of the keys then becoming 
 apparent, as will be seen in the following, in which the chords elided in No. 77 
 are added (and marked with an x). 
 
 j In the next specimen examples the omitted steps are shown by parenthe- 
 ses, whatever attractiveness there may be in the progressions being lost if 
 these elided chords are added.
 
 76 
 
 MODULATION 
 
 With this elision of chords, as is shown in the subsequent illustrations, 
 progressions appear that are subtle and fascinating, even puzzling to a 
 listener unfamiliar with the procedure; here again we have what is simply a 
 succession of keys (or chords) without modulation of the customary sort 
 (14). 
 
 It is also true (as was the case with the device discussed in the preceding 
 chapter) that this scheme is rather of harmonic interest and value than 
 applicable in modulation, for it is available more as an adjunct than as a 
 final means. 
 
 The two following examples show this; it will be seen that the chords 
 marked x in each case begin a normal modulation, this rapid way of getting 
 to them being sometimes well worth while; for the road between Gb and 
 g, and C and /# is by no means an obvious one. 
 
 J. 
 
 -J.
 
 MODULATION 
 
 77 
 
 . J' J uj 
 
 fe- i -f IjfJ- "i 1 ! 1 
 u r r KV f 
 
 ^F=^=^=g=P : |g 
 
 
 F F 
 
 In these illustrations third-relationship is clear; there are, however, 
 great differences in the attractiveness of such changes of key; in No. 10 
 (Chapter III), in which the change of tonics is purely one of an ordinary 
 succession of keys, there is lacking the piquant element of unexpectedness 
 felt in Nos. 11 and 13. The following table gives the most striking of these 
 third-relationships . 
 
 -- 
 
 -<5>- 
 
 kJ. J.kJ. 
 
 1" 
 
 d= ll 
 
 9t 
 
 
 74. 
 
 WAGNER: "Parsifal' 
 ^ 
 
 2t C t 
 
 P^ 
 
 :i^=ih4 
 
 (In No. 74, db-atj is enharmonically equivalent to the 3d, c#-a). 
 
 76. 
 
 CESAR FRANCK: Piano Quintet 
 
 e
 
 78 MODULATION 
 
 Hnr-^fer-iE-ite- 
 
 ==F= 
 
 
 In the following from Liszt there is a drop downward of a major 3d from 
 V 7 of C# to the tonic of e minor, the tonics of c% and E being elided. 
 
 76. 
 
 LISZT: Sonetto 104 del Petrarca 
 
 t**f f j 
 
 s=s 
 
 * * E * * = +\ 
 
 *te 
 
 WAGNEB: "Parsifal" 
 
 -b-tea 1 1- -b^-r-k bv fc-A-^r^ n 
 
 
 
 =4= 
 
 II
 
 MODULATION 
 
 79 
 
 MACKENZIE: "Dream of Jubal" 
 
 In choosing keys for different movements of a composition, or for sec- 
 tions of a piece, this idea is sometimes carried out. In the following the 
 steps between Eb and 6 are as follows, e\> and Gi? (f#, the dominant of 6), 
 being in fact supplied by the composer in a modulatory passage. 
 
 SCHUBERT: Impromptu, Op. 90, No. 2 
 
 CHAPTER XII 
 
 A TABLE OF MODULATIONS 
 
 39. IN the following modulations the chief objects aimed at are clearness 
 and simplicity; the one first given is in each case offered merely as being the 
 shortest way (not always a desirable one), while in the others it has been 
 intended to furnish a fairly musical road between the two keys. Another 
 form is also to be recommended in some cases, i.e., to proceed from a key 
 to its dominant (with minor keys to the dominant with minor third), and to 
 then consider that dominant as a new tonic from which another similar
 
 80 
 
 MODULATION 
 
 progression is made to the dominant of the latter, this last being regarded 
 as the final tonic; e.g., C to G (I-V) then, regarding G as I, G to D (I-V), in 
 this way progressing from C to D with smoothness and in a manner that will 
 at least pass muster musically; similarly in minor keys (a to e, and then 
 e to 6). A like procedure may be employed with sub-dominants (C to F 
 and then F to Bb; o to d and d to g). 
 
 40. While the authentic cadence has long been recognized as useful, 
 through the extremely definite character which it possesses, it is far from 
 necessary; a plagal one, perhaps strengthened by n 7 , is quite conclusive, 
 f orming a desirable alternative (a) ; neither need there be any alteration of 
 notes by #, b or ty (6) ; as the authentic cadence can be quite as well introduced 
 
 / 
 
 by IV 7 (c), ii 7 (d) ,or a suspension (e), the use of the ? chord is by no means 
 the only way of enforcing this cadence. 
 
 tfTT ~Hr 
 
 IV7
 
 MODULATION 
 
 81 
 
 41. In forming a general scheme of modulations, the plan is adopted of 
 starting in each case with the key of C or c; the figures n, etc., indicate the 
 degree of the scale to which the modulation is to progress, all alterations by 
 accidentals being included, e.g., C to D# (Eb), Db, etc.; while in case a scale 
 is impractical in one form with sharps or flats, the convenient alternative is 
 offered (e.g., not D# but Eb). 
 
 It is, of course important to transpose in all cases. The use of suspen- 
 sions, appoggiaturas, passing-notes and occasional chromatic alterations is 
 desirable, as making modulations more musical and interesting as well as 
 more flexible. 
 
 I-V 
 
 n 
 
 
 
 
 J 
 
 
 ,. 
 
 j 
 
 
 
 1 
 
 
 
 
 
 
 
 (J .) 
 
 
 
 h 
 
 
 
 ^ 
 
 i L/ 
 
 : S< 
 
 - 
 
 
 -J 
 
 
 
 
 
 
 
 
 
 
 
 $9 *f- 
 
 ^ 
 
 I^K^ 
 
 
 
 
 
 ^ 
 
 
 ^ 
 
 
 
 
 r 
 
 
 
 f 
 
 
 r 1 ^ 
 
 T 
 
 ^j 
 
 ^ 
 
 . 
 * K~^*ii 
 
 I" ^ 
 
 -^ 
 
 's 
 
 - 
 
 '\ 
 
 
 " 
 
 1 
 
 V 
 
 Q 
 
 
 S3 
 
 
 "' 
 
 
 h-02-! 
 
 -f 5i: - ! 
 
 
 
 
 
 
 
 ' f 
 
 
 
 
 
 II 
 
 E3Zp 
 
 -f 
 V 
 
 I 
 
 37 
 
 L i l 
 
 II 7 VIl' 
 
 r 
 
 
 
 
 
 f* 
 
 
 
 
 
 
 
 In (a) there is I J -V, (6) u 7 -V, (c) a suspension to V, (d) a suspension 
 introduced by n 7 , (e) vn 7 introduced by n 7 , and (/) V introduced by an 
 appoggiatura.
 
 82 
 
 MODULATION 
 
 C to g. A desirable way is given by the second one, in which the first 
 bb takes us 4 out.of C, but leaves a doubt as to what key is coming (intensi- 
 fied by the ambiguous vn 7 ), until a V 7 settles the question; much of the 
 naturalness results from vn 7 . 
 
 m*-*-*- 
 
 
 -*& 1 f9 ' 
 
 1 
 
 vii 07 V 7 
 
 This modulation can also be effected through subdominants, and then to 
 relative minor (C to F, F to Bb, Bb to g) : 
 C to Gb (F3) : cf : C-F# (I-IV). 
 
 C to G# (Ab) : cf : C-Ab (I-VI). 
 C to jr# (ab) 
 
 
 
 I 
 
 V 7 vii 07 
 
 c to G (or gr) 
 
 ^^ ~~Q 
 
 ~^L .-. 
 
 ^ V 
 
 L
 
 MODULATION 
 
 83 
 
 J 
 
 f(T\^ VA & 15 n Tl ro n- 
 
 
 
 ** > &"./ 
 
 J i i I ~ -T i r 
 
 1 or 
 -&- 4 \ \' ^ 1 i 
 
 J w tp ^* ^^"^ 
 
 
 13 H 
 
 -^ U uti f5 1 ^ * 1^"' 
 
 \ H 
 
 "** r ' 1 1 
 
 ^ V ^ i rl 
 
 o+ r* 
 
 4+ 
 3 
 
 c to g. In the next one the principle is followed of going SL step beyond g by pass- 
 ing through d (26); the return to g, as final, is rendered attractive by this device. 
 The Tierce de Picardie enables us to end in G as well. 
 
 (modal) 
 
 
 __^^i?q =1 /I g ' 
 
 L \ Li L^-V-^g)/-! i 
 
 I 
 
 V 7 vii 07 
 
 c to 
 
 ?ei 
 
 
 g*^";g 
 
 ^*~ 
 
 m 
 
 j. 
 
 ws*- 
 
 A longer modulation is, however, preferable. 
 
 
 
 V 7 
 
 V 7 
 
 c to pb (ft) : c/. c-/ft (I-IV). 
 c to G (Ab) : cf. c-Ab (I-VI). 
 c to 0# (ab) : qf. c-ab (I-VI).
 
 84 
 
 CtoF 
 
 MODULATION 
 I-IV 
 
 j=rrTJ-id 
 
 i 
 
 r T 
 
 "tt-ra 
 
 ^ 
 
 
 i 
 
 V 7 
 
 fl J. J J Uj J \"f\ =f 
 4^ - t t |g 
 
 1 
 
 J 
 
 faUJ^- 
 
 ^- 
 
 i 
 
 V 7 
 
 C to /. Observe that the chord of the 6th is also an efficient factor in 
 
 
 
 a cadence, as well as a pleasant change from the ? chord: the vn 7 adds 
 interest to the second example. 
 
 .^m=^-^>* r ^=1 
 
 1 
 
 
 V 7
 
 MODULATION 
 
 85 
 
 
 The ambiguous vn 07 is an aid to this very remote modulation; the first 
 two measures can also be used in the modulation C to 6. 
 
 C to /#. The same as the preceding, except that the last four measures 
 will be in /#. 
 
 c toF 
 
 ^=t 
 
 ^ 
 
 1 
 
 S^s 
 
 fe 
 
 i 
 
 5t* 
 
 i 
 
 te-i-fg J 14 
 T I i^-l 
 
 i 
 
 r 
 J- 
 
 LJ 
 
 VI1 07 
 
 C tO/ 
 
 V7 
 
 : ^. c-Gb (I-V). 
 
 This can also be made by traversing several keys according to the Circle 
 of Fifths, although the process is rather mechanical (c-G-e-B or b-F#).
 
 80 
 
 MODULATION 
 
 Cto A 
 
 I-VI 
 
 VII 07 
 
 C tO O 
 
 i'lUjL 
 
 gig 
 
 w 
 
 B 
 
 rrT^ 
 
 J- 
 
 ffi 
 
 r 
 J. 
 
 r 
 
 6+ 
 
 / I 
 
 In (a) the augmented ^ shows itself as especially available, resolving 
 
 to both major and relative minor keys: the ending is modal. In (b) there 
 is no alteration by accidentals, the chord of F major being a Bridge Chord; 
 this modulation is, however, not so strong as the other two.
 
 MODULATION 
 
 87 
 
 Cto 
 
 
 
 
 
 ^ 
 
 J> L I I 
 
 1 
 
 
 ! 
 
 fc* 
 
 Ctoab (&S): <jf. C-srS (I-V). 
 C to AS (Bb): c/. C-Bb (I-VII). 
 C to alt (6b): c/. C-6b (I-VII). 
 
 c to A 
 
 
 
 E t 
 
 _. u o I r- 
 
 v 7 
 
 ,_? 
 
 
 J .faj fc 
 
 = 
 
 I 
 
 The progression | | is useful when it is desired to quickly get away 
 
 from a key, the second chord under it being neutral, and available as a 
 Bridge Chord, e.g.
 
 ss 
 
 MODULATION 
 
 -d 1 i - 
 
 =F 
 
 s 
 
 ^Ni 
 
 =l 
 
 The progression can be made through g and d to A, as follows. 
 
 +* 
 
 ^ 
 ff 
 
 II 
 
 V 7 
 
 c to a. The modulations c to A can be used for this one also by simply 
 changing the last chord to a minor. 
 
 -M=J4^^^^=-===^ 
 
 6+ 
 5 
 
 c to A'? 
 
 iBE! 
 
 ^1 
 
 ^ te 
 
 r 
 
 a> aJ I g , J 
 
 K^
 
 MODULATION 
 
 c to b- 
 
 6^ 
 
 4=h 
 
 -- 
 
 
 
 
 V 7 
 
 i \\K& 
 
 p 
 
 ? 
 
 - 
 
 LUTl-C-pj^!p 
 
 II 
 
 r 
 
 This obscure modulation is aided by vii 07 . 
 
 ctoAS(Bb): c/. c-Bb (I-VII) 
 c to aid (6b): cf. c-6b (I-VU). 
 
 I-I 
 
 CtoCb (B): qf. C-B (I-VII). 
 Ctocb (6): cf. C-6 (I-VII). 
 CtoC(Db): c/. C-Db (I-H). 
 C to ctf (db).
 
 90 
 
 MODULATION 
 
 ctoCb(B): cf. c-B (I-VII). 
 ctocb (6): cf. c-b (I-VII) 
 c to Ctf (Dt>): cf. c-Dl> (I-II) 
 c to ctf 
 
 
 T 
 
 J 
 
 
 
 
 f\ j 
 
 Or through d and A, and then arriving at c# by a ^ chord; the passing 
 note d# contributes to the naturalness of this progression. 
 
 :?;., 
 
 ;^_ 
 
 :-] H-F 
 
 S^ 
 
 
 
 ^K 
 
 . ^i*g ,U^ 
 
 f^T^R% 
 
 vn 7 A: 
 
 6+ 
 5 
 
 S 
 
 
 teff 
 
 * 
 
 I-II 
 
 C to D. A fairly musical way of obtaining this unpromising modulation 
 
 6+ 
 
 is by the enharmonic change at 4+. 
 
 3
 
 MODULATION 
 
 The following is practicable, but too abrupt. 
 
 91 
 
 TT 5 
 
 'Tsr 
 
 1 
 
 -25 pit |i 
 
 Or by means of a complete modulation to G, followed by a similar one to D. 
 C to d. 
 
 d: 
 
 foE: 
 
 ~r \ 
 
 Or to Db through a previous modulation to At>. 
 Ctodb (c#): cf. C-c (I-I). 
 C to D# (Eb): c/. C-Eb (I-III). 
 Ctodtt(eb): cf. C-eb (I-III). 
 
 c to D. 
 
 tr 
 
 ^^ j
 
 92 
 
 MODULATION 
 
 i 
 
 ^^ 
 
 =Y- 
 
 i 
 
 VII 07 
 
 c to d. 
 
 A,. J Ji n^ 
 
 i 
 
 ^_1O3. 
 
 3SO- 
 
 ^H 
 
 J t J 
 
 rtr-Hh! 
 
 3i 
 
 r 
 
 I 
 
 Aft J Jirahte 
 
 IK" ^ - -C2_mH 33 
 
 a 
 
 
 iZj"ku>J. 
 
 ag 
 
 e 
 
 " "TiJ J 
 
 5> 0-r-M *- 
 
 P ^ 
 
 ^r^ 
 
 I 
 
 ^S 
 
 ? 
 
 *^^ 
 
 n' V 
 
 c toD[>. 
 
 JbJlbJ Jfc/T^-r^T: ^ bJ J 
 
 i g^ verves & w vcJ lyT K^Tf^V V ^ 
 
 ^a 
 
 ;, (^Tl 5^11 
 
 iJ 
 
 g 
 
 ctodb (c#): qf. c-c# (I-I). 
 c to D# (Eb): cf. (^Eb (I-III). 
 ctodtf (eb): cf. c-eb (I-III). 
 
 C toE 
 
 I-III 
 
 I 
 
 
 * 
 
 3e 
 
 -
 
 MODULATION 
 
 93 
 
 i 
 
 lp 
 
 $ 
 
 ^ 
 
 1 
 
 -<g . -jy 
 
 6+ 
 5 
 
 6+ 
 
 4 
 
 3 
 
 C to e 
 
 
 itif: 
 
 ~f 9 ^^f^ 
 
 tX k/ 
 
 1 
 
 VII 07 
 
 C to E[> 
 
 -te 
 
 i 
 
 r 
 
 -^g- 
 
 p 
 
 :fe 
 
 I 
 
 ii 7 V 
 
 
 r 
 
 i 
 
 - 
 
 
 
 VII 07 
 
 ^^^ 
 
 ta 
 
 
 ~r 
 
 VII 07 VII 07
 
 94 
 
 MODULATION 
 
 RH ^ 
 
 
 
 1 
 to 
 
 r 
 
 "fis 
 
 i 
 
 
 T~l 1~~ 
 
 
 frj < 
 
 - 
 
 b 
 
 * fa 
 *l 
 
 r~ 
 
 > 
 
 -\*r 
 
 hi 
 
 i ' 
 
 5g J- 
 
 r- 
 
 j 
 
 Rf-fc 
 
 V* V (g a 
 
 
 M 
 
 r 
 
 
 
 u 
 
 , 
 
 r^~~H 
 
 -^ 1 *- 
 
 y 
 
 
 
 ^t : 
 
 
 
 -9&-i 
 
 
 
 1 
 
 
 
 
 T 
 
 i 
 
 f -r- 
 
 T 
 
 -'-. 
 
 This gradual progression through /, 6b, Gb to e\> is preferable to shorter 
 modulations; the link of Gb, however, could be omitted without disad- 
 vantage. 
 
 ctoE - 
 
 >zfc= 
 
 *?Fr 
 
 SI 
 
 
 c to e 
 
 VII 07 
 
 c to 
 
 / 
 
 ?m4- 
 
 H 
 
 1 
 
 
 
 
 II 
 
 
 1 
 
 (q)^P4 
 
 f . 
 
 >, *' 
 
 
 
 
 H 
 
 
 
 ^jZ SL_ 
 
 9 
 
 J- f 
 
 f^- 1 >-7 
 
 '- -J. . 
 
 ^-^ 
 
 _ 
 
 ^^ 
 
 ' r 
 
 i j 
 
 
 
 / 
 
 C^\ * In ^ 
 
 
 
 
 
 ^* 
 
 ^ ii 
 
 
 1 
 
 y * r *" - 
 
 i 
 
 
 
 
 
 1 
 
 
 v 
 
 V |^ : 
 
 ^ P? 
 
 ? r "^ 
 
 
 
 s 1 
 
 H 
 
 
 A u 
 
 i ..r i 
 
 
 r 
 
 
 
 
 -<s>- 
 ^ 1 
 
 
 L/ 17 f> 
 
 j W J- 
 
 V- 
 
 1 /h)\ J | 
 
 
 s 
 
 1 fv 
 
 
 
 (&)" ''If ' 
 
 
 P- 
 
 m 
 
 ' l ' 
 
 , 
 
 
 - m 
 
 * 1 - t 
 
 
 
 1 ^ 
 
 H 
 
 V 
 N 
 
 ;g j. r 
 
 J ;J 
 
 ' 
 
 \ 
 
 1 N 
 
 N 1 J S 
 
 a^d m 
 
 -7-M-l 
 
 ^ h *A 
 
 i 
 
 
 
 L 
 
 
 ^-j 
 
 * * 
 
 M m 
 
 - 
 
 VII 07
 
 MODULATION 
 
 95 
 
 c to 
 
 
 
 
 J: 
 
 =^$b=g: 
 
 
 
 
 I u I i 
 
 -Gr 9th _&_. 
 
 
 I-VII 
 
 C toB 
 
 
 
 6+ 
 5 
 
 J 
 
 
 C to 6 The preceding modulation is also practicable for 6. 
 CtoB> 
 

 
 96 
 
 MODULATION 
 
 
 rr 
 
 
 ^ 
 
 C to 
 
 5JE=d 
 
 - 
 
 =& 
 
 ^ 
 
 -{- b-<g- bg< k*; b J 
 
 -(S2- 
 
 Or C to / or F, and then to 6b 
 c to B 
 
 ^* t=u 
 
 
 6+ 6 
 5 4 
 
 I N k _&JL i N | 
 
 1 r~1 ! .^ xi F 
 
 
 r\ B. 
 
 Vof 
 
 tJ 
 
 I 
 
 rifT^" "f 
 
 The enharmonic change facilitates the progression.
 
 MODULATION 
 
 97 
 
 c to b 
 
 to: 
 
 ^m 
 
 i 
 
 s 
 
 6: 6+ 6 
 5 
 
 6 V* 
 
 
 I I 
 
 b- fg I n ~ 
 
 P^Hr-^ 
 
 
 
 
 c: VT 6: 6+ 
 5 
 
 Observe that while the change from c to 6 can be made instantly by the 
 enharmonic alteration (V 7 -g ), the modulation must be considerably 
 lengthened if it is to appear as a natural musical expression. 
 
 J J i J J 
 
 1^ I J 7 iTT 
 
 E" ^VJ: 
 
 if-^r 
 
 r 
 
 P
 
 98 
 
 MODULATION 
 
 f 
 
 rr 
 
 ^ 
 
 1 
 
 c to 6b 
 
 
 r r f 
 
 ->- 
 
 Zfc 
 
 ^ 
 
 (Modal) 
 
 Ff=f 
 
 Or from c to /, and then to 
 
 Modulate by playing or writing g to Eb; /# to E; Ab to /; E to g%; 
 /to Db; 6b to Gb; /# to G through D; e to F# through b; E to C through o; 
 D to Bb through 9; F^ to g through 6 and D; Ab to g (by j? + J; A to ^S 
 
 through c (vn 7 ); B to G through e; Db to F through 6b (vn 7 ); Eb to A 
 through g and D; F to Eb through Bb and g; Gb to 6 (enharmonic); Bb to 
 D through g; D to /#; E to F through a; Ab to 6b through Db; G to /# 
 through 6; G to Eb through c; B to Eb through gr# (enharmonic); Eb to 
 
 Cb through ab; E to F through a; Db to bb (by ^ + V a to p through d; 
 a to / through F and 6b.
 
 Alteration of 3d or 5th by accident- 
 als, 54 
 
 Augmented chords of 6th, etc., derived 
 
 in various ways, 55 
 probable derivation, and resolu- 
 tions, 56 
 
 Augmented 6-5 chord identical in 
 sound with dom. 7th, 21, 58 
 
 Augmented chord of 6 with doubly 
 augmented 4th, 58 
 
 Bridge chords, 21 
 
 Change of chords (keys) through voices 
 
 moving independently, 62, 67 
 Circle of 5ths, 4 
 
 Diminished 7th chords, 41 
 
 ambiguous, 42 
 
 resolutions of, 42 
 
 changes of key resulting from lower- 
 ing different factors, 42 
 Dominant 7th chords, 22 
 
 in a series, 27 
 
 altered to dim. 7th chords, 28 
 
 (illustration of uses), 49 
 
 Elision of steps in chord successions, as 
 
 an element in modulation, 16, 75 
 Exercises in modulation: 
 
 by dom. 7th, 35 
 
 by dim. 7th, 50 
 
 by augmented chords, 63 
 
 Fifths, circle of, 4 
 relationship by, 4, 12, 79 
 
 Harmonic changes by elision of chords 
 (keys), 16, 75 
 
 Modulation: transient, 7 
 
 apparent, 7, 10 
 
 alteration of notes not necessary, 10 
 
 not produced by a mere succession 
 of keys, 1 1 
 
 diatonic, chromatic, enharmonic, 19 
 
 to dominant, 4, 22 
 
 to subdominant, 24, 35 
 
 to relative minor, 23 
 
 to relative major, 23 
 
 by dominant 7th, 22 
 
 by diminished 7th, 41 
 
 by augmented chords, 55 
 
 table of, 79 
 Modal ending, 25 
 
 Neapolitan 6th, 62 
 
 Relationship by 3ds, 12, 16, 77 
 by 5ths, 4, 12, 79 
 
 Scales, forms of minor, 1 
 
 Third relationship, 12, 16, 77 
 Table of modulations, 79 
 
 99
 
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