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NOVELLO, EWER AND CO.'S MUSIC PRIMERS.X^ 
EDITED BY SIR JOHN STAINER. 



MODULATION 



HY 



JAMES HIGGS, 



MUS. BAC., OXON. 



PRICE TWO SHILLINGS. 

In Paper Boards, Two Shillings and Sixpeme. 



LONDON 6- NKW YORK 

NOVELLO, EWER AND CO. 



Mr 



INTRODUCTORY. 



IN this Primer on Modulation an attempt is made to show something of that inter-relation of keys 
which is so prominent a feature in modern music, to exhibit some of the points of contact that unite various 
tonalities one to the other, and to show that no combination or chord so exclusively belongs to any one key 
that it cannot be employed in other keys. 

The diatonic and chromatic contents of a key are therefore shown at the outset in somewhat of detail 
on the basis of the teaching of the late Professor Sir G. A. Macfarren. Tables are given, in which the 
fourfold use of triads or common chords is displayed, according as a chord being (a) diatonic in primary 
key is quitted as another diatonic chord of another key; (6) diatonic in primary key is quitted as 
chromatic in another key; (c) chromatic in primary, but quitted as diatonic in new key; or (d) being 
chromatic in primary, is quitted as another chromatic chord in another key. 

The several most usual and potent chords of modulation are next passed in review. The essence of a 
modulation is held to consist in the sequence of dominant and tonic harmony in a new key, although the 
special classification of a modulation, whether transitory or cadential, must depend upon the length of 
stay in the new key, position of chords employed, place in rhythm, and probably many other considerations. 
The frequency and habit of modulation is so common in modern music, that the ear of the listener has 
become accustomed to groups of keys being associated and having their harmonies interchanged, so that 
much which, if technically analysed must be regarded as modulation, passes without recognition of the 
fact that the original key has been quitted. 

In the early days of modern music the appearance of an accidental was the almost sure harbinger of a 
change of key, and, as the event was comparatively rare, the continuance was often proportionately long. 
Perhaps a useful comparison may be instituted between tonality in music and habits of travelling. Formerly 
when travelling was difficult, a journey of but a few miles involved time, thought, preparation and endurance, 
and the traveller, by loss of time, by fatigue and discomfort, had but too keen a sense of having been away 
from home. Now facilities for locomotion are so great, that breakfasting in London, one may easily travel 
a couple of hundred miles, transact business, and return in time to dine with little sense of having been away 
at all; but let the same man travel a quarter of the distance and sleep out of town (in fact make a "perfect 
cadence") and he will at once realize that he has been from home. The parallel holds good in tonality. 
Facilities, by use of chromatic harmonies and other means, are so great for combining features of different 
keys and passing out of a key, that often only those modulations which are truly cadential are regarded as 
departures from the principal key; this may be very natural, but it is hardly systematic or technically 
correct. 

After the explanation of the nature and means of modulation a considerable collection of extracts from 
classical writers is added ; each is annotated as seemed necessary. The extracts are taken generally from 
familiar works, in order that the student may derive further advantage from studying each example with its 
context. Two complete movements are also inserted, with detailed examination of the modulations, thus 
showing not only how, but when and where modulations are made. Next follows a set of modulations from 
C to each tonic above. The modulation is shown by five or six different methods in each case. The Primer 
concludes with a set of exercises, and its object will have been attained if any one who reads and studies it 
is induced to observe and tabulate for himself those wonderful possibilities which result from the inter- 
relationship of tonality, and are among the most distinguishing characteristics of modern music. 



CONTENTS. 



INTRODUCTION. 

CHAPTER I. PAGE 

Definition of Modulation Importance of knowledge of Modulation for analysis and construction 
Contents of a key Accidentals Diatonic and chromatic chords in a minor key Diatonic and 
chromatic chords in a major key Illustrative examples Summary of harmonies, including each 
note of chromatic scale ... ... ... ... ... ... ... ... ... ... i 7 

CHAPTER II. 

Natural and extraneous Modulation Attendant keys Tonic chords of attendant keys all included 
in notes of primary scale Modulation transient or complete Gradual or sudden Diatonic 
chromatic or enharmonic Difference between enharmonic Modulation and a mere enharmonic 
change of notation Dominant seventh a key-defining chord Subdominant and leading notes 
the limiting notes of the scale ... ... ... ... ... ... ... ... ... 8 u 

CHAPTER III. 

Modulation by means of chords common to two keys, or by chords connected by one common 
note Major diatonic concords- changed into other diatonic concords of other keys Major 
diatonic concords changed into chromatic concords of other keys Chromatic concords changed 
into diatonic concords of other keys Chromatic concords of primary key changed into other 
chromatic concords of other keys Modulation by retaining root successively as third, fifth or 
seventh of a new chord Modulation by retaining third of primary chord as root, fifth or seventh 
of new chord Modulation by retaining fifth as root, third or seventh of new chord Modulation 
by retaining note of dominant triad as a note of new dominant harmony... ... ... 12 16 

CHAPTER IV. 

Compound Modulation Major tonic changed to minor and so to attendants of minor Minor tonic 
changed to major and so to attendants of major Compound Modulation from a major key 
through minor form of subdominant and so to attendants of that key ... ... ... ... 17 18 

CHAPTER V. 

Enharmonic Modulation The diminished seventh Varied notation Four roots, each available on 
three different degrees of the scale and in two modes Affords direct connection between each 
of the twenty-four scales Remarks on diminished seventh from keyboard point of view Cause 
of the power of the diminished seventh for purposes of Modulation Diminished sevenths may 
follow one another chromatically The minor thirteenth and its enharmonic power The aug- 
mented sixth and dominant seventh enharmonically considered ... ... ... 19 23 

CHAPTER VI. 

Analysed examples of sundry modulations from the works of the Great Masters ... ... 24 38 

Detailed examination of the modulations in the First Movement of Beethoven's Waldstein Sonata ... 39 50 

Summary of the above Modulations ... 5 

Detailed Examination of the Modulations in Schubert's " Domine Deus" (Mass in F) 52 53 

CHAPTER VII. 
Tables of Modulation by various meani from C to each other tonic in chromatic order : 

C to D>. C to G. 

C to D. C to At>. 

C to Eb. C to A. 

C to E. C to Bt>. 

C to F. C to B. 

C to FS (G>). 
Exercises in Modulation 6164 



5461 



LIST OF EXTRACTS FROM THE WORKS OF THE GREAT MASTERS 

EMPLOYED AS ILLUSTRATIONS. 



BEETHOVEN 



BRAHMS 

SCHUBERT 

BRAHMS 

GOUNOD 

BEETHOVEN 



MOZART 
BEETHOVEN . 
MOZART 
BEETHOVEN . 



HANDEL 
SCHUBERT . 

)j ' 

MOZART 
HANDEL 
SCHUMANN , 
BEETHOVEN . 
MOZART 
SCHUMANN . 
BEETHOVEN . 
MOZART 
BEETHOVEN . 
SCHUBERT , 
BEETHOVEN 

ft 
MOZART 



BEETHOVEN 

ROSSINI 

HANDEL 





PAGE 




Air in G 


I 


HAYDN 


Theme Ab, Op. 26 


I 


SCHUMANN ... 


Sonata No. I, Op. 27 


2 


WAGNER 


Requiem, Op. 45 


5 


BEETHOVEN ... 


Mass in E7 ... 


6 




Requiem, Op. 45 ... 


6 


D 


Chorale 


Q 


BACH... 


Sonata, Op. 13 


y 
10 




Sonata, Op. 13 


II 





Sonata, Op. 27 


17 


BEETHOVEN ... 


Sonata, Op. 31 


17 


HANDEL 


Sonata, E minor (Violin and Piano) 


17 





Sonata, Op. 10 


18 


BEETHOVEN ... 


Symphony ("Jupiter") 


18 


SCHUBERT ... 


Second Symphony ... 


18 


BEETHOVEN ... 


Fifth Symphony 


21 


,, 


" Messiah " ... 


2 




March, Op. 40 


24 





March, Op. 27 


24 


,, 


Sonata in D 


25 


,, 


Overture (" Lotharius ") 


2 5 


SCHUBERT 


Piano Works ... . . 


25 


MOZART 


Andante, Op. 35 


25 


BEETHOVEN ... 


" Don Juan " 


26 


SCHUBERT ... 


Piano Works, Op. 4 


26 


SCHUMANN ... 


Sonata, Op. 13 


26 


SCHUBERT .'.. 


Sonata 


26 


MENDELSSOHN 


Sonata No. i, Op. 2 


26 


SCHUMANN ... 


March, Op. 55 


27 


BEETHOVEN ... 


Sonata, Op. 79 


27 


MOZART 


Sonata, Op. in 


27 


,, 


Sonata, C minor 


27 


SCHUBERT 


Sonata, C minor 


27 


HAYDN 


" Don Juan " 


28 


BEETHOVEN ... 


Sonata No. 2, Op. 2 


28 


,, 


" Stabat Mater " 


28 




" Solomon " 


28 


SCHUBERT ... 



"Creation" 28 

Pianoforte Works ... ... ... 29 

"Lohengrin" ... ... ... 29 

Sonata, Op. 77 ... ... ... 29 

Sonata, Op. go ... ... ... 30 

Sonata No. :, Op. 2 ... ... 30 

English Suites ... ... ... 30 

English Suites ... ... ... 30 

English Suites .,. ... ... 30 

Finale, Second Symphony ... 31 

Overture (" Alexander ") ... ... 31 

Overture ("Julius Caesar ") ... 31 

Sonata, Op. 13 ... ... ... 31 

March, Op. 40 ... ... ... 32 

Sonata, Op. 14 ... ... ... 32 

Sonata, Op. 10 ... ... ... 32 

Sonata, Op. 2 ... ... ... 32 

Sonata, Op. 2 ... ... ... 33 

Sonata, Op. 14 ... ... ... 33 

Sonata, Op. 2 33 

March, Op. 27 ... ... ... 33 

First Finale (" Don Juan ") ... 34 

Sonata, Op. 13 ... ... ... 34 

March, Op. 121 ... ... ... 34 

Piano Works, Op. 9 ... ... 34 

March, Op. 40 ... ... 35 

" Lauda Sion " ... ... ... 35 

" Rose's Pilgrimage," Op. 112 ... 35 

Sonata, Op. 2 ... ... ... 35 

Quartet No. 9 ... ... "-35 

Violin and Piano Sonata ... ... 36 

Sonata, Op. 53 36 

Symphony in D ... ... ... 37 

Sonata, Op. 2 ... ... ... 38 

Complete First Movement, Wald- 

stein Sonata, Op. 53 ... 39-50 

" Domine Deus " (Mass in F) 52-53 



MODULATION. 



CHAPTER I. 

MODULATION, in the modern acceptation of the term, is the art of passing from one key or scale to 
another. 

A knowledge of modulation is of the greatest possible importance to the student, alike for the purpose 
of analysis, and construction. Before entering on the consideration of the varieties, signs, or means of 
modulation, it will be necessary to devote a few words to the consideration of the contents of a key, since 
it is essential that the chords possible in, or properto, a key should be well understood before progress can 
be made in recognizing when or how a key is quitted. 

At first it may seem that the integrity of a key can only be preserved by the exclusive use of notes 
belonging to the particular scale, but consideration of the very frequent employment of chromatic notes, 
especially in modern music, will at once show that the appearance of one or more accidentals does not, of 
necessity, indicate modulation. In the following example from Beethoven, it is evident the DJJ is a mere 
chromatic passing note that in no way affects the harmonic progression : 

BKKTHOVEN. 



Ex. i. 



*' 



* 






. 



As any single part may employ chromatic progressions, so certain definite foreign chords may be 
introduced into a key without necessarily producing modulation. The direction of modern musical thought 
and practice has been thus to extend the boundary of each individual key by affiliating to it some of the 
principal harmonies of neighbouring keys. Such chords, although more or less indicative of keys other than 
the primary key, if they do not reach the goal they threaten but return to the first key, are generally 
regarded as chromatic chords in that key thus in the next example the chord marked * may seem to be 
borrowed from the key of E7, but because it at once returns to a characteristic chord of the primary key, it 
is regarded as a chromatic chord in A7. 



Ex. 2. 




So in the next example the chord * D in this context might seem to be the subdominant chord of the 



submediant key A, but the unquestionable tonality of the harmony on either side of the chord referred to 
stamps it as a chromatic harmony in the primary key of CJ minor. 



BEETHOVEN. 



Ex. 3. 




The following tables are intended to exhibit, according to the teaching of the late Professor Sir 
G. Macfarren, the principal chords proper to, or possible in, a key. It is convenient to show the chords 
belonging to a minor key first and to class them as (a) diatonic concords, (6) diatonic discords, (c) chromatic 
concords, (d) chromatic discords. It will be observed that the leading note of a minor scale although 
expressed by an accidental is regarded as diatonic. 



THE PRINCIPAL DIATONIC AND CHROMATIC CHORDS IN A MINOR KEY. 

DIATONIC CONCORDS. 
n , () (b) (c) (d) (e) (/) 



Ex. 4. 



(^ g ; ; 


g S | | 


H ^f* i 


*-K-f: 1" 


jpl s^m 


tr e ^- * ' 


-*- 


J=> 99 
\ ^ ^ 


u_ -*- 




(e^r 7^3 * 






w 




6 6 
4 


6 6 

4 


\ 6 t|6 
4 


6 6 


6 



(a) Tonit triad and inversions. 

(6) Subdominant triad and inversions. 

(c) Dominant triad and inversions. 

(d) Submedjant triad and inversion. 

(e) Inversion of diminished triad on 2nd of scale. 
(/) Inversion of diminished triad on leading note. 



DIATONIC DISCORDS. 



(b) 



(d) 



Ex. 5. 



br^h \T 








* 


1 h "&'! 


1 GJ ** r 'll b^ ~tf^ &c: tl 






-Z- 


-S 

1 




L_a I ^__n c-! jj 


i 
\ 


6 

5 


M. o * cc 


1 


9 7 

7 


11 7 6 13 13 

* 5 



() Dominant 7th and inversions. 

(b) Dominant minor gth, diminished yth on leading note and other inversions. 

(c) Dominant nth and inversions. 

(d) Dominant minor i3th and inversions. 

t The leading note of a minor key although expressed by an accidental is accounted diatonic. 



CHROMATIC CONCORDS. 




Ex.6. 



gj ..*_ Eg^ 



XJ 



e 

B 



(a) Triad on flat 2nd and inversion. 
(6) Triad on supertonic and inversion. 



CHROMATIC DISCORDS. 
fa) 



(*) 



<0 



Ex. 7. 









^ g 




II 



4 



18 



7 

s 



iii Supertonic 7th and inversions. 

(6) Supertonic minor gth, diminished 7th on raised subdominant and other inversions. 

(c) Supertonic ijth and inversions. 

(d) Chromatic tonic 7th, gth and i3th with inversions. 
(<) Augmented 6th on flat 6th with inversions. 

(/) Augmented 6th on flat 2nd with inversions. 



THE PRINCIPAL DIATONIC AND CHROMATIC CHORDS IN A MAJOR KEY. 

The chords shown as belonging to, or possible in, a major key are more in number than those shown 
in a minor key, since all chords shown here as proper to a minor key (except those derived from the tonic- 
triad) are available in the major while the converse does not hold, the minor key is not enriched from the 
major. 

DIATONIC CONCORDS. 

(*) If (<f) V) (/} <g)* 



Ex.8. 






4 



I 

I 



(a) Tonic triad and inversions. 

(6) Subdominant triad and inversions. 

d i Dominant triad and inversions. 

(d) Supertonic triad and inversion. 



(e) Submediant triad and inversion. 
(/) Inversion of triad on leading note. 
(g) Mediant triad and inversion. 



* Chiefly used in sequence. 



CHROMATIC CONCORDS. 

, () (*) W 



Ex. 9. 




S= 



a 



() 



(a) Triad on flat 6th and inversion. 
(6) Triad on flat 2nd and inversion. 

(c) Chromatic triad on supertonic and inversion. 

(d) Minor triad on subdominant and inversions. 

(e) Inversion of diminished triad on supertonic of min.or scale. 



DIATONIC DISCORDS. 

(a) (t) 



Ex. 10. 



yg g 


; s i 


H^ ^^SHH^zzzp^} 


r^j 




f m m \ 


1 II W * 






~m_ 1 


* 
1 * *i 


-s H 


Ez 




&c. 




7 


644 
532 


9764 11 7 6 13 
753 57 



(a) Dominant 7th and inversions. 

(6) Dominant major gth and inversions. 

(c) Dominant nth and inversions. 

(d) Dominant i3th and inversions. 



CHROMATIC DISCORDS. 



Ex. n. 



fc^ 


f- 


"tti f~^ 


rjS * &c - 


'^ 


f 


^ 


^S ^tt^iS ^^ 


tj "^ 




* r 


ffs p 


i 


n 


1 1 




@ ey 


_fi*_ 


f 


g * *" 


^s>- 





&c fj <s &c.- 


-j <> &C.-JJ 


7 


6 

5 


6 J4 
4 2 
3 


t>9 t>7 9 
7 7 

* * 


7 




7 

8 


18 
7 
1 



(a) Supertonic 7th and inversions. 

(b) Supertonic minor gth, diminished 7th on raised subdominant and other inversions. 

(c) Supertonic major gth, 7th on raised subdominant and other inversions. 

(d) Supertonic minor I3th and inversions. 
() Supertonic major i3th and inversions. 



CHROMATIC DISCORDS (continued). 
(<> () W 



(0 



(f) 



(*) 



m i *-F* ' 



Ex. 12. 



90 



t7 6 



-*e. 



+*, 



" 



\. 



9 b7 



018 



18 
77 



g^a 



(a) Tonic chromatic 7th and inversions. 

(b) Tonic minor gth diminished yth on mediant and other inversions. 

(c) Tonic major gth and inversions. 

(d) Tonic minor I3th and inversions. 

(e) Tonic major I3th and inversions. 

(/) Augmented 6th on flat 6th with inversions. 
(g) Augmented 6th on flat 2nd with inversions. 

So long as the chords enumerated above are employed with the restriction that each chromatic 
harmony is followed by a harmony diatonically characteristic of the primary key or by another, but 
antagonistic, chromatic harmony no modulation is made; on the other hand whenever chords proper to, or 
possible in, a new key are confirmed by the use of dominant and tonic harmony of such new key, modulation 
takes place. 



The following examples of the use of chromatic harmonies will be instructive. It will be seen, though 
abounding in the use of accidentals, no real modulation occurs in either extract. 



Poco A ndantf e con espresitoiu. 



JOHANNES BRAHMS, from the " Requiem," Op. 45. 



Ol TrJr f^* 

/) C</^ < ru/<. Ugato. 



9^- 



rrrr rrrr rrrr 



rrrr rrr r r r r^r r r 




rr r r r r r r rr rr 



f fff f fff f 



From SCHUBERT'S Mass in Et>. 




bfc 



3 



^3 



r 



Ky 

i , 



n - e. 



S" 1 



f 



III. 



JOHANNES BRAHMS, Op. 45. 




SUMMARY, 

NAMING THE SEVERAL HARMONIES OF WHICH EACH NOTE OF THE CHROMATIC SCALE OF C 

FORMS A PART. 



Root of tonic series, third of triad on flat sixth and of augmented sixth, fifth of subdominant, 
seventh of supertonic series. 

Root of chromatic chord on flat 2nd, bass of augmented 6th, minor gth of C (tonic minor gth). 

Root of chromatic supertonic' series, root of diatonic supertonic, 5th of dominant, tonic 
major gth. 



Minor gth of D, (chromatic supertonic gth), part of dominant minor i3th. 




Third of tonic series, root of diatonic triad, part of dominant major I3th. 



Root of subdominant triad major and minor forms, 3rd of triad and augmented 6th on flat 
2nd, 7th of dominant, 3rd of diatonic triad on supertonic. 






Third of chromatic supertonic series, part of augmented 6th on flat 6th. 
Root of dominant series, 5th of tonic series. 



y L Root of triad, 3rd of minor form of subdominant, 5th of chromatic chord on flat 2nd bass 

of augmented 6th, minor gth of dominant. 




Root of diatonic triad, 3rd of subdominant, 5th of supertonic series, 131)1 of tonic. 



7th of tonic chromatic series. 



3rd of dominant series, 6th on flat 2nd. 



As each note of the chromatic scale is here shown as forming part of various chords available in the 
scale of C, and as these same notes (although sometimes under other names) are the constituents of every 
other chromatic scale, it follows that every note has not only its power of combination, as here exhibited, 
but, under the condition of becoming other degrees of other chromatic scales, the whole of the combinations 
shown among the twelve degrees are really applicable to each degree. 



8 



CHAPTER II. 

MODULATION as regards the key to which it may be made is divided into (a) Natural Modulation 
and (6) Extraneous Modulation. 

Natural Modulation is where we pass from a given key to either of its attendant keys ; Extraneous 
Modulations are modulations to keys other than the attendant keys. 

The attendant keys are those having the same signature as a given key, or one sharp or flat, more 
or less; in other words the attendants are the relative (minor or major), the dominant and subdominant 
keys and their relatives (minor or major). 

In the following diagram major keys are indicated by capitals and minor keys by small letters. 



KEY OF 

I 
F-<-C->G 

4" I I 



KEY OF 



EXAMPLES. 
KEY OF 



I 



III 
c g d 

KEY OF 
.^_ + 

v v" 

E b B b F 



KEY OF 



III 

e b iff 

KEY OF 

I 

e^b-^J?f 

III 
G D A 



The final chords of all these keys will be found among the notes of the primary scale, but the seventh 
note of the ascending major scale and the seventh note of the descending minor scale cannot be tonics, 
because the scale does not furnish a perfect fifth to such notes. 



ATTENDANTS OF B MAJOR. 



Ex. 13. 












W 


ATTENDANTS 


OF C 


MAJOR. 


41} 9. 


f 


=*= 


fr 


g, 




t) -&~ 


j- 












8 


o 


g 


s 


o 




B 


c 


"rt* 




c 




a 


E 


s 


E 


S 


(b) 


ATTENDANTS 


OF A 


MINOR. 




fn\ *^ 


^ 




5, 


f 





J 








t _J 


c ~*=r -- 













o 


o 




V 




c 


c 






s 


E 


& 


s 


E 



./ L P 




~s c 


- ^ * 


^ 4. 4 
i 
a 


=|F= 

c 

is 


-^ fc 

.s .s 

s s 


o 

c 

a 



(d) 



ATTENDANTS OF G MINOR. 



-*-*- s-^- 



S S S . E E 

The importance of the modulation will largely depend on the form and position of the dominant and 
tonic chords: if they are both in root position and coincident with the end of a phrase the modulation is 
felt to be important; if either of these characteristics be wanting the modulation is less important; but it 
should be noted that important modulations are often made in an incidental way but confirmed by the use of 
more important positions of the necessary harmonies at the appropriate point. 

Modulation is transient or complete. The form of the chords employed whether having the root in the 
bass, or being inversions, the length of the modulation and its place in the rhythm are all important 



f ictors in determining to which class any modulation belongs ; an example will best show how to distinguish 
modulations in this respect: 

GOUNOD. 

-> J- 



j J J JJ| J q^rir^FJ 

r r ET'T r r r V 




'- 



* 



r 



11 



r 



r 



In the above extract we have in the first bar a transitory modulation from Bb to E7. We know the 
key to be Bb from the bass note which from the law of inertia the mind naturally regards as a tonic. We 
recognize a modulation by the succession of dominant and tonic harmonies in another key, both chords 
being however in inverted position, occurring at an unimportant part of the rhythm and of very short 
duration, it is a transitory modulation ^contrast with this the cadential modulation into C minor at the end 
01 the extract where the several harmonies have been converging upon and defining the new key. The 
particular form of the bass A (7, F, G, the notes on either side of the dominant proclaiming its importance; 
the 5 on the sub-dominant pointing to those of experience the coming cadence as plainly as if already 
heard. These are among those habits of progression which the student cannot too closely observe. 

Natural modulation may be either gradual or sudden. It is gradual when it is approached through a 
chord that belongs both to the primary key and also to the key of modulation. It is sudden or abrupt when 
the chord that precedes the modulating chord does not belong to the new key. The following examples 
are from Sir John Goss : 



Ex. 14. 



GRADUAL. 




(6) 



ng^ 



^ 



SfDDEN. 





3 II 



I " I " I -H 



The modulation at (a) is gradual because the second chord belongs both to the key of C and of G. 
The modulation at (b) is gradual for a similar reason. The second chord belongs both to the key of C and 
also to F. On the other hand at (c) the modulation is sudden because the second chord belonging to the 
key of C does not belong to the key of G, and at (d) the second chord belonging to the key of C does not 
belong to the key of I ; . 

Modulation as concerns its means is either diatonic, chromatic, or enharmonic. In diatonic modulation 
some chord is found which is common as a diatonic chord, both to the original key and to the key of 
modulation. In the following example while the first three chords are in the key of C and the last three 



IO 



in the key of G, the third chord is really approached as the tonic chord of C, but quitted as the sub- 
dominant of G, it is therefore common to the two keys. 



Ex. 15. 



S* C2 


" t^ 






e H 


) g 


, ' i^, 






H 


p> f- 








B 


(& CT 




s> 


1 5 U 



In chromatic modulation, a note or chord is taken which is chromatic either to the primary key or to 
the key of modulation. In the next example, allowing the first chord to indicate the key of C, the second is 
chromatic in that key (minor triad on subdominant), but it proves to be also the minor chord on the second 



Ex. 16. 





-tg j^ 




IT2J 
23 


^^^| 






jjZSi 








, 




^-^ 


F^ 1 


-te^ d 


-ud 1>^ 


1 2i 



In the next example the fourth chord diatonic in the key of C, is discovered to be the chromatic super 
tonic triad in the key of Bt>. 



Ex. 17. 



g -*_ cx-** i >j b.^ 



ffih 



Enharmonic modulation is that in which by reason of a change of name of one or more notes of a 
chord, the sound or sounds remaining, the several notes of such chord become other degrees of another 
scale, with new associations and obligations. 

In the subjoined extract at (a) we have a chord of minor gth on D as a root ; at (b) immediately 
after we have the same sounds, only that which was called Eb is now Djf, the root is changed to B, and 
we pass into the key of E minor. 



Ex. 18. 



BEETHOVEN. 




w 



In connection with the subject of enharmonic change, it may be useful to point out that a change of 
all the notes of a chord, from a sharp to a flat notation, is not enharmonic modulation, as it is sometimes 
inaccurately called. In the following example the distance from A|? minor to E major looks very wide, but 



II 



it is evident the composer might have written the first bar as a chord of GJ minor, when the progression to 
the chord of B would have been quite simple. Of course, Beethoven was led to express the first chord of 
the extract as he has done, by reason of the previous context. 



Ex. 19. 



BEETHOVEN. 




The chord of the dominant 7th, as one of the most frequent means of modulation, must receive 
a little special attention. This chord contains what may be termed the two characteristic, or limiting, 
notes of the scale (i.e. the leading note and the sub-dominant). When this chord is followed by the tonic 
triad the key is fully defined ; hence the well-known rule of modulation : " The new key is entered through 
its dominant." It is true the new key may be indicated by other chords, and certain habits of progression are 
often influential in introducing modulation, yet in all cases dominant harmony, in some form, is essential 
to establish and confirm the new key. 

The power of the dominant 7th to define the key is due, as stated above, to its containing the 
limiting notes of the scale. The chord 




cannot diatonically belong to any other key than C, 

because if it belonged to any other key than C, it must belong to a key requiring either sharps or flats in its 
signature. If a key with sharp signature, there must be at least one sharp, and that would be FjJ, but here 
we have Ffe, so the chord cannot diatonically belong to a key with a sharp signature. If, in the same way, 
we examine keys with flat signatures, such keys must have at least one flat, and that would be B7 ; but 
here the note is B||, so the chord cannot diatonically belong to a key with a flat signature, and must, 
therefore, be in C. 

r\ j| ^l 

Of course it is the same with corresponding chords in other keys, thus in the chord (fo 'i8 

C# asserts the key has at least two sharps, while the G !3 declares it has not three. The key, therefore, to 



which the chord diatonically belongs is D. So again in this chord 



At? asserts the key has 



**s 

at least three flats, while the D|| declares it has not four. The key, therefore, is K!. 

Whatever has been said as to the key-defining character of the dominant 7th applies with equal 
force to the whole series of dominant discords, the minor and. major gth, and the derived chords of leading 
and diminished /ths, &c. 



12 



CHAPTER III. 

BY far the largest number of modulations are effected either (a) by finding a chord common to the 
two keys, or (b) by finding chords which, although belonging to different keys, have at least one common 
note. 

Dealing with the case of chords common to two keys, it will be instructive to examine in detail 
the manner in which common chords may be related to one another ; four cases arise : 

(1) A diatonic chord may become some other diatonic chord in another key. 

(2) A diatonic chord may become a chromatic chord in another key. 

(3) A chromatic chord may become a diatonic chord in another key. 

(4) A chromatic chord may become some other chromatic chord in another key. 

The tables of chords which follow are confined to the employment of major chords, because they 
are far more valuable for the purpose of modulation than minor chords, and to have included minor chords 
would have extended the tables to an unnecessary lerfgfh. Only one form of the final chord is given, 
according to the nearness of relationship ; but as every dominant is, as a mere chord, equally the dominant 
of the major and minor form of the tonic, the number of examples may be considered as doubled. 






MAJOR DIATONIC CONCORDS CHANGED INTO OTHER DIATONIC CONCORDS 

OF OTHER KEYS. 



Ex. 20. 



-9 


- H VJ b J 




^ | %J r j gj 


I r^ T| 


j 


S I' 8 




: ^ F J~ 


" fl 


S^ C^ _ 


_C2 






II 



(a) Tonic quitted as subdominant of new key. 

(b) Tonic quitted as dominant of new key. 

(c) Tonic quitted as sixth degree of new key. 



Ex. 21. 





| 






(6) * 
ra ^ 


-t 




r^ 










1 H 


5ti2 ^ 2 22 g 




- 




1 ^ 




1 


-< 


s 


>- 




ro II 


^^ ^^ V& ^ 






1 


^j 




^s 1 


1 ca 








(T-^ II 



(a) Subdominant quitted as tonic of new key. 

(b) Subdominant quitted as dominant of new key. 

(c) Subdominant quitted as sixth degree of new scale. 



Ex. 22. 




(a) Dominant quitted as tonic of new key. 

(b) Dominant quitted as subdominant of new key. 

(c) Dominant quitted as sixth degree of new key. 



MAJOR DIATONIC CONCORDS CHANGED INTO CHROMATIC CONCORDS 

OF OTHER KEYS. 



Ex. 23. 



(6) 



9 ti 




(a) Tonic quitted as flat 2nd of new key. 

(6) Tonic quitted as chromatic supertonic of new key. 

(c) Tonic quitted as flat 6th of new key. 




s 






2 



Ex. 24. 







(a) Subdominant quitted as flat 2nd of new key. 

(b) Subdominant quitted as chromatic supertonic in new key. 

(c) Subdominant quitted as flat 6th in new key. 



Ex. 25. 




(a) Dominant quitted as flat 2nd of new key. 
(6) Dominant quitted as supertonic of new key. 
(c) Dominant quitted as flat 6th of new key 



14 
CHROMATIC CONCORDS^CHANGED INTO DIATONIC CONCORDS OF OTHER KEYS. 

la\ * (b) *. (c) * (d) * 



:fc5 



Ex. 26. 



>c? 



W| 



"7^~ 



~^3~ 



(a) 'Flat 2nd quitted as subdominant of new key. 
(6) Flat 2nd quitted as dominant of new key. 

(c) Flat 2nd quitted as tonic of new key. 

(d) Flat 2nd quitted as flat 6th of new key. 



Ex. 27. 



32 ~ 



(a) Chromatic supertonic triad quitted as tonic of new key. 

(6) Chromatic supertonic triad quitted as subdominant in new key. 

(c) Chromatic supertonic triad quitted as dominant in new key. 

(a) Chromatic supertonic quitted as flat 6th in new key. 



,() 



(6) 



(c) 



7T ra R3 ^~~iJ^~ 


L -s H z? 


Lf .j 




?^j L*fd 


K 


^ 


3 H 


>- u 


- 7^3^ ^ 
" ^ 7 

7^^ n 


s 




b* _ b_ 






-J 2 -?^ U 
-^ H 






H -G* 


*tr^> 


= H 



Ex. 28. 



(a) Flat 6th quitted a.s tonic of new key. 

(b) Flat 6th quitted as subdominant of new key. 

(c) Flat 6th quitted as dominant of new key. 

CHROMATIC CONCORDS OF PRIMARY KEY CHANGED INTO OTHER CHROMATIC 

CONCORDS OF OTHER KEYS. 

(a) * (6) * 



Ex. 29. 






(a) Flat 2nd quitted as chromatic supertonic of new key. 

(b) Flat 2nd quitted as flat 6th of new key. 



Ex. 30. 




(a) Chromatic supertonic quitted as flat 2nd of new key. 
(6) Chromatic supertonic quitted as flat 6th of new key. 







(a) 



(6) 



z-rf . ^-r 




Ex. 31. 



(a) Flat 6th quitted as flat and of new key. 

(b) Flat 6th quitted as chromatic supertonic of new key. 

In the foregoing paragraph and examples, connection of keys has been shown by an entire chord being 
retained,* but used on a different degree of the scale from that on which it was originally employed. A 
method of modulation will now be shown wherein a single note of a chord is retained as a note of dominant 
harmony of a new key. For simplicity the first chord used shall be the tonic 'triad, and the dominant chord 
in which it is retained shall be a dominant 7th, but the principle is capable of far wider application, 
since any note of an unprepared discord may remain to become any other note of any other unprepared 
discord: thus root may change to jrd, 5th, yth, minor or major gth, nth, .minor or major I3th; so the third 
may change to root, 5th, 7th, gth, &c., and so"of every other note. 



MODULATIONS BY RETAINING ROOT AS NOTE IN NEW DOMINANT HARMONY. 




Ex. 32. 



(a) Root retained as root of new dominant. 
(6) Root retained as 3rd of new dominant. 

(c) Root retained as 5th of new dominant. 

(d) Root retained as 7th of new dominant. 

* It U convenient to say " retained." The reader must regard each chord marked * a* split in two, the first half being the 
described chord in the original key, and the second half as that indicated in the new key. 



i6 

MODULATIONS BY RETAINING THIRD OF PRIMARY TONIC AS NOTE OF NEW 

DOMINANT HARMONY. 

(b) (c) 

m 



Ex. 33. 




^z~- 



(a) Third of first chord retained as root of second. 

(b) Third of first chord retained as 5th of second. 

(c) Third of first chord retained as 7th of second. 

MODULATIONS BY RETAINING FIFTH OF PRIMARY CHORD AS NOTE OF NEW 

DOMINANT HARMONY. 



Ex. 34. 




(b) 



i 



(a) Fifth of first chord retained as root of dominant. 
(6) Fifth of first chord retained as 3rd of second chord, 
(c) Fifth of first chord retained as yth of second. 

It will be seen that each tonic, except that of the minor or major 3rd, and of the augmented 4th 
(i.e. in the key of C the keys of Eb, Eh, and FJf), may be directly reached if one or other of the notes of the 
original tonic triad be retained as a note of new dominant harmony. These three may be conveniently 
reached by retaining a note of the primary dominant triad. 



MODULATIONS BY RETAINING NOTE OF DOMINANT TRIAD AS NOTE OF NEW 

DOMINANT HARMONY. 

() (b) (c) ^ 



Ex. 35. 



(a) Fifth ol dominant triad retained as 3rd of new dominant chord. 
(6) Third of dominant triad retained as root of new dominant chord. 
(c) Third of dominant triad retained as 7th of new dominant chord. 



CHAPTER IV. 



Modulation to remote keys is often effected by two or more steps; this is called Compound Modulation. 
For the purpose of compound modulation the mode of a tonic may be changed, and modulations made to 
the attendants of the new key. In the following example E major changes to E minor, and modulation is 
made to C major and B minor, both attendants of the new key. 



litl THOVKN, Op. 27. 




The above change is often made, and another familiar example may be quoted. The change in this case 
is from B major to B minor, but with the common dominant intervening. Notice the third bar. 



BEETHOVEN, Op. 31. 



Ex. 37. 




A change is sometimes, but more rarely, made from minor to major. The next extract, from a violin 
sonata by Mozart, will illustrate this : 



W. A. M CHART. 






Ex. 3.S. 




The change, as shown above, from minor to major direct is not very frequent ; but, effected through the 
ominant, common alike to the minor and major, the change is very famili; r. 



18 



BEETHOVEN. " Finale." Op 10, No. i. 




39- 



Compound modulations are often made through the minor form of the subdominant of a major key and 
then on to one or other of its relatives. See Examples by Mozart and Beethoven. 



Ex. 40. 



MOZART. "Jupiter" Symphony. 
Arr. by HUMMEL. 




f f f .F' 




i 




s 



' f r r 



^ 



Lit* 8 g 



i 



' -^~ T^- L~~ 



^ J.---J- 



i 



V 




j 

s i 



In the above Example (40) the tonic chord of C is followed by the minor form of subdominant and 
further modulation to D 1 ? attendant of F minor. The return is really by the dominant 7th on At? being 
treated as augmented 6th in C major. 

BEETHOVEN. Scherzo, and Symphony. 

' ' *; - -9r _^_ Arr. by HUMMEL. 



Ex. 41. 



/ly-* 




* 


( . j 




3 i B 




-F^ 


Bf* P 




- 


\ 


* 


i ! J -1 n 


=M=^ 


^=i r- 


[\^L J 

nHMFi 


i 

^= 


-ti (2 


rn^- 

4-n^ 



The new tonic A being established is followed by minor form of subdominant of that key. The 
modulation afterwards continues to.Bb, relative of D minor. 



CHAPTER V. 



ENHARMONIC MODULATION. 

The general nature of enharmonic modulation has been already explained (fee page 10). The 
most important chords employed in this way are (a) the diminished 7th, the augmented 5th or minor I3th, 
the augmented 6th, and dominant 7th. 

The diminished 7th, as is well known, arises from the chord of the minor gth with its root omitted, the 
chord thus consists of three minor thirds superposed one on the other. 

Q j This chord, or any other diminished 7th may, according to the notation used, 

O n ^ be expressed either as a 7th, g, *, or , with the result that the root of the chord will 

9J be different in each case. 



Ex. 42. 



As each root may be dominant, supertonic, or tonic of either a major or minor key, we have 4 roots x 3 
possible positions of chord x 2 modes = 24; so by this one chord we may modulate directly into every 
major and minor key, as shown in the next table. 

Ex. 43. 

(a) ROOT AS DOMINANT, (b) ROOT AS Sf TEUTONIC. () ROOT AS TONIC. 








97 9 



t7 '2 



t>7 



, 

t>7 



;r , 



Ex. 44. 

(a) ROOT AS DOMINANT. (b) 



ROOT AS SUPF.RTONIC. 



ROOT AS TONIC. 



= 




s 



6 

= 



& G 



fJ W 



-Z2L 



Ex. 45- 

(<j| ROOT AS DOMINANT. (6) . ROOT AS SUPERTONIC. 



ROOT AS TONIC. 




I 

8 

f* 

*< , . 


: 

=*=! 


M 
: 

.. 

I! | 


ffi 

'. 

=to 


: 
: 
1 

I ? 


?; 

: 

- 

* n II 


J6 C'. 
Jl ||5 
5 
JSZ ( 


1 

^rF 


M 
84 6 
8 

J2 $Q_ 


^ 


*8 

F^~ 


i 

6 

^ 


: 
5 "- 


Cd jpt_ 


-3= 

W ^ 


M 


,-' 


- . 


> w . r 11 : 


: . r II' 


E , 
SH 


? j 


^ur_ 


jhy. 


-" II 



20 



Ex. 46. 

(a) ROOT AS DOMINANT. (b) 



ROOT AS SUPERTONIC. 



'(*) 



ROOT AS TONIC. 



2- b 



06 
4 
2 



56 
4 

2 



be 

P4 4 f>4 

bs b 2 bs 



be 

4 
2 



be 

4 
2 



s* 



^F"" w 

It is worthy of notice that there are only three essential varieties of this chord on a pianoforte or other 
keyed instrument, as the following example will make plain : 

"^ ^_ if w _ ^_ 



Ex. 47. fF 



It will be seen that the chords written in semibreves ascend semitonically, and that the first inversions 
of each of these chords continue the ascent, and the second inversions still carry through the process, 
which may be prolonged through the whole compass of the keyboard. 

The three chords given above may be expressed in no less than sixty varieties of notation, having regard 
to the variety of accidental required, according to key, position, and mode. 

The first of the above chords, as : 

DOMINANT. SUPERTONIC. TONIC. 

3 .4 5 6 












It will be observed the above table contains twenty-ibur varieties of notation, but the third and sixth of 
each set are identical, so there are twenty varied notations of the first chord. There will, of course, be the 
same for each of the other original chords, making sixty varieties of notation for the three chords. These, 
may, under suitable circumstances, be interchangeable one for the other. The combination taken, say 
as a diminished yth on the leading note of C major, may be quitted as either of the other twenty- 
three chords. 

The immense power of the diminished 7th, as a modulating chord, is due to the fact that every 
possible dominant, supertonic or tonic, is either already a note present in the chord, or, at most, may be 
reached by upward or downward semitonic movement of one or other of its notes. 



Three cases arise (a) one note may fall a semitone while the others remain, and the chord becomes a 
dominant 7th, or an inversion of a dominant 7th ; (b) one note may remain, and the others, each rising one 
semitone, the chord again becomes a dominant 7th, or an inversion of a dominant 7th ; (c) one note may 
rise and the other notes adjust into some form of a tonic chord, the raised note becoming the dominant. 



lix. 49. 




i. Dominant of A?. 
3. Dominant of D. 



2. Dominant of C?. 
4. Dominant of F. 




6. 



J. 



5. Dominant of A. 
7. Dominant of E">. 



6. Dominant of C. 
8. Dominant of Q*>. 





9. Tonic chord of B?. 
II. Tonic chord of F?. 



10. Tonic chord of D5. 
12. Tonic chord of G. 



In Nos. I to 4 the lowered note is shown in minim notation. In Nos. 5 to 8 the retained note is 
shown in minim notation. In Nos. 9 to 12 the raised note is shown in minim notation. In every case the 
altered or retained minim is the dominant. 

Diminished 7ths may follow one another chromatically, the whole chord rising or falling together, 
as in the following example, where the chords are respectively built on tonic, supertonic, and dominant roots 
in the key of A : 



Ex. 50. 



8 



-_ -^ 



Roots. A 



In the first movement of the symphony in C minor, Beethoven writes: 



Ex. 51. 




When it is remembered that a chord of diminished 7th may be taken on either of three degrees of 
the scale (on leading note, on raised subdominant, or on major 3rd), it may be necessary to give a word of 
caution lest the too great facility with which it may be used, induces an undue frequency in its 
employment. 



The simplest form of the chord of minor i3th (root, 3rd and i3th) is a chord having somewhat 
similar powers to that of the diminished 7th, and for a similar reason, the equidistance of its several notes 
(here of equivalent magnitude to major 3rds) which allows of corresponding but more limited enharmonic 
variation. 



The chord 




= when brought close 



>~~~ ' s not unfrequently written as an augmented 



5th 




:; such the original chord truly is when inverted (n 



According to the notation employed, either note may be root, 3rd or I3th, and this on either of three 
degrees, viz., dominant, supertonic, or tonic; and the chord on each of these degrees is the same in both 
the major and minor modes, hence we have 3 roots x 3 degrees of the scale x 2 modes, 3 x 3 x 2 = 18 
different resolutions. 

The three aspects of the given chord are 



Ex. 52. 




ite; 






TABLE OF ENHARMONIC VARIATIONS OF MINOR THIRTEENTH.* 

(a) ROOT AS DOMINANT. (6) ROOT AS SUPERTONIC. (c) ROOT AS TONIC. 



122: 



Ex. 53. 



2?- 



-22. 



(a) ROOT AS DOMINANT. (b) ROOT AS SUPERTONIC. 



ROOT AS TONIC. 



Ex. 54. 



LCD its? II tte 






* *-~ - 1 "* '*'--' r "^^ 












i' # 




^ ifo ll=> 


^^- 


7 ' i 
e< 5^ 


j r; It"^-^ ^ \ 


r ^ ^ "-4 



(a) ROOT AS DOMINANT. (6) ROOT AS SUPERTONIC. 



ROOT AS TONIC. 



rz? 



^^S 



HB 



Ex. 55. 



* The position of the chord has been changed with each change of root, in order that the chord may appear in an 
effective position. 



23 



It remains to notice the enharmonic change of the augmented 6th into the minor 7th, or conversely, 
the change of a minor yth into an augmented 6th. The seat of the augmented 6th is upon the sixth 
degree of a minor key, or on the flattened 6th of the major key, or upon the flat 2nd of the scale ; when 
changed into a 7th, such 7th may be either dominant, supertonic, or tonic of the new key: 



Ex. 56. 




- 



m 



Jta: 






(a) Augmented 6th becomes dominant jth of new key. 
(6) Augmented 6th becomes supertonic 7th of new key. 
(c) Augmented 6th becomes tonic 7th of new key. 

or, conversely, a 7th may be changed into an augmented 6th : 

J -I J- I 

^ - ^o < * ** 



Ex. 57. 



*> r r 



d 



CHAPTER VI. . 



Having now passed in review some of the principal means of modulation, it will be interesting and 
profitable to examine a few extracts from the works of great composers, and to observe how they have 
employed the means which have been described. Before doing so, it may be well to explain the importance 
cf'observing the conditions under which modulations occur. 

Extraneous modulation most frequently takes place, not as a departure from the primary key, but 
as departures from related keys. The free fantasia, or development section of the duplex form, is the place 
of all others where we are most likely to meet with remote modulations. Again we often find keys in near 
juxtaposition that seem remote, while in reality they are natural modulations from a common principal key. 
The following extract from Handel shows a transition from D minor to C minor. For the moment it may 
look like an example of extraneous modulation, but on examination it is seen that each of these scales is 
related to the primary key B^ : 

" His yoke is easy " (Chorus in 



Ex. 59. 







EXAMPLES OF MODULATION FROM THE WORKS OF GREAT MASTERS. 



I. B? to B minor. 



SCHUBERT, Op. 40. 




The original key is D major. A well-established modulation is made to Bt>. This note is enhar- 
monically changed into AJ, leading note of B minor. 



II.. From A to BP. 



SCHUBERT, March in D. 




. 3 13^*33.3 tf-3 



The key of A being reached at the end of the first section, the note A is retained as leading note of Bb. 
The modulation is subsequently fully established. 



III. A minor to H>. 



MOZART, Sonata in D. 





l *U. -Jj. -^tJ ^ , J: 

r -IK *i|T' -[T i i|V ^f F| 






This example shows major followed by minor. The subsequent progression shows root and yd 
retained as 3rd and 5th in the dominant harmony of the flat 2nd. 



IV. D major through A minor to E minor. 



HANDEL, Overture to " Lotharius." 




Notice here, going beyond, and reaching the key to which the ultimate modulation is made from the 
other side, A minor, first reached, is evidently more distant from D than E minor. A minor is reached 
by substituting the minor for the expected major chord on the dominant. 



V. A to 



SCHUMANN. 




F^ ^ 



Disregarding the consecutives and the resolution 
in another region, the progression is clear if re- 
garded as a dominant 7th, followed by an aug- 
mented 6th, euharmonically changed into another 
7 th. 




VI. F to Gb and back to original key 



BEETHOVEN, Op. 




Tonic becomes leading note of new key ; afterwards, 3rd of Gt? becomes 7th of C as dominant in F, 
as is often the case in resolution of Neapolitan 6th. 



VII. D minor to E7. 



-Q 1 




1 ^ V * 


bp- 


, f_t 






| Cj* 1 C >-a r 


= r r' c 


L^ 1 Z K 


J ! 




i ff~fi & ft" 

i " 8 S *i 3-55 


-4-= J E 




|W|,</ . 






i i?&> i= ' 


-J 



Retained notes root and 3rd of tonic chord becoming 3rd and 5th of new dominant, combined with 
chromatic movement. The 7th on B!7 appears, at first, to the ear as an augmented 6th in D minor. 



VIII. C to D?. 



SCHUMANN, Op. 4. 



= 



-^r- 



Augmented 5th (tonic i3th) becomes new dominant. 
IX. C minor to 

-2- 



I 



-_g: *_i- t , ', ' 

) . b t? te i kg r? i rt.^-j 

' U u f^S [~ ^p- L r-Si ^^H ,^j 

^g= | P 1 = : eS : = I a h g 

/S7 



, BEETHOVEN, Op. 13. 



^ 




fe 







Inversion of chord on 6th degree of C becomes inversion of new dominant of Dt?. 
X. A minor to B minor. 



MOZART. 




Here there is no note in common, but the 6th on A, sounding like a Neapolitan 6th in E minor, is 
followed at once by an augmented 6th in B minor. 



XI. Bb minor to C minor (both attendants of original key). 



BEETHOVEN, Op. 2. 



m 



r 



i 



- 



Z==3 







In this modulation there is neither a chord common to both keys nor a note common to both chords. 
Ab, taken as flat yth in a descending scale from Bb, is discovered to be the flat 6th bearing an augmented 
6th in the scale of C minor. 



XII. A9 to B (major followed by miuui). 



SCHUBERT, Op. 55. 




This chord is an enharmonic variation of the chord on flat 6th of scale of Ab, requiring notation of 
Ft? and Cb. The major is exchanged for the minor of the same root, which is subdominant in B minor. 



XI 11. G minor to 



BI-:I:IHOVKN, Op, 79. 



: 



1 



- 



-*- 



eifireuivo. 






m 



Chord of G tonic in original key is quitted as sixth in 15"*. 



XIV. C minor to E>. 



BUETHOVKM, Op, in. 




* B5, which gives the hrst indication of change of key, is, however, the melodic minr /th of C minor, 
and only at t do we get real dominant harmony; inversion of major gth, root B?, and this is an equivocal 
chord. It might have proved a 7th on second of scale of C minor, or some prefer to regard such a chord 
as an nth on G. It is the context that decides the ear to know the chord as a dominant harmony of E">. 



XV. C minor to Et>. 



MOZART. 




The key of the minor 3rd above is often attacked direct, the original tonic being Gth in new key. 
XV. (a) C minor to Et>. MO/ART. 






"J 





g* p f r i IT 

SH J I t 



~F 

1 r 



28 



XVI. Bbto D. 



MOZART, " Don Juan." 



I I 






The GJt in bar 2 is really taken by the ear as At>, making a dominant jth on E9, but it is quitted as 
Gjf, the augumented 6th on Bb. The modulation is essentially enharmonic. 



XVII. Bt to D. 



BEETHOVEN, Op. 2. 




Chord marked * supertonic minor gth in D minor 3rd and z>th of previous chord (6th degree in D 
minor), retained as yth and gth. 



XVIII. A minor to C (expressed as D9) and back to primary key. 

tr 



ROSSINI, " Stabat Mater." 
tr 




The chord * is quitted as chord on flat 6th of CjJ (enharmonic equivalent of DO). In bar 4 the 
becomes CJf leading note of D minor, through which a return is made to the original key. 



XIJC. & minor to G minor. 

b sL= i tJ-, 



HANDEL, " Solomon. 



^ 









I 















f 



, h_ 

Cj l r r 






r 



E 



Dominant yth of Ab becoming by enharmonic change augmented 6th on 6th degree in G minor. 



XX. E minor to 



"' Song. 



HAYDN, "Creation." 










y r r 



g 



i 



+4^- 



-7: 



^LLLflLLf 'Igirgff ^Rfjjw* 5 ? 




^B 

This extract beginning in G, passes through A minor, G, E minor, attendants of original key C. The 
root and 3rd of E remain as 3rd and 51)1 * of C (dominant of F), this resolves on chord of flat 6th, which is 
changed into subdominant of A? major, and the familiar movement of the bass establishes that key. 



xxi. B t.. K?. 

tl 



SCHUMANN. 




B (enharmonically O) quitted as flat 6th of new scale. 



XXII. Ai> to D and back. 






WACNEK Lohengrin." 



; -r 









i-> 







-' - 




A3 is followed by chord on flat 6th, this by major triad on C&. The C7 chord (enharmonically B) is 
changed to B minor, relative of D. D major is followed by I) minor, that in turn by its relative F, the 
root of which * remains as a member of the added 6th on the subdominant of original key Ab. 



XXIII. D minor lu A?. 

BEETHOVEN, Op. 77. 




Dominant minor gth of primary key. 
enharni"iii<-ally changed to dominant 
minor 9th of new key. May be ex- 
pressed thus: 



I 

* '-'-*." ': * 



XXIV. A minor to Et>. 



BEETHOVEN, Op 90. 



AAAA , UAAAAA 




The At? at the beginning of the third bar of the extract, strikes the ear as GJf. The enharmonic 
treatment of that note as A!? and of the Btj as C7, makes the last chord of bar three an inversion of a 
minor gth on Bi7 dominant of E^. 



XXV. F minor to C minor. 

rH^( 



BEETHOVEN, Op. 2- 




Implied 5th of first chord becomes yth of new supertonic. 



XXVI. From E to B minor. 



BACH, English Suites. 




Root of first chord retained as 7th of FJf, dominant of B minor. 



J. S. BACH. 



XXVII. A to E via B. 



j=W T-f F^~^=\ 


i^- ^ J/ * 


r ! 





r^rlt-* r = E- SP" 1 

Eg*/ r 1 I P ?: 


m -?- f<*- -*- - 

= r ' r r 


*- 


-f^ - 



Passing through B, and so attacking the new key from beyond. 



XXVIII. From A to E through D. 



BACH, English Suite. 




The converse of the former example. 



BEETHOVEN. Finale of 2nd Symphony, air. by HUMMEL. 




The key of G has been established, but the chord, used as subdominant, would appear to proceed 
through GJ (expressed as A!?), bearing an inversion of augmented 6th and so returning to primary 
key of D ; or, the approach to the chord may be from G quitted as dominant of C minor to dominant of its 
relative E7, by means of implied enharmonic treatment the chord being afterwards quitted as an inversion 
of augmented 6th. 



XXX. G major to D minor, afterwards changing to D major. 
m S3 



HANDEL, Overture to "Alexander." 
tr 




Compare with No. IV. 



XXXI. From A to 1C minor and back. 



HAMU L, Overture to "Julius Csesar." 



i' 









.=fe 



- 



The chord of E minor, * is introduced as a chord on 2nd degree of D, and is followed by chromatic 
harmony on supertonic of new key. 



XXXII. At> minor to E. 



BEETHOVEN, Op. 13. 



. 



T 




Cb enharmonically changed to Bb, or more simply that the first chord is the chord of G minor, and 
the second the dominant of E. (See page n.) 



XXXIII. Dl? to A minor. 

Q 



SCHUBERT, Op. 40. 
* ** 




----- . 

LL r irr 



Dominant of first key becomes leading note of second key. The last Ab of first bar is treated as Gjf 
leading note of next harmony. 



XXXIV. A to F, and on to E. 



BEETHOVEN, Op. 14. 




: ^ 



Flat 6th of A* becomes tonic in F, and the new tonic F* is quitted as chromatic chord on flat 2nd 
of E. The note Ct 5th of the first chord, bar 4, remaining to become minor gth of new dominant B. 



XXXV. D to Bt7. 



BEETHOVEN, Op. 10. 



P 



fcfc 



&c. 



By deceptive cadence, flat 6th of original key becomes new tonic. 



XXXVI. A to F. 



BEETHOVEN, Op. 2. 




Tonic root has minor gth added, the gth remains as yth of new dominant root. 



33 



XXXVII.-D minor to B?. 



BEETHOVEN, Op. a. 




col. 8va. 
The key of D minor being established the new tonic is quitted as 3rd of 13!?. 



liKETHOVEN, Op. 14. 




Founded on a form of deceptive cadence. The minor 6th of E becomes tonic in C. 



XXXIX. A through D to B&. 

Jt 



BEETHOVEN, from Rondo, Op. 2. 




" Filth of chord of L) remains to become 3rd of F as dominant of Bt7. 



S< HUBERT, Op. 27. From a March in C. 




The primary key is C major. The key of A major having been reached modulation is made to F by 
retaining the 5th of the first chords as 3rd of the second harmony. A latent connection exists between 
these harmonies in the key of K major, in which the first chord would be subdominant and the second an 
enharmonic variation of the augmented 6th on the flat 6th of that scale. 



34 



MOZART, " Don Juan." (First Finale.) 




Fifth of first chord remaining as third of second chord, relationship as between dominant triad of 
minor key and dominant 7th of relative major, i.e., as between dominant of C minor and Eft. 



XLII. G minor to E minor. 



BEETHOVEN, Op. 13. 



~ - * * ** v& wr 




Minor gth of chord on D enharmonically changed into 3rd of chord on B. 
XLIII. B!> to G. SCHUBERT, Op. 121. 

JL*- 










m 



pg 

"*" B* "*" 



-i-3- 



In the above the bass note that resolves each discord, instead of bearing the expected first inversion, is 
made a new dominant, the 5th of each chord in turn becoming yth of new chord. So we have a suggested 
but incomplete sequence of Ei?, C, A. 

XLIIlA. From dominant of B to A" 1 . R. SCHUMANN, Op. 9. 



S 






; 



^ 



The connection of the two keys is less remote than the notation would appear to indicate. GJf minor 
is the relative of B. The major mode is substituted for the minor and expressed as Ab. 
The following may make the connection of the chords more plain : 
XLIIlB. 




It will be seen the 3rd of the first chord remains to become the 5th of the new dominant harmony. 






35 



XL1V. fj \nnior to D and on to B. 



SCHUBERT, Op. 40. 




In the first case *A is taken as 6th of CJJ minor, but bearing a $ 7th, becomes dominant of D. In the 
second case the 3rd of chord of Ut, becomes root of dominant of B. 



XLV. E minor to D major. 

09 J* 



MtsotLssoHN, " Lauda Sion. 



-I \- 




* 



. 



! 




=.- 



~ 




! 



-3- 



' 







" 



The modulation is from E minor to D, through G and B minor. The harmonies in the second, third, 
and fourth bars are consistently possible in G, in the fifth bar by an enharmonic change of B^ to AjJ; the 
key of B minor is reached, and then we pass to the key of D. An allusion to the relative is a frequent 
incident in cadential modulation. 

XLVI. G to F (both attendants of principal key C). 
SCMUUAMM. M Thn Rosa's PiliTiiiiairR _" Oi 



SCHUMANN, "The Rose's Pilgrimage," Op. 112. 







G major changed to G minor, and jrd B? retained as jth of new dominant. 

BEETHOVEN, Scherzo, Op. 2. 



XLVII. A through FJ minor to G$ minor. 

H 




First the chord of B * second in A is quitted as subdominant of F$ minor ; this is followed by t sub- 
dominant and dominant of Gg. 

XLVIII. DP to C minor. MOZART, from Quartet No. 9. 



p 


^ 


" IV f" ~t 


B 


trss: - 


F ^ f s&s = , =a= , i 



The chord marked *, approached as dominant of D!?, is quitted as an augmented 6th in C minor. The 
mass of harmony that follows is regular, although the progression of individual parts is free. 



The following are examples of more extended and sequential modulations : 
XLIX. From BP minor to B minor and on to C minor. W. A. MOZART. From a Violin and Piano Sonata. 






Bb as tonic in the first two bars becomes in bar 3 a new leading note (enharmonically expressed as AJf) 
in B minor ; the note B afterwards undergoes a similar change of position, and becomes in bar 8 leading 
note in C minor. 



L. 



SCHUBERT. From Sonata, Op. 53. 






3^3=3 



3=3 



g=:S 



(5) 



(6) 



-(9) 



f frfrr 



37 




The connection of harmonies in the above extract is that of the subdominant and flat 6th of a key, 
chord of C, chord of E? (bars 5 and 6). The same progression is repeated between the chords of Bt> and 
G? (bars g and 10). In bar 13 B7 and D7, enharmonic variations of AJJ and CJJ, make part of the 
dominant chord of B minor. The chord on its 6th degree is employed as the dominant of C (bar 16). 



HAYDN. From Symphony in D. 
Andante. 






G major is followed direct by G minor (bar 4). The chord on the 6th degree of G minor is established 
as new tonic (bars 5 to 9). The same note, Eb, in bar n, is employed as bass of augmented 6th. D, 
reached as dominant, is dwelt upon for five bars beyond the present extract, and so effects the return to G 
major. 



LII. 



BEETHOVEN, Op. 2, No. 2. 




The above extract commences in the key of A minor. The GJf part of a diminished 7th'in bar 3 is 
quitted in the next bar as Ai? minor gth on dominant of C. In bar 7 B is part of a diminished yth, but in 
the following bar it is quitted as C?. minor gth, on Bl? as dominant of E 1 ?. In bar u D, part of diminished 
yth, remains to become in bar 12 the root of a dominant yth in G ; this note in turn bears another dominant 
yth. The bass is afterwards sharpened leading to A (bar 15), as previously a dominant 7th is first 
employed ; the bass is again raised, and we reach B minor (bar 17), and now A, employed as an nth on E, 
leads through a prolonged use of dominant harmony to the principal key. 

It is not enough to possess the power or skill to modulate, it is pre-eminently necessary for the 
musician to know when to modulate. As has often been pointed out, a mere senseless rambling in and out 
of different keys, is not in itself a source of pleasure ; but the power of appreciating when variety has 
exhausted its means within a key, and the skill to glide out of the original key into some other, or by a 
sudden surprise to assume at the right moment a new tonality (the chord of modulation carrying its 'own 
iustiflcation to the mind of the intelligent listener) these are among the most potent charms of modern 
music, and plan or design is shown at least to as great a degree in the balance and contrast of the keys 
chosen, in which to display manipulation of the theme, as in the thematic treatment itself. 

The student is strongly advised to analyze many movements of various kinds on some plan similar to 
that now employed to exhibit the modulations of the first movement in Sonata C, Op. 53 (Waldstein), 
Beethoven, and "Dominus Deus," Mass in F, Schubert. 



PIANO. 
cJ_88. 



39 

FIRST MOVEMENT OF WALDSTEIN SONATA, WITH NOTES ON THE 

MODULATIONS. 

_ i^ ^k""'\ L> v ' B " OV H. P- 53- 

[ ' AlUfro cun bno. ^ \2?- *$* * f ' ___^ "^^ 

^TVT~~ ~ ~ > mm ^ *9m+ ft ~^ t m^m* I i 1 * ^^ ^^ ^^ 

iH*s 






p^ 



^ 



Ws.jJJJIII JJJJJJ jjl ;Jj J JJTTrjjJJJJS 

-j*M^.MMjij|. 
******"* -tr-mt-0-0 --tt-0-tt "tr -f-*t r -* -g-tt -*-?* **-*-*-*-*-* 

* r>. j 




J7T37t73 



=-7= =t 







Bar i. C major. 

Bar 2 4. Dominant and tonic harmonic* of G. (Modulation 

very Iraniient.) 
Bar 5 7. Subdominant, dominant and tonic harm.iiei of F. 

(Modulation trannit 
Bar 8 10. Approaching through minor form of tubdaminant. 



Bar it 12. Dominant and tonic of C minor. 

Bar 13 14. Return to C major. 

Bar 15 17. Dominant and tonic of G. (Compare with 3 4.) 

Bar 19 21. Dominant and tonic of A minor. 

Bar 22. Augmented 6ih on 6th of K minor leading to 

Bar 23 34. Dominant of E u>ed ai Pedal. 




V 81*'. 



P 33 



I f^\ r -I *J- 

+TGT V ^f *f 



CTfFf 



I 

cres. 34 , 35 36 

* * ft*- dolce e molto legato. 



* 



1 



* 



^P 



S 



* 



-iT 
i 






f^ 1 *^ 1 



37 



39 



i 40 



42 







,r 




Bar 35 74. E major (the second subject begins in bar 35). Bars 36, 40, /" an( j 4 g contain avoided or deceptive cadences from 
dominant of C]t minor. 






59 



-*----* - * 

I r 






^ -. .. 



'r^* 




Ban 64 and 6j. Chromatic lupertonic harmony in E. 



| Ban 74 and 75. Dominant and tonic of A minor 







I* * 



^-#^4=^ 

83 cres. 84 



m 



80 



81 | 



cres 82 



I I ! 







=P=H 



f 



85 



1 ores. 86 
I. 



87 







Bar 76 78. E minor. 

Bar 78 80. A minor. 

Bar 80 84. E minor. 

Bar 84 85. C major. (At this point the " repeat "commences.) 

Bar 86 go. F major. 

Bar 9192. Dominant and tonic of C major. 



Bar 93. Mode changes from major to minor and the chord 

proves to be subdominant in G minor. 
Bar 94. Dominant of G minor. 

Bar 95 99. G minor. 
Bar 99103. C minor. 
















r> f M 


t^-r^ : 1 1 


r-"^. 


c/ 

111 


W 
r ' 112 





_rH .JH rT 
; - 


^f^f^-^rr^,- 




=^ 


* i j * 

4-- ,, 


"If^ 



.,._u. ,. 



l5nEs.----.-r 




Bar 103 104. Dominant and tonic of F minor. 

Bar 104109. Sequence of prepared icventhi in laat inversion. 

Bar 1 10. Dominant and tonic of F minor. 

Bar lit. Augmented 6th, on D?, leading to 

Bar 112 115. Prolonged uie of harmony of C (dominant in F.) 



Bar 116117. *' major. 

Bar 118119. F become* dominant of in. 

Bar no 121. B,T 

Bar 122 113. B? aa dominant. 



44 







Bar 124 126. E|? minor (second inversion). Here a change 
of notation occurs, B[> being next written 
as A4 and Gf as Fj. (Se Note, page 51.) 

Bar 126127. ^t as dominant of B minor. 

Bar 128 129. B minor. 



Bar 130 131. Dominant of C. 

Bar 132 133. C minor. 

Bar 134. Chromatic chord on flat 2nd of C. 

Bar 135. Chromatic supertonic harmony in C. 

Bar 136 155. Mainly dwelling on dominant of C 




Bar 156. Return to principal subject and original key. i Bar 168. 

Bar 157 159. Dominant and tonic of G. 

Bar too. Subdominant in F. Bar 169. 

Bar 161 163. Dominant and tonic in P. Bar 170. 

Bar 164165. Approaching C minor. 

Bar 166167. Dominant and tonic of C minor. 



to 

vi/ 
Pause on sixth of C minor quilted as dominant 

in Dp. 
Tonic in Dp. 
Pause on B? as 6th of Dp, quitted as dominant 

ofEp. 



W 171 172 crcs. 173 ,-_ 174 



^.rjrj.F JF KK^ !J 



_ r _ r _ r -rr .r , f 

^ ryr Frf F=rt 3^fc: 



r ^H^ 



/ y isg^/ j/- jf 

>trir ,rr '>fg'./a 



' ' ^ SF- 4- -F- -- -F-,! -- i -F-I 




Bar 171. Et>. 

Bar 172. Chromatic harmony of D as supertonic in coming key of C. 

Bar 173. Dominant of C. 

Bar 174. C major 



Bar 175 177. Dominant and tonic of G. 

Bar 179 181. Dominant and tonic of A minor. 

Bar 184 195. On E as dominant of A. 

Bar 196. A major. Second subject. 



^^^jjy^^i 

i "r*^ -it-. 







209 



r^ - , : r * ~""7 

;- ( -5 ' w 9 m m 

*" " 



( 

V 

' 



- rriiJTn 



210 



:' 






*'^ffff f *'*v5'frgs 



221 




222 



223 



224 










I iii iii iii i 



Bar 200. A minor. 

Bar 201203. C major. 
Bar 304205. A minor. 



Bar 206 107. C major. 

Bar 208 209. A minor. 

Bar 210 220. C major. 
Bar 211 223. Dominant and tonic of F. 



errSE^fTTj 1 1 r A i TTT1 tf r ; 



t=i 



225 



226 



V 2 



1^3- 



22 J 



y^yrjt 



ii iii i T i i iii 





^344^b4jffiTO 

*--*- WW-al-r:**^* J:i5 




Bar 225 226. Chromatic supertonic harmony in C. 

Bar 227 235. C major. 

Bar 235 237. F minor. 

Bar 238 239. C becoming dominant. 

Bar 239 241. F major. 



Bar 241 245. C major. 

Bar 245246. F. 

Bar 246 248. F minor. 

Bar 249250. D[? taken as fiat 6th of F, employed as new tonic. 

Bar 250251. Dominant and tonic of Ap 



'/ 





" ""CUi 



269 



m 





Bar 252 253. Dominant and tonic of B? minor. 

Bar 254 255. Dominant and tonic of C minor. 

Bar 256 262. C with varioui chromatic harmoniei. 

Bar 262 264. Dominant and tonic of D minor. 



Bar 265267. C major. 

Bar 267268. Dominant and Ionic of A minor. 

Bar 269 270. C. 

Bar 270274. Sequence. 









1 ^"^ 


^~-- 


| 


fc ' 


f * - 


^ 


^ 


E i 


O- 


^^TN 

[\y r-j "*" "-' 
1 ' j ^ K^^.I '^ 1 


40 

, 




285 

~~i -- i 


286 




e> 
-&^ ^ 


287 

~- 

d 


i i 
p 288 


1 


i 


289 




cr. 290 p 


11 


H <d 




-%^ 












v 






/nV S 






J 


















(W. 11 










/m 


P #S 


J 


fs 




J 


i 3gg 





T"^ 




1 




vF~ 


| f* 


R__ 






3 






r ^ 








' 















~i J^jlJ^'qrgp 




Bar 275 284. C major. 

Bar 284. A minor. 

Bar 285. Deceptive cadence. 

Bar 286288. C major. 

Bar 288 289. A minor. 

Bar 289. Deceptive cadence. 



Bar 290 -296. C major. 

Bar 296 297. Dominant and tonic of G. 

Bar 297 298. Dominant and tonic of F. 

Bar 298. Chord of F minor quitted as minor form of 

subdominant in C. 
Bar 298 300. C major. 



I 



SUMMARY OF THE MODULATORY ANALYSIS OF THE FIRST MOVEMENT 
OF SONATA IN C. (BEETHOVEN, OP. 53.) 



i. C major. 

2 3. Dominant and tonic harmony of C (modulation 

very transitory). 

5. Subdominant of F. 

67. Dominant and tonic harmony of F (modulation 

very transitory). 

8 10. Approaching 

ii 12. Dominant and tonic of C minor. 

13 14. Return to C major. 

15 17. Dominant and tonic of G (compare with 2 4). 

1921. Dominant and tonic of A minor. 

22. Augmented 6th on 6th of E minor, leading to 

23 34. Dominant of E. Used as a pedal. 

35 74. The second subject begins in bar 35. 

Bars 36, 40, 44 and 48 contain avoided or de- 
ceptive cadences from dominant of C ; minor. 
Bars 64 and 65, chromatic supertonic harmony 
in E. 

74 75. Dominant and tonic of A minor. 

7678. E minor. 

78 80. A minor. 

80 84. E minor. 

84 85. C major (at this point the repeat commences). 

8690. F major. 

9192. Domiuant and tonic of C major. 

93. Mode changes from major to minor, and the 

chord proves to be subdominant in G minor. 

94. Dominant of G minor. 
9599. G minor. 

99103. C minor. 

103 104. Dominant and tonic of F minor. 

104 109. Sequence of prepared 7ths in last inversion. 

no. Dominant and tonic F minor. 

in. Augmented 6tb on I)?, leading to 

1 1 2 115. Prolonged use of harmony of C (dominant of F). 

116117. F major. 

118 119. F becomes dominant of B?. 

120 121. Bf. 

122 123. ivy as dominant. 

124 126. E!> minor (second inversion). Here a change 

of notation occurs, Bt> being next written as 

AS, and G) as F* 

126127. 1 J as dominant of B minor. 
128 129. B minor. 
130131. Dominant of C. 
132 133. C minor. 

134. Chromatic chord on flat 2nd of C. 

135. C bromatic supertonic harmony in C. 
136 155. Mainly dwelling on dominant of C. 

156. Return to principal subject and original key. 

157 159. Dominant and tonic of G. 

160. Subdominant in F. 

161 163. Dominant and tonic in F. 

164 165. Approaching C minor. 



BAR 

166 167. Dominant and tonic C minor. 

1 68. Pause on 6th of C minor, quitted as dominant 

in Dt>. 

169. Tonic in D!>. 

170. Pause on B7 as 6th of D7, quitted as dominant 

of E7. 

171. E?. 

172. Chromatic harmony of D as supertonic in 

coming key of C. 

173. Dominant of C. 

174. C major. 

175 177. Dominant and tonic of G. 

179181. Dominant and tonic of A minor. 

184 195. On E as dominant of A. 

196. A major. The second subject. 

200. A minor. 

201 203. C major. 

204 205. A minor. 

206 207. C major. 

208 .209. A minor. 

210 220. C major. 

221 223. Dominant and tonic of F. 

225 226. Chromatic supertonic harmony in C. 

227235. C major. 

235237. F minor. 

238 239. C becoming dominant. 

239 241. F major. 

241 245. C major. 

245246. F. 

246 248. F minor. 

249 250. D? taken as flat 6th of F employed as new 

tonic. 

250 251. Dominant and tonic of At>. 

252 253. Dominant and tonic of B? minor. 

254 255. Dominant and tonic of C minor. 

256 262. C with various chromatic harmonies. 

262 264. Dominant and tonic of D minor. 

265 267. Dominant and tonic of C. 

267 268. Dominant and tonic of A minor. 

269 270. C. 

270 274. Sequence. 

275284. C major. 

284. A minor. 

285. Deceptive cadence. 
286288. C major. 

288 289. A minor. 

289. Deceptive cadence. 

290296. C major. 

296297. Dominant and tonic of G. 

297 298. Dominant and tonic in F. 

Chord of F minor quitted as minor form of 

subdominant in C. 

298 300. C major. 



* The chord written as J on B7, in bar 125, passe* by enharmonic change of B7 to A& 
and of G? to FjJ to a g on AJJ. The remote key attained, together with the change 
of notation, makes this look more complex than it is in truth. Transposed to a key 
that does not require change of notation, this is the substance of the progression : 



-49- 







" DOMINE DEUS," WITH NOTES ON MODULATION. 



PIANO. < 




A , ^ 


1 














^VJ- 


ffST" 


J J 




It? s 1 


7 f tj 

K. 
* ^ 


|T 
* 1 





: 






_ 
J 


r 8 S 


(Lr ' 
- 

c $" 
F 


9 ~ 

1 f f f-^= 


= H =z i 


^^Q 


r r 


* ' 


k 


a* 









L-J 


- 


LJ CJ t- ' 


-fl^- 1 



r fl 1 




=^ 






-* 


J 1 


-^ 


t ^>a-^" 







J J 






=ir 






=s=\ 


ny'-^* 
& -T 


F=^ 
f-H> 


^ 

ai 


- 

^ 


J 




o 


-f 


11 ' 

Ml ^ f 


r ^ 





* 
- 




1 


2 




J 


. 

J - 


M b r 


4= 






^ 








^ CJ C^ 


E= 




1 r 1 























= - I i.^ i i j. =qa)= 


^ 




.tti* 




r 


' 


J 


s^ 


^ 



- 

=1 


33 
f= 


bg Lf F 1 

1 15 ^_^ r , 


zfe 


jjj 


^13 

F r 


-i* 


&-> 1 ""- *-\ r 
^ cJ ^ i-J [ 






E 




s 


^= 


> 


Bar i. D minor. 
Bar 2 3. F major. 
Bar 3 4. A minor (chord of G supertonic in F). 
Bar 5. F major. 
Bar 5. Bl? (very transitory). 
Bar 67. F. 


Bar 7 9. D minor. 
Bar 9 10. G minor dominant quitted as super- 
tonic in C. 
Bar n. C minor. 
Bar 12 14. G minor. 
Bar 1415. C minor. 



53 






Bar 16. G minur. 

Bar 16 19. D minor. 
Bar i g 20. F major. 



Bar 20 21. A minor. 
Bar 22 24. D minor. 



SUMMARY OF THE MODULATOKY ANALYSIS OF " DOMINUS DEUS," FROM 

THE MASS IN F. (SCHUBERT.) 



BAR 

i a. D minor. 

a 3. F major. 

34. A minor (chord of G supertonic in F). 

}. F major. 

5. Bt> (very transitory). 

6-7. F. 

79. D minor. 

9 10. G minor dominant (quitted as supertonic in C). 



BAR 

ii. C minor. 

12 14. G minor. 

1415. C minor. 

16. G minor. 

16 19. D minor. 

1920. F major. 

20 21. A minor. 

2224. D minor. 



These modulations are almost exclusively to attendant keys. 



54 



CHAPTER VII. 

The following pages contain modulations from C major to each diatonic and chromatic interval. Five 
or six different means are shown for effecting each modulation, and return modulations to C major are added 
in each instance. 

Wherever a modulation occurs from .the primary key there must be by some means a return ; such 
return may be direct or circuitous ; when direct the return modulation is seldom effected by as striking a 
harmony as that by which the outward modulation was introduced in fact as the ear is better prepared for 
the returning tonality it does not need so much that is characteristic to justify its re-appearance ; yet it is in 
this matter of the return that the inexperienced most often betray their want of resource. 

A short explanation is appended to each example. It would have been easy to have added to the length 
of the book by transposing these examples to start from each key, but it will be far more profitable for the 
student to make such transpositions for himself or herself. The modification necessary to make these 
modulations available to or from a minor key will be evident. 



TABLES OF MODULATION FROM C TO EACH OTHER TONIC IN CHROMATIC ORDER. 

In the tables which follow, the first semibreve chord in each example represents the key from which 
the modulation is made. This is generally given in root position, but sometimes, for convenience, the first 
inversion is employed. The second semibreve indicates the key reached ; this and the immediately 
preceding chord in each case stand in the relation of tonic and dominant harmony of the new key, but the 
inverted positions of these chords are frequently used, as the object is merely to show the essence of the 
modulation : the confirmation of the modulation should be added in each case. In like manner the chords 
added to effect the return to the original key often require corroboration. 



V 



C TO Dt?. 



(Enharmonic change is indicated by the use of quaver notation.) 



-f*s? 



fl) i f; i * g hg- 



^^ 



m <^> 



<&- 



-W- 



Neapolitan 6th becomes new tonic. 



# Chromatic flat 6th of primary 

becomes dominant of new key, 

tonic of primary becomes leading 

note of new key. 




1 If r ' 




Inversion of dominant minor gth becomes 
inversion of new tonic minor gth. 



Inversion of supertonic minor gth becomes 
inversion of new dominant minor gth. 



55 



*-"'- 



Inversion of primary tonic gth becomes 
inversion of new supertonic gth. 



iMi 



: 



m 9a> 



Minor ijth of C resolved as minor 
1 3th of A? . 



C TO D. 



z B 



3rd and 51 h retained as part of 
new dominant. 



Inversion of dominant minor gth becomes 
inversion of supertonic minor gth. 



r^ 



Inversion of supertonic minor gth quitted 
as inversion of tonic minor gth of new key. 




^ -' 



Inversion of tonic minor gth becomes inversion of 
dominant minor gth of new key. 



? 



Tonic minor i jth of primary key quitted 
as supertonic 131(1 of new key. 






C TO Eb. 



if 

<T1- 

| ' 



m " r ~- r 



'; >; 



Minor form of subdominant becomes 
minor second of new key. 



Chord on flat 6th quitted 
subdommant of new key. 



Inversion of dominant minor gth 

quitted as another inversion of 

dominant minor gth of new key. 






Inversion of supertonic gth quitted as another 
inversion of supertonic gth of new key. 



TTTTT 



Inversion of tonic gth quitted as another inversion 
of tonic gth of another key. 



C TO E. 



Tonic of primary key, quitted as flat 6th 
of new key. 



q) g 



: 



Triad on 6th of key, quitted as minor 
form of new subdominant. 



t ^ ^ jj(S 3 cr L-fc - 

) o * jfr US' "^g e^- 



ffl 



Inversion of subdominant, quitted ae 
Neapolitan 6th of new key. 



Minor I3th of primary tonic becomes minor 
of new key. 



Ik 



Inversion of supertonic gth becomes inversion 
of new dominant gth. 



Jl 



Inversion of tonic minor gth becomes inversion of 
supertonic minor gth. 



Inversion of dominant minor gth becomes inversion 
of new tonic minor gth. 



g 



Tunic becomes new dominant. 



57 
C TO F. 



? % 



Dominant minor gth becomes supertonic 
minor gtb. 



m 



ii 



Supertonic minor gth becomes new tonic 
minor 9th. 



e^ 
~v 



Tonic minor gth becomes dominant minor gib. 



- H - - 



Minor i jth of primary tonic quitted as 
minor i jtli of new dominant. 



C TO Ftf (Gb). 




Flat 2nd (Neapolitan 6th) quitted as dominant 
of new key. 



Inversion of dominant minor gth become* 
inversion of dominant minor 9th of new 
key. 



Dominant triad quittted as that on flat 2nd of 
new key. 




Inversion of supertonic minor yth quitted as inversion of 
supertonic minor 9th of new key. 



??*=* 



pr- 

Inversion of tonic minor gth quitted as another inversion 
of tonic minor gth of new key. 



_a=?_ 



Minor i$th of primary tonic quitted as supertonic 
minor i$th of new key. 



C TO G. 



IZ2I 



Tonic quitted as subdominant of new 
key. 



:g= 



~f=3~ 



Flat 6th of primary becomes flat and of 
new key. 






E 



Supertonic minor gth of primary quitted 
as dominant minor gth of new key. 



Tonic minor gth becomes supertonic minor gth of 
^, .minor gth of new key. 




Dominant minor gth quitted as tonic 
minor gth of new key. 



C TO Ab. 






Chromatic chord on flat 6th quitted 
as new tonic. 



Neapolitan 6th quitted as inversion 
of new subdominant. 



59 



Minor form of subdominant quitted as 6th of 
new key. 



a 



Inversion of tonic minor gib quitted as inversion 
of dominant minor gth of new key. 



^^ 



Tonic minor I3th of primary key quitted as 
tonic minor ijth of new key. 





*" sg * " H 


R\ *s 7 w f rS 1 
W. (tS 

^ ?*. 


^g i ^ ^ II 

* q ? 


tL ~5 B , 


B 



Inversion of dominant minor 9th quitted as 
inversion of supertonic minor gth. 




- ' 



-w- 



Inversion of supertonic minor gth quitted as 
inversion of tonic minor gth of new key. 



C TO A. 




Chromatic supertonic triad Quitted as sub- 
dominant of new key. 




Subdominant becomes flat 6th of new key and bears aug- 
mented 6th. 



ra * 



^: * ; ^ 



Third of primary key retained as root of 
dominant of new key. 



P 8 



Tonic minor I3th of primary 
quitted as dominant minor ijth of 
new key. 



6o 



Inversion of dominant minor gth becomes 

another inversion of dominant minor gth of 

new key. 



-*-tpr 



g 



Inversion of supertonic minor gth becomes inversion 
of tonic minor gth of new key. 



Inversion of tonic minor gth becomes another 
of tonic minor gth of new key. 



C TO Bt>. 



Tonic of primary key quitted as chromatic 
supertonic triad of new key. Retained note. 



Inversion of supertonic minor gth quitted as in- 
version of dominant minor gth of new key. 



Inversion of tonic minor gth quitted as 
inversion of supertonic of new key. 



Tonic minor I3th of primary key 
quitted as supertonic of new key. 






Inversion of dominant minor gth 

quitted as inversion of tonic minor gth 

of new key. 



/ 



61 
C TO B. 



^-g* 



First inversion of tonic triad quitted as 
Neapolitan 6th of new key 



s. 



8 



II 



Inversion of tonic minor gth 

quitted as inversion of dominant 

minor </h. 



6 5 ii^= 



&*- 



* 



Dominant 7th of primary becomes augmented 6th of new key. 







Inversion of supcrtonic minor 9th quitted 
as inversion of tonic minor <yth. 




-.. ^1 



Inversion of dominant minor <jth quitted as 
inversion of supurtonic of new key. 



EXliRCISliS IN MODULATION. 

The student should now work the following exercises. In doing this, it will be desirable to extend 
each exercise into a regular phrase, say of four bars; the modulation, if made early in the phrase, should 
be duly confirmed, and care taken to attain variety in the approach of the cadence. It will be found useful 
to work in various rhythms : the following may illustrate what is meant : 

D to G. 



D to Bf. 



P^P 



Sr:| 



T-Tr 



- :' 



J I 



62 

Exercise i. Name the attendant keys of A, B, and Eb major, and of G, Bb, and Eg minor. 



j. Quit this chord (given as tonic in Ab) 

(a) As a subdominant chord. 

(b) As a dominant chord. 

(c) As chord on sixth of that minor key to which it diatonically belongs. 

(See example 20.) 



EE 



3. Quit the second chord (given as subdominant) 

(a) As a tonic chord. 

(b) As a dominant chord. 

(c) As chord on sixth of that minor key to which it diatonically belongs. 

CSee example 21.) 



4. Quit the second chord (given as dominant) 

(a) As a tonic chord. 

(b) As a subdominant chord. 

(c) As 6th of that minor key to which it diatonically belongs. 

(See example 22). 



5. Quit this chord (given as an inversion of tonic) 

(a) As an inversion of chord on flat 2nd of key (Neapolitan 6th). 

(b) As chromatic supertonic harmony of a new key. 

(c) As harmony of flat 6th of a new key. 

(See example 23.) 



6. Quit the second chord (given as inversion of subdominant harmony) 

(a) As inversion of chord on flat 2nd of a key (Neapolitan 6th). 
(6) As chromatic supertonic harmony of a new key. 
(c) As harmony of flat 6th of a new key. 
(See example 24). 



7. Quit the second chord (given as inversion of dominant harmony) 

(a) As chord on flat 2nd of a key (Neapolitan 6th). 

(b) As chromatic supertonic harmony of a new key. 

(c) As harmony on flat 6th of a new key. 

(See example 25). 



8. Quit the second chord (given as chromatic harmony of flat 2nd) 



(a) As tonic harmony of new key. 

(b) As subdominant harmony of new key. 

(c) As dominant harmony of new key. 

(</) As 6th of minor key to which it diatonically belongs. 
'.See example 26). 



9. Quit the second chord (given as chromatic chord on the supertonic) 



(a) As tonic of a new key. 

(6) As subdominant of new key. 

(c) As dominant of new key. 

(d) As flat 6th oi a new key. 

(See example 27). 



10. Quit the second chord (given as chord on flat 6th of key) 

(a) As tonic of new key. 
(6) As subdominant of new key. 
(c) As dominant of new key. 
(See example 28). 



> , 












I* " "* 








OS 


n ti3 


/ 


flp U S 






L J- 




a 




< 



ii. Quit the second chord (given as inversion of chromatic chord on flat 2nd) 



(a) As chromatic supertonic. 
(6) As flat 6th. 

;See example 29). 



:; 



12. Quit the second chord (given as chromatic supertonic) 



(a) As flat second of a key. 

(b) As flat 6th of a key. 

(See example 30). 



1 



' o- 



^ > 



13. Quit the second chord (given as chord on flat 6th) 



(a) As flat 2nd. 

(b) As chromatic supertonic. 

(See example 31). 



=. s - ^ 



MA 

6 " 






6 4 

14- Convert each note of the given chord successively into root, 3rd, 5th, or 7th 
of a dominant 7th, and resolve. 
(See examples 32 34). 



m 



15. Modulate from chord of Bb to Dt?, D, and E major, use but one intermediate concord, and proceed 
to 7th by a retained note. 

(See example 35.) 

16. Modulate from B major through B minor to relatives of B minor. 

(See example 36.) 

17. Modulate from C minor through C major to relatives of C major. 

(See example 38.) 

18. Modulate from Bi7 through Eb minor (minor form of subdominant) to relatives of Eb minor. 

(See example 40.) 

19. Modulate from B minor through F$ (dominant of B minor) to relatives of FJf. 



20. Enharmonically vary each of these diminished 7ths. /f. \rS &j I 5 ^ Mark 

yj ) ,^ [ | *? \ \ j^ || 

each root and resolve each chord t7~ ir^~ 

(a) As dominant. (6) As supertonic. (c) As tonic discord. 
(See examples 42 46.) 



21. From given chord, $ & 1 - '- modulate by one intermediate chord to each of the twelve major 
and minor keys. 

(See examples 43 46.) 

22. Modulate from D to E, F, and A, by diminished 7th on leading note of new key, showing the same 
chord in relation to the primary key by enharmonic variation. 

(See example 42, and Modulations, pp. 54 61.) 

23. Modulate from Bfr to A, G, and F#, by diminished 7th on raised subdominant of new key, showing 
that chord first as it would be expressed in relation to the primary key. 

(See example 42, and Modulations, pp. 54 61.) 

24. Modulate from A to C, E, and Eb, by diminished 7th on 3rd of new key, showing that chord 
first as it would be expressed in relation to the primary key. 

(See example 42, and Modulations, pp. 54 61.) 

25. Modulate from E7 to Dt7, G to Ab, and Al? to D, in each case by dominant minor I3th of 
primary key. 

(See examples 53 55.) 

26. Modulate from D minor to Eb, A to Eb, and G to Eb, in each case by enharmonic variation of an 
augmented 6th in primary key. 

(See example 56.) 

27. Modulate from F to B, G to B, and G to FJf, in each case by enharmonic variation of a 
dominant, supertonic or tonic chromatic 7th. 

(See example 57.) 

28. Mention all the possible functions, within one key, of each note of a chromatic scale. 

29. Show at least four modes of modulation to every other key from D, E, Ft], and Ab. 



CARS 



WELL 



MT 
52 
H54 



Higgs, James 
Modulation 



UNIVERSITY OF 


Toor,ro 


EDWARD JO 

MUSIC L: 


.'J.N3ON 
HAjiV