Fugal analysis : a companion to "Fugue"

3^1

LIBRARY

Brigham Young University

IN MEMORY OF

Georqe Fitzroy

GEORGE V, ~ZROY

The Boston

Music Company(g. schirmer)

Boston, Mass.

AIT"

H

}^ GEORGE W. FITZBC1993

AUGENER'S EDITION, No. 9186.

FUGAL ANALYSIS:

A Companion to "Fugue;"

BEING A COLLECTION OF FUGUES OF VARIOUSSTYLES, PUT INTO SCORE AND ANAL YZED

BY

EBENEZER PROUT, B.A. Lond.

Professor of Harmony and Composition at the Royal Academy of Music;

Author of "Harmony : its Theory and Practice""'Counterpoint: Strict

and Free" "Double Counterpoint and Canon" "Fugue" <2rv.

-

NEW YORK:

G. SCHIRMER, 35, Union Square.

HAROLD B. LEE LIBRARYBFUGHAM VOUNO UNIVERSITY

PROVO, UTAH

PREFACE

The present volume is intended as a supplement to, or (to speak

more accurately) the complement of, the author's recently pub-

lished work on Fugue. In the course of that work it was more

than once remarked that the student could learn more from the

actual analysis of fugues than in any other way. As the limits

of the preceding volume did not allow the introduction of more

than a very few specimens of complete fugues, the present one

is intended to supply the deficiency.

In making the selection of fugues here given, several things

had to be considered. First and foremost, the author felt it to be

of importance that all the examples should be music, in the best

and truest sense of the term. For this reason, every fugue in the

volume is by a composer of acknowledged eminence ; and no

specimens are included of the works of musicians who, like

Kirnberger, Eberlin, or Albrechtsberger, are little known except

as fugue writers or theorists. Had technical correctness been the

only consideration, the selection would have been very different

from what it is. Some of the numbers in this volume {e.g.

Fugues 3 and n) have been included, among other reasons, to

show how much freedom the great masters sometimes allow

themselves in fugal writing. On the other hand, no mere dry

scholastic exercises, however meritorious from a university

examiner's point of view, have been allowed a place in the

volume.

Another important consideration was that of variety, both in

form and details. The possibilities of fugal construction are

practically almost exhaustless ; and, though it has been impossible

within the compass of one volume to exhibit every form of fugue,

it may at least be claimed for this collection that all the most

iv Preface.

important variations in fugue form are illustrated, and that every

fugue has some feature peculiar to itself, and not seen in any of

the others.

It will probably be a matter of surprise that, with one single

exception (No. 12), no fugues are included from that incomparable

masterpiece, Bach's ' Wohltemperirtes Clavier.' As a matter of

fact, it was originally intended to give several specimens from

that work ; but, happening to meet his friend, Mr. James Higgs,

and learning from that gentleman that he was at present engaged

in preparing an analysis of the whole ' Forty-Eight,' the author at

once modified his plan, feeling sure that Mr. Higgs's analyses

would be so good as to render any others superfluous. The

fugues already selected from the * Wohltemperirtes Clavier' were

therefore replaced by others, and the author strongly recommends

all earnest students to obtain Mr. Higgs's work as soon as it

is published. He understands that an English translation of

Dr. Hugo Riemann's analysis of the * Forty-Eight ' is also shortly

to be published ; this will be found another valuable aid to

the student. The one fugue of the * Forty-Eight ' which is

retained in this collection is inserted, as will be seen, with a

special object—to afford a comparison between the different

treatment of the same subject by different composers. In the

vocal fugues, the words have in all cases been omitted, partly

because a considerable saving of space is thereby effected, but

still more for the sake of clearness. The marks indicating the

subject or answer, episodes, etc., would have been more difficult

to distinguish had the spaces between the staves been filled up

with words. For the same reason, numerous unimportant instru-

mental parts, generally mere fillings up of the harmony, are also

omitted. AVhere the instrumental features are important to the

structure of the composition, they are added in small notes. ^

While it is hoped that these analyses will be found fairly

complete, the author cannot claim that they are in any wayexhaustive. This is especially the case with the fugues by Bach.

As has often been said of the Bible and Shakespeare, every time

we read Bach we find some new beauty in him that we had never

Preface. v

observed before. Even in the case of so familiar a fugue as the

" St. Ann's " (No. 20), which the author had known by heart for

thirty years, he found, on analyzing it for this volume, several

points of interest which he had never previously noticed. Nodoubt in many of these fugues much has been overlooked ; the

author trusts that enough has been said to put the student on the

track of further discoveries for himself.

In the arrangement of this volume, the author has followed

as nearly as he could that of the companion work on Fugue.

First come fugues on one subject, without and with regular

countersubjects ; these are followed by specimens of fugues

by inversion, augmentation, and diminution. No examples of

Fughetta are included here, as four complete specimens had

already been given in Chapter X. of Fugue. The first part of

this volume concludes with four different fugues on the same

subject by Bach, Handel, Haydn, and Mozart. The comparison

of these will, it is hoped, prove both interesting and instructive.

The second part of the volume shows fugues on two and three

subjects, fugues on a choral and canto fermo, and fugues with

independent accompaniments. The last number in the volume

may be regarded as a kind of " grand finale;" it is given as a

marvellous example of the combination of nearly all fugal devices

in one piece. As the chorus in its original form is only to be

found in the Bach Society's edition, which is by no means

universally accessible, its introduction here will be welcome. It

will also afford the student an opportunity of acquiring the

invaluable power of reading from a full score.

As it is important that the student should know how to make

analyses of fugues for himself, full instructions on this point are

given in the introducticn to the present volume. Far deeper

insight into fugal construction will be obtained by making analyses

for one's self, than by reading any number of analyses made by

others.

It will be noticed that the tabulated analyses given at the end

of each fugue differ very widely in their details. In the earlier

numbers certain points are mentioned which it was not thought

vi Preface.

needful to notice later, as the student would become accustomed

to observing them for himself without such help. It is hoped,

however, that nothing of real importance has been overlooked.

The preparation of this volume, the plan of which, it is

believed, is somewhat novel, has been an especially interesting,

though necessarily somewhat laborious task. The author, how-

ever, felt it likely to be of such great utility, that, as he desires to

make this series of works as complete as possible, he could not

well omit it. If the reading of it gives half as much pleasure to

the student as the writing has done to the author, he will be

amply compensated for the time and labour spent in compiling it.

London, March, 1892.

TABLE OF CONTENTS.

PAGE

Introduction „ i

fart I.

FUGUES ON ONE SUBJECT.

Section (a).—Fugues without a Regular Counter-

subject.

1. J. S. Bach : Fugue in D minor (' Art of Fugue,' No. 2) 5

2. G. F. Handel : Chorus, " Preserve him for the glory of thy

name " (' Saul') 14

3. J. Haydn :" Kyrie eleison" (5th Mass) 19

Section (b).—Fugues with more or less regular

Countersubjects.

4. J. S. Bach : Fugue in D minor (' Art of Fugue,' No. 4) 27

5. J. S. Bach : Organ Fugue in G minor 38

6. J. S. Bach : Organ Fugue in D minor (Dorian) 52

7. J. Haydn :" In gloria Dei Patris " (5th Mass) 66

8. F. Mendelssohn : Fugue in D minor, for Organ, Op. 37, No. 3... 73

Section (c).—Fugues by Inversion, Augmentation, and

Diminution.

9. J. S. Bach : Fugue by Inversion ('Art of Fugue,' No. 5) 80

10. J. S. Bach : Fugue by Augmentation and Diminution ('Art of

Fugue,' No. 7) 88

11. R. Schumann : No. 5 of 'Six Fugues on the name Bach,' Op. 60 98

Section (d).—The same Subject treated by different

Composers.

12. J. S. Bach: Fugue in A minor (' Wohltemperirtes Clavier,' No

44)

13. G. F. Handel : Chorus, " And with his stripes " (' Messiah ') ..

14. J. Haydn : Fugue from the Quartett in F minor, Op. 20, No. 5 ..

15. W. A. Mozart :" Kyrie " from the ' Requiem '

107

112

117

128

viii Table of Contents.

fart XL

FUGUES WITH MORE THAN ONE SUBJECT ; FUGUES ON ACHORAL AND CANTO FERMO ; ACCOMPANIED FUGUES.

PAGESection (e).—Double and Triple Fugues.

16. C. H. Graun : Double Fugue, " Christus hat uns ein Vorbild

gelassen" ('Der Tod Jesu') 135

17. L. Cherubini : Double Fugue, "Cum sancto spiritu " (2nd Mass) 145

18. Leonardo Leo : Triple Fugue, " Tu es sacerdos," from the " Dixit

Dominus " in C 158

Section (/).

—

Fugues on a Choral and Canto Fermo.

19. J. S. Bach: Fugal Treatment of the Choral "Jesu, Leiden, Pein

und Tod," from the Cantata, ' Himmelskonig, sei willkommen' 165

20. J. S. Bach : Organ Fugue (" St. Ann's ") in E flat, in five parts ... 171

Section (g).—Accompanied Fugues.

21. W. A. Mozart : Choral Fugue, " Pignus futurae," from the Litany

in B flat 190

22. F. Mendelssohn : Final Fugue from the 42nd Psalm 202

23. J. S. Bach : Double Fugue on a Choral, from the Cantata * Es ist

nichts gesundes an meinem Leibe ' ... 221

SIGNS AND ABBREVIATIONS.

S = Subject.

A = Answer.

{N.B.—In the tabulated analyses at the end of each fugue, the letters

S ATB refer to the soprano, alto, tenor, and bass voices.)

CS = Countersubject.

var. ss varied (of the Subject or Countersubject).

inv. = inverted.

aug. = augmented.

dim, = diminished.

? bs incomplete. The lines,show the extent of Subject, Answer,

or Countersubject. S ?1

indicates that the first part of the Subject is

wanting ; S ?, that the end is wanting ; S ? ?, that only a partof the middle of the Subject is present, both the beginning and end beingwanting.

Fugal Analysis.

INTRODUCTION.

Of all existing musical forms, that of fugue, as we find it in

the works of a great genius, such as J. S. Bach, is certainly one of

the most perfect, and, to an earnest musician, one of the mostinteresting. The idea, popularly entertained, that fugues are

very dry, arises partly from the fact that many fugues have

been written by composers destitute of genius, and possessed

of little beyond merely technical skill, but still more from the

fact that a fugue requires a considerable amount of theoretical

knowledge on the part of the hearer to appreciate it fully. It is

not a mere succession of interesting melodies, following oneanother with no necessary logical connection, but, as we have

said elsewhere, an organic growth, the whole of which is

developed from one or two themes, sometimes of extremesimplicity, according to certain artistic principles and well-

understood methods of procedure. Unless, therefore, the player

or hearer of a fugue is able to analyze its construction and trace

its developments, he can derive but little pleasure from it as a

composition. The present volume is intended to aid him in this

important matter ; and in this introduction we propose to showhim how to set about making an analysis for himself, before weproceed to analyze a selection of fugues for him.

Though all regularly-constructed fugues follow the samegeneral plan, there is an infinite variety in their details. In

the twenty-three fugues contained in the present book, there

is not a single one which does not illustrate some point not

shown in any of the others ; and even this volume does not

pretend to be exhaustive. It contains, however, a sufficient

number of examples of different styles to enable a student

who has fully mastered its contents to analyze any others for

himself without difficulty.

A knowledge of the treatise on Fugue, to which this is acompanion, is pre-supposed throughout this work. It was said

in that volume that more can be learned by analysis than

in any other way ; and to that we may here add, that the

careful analysis of fugues by the student himself will teach himmore than he can learn even by reading this book.

If the student wishes to analyze a fugue written for the organ

or pianoforte, we most strongly advise him, if he can spare the

time for it, to begin by putting the fugue into score—that is,

to write each of the voices on a separate staff, and in its proper

B

2 Fugal Analysis. [introduction.

clef. He will be astonished to find how many points he will

notice in this way which would almost certainly escape his

attention when he has two, and sometimes three, voices written

on the same staff. This is especially the case when, as so

frequently happens with fugues, there is any crossing of the

parts.

In putting a fugue into score, care will sometimes be neces-

sary with the middle voices, otherwise fresh entries may bedisregarded, or put in the wrong part. In Bach's ' St. Ann's

'

Fugue, for example (No. 20 in this volume), at bar 89, an

inexperienced student, transcribing the fugue from the organ

copy, would be extremely likely to regard the entry of the first

bass as the continuation of the tenor part. This will be seen

at once by examining the original. In some cases (for instance

in Mendelssohn's D minor fugue, No. 8 of this collection) muchthought was required in consequence of the crossing of the parts

to decide the progression of the voices. No rules can be given

in this matter ; if there appears to be a crossing of the parts, the

student must look for the place where they re-cross. Sometimes,especially in Handel's and Mendelssohn's instrumental fugues,

the composer altogether forgets that his parts have crossed, andomits to put them right again. In such a case there is "nothoroughfare " ; and if the student finds himself in a blind alley

of this kind, the best thing he can do is to abandon the scoring

of the fugue as a hopeless job. We have ourselves had to dothis with more than one of Mendelssohn's fugues. With thoseof Bach, there is never any danger of this kind.

Having put his fugue into score, the student will next proceedto analyze it. The first thing to do is, to determine the limits

of the subject, or subjects, if there are more than one. Fullinstructions on this point will be found in Chapters II. and III.

of Fugue. Next notice whether there is any countersubject, andif there be, whether it accompanies the whole, or only a part ofthe answer. Observe also at what interval the double counter-point is—whether in the octave, tenth, or twelfth. Of course,in an enormous majority of cases it will be in the octave. Seewhether there be any codetta, either before the entry of theanswer, or between any later entries in the exposition. If therebe one, take careful note of it, as it will very likely be subse-quently made use of in the course of the fugue.

As soon as all the voices have entered with either subject oranswer, the student should carefully examine what follows, to seewhether or not there is the additional entry spoken of in Fugue,§ 186. If there be, he must remember that this forms part ofthe exposition. If there be not one (as will probably be the casewhen the subject is announced by a middle voice), he will nextfind either the first episode or a counter-exposition— mostfrequently the former. Let him very carefully notice the keyof the next entry following the first episode. If it be the tonic

Introduction.] FUGAL ANALYSIS. 3

or dominant,* we shall find either a counter-exposition, complete

or partial, or the additional entry spoken of above, which is

occasionally, though rarely, introduced after the first episode,

instead of before it. In either of these cases, the episode andthe following entry, or entries, belong to the first section of the

fugue ; but if the episode modulates so as to introduce an entry

in some other key, it will form the beginning of the middlesection. (Fugue, § 293.)

The examination of the episodes will be found one of the

most interesting, as well as one of the most important parts of

fugal analysis. Occasionally they are constructed from absolutely

fresh matter; but in the very large majority of cases they are

made from materials already met with. Here careful comparisonis needed. The student must see whether the episodes are

formed from fragments of the subject, countersubject, or codetta

(if there be one), or from some of the incidental counterpoints.

He must also notice how they are so constructed—whether bysimple sequential treatment, by inversion, augmentation, or

diminution, or any combination of these. In Chapter VII. of

Fugue, he will find examples of all kinds of episodes ; he mustbe on the watch for any or ail of the devices there explained andillustrated. But the resources of episodical construction are

practically so exhaustless, that it is quite possible that he maymeet with episodes of a pattern not shown in any of the examples

we have given.

The middle entries of the fugue will next claim his attention.

He must notice whether these entries are isolated, or in groups.

On this point, a word of caution may here be given. Occa-sionally the student may be inclined to regard two consecutive

entries as isolated, when they really belong to the same group.

For instance, in Fugue 13 of this volume, there is a middle entry

ending in bar 52, while the following does not begin till bar 55.

In this case both belong to the same group, because they bear

to one another the key-relation of subject and answer; and the

intermediate passage is codetta, not episode. Another goodillustration of this point will be seen at bars 35 to 37 of the first

fugue in this volume The order of the keys in these middleentries must always be carefully noticed ; and when the subject

is found again in the key of the tonic, the student must see fromwhat follows whether or not he has reached the final section of

the fugue. The rule given in Fugue, § 302, will be a safe guide

for him.

If the fugue contains any stretti, the first will mostly be metwith in the middle section, though they are occasionally to beseen in the exposition. These must be carefully looked for, and,

if found, there are several points to be noticed with regard to

* Sometimes (as in Fugue 7 of this volume, bar 26) the first group of middleentries begins in the dominant. In such a case, the key of the following entrywill show whether or not there is a counter-exposition.

4 Fugal Analysis. [introduction.

them. See, first, how many voices take part in them, at whatintervals, and at what distances of time. Observe also how muchof the subject is given by each voice—whether each discontinues

the subject on the entry of the next, and, if not, how much of it

is carried on beyond the next entry.

The devices of inversion, augmentation, and diminution are

sometimes found in the middle section of the fugue. Thesemust be carefully watched for, as must also the modifications in

the form of the subject itself (see Fugues 4 and 11), and the

incomplete entries of subject or answer. These last are some-times likely to be overlooked, especially if, as occasionally

happens (see Fugue 18), both the beginning and end of the

subject are wanting.

The analysis of the final section will in general offer but little

difficulty. The entries will now all be in the tonic and dominantkeys ; these may or may not be divided by episodes. Be on the

watch for stretti here, and also for pedal points. If there be acoda, note where it begins.

The directions here given refer to simple fugues—that is,

fugues with one subject, and to those double fugues in which the

two subjects are announced together. In the case of doublefugues in which each subject has a separate exposition (see

Fugue 16), it will be remembered that the form is different, as is

fully explained in Fugue, Chapter XL The method of analysis

will, nevertheless, be the same, the difference being merely in thedivision of the sections of the fugue.

With a fugue upon a choral, the analysis will vary accordingto the form chosen by the composer. If each line of the choral

receives a separate exposition, as in the fugue by Bach, given in

Fugue, § 422, there will be as many sections as there are lines.

In Fugue 19 of this volume, where sometimes one line, andsometimes two, of the choral are treated separately, the numberof sections will be the same as the number of expositions. Butif the subject of the fugue be quite independent of the choral,

the latter being treated as a canto fermo, as in the example byBach in Fugue, § 427, or in Mendelssohn's third Organ Sonata,the form of the fugue will not be affected by the presence of thechoral.

It will greatly assist the student if he marks the entries ofsubject and answer, and the episodes, as we have done through-out this volume. When his analysis is completed, he will alsodo well to tabulate the results, as is here done at the end of eachfugue.

We have fully explained in this introduction the exactmethod we ourselves pursued in making all the analyses in thisvolume ; and we can assure the student that he will find thework of scoring and analyzing fugues, though somewhat long,truly fascinating, if, as we assume, he has sufficiently studied thesubject to be able to appreciate its beauties.

Fugue l.J Fugal Analysis.

PART I.

FUGUES ON ONE SUBJECT.

Section (a). Fugues without a regular Countersubject.

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As this volume contains several examples from Bach's ' Artof Fugue,' it will be well to give here some account of that

work. It was written to show the varied possibilities of fugal

construction, and consists of a series of fugues and canons,all founded upon the same subject, which, however, appears in

the different numbers of the work in various modifications. Its

original form is

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and in this shape is combined with itself in inversion, augmenta-tion, and diminution. (See Fugues 9 and 10 of this volume.) It

Fugue I.] FUGAL ANALYSIS. II

is subsequently further modified, and combined with other sub-

jects in double counterpoint of the octave, tenth, and twelfth;

and finally Bach gives two fugues, one for three and the other

for four voices, which are treated by inverse contrary movementin all the parts. Besides this the work contains a number of

canons on the same theme, and at the end is printed a long

triple fugue, an analysis of which was given in Fugue §§ 400-403,which was no part of the original work. Its introduction is dueto the fact that the ' Art of Fugue ' was not published till after the

composer's death, and the editor was not certain as to the author's

intentions.

Composed in the last year of Bach's life, the ' Art of Fugue

'

shows his stupendous genius in its fullest maturity, and contains

many of the most perfect specimens in existence of fugal writing.

Being written with a distinctly educational purpose, the work is

especially valuable to the student and to the teacher, becauseBach here deliberately sets to work to show how fugues should

be written. The different numbers may therefore be taken as

models for our guidance ; and it is for this reason that we haveincluded several of them in the present volume.

The fugue now before us is so simple and straightforward in

its construction that it will not need a very long analysis.

Though it has no countersubject, remarkable unity is given to

the whole work by the persistent dotted-note rhythm first heard in

the fourth bar, which is continued without any intermission what-

ever until the final chord.

The exposition extends to the beginning of bar 17. As the

subject commences with a leap from tonic to dominant, the

answer is tonal, according to the usual rule (Fugue, § 86). Asthe subject does not modulate, the only alteration made is in the

first bar.

The last four notes of the subject S_.|g

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gj

must be

particularly noticed, because they are the germ out of which the

whole of the counterpoints accompanying the subject are de-

veloped. Sometimes this figure appears, treated sequentially

in the same voice, either by direct or inverse movement

—

e.g., in

the tenor of bars 9 and 10 (direct), and in the alto of bars 39, 40(by free inversion) ; at other times, as we shall see directly, the

figure is employed in imitation between the different parts ; andin one place (bar 70), the rhythm only is preserved, and is divided

between the treble and alto. The first example of imitation will

be seen at bar 8, where the counterpoint is announced in the

tenor, imitated in the sixth below by the bass, and this in its turn

in the ninth above by the tenor. In bar 1 1 the bass is imitated

by the tenor in contrary movement. It is impossible to point out

all the imitations throughout the fugue ; this would take too long.

12 Fugal Analysis, [Fugue i.

We have said enough to show the student how to find them for

himself.

The exposition is followed at bar 17 by the first episode, con-

structed from the figure above quoted, and leading to a full

cadence in the dominant at bar 23. Here begins the counter-

exposition. Observe that the beginning and end of the subject

are altered in the alto. The change in bar 23 gives Bach an

opportunity to introduce the tenor and bass in imitation of the

figure ==^jj^ =::. The end of the subject is altered because

the answer in the treble enters one bar sooner than before ; there

is, in fact, here a partial stretto—the only one in the fugue. This

counter-exposition departs from the usual practice, inasmuch as

the voices which before had the subject do not now have the

answer, neither does the answer lead, and the subject reply.

The passage of imitation in all the voices at bars 35 to 37might possibly be considered as a second episode ; but as the

following entry of the tenor in bar 38 is clearly the answer to

that in the bass at bar 31, and certainly forms part of the

counter-exposition, it is better to regard bars 35 to 37 as acodetta, such as is often found in the exposition, but less fre-

quently in the following part of a fugue.

The counter-exposition ends at bar 42. Hitherto all the

entries of the subject have been in the keys of the tonic anddominant ; but our second episode (bars 42 to 44) introduces

an entry in the relative major. It therefore belongs to the

middle section of the fugue, which begins at bar 42 ; and it

will be seen that the first section occupies exactly half of the

whole fugue.

There is here only one group of middle entries, and it

presents one or two points for comment. Note in the first placethe alteration in the last note of the subject, at bar 49. Suchslight modifications are very common in the middle entries of afugue, and we shall meet with many similar examples in this

volume. It will also be seen that in the entries at bars 49 and53 the first note of the subject is altered. It looks at first sight

as if we had here an entry of the answer ; but if it were, theinterval between the second and third notes would be a second,and not a third. Besides this, the key-relationships of the entries

are not those of subject and answer. At bar 45 the entry is in

F, at bar 49 in G minor, and at bar 52 in B flat. Just as in

tonal fugues we often find a real answer in the later entries,

where a tonal has been given at first, so we sometimes (as here)see the subject taking a form which resembles the tonal answer.Throughout this volume, whenever the entries are at irregulardistances, we shall mark them with S in all cases of doubt. Thestudent should note the various incidental double counterpointsin this middle group of entries. Bar 46 compared with bar 54

Fugue I.] FUGAL ANALYSIS, 1

3

shows inversion in the twelfth ; and bars 49 and 53 are written in

double counterpoint in the fourteenth.

The third episode (bars 57 to 60) brings us to the final section

of the fugue, in which subject and answer reappear in the tonic

and dominant keys. Here each successive entry is divided fromthe preceding by an episode. This, though hardly to be called

unusual, is not very often met with. More frequently the final

entries are either in stretto, or, if not, follow one another without

any break. Observe that at bar 69 the entry of the answer in the

tenor is varied by means of syncopation.

This fugue is an admirable example of how much variety is

possible with a very small amount of material. The persistent

employment of the dotted figure of the counterpoint never

becomes monotonous. Compare the five episodes, and note

how each one differs from all the others, though the same figure

is used in each. Here we see something akin to that " thematic

development " so invaluable in the higher branches of composi-tion, which Beethoven employed in such a marvellous way, andof which we shall have to speak in a later volume of this series.

Analysis of Fugue 1.

First Section—Bars 1 to 42.

(a) Exposition. Subject (B), D minor, bar 1.

Answer (T), A minor, bar 5.

Subj. (A), D minor, bar 9.

Ans. (S), A minor, bar 13.

(b) Episode I. (bars 17 to 22).

(c) Counter-exposition. Subj. (A), D minor, bar 23.

Ans. (S), A minor, bar 26.

Subj. (B), D minor, bar 31.

Ans. (T), A minor, bar 38.

Middle Section—Bars 42 to 60.

(d) Episode II. (bars 42 to 44).

(e) Middle group of entries. Subj. (S), F major, bar 45.

Subj. (A), G minor, bar 49.

Subj. (B), B flat, bar 52.

(/) Episode III. (bars 57 to 60).

Final Section—Bars 61 to 84.

(g) Subj. (B), D minor, bar 61.

(h) Episode IV. (bars 61 to 69).

(/) Ans. (T), A minor, bar 69.

(/) Episode V. (bars 73 to 78).

(k) Subj. (S), D minor, bar 79.

14 Fugal Analysis. [Fugue II.

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Handel's fugues in general differ considerably from Bach's in

their greater freedom of form, and in their being less polyphonic.

In the fugues for the harpsichord the freedom is carried to suchlength as often to obscure the clearness of the part writing.

This the student can easily see if he attempts to put them into

score. He will find it at times almost impossible to follow the

progression of the different voices. We have therefore chosena choral fugue, and one of the most regular in construction, for

this work. Only a short analysis will be needful.

The answer is tonal, only the first note being altered ; there is

no countersubject. At bar 8 will be seen a good example of the

"inganno" (Fugue, § 165). The exposition ends at bar 18, in

which bar the first episode begins. This is made from a sequential

treatment of the last bar of the subject, by tenor and bass

alternately, which accompanies a canon in the fifth belowbetween soprano and alto. There is no regular counter-exposition,

as in the preceding fugue, but there is an entry of the subject in

the original key at bar 23, preceded at bar 22 by an entry in the

treble of the first bar of the subject, forming a partial stretto.

These entries, therefore, with the episode that precedes them,belong to the first section of the fugue.

The middle section begins at bar 27. At bar 28 the first

complete stretto for all the voices is seen ; notice that only the

last entering voice (the bass in bar 31) gives the entire subject,

each of the others discontinuing it when the next voice enters.

The counterpoints accompanying the various entries illustrate

what was said above as to the difference in style betweenHandel's and Bach's fugues. The part-writing here is muchsimpler, and the voices often move together in plain three- andfour-part harmony, instead, of in florid counterpoint. Thesmall notes in bars 20, 21, and 31 give the alterations madein the voice parts to keep the subject in a convenient compass

;

the lower notes are for the orchestra. At bar 36 is anotherpartial stretto in C minor. The second episode (bars 41-44)is made from the latter part of the subject in a modified form, as

will be seen by comparing the alto of bar 41 and the treble

of bar 42 with bar 4.

1

8

Fugal Analysis. [Fugue ii.

The final section of the fugue begins at bar 44 with the entry

of the answer in D minor. As it begins with the leap of a fifth

from dominant down to tonic, it looks as if it were an entry of

the subject ; that it is really the answer is shown by the imme-diately following entry being in G minor. We have here (and

again in bar 58) a real answer instead of a tonal one ; this is con-

tinually to be met with in the middle and final sections of tonal

fugues. In the Fugue No. 1, we saw at bars 49 and 53 the con-

verse case ; the subject took the form of the tonal answer. At bars

48 and 49 is another partial stretto; and at bar 52 is a somewhatunusual point—the subject, which is begun by the soprano, is

transferred to, and completed by the bass. The third and last

episode (bars 53-56) is made, like the first, from a sequential

treatment of the last bar of the subject; but the distribution

between the voices is different, as also is the accompanyingcounterpoint. At bar 56 begins the last stretto ; observe in

bar 58 the alteration in the answer—a major third instead of a

minor. Note also, as an irregularity, that the bass (the last voice

to enter) does not complete the subject {Fugue, § 252).



(a) Exposition (bars 1 to 18).

(Order of entry, TASB.)(b) First episode (bars 18 to 22).

(c) Additional entry, with partial stretto, in G minor(bars 22 to 27).


(d) First group of middle entries in B flat, with stretto in all

the voices (bars 28 to 35).(e) Connecting bar (bar 35).

(/) Second group of middle entries in C minor, with partial

stretto (bars 36 to 41).

(g) Second episode (bars 41 to 44).

. Final Section.

(a) Answer (A) followed by subject (B and S), (bars 44 to 53).

(l) Third episode (bars 53 to 56).

(J) Final stretto followed by coda (bars 56 to 64).

N.B.—In the above fugue, as in several of those that follow,

a few notes of the orchestral accompaniment which completethe harmony have been omitted to show the fugal constructionmore clearly.

Fugue IIl.j FUGAL ANALYSIS.

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69 70

This is a very interesting fugue, of somewhat unusual con-

struction, inasmuch as after the exposition the subject appearsonly once (bar 44) in its complete form. We have, nevertheless,

selected it for analysis as a very instructive example of the wayin which great unity of design can be combined with very free

treatment. It " hangs together " so well that it is very doubtful

whether anybody hearing it without any previous acquaintancewould notice any irregularity in its form.

In the exposition of this fugue (bars 1 to 14) we find a nearer

approach to a regular countersubject than in either of the pre-

ceding fugues of this volume. The counterpoint in the alto of

Fugue III.] FUGAL ANALYSIS. 25

bars 9 to 1 1 is the same as that in the bass of bars 3 to 6 ; butthere is sufficient difference in the other counterpoints accompany-ing the entries to prevent our being able to regard it as a true

countersubject. At bar 12 is an additional entry in the bass, suchas we often find when an outer part leads. If the counterpoint

we have just spoken of were a real countersubject, it ought to

appear in bar 12 in the treble—the voice that last entered; instead

of which it is in the tenor. It should be said that in bar 12 the

bass is still really the lowest part, as it is doubled in the loweroctave by the double basses.

The middle section of this fugue begins at bar 14 with the

first episode (bars 14 to 17). This is made from a sequential

treatment of the last part of the subject, and leads to an isolated

entry (partial) of the subject in A minor (bar 17). This is given

to the bass—the voice by which the last entry was made (bar 12).

Here we see how little the old formal rules were observed by the

great masters; one of these rules was that no two consecutive

entries of subject or answer should be in the same voice. Theoccasional small notes in the bass, as at bars 14, 15, and later in

the fugue (bar 43, &c), show that the orchestral bass is in-

dependent of the vocal.

The second episode (bars 19 to 28) is made from the last

notes of the subject, treated both sequentially and by imitation,

and combined in bars 21 to 23 with the inversion of the figure

EEte4j"~bg=: in the first bar of the subject. This episode

modulates to E minor, introducing in that key another partial

entry of the subject (alto, bar 29). This is followed by the third

episode (bars 30 to 43)—the longest and one of the mostinteresting in the fugue. The first part of it (bars 30 to 38) is

mostly founded on the same quaver figure which we saw treated

by inversion in the preceding episode ; from bar 38 to bar 40Haydn works the semiquaver figure of bar 2 by sequential

imitation, and bars 41 to 43 are developed from the last notes of

the subject. At bar 44 we find the only complete entry of the

subject after the exposition (soprano, F major), which is followed

by another rather long episode (bars 46 to 55). This commenceswith a sequential continuation by the tenor of the last bar of the

subject (bars 46 to 48). It will be seen that this is a free inver-

sion of the first episode, bars 15 to 17. The following passage

(bars 49 to 52) should be carefully compared with the secondepisode from bar 21 to bar 23 ; it will be seen that the material

is the same, but the treatment quite different. Note also the

entries of the first notes of the subject at bars 49, 51, 53, and 54.

This fourth episode, leading back to the key of C, introduces

the final section of the fugue at bar 56. This commences with a

partial entry of the subject by inversion (bass), followed by the

answer (tenor), also inverted, in stretto at half a bar's distance.

The alto and treble follow, again at half a bar's distance. The

26 Fugal Analysis. [Fugue hi.

rests in the tenor and bass at bars 59 and 60 are somewhatunusual ; more frequently during the continuation of the stretto

the voices that first entered continue with free counterpoint. Theentry of the subject (incomplete) in its direct form (bar 61) leads

to a dominant pedal (bars 63-66), and a short coda, formed fromsequential groups of semiquaver figures in the bass, taken fromthe subject, conclude the fugue.




(Order of entry, B T AS., with additional entry for B.)


(b) First episode (bars 14 to 17).

(c) First middle entry (B), A minor, bar 17.

(d) Second episode (bars 19 to 28).

(e) Second middle entry (A), E minor, bar 29.

(/) Third episode (bars 30 to 43).

(g) Third middle entry (S), F major, bar 44.

{h) Fourth episode (bars 46 to 55).


(1) Stretto on inverted subject (bars 56 to 60).

(/) Partial entry of subject (B), bar 61, leading to

{k) Dominant pedal point (bars 63 to 66).

(/) Coda (bars 66 to 70).

It is worthy of notice that all the middle entries in this fugue

are isolated, and that as nearly as possible half the entire fugue

consists of episodes.

Fugue IV.] Fugal Analysis.. 27

Section (if).—Fugues with more or less RegularCOUNTERSUBJECTS.

No. 4.—J. S. Bach. Fugue in D minor ('Art of Fugue,' No. 4).

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Fugue IV.J Fugal Analysis. 35

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The subject of this fugue is the inverted form of that which

we saw in Fugue i of this volume. As in its original form, it

takes a tonal answer. There is a regular countersubject, but

it is fitful in its appearances, and the beginning and end are

sometimes modified. This is by no means uncommon with a

countersubject (Fugue, §§ 170, 269).

The exposition of this fugue (bars 1 to 19) is quite regular,

the countersubject being given in each case to the voice which

has just completed the subject or answer. It will be seen that

the first three notes of the countersubject are altered when it

appears m the alto.

The middle section commences at bar 19 with the first

episode. This is made from the last notes of the subject,

imitated in contrary movement and treated sequentially. Weshall find as we proceed that the later episodes are developed or

varied from this one.

At bar 27 we come to the first group of middle entries—Sub-

ject (soprano) in F major ; Answer (alto) in C major, followed

immediately by Subject (tenor) in G minor, and Answer (bass)

in D minor. It must be noticed that the answer of the alto in

bar 31 is real, and not tonal—a case of constant occurrence in

tonal fugues—and that of the four entries only one (bars 35 to 38)

is accompanied by the complete countersubject. It is entirely

wanting against the soprano and alto entries, and only fragments

of it are given against the bass. We see a snatch of it in the

tenor of bar 40, transferred to the treble in the following bar.

(Compare Fugue 2 at bar 52, where the subject is divided between

two voices.)

The second episode (bars 43 to 60) is, like the first, con-

structed from the last part of the subject. All the episodes

of this fugue are most instructive, and deserve very close

examination. To analyze them fully would require far morespace than we can spare \ we can only indicate one or twopoints, leaving the student to discover others for himself. If

bars 44 to 47 are compared with bars 20 to 22 of the first

episode, it will be seen that what were then soprano and bass

36 Fugal Analysis. [Fugue 1v.

are now inverted in the twelfth as soprano and tenor ; and, at

the same time, the former alto and tenor are now inverted

in the octave as alto and bass. Bars 48 to 50 are a sequential

continuation of bar 47. From bars 53 to 57 we have a canon,* 4 in 2,' the tenor and bass being the inversion in the twelfth of

the soprano and alto.

The second group of middle entries (bars 61 to 69) presents

some new features. We see here the subject modified in formfor the purpose of modulation. The bass entry (bar 61) begins

in C major and ends in G minor ; the tenor (bar 65) begins in

G minor and ends in D minor. We have marked both with1S,' as the tenor can hardly be regarded as the answer to the

bass here. Both these entries are accompanied by a portion

only of the countersubject.

The third episode (bars 69 to 72) should be compared with

bars 19 to 22 of the first episode, of which bars these are a free

variation. The third group of middle entries—subject (alto),

bar 73; answer (soprano), bar 77—shows us the same altered

form of the subject that we saw at bars 61 and 65. Observealso that we call the entry at bar 77 "answer," because it is anexact transposition to the fifth above of the entry in bar 73.

The countersubject does not accompany either of these entries,

though the accompanying counterpoint in bars 73 and 74 bears

some affinity to it. It will further be seen that at bar 79 there is

a distinct modulation beyond the related keys. The harmonyis that of the supertonic minor ninth of E minor—an unrelated

key to the original tonic. In the next episode (bars 84 to 86)will be seen a modulation to another unrelated key, C minor.

Though Bach generally adheres to the old rules as to modulation,

we see from these passages that he had no scruple as to breaking

them upon occasion. It must be remembered that the 'Art of

Fugue' was written with an educational purpose; and we maysafely presume that Bach introduced nothing which he did not

consider to be correct.

The fourth episode (bars 81 to 106) is the longest in the

fugue, and one of the finest. Let the student compare it

carefully with episodes 1 and 2, and see how many new com-binations are obtained with the old material.

The final section of the fugue begins at bar 107 with an entry

of the subject in the tenor, accompanied in the soprano by a

part of the countersubject combined against a different part of

the subject (the chromatic figure of quavers coming in the first

half of the bar instead of the second) ; while the bass gives asyncopated imitation of the subject itself. The answer in the

soprano (bar in) is varied by syncopation, and freely imitated in

the sixth below by the alto. These two entries are followed bythe fifth and last episode (bars 115 to 128). Compare bars 119to 122 with the second episode, bars 47 to 50, and note also

that the alto in bars 124 to 126 is the inversion of the bass of

Fugue IV.] FUGAL ANALYSIS. 37

bars 1 20 to 122. The fugue ends with the entries of the subject

(varied) in the tenor, bar 129, and in its original form (alto),

bar 133.



(a) Exposition (Order of entry, S A T B).


{b) First episode (bars 19 to 26).

(c) First group of middle entries. Subj. (S), F major, bar 27.

Ans. (A), C major, bar 31.

Subj. (F), G minor, bar 35.

Ans. (B), D minor, bar 39.

{d) Second episode (bars 43 to 60).

(e) Second group of middle entries. Subj. varied (B), bar 61.

Subj. varied (T), bar 65.

{/) Third episode (bars 69 to 72).

(g) Third group of middle entries. Subj. varied (A), bar 73.

Ans. varied (S), bar 77.

{h) Fourth episode (bars 81 to 106).


(/) Subj. (T), D minor, bar 107.

Ans. varied (S), A minor, bar in.

(J) Fifth episode (bars 115 to 128).

(k) Final group of entries. Subj. varied (T), bar 129.

Subj. (A), bar 133.

It will be seen that this fugue, though one of the finest andmost perfect in construction that can be found, contains not the

least approach to a regular stretto.

38 Fugal Analysis. [Fugue v.

No. 5.—J. S. Bach. Organ Fugue in G minor.

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113 114 115

We have chosen this fugue as our next specimen, not only

because it is one of the best-known and most popular of Bach's

organ works, but because it is a very fine example of a fugue

with a regular countersubject. In its construction it is simple

and straightforward, and its analysis offers no difficulties.

The answer is tonal; but the first note is the only onealtered. The intermediate modulation to the relative major is

imitated exactly in the answer (Fugue, § 83). The countersubject

does not accompany the whole of the answer. The codetta

before the entrance of the third voice (bars 7 to 9) is developedsequentially from the first half of bar 7 of the alto. The coun-

terpoint in the soprano of bars 11 and 12 accompanies the

subject and countersubject so frequently that it might almost

be -considered as a second countersubject ; the three voices in

bars 11 and 12 are written in triple counterpoint, and in the

course of the fugue five of the six possible positions are em-ployed, as may be seen by comparing bars 11, 23, 26, 38,

and 104.

The exposition ends at bar 17, and the first episode (bars 17to 21) leads to a counter-exposition (bars 21 to 32). Here the

first two entries are the same as in the exposition, which is

unusual, though the additional entry of the subject in the treble,

so as to allow the bass to have the countersubject, is quite

regular. As is often seen in a counter-exposition, only three ofthe four voices have an entry of subject or answer.

The middle section of the fugue begins with the secondepisode, at bar 32. The student should by this time be sufficiently

accustomed to analysis to be able to discover for himself the

material from which the episodes are constructed; in future,

therefore, we shall only notice any special points in them that

need comment.There are no groups of middle entries in this fugue. On

examination it will be found that all the middle entries are

isolated. The first is seen at bar 36, and is for the tenor. It

should be noticed that in this fugue (as in some others in the

volume) the words "alto" and "tenor," as applied to the middle

5<d Fugal Analysis. [Fugue v.

voices, refer merely to their relative, and not to their actual

position. It is comparatively seldom that so wide a compass is

given to the middle parts as here

—

e.g., the alto in bars 44 to 47,and S3, 54.

The third episode is founded on the first part of the subject

treated sequentially in the tenor, and accompanied by a canon in

the fourth below for the treble and alto. It leads to an entry of

the subject (bar 43) in the treble, in D minor, slightly varied

in form at the beginning, and accompanied by a new sequential

figure in the alto, varied from the countersubject. The fourth

episode (bars 46 to 50) leads to another entry in D minor, also

in only two-part harmony. Note that bars 51 to 53 are the

inversion in the octave of bars 44 to 46. This is the justification

for there being two consecutive entries of the subject in the samekey, which is rather unusual.

The fifth episode, only one bar in length, introduces the

subject in F major (bar 54). The sixth episode (bars 57 to 65)should be specially noticed, as it contains a new figure, first seen

in the alto iz^ggpizz of which much use is made later in

combination with the semiquaver figure in the bass of bars 57, 58.

Compare this episode, as far as bar 60, with the seventh and ninth

episodes (bars 68 to 72, 82 to 86, and 89 to 93). The next entry

of the subject (bar 65, tenor) is in the tonic key. In longer

fugues this is neither infrequent nor undesirable. It is not

needful to dwell on the following entries in C minor (bar 72), andE flat (bar 79), and we therefore pass on to the ninth episode

(bars 82 to 93). Besides the varied positions of the combination

first seen in bars 57, 58, to which we have already called attention,

there is an interesting point at bars 86 to 89. A sequence formedfrom the first half of bar 48 is combined with an augmentation of

the important figure of counterpoint first seen in the soprano

of bar 11, which we said was almost like a second countersubject.

The final section of the fugue begins in bar 93. The subject

is not accompanied by the countersubject in its original form;

but we have here a transposition (with slight modifications) of

part of the middle section (bars 44 to 53). It is very rare in

a fugue to find so long a passage repeated almost exactly in adifferent key; but here there is so much variety in what has

intervened that no effect of monotony is produced. At bar 103is the only attempt at stretto in the whole fugue—the alto

entering before the tenor has quite completed the subject. In the

last entry, we see a new variation of the countersubject (alto, bar

in), and in the final cadence additional voices are introduced.

Fugue V.] FUGAL ANALYSIS. r i

Analyst's of Fugue J.

First Section—Bars i to 32.


(Order of entry, SATB.)(b) First episode (bars 17 to 21).

(c) Counter-exposition (bars 21 to 32).



(e) Entry of subject (T), B flat, bar 36.


(g) Entry of subject (S), D minor, bar 43.

(h) Fourth episode (bars 46 to 50).

(/) Entry of subject (A), D minor, bar 50.

(/) Fifth episode (bars 53, 54).

{k) Entry of subject (B), F major, bar 54.

(/) Sixth episode (bars 57 to 65).

(m) Entry of subject (T), G minor, bar 65.

(n) Seventh episode (bars 68 to 72).

(0) Entry of subject (S), C minor, bar 72.

(/) Eighth episode (bars 75 to 79).

(q) Entry of subject (A), E flat, bar 79.

(r) Ninth episode (bars 82 to 93).


(s) Entry of subject (S), G minor, bar 93.

(/) Tenth episode (bars 96 to 100).

(u) Entries of subject (T), bar 100; (A\ G minor, bar 103.

(v) Eleventh episode (bars 106 to no).(w) Final entry of subject (B), G minor, bar no.(x) Coda (bars 113 to 115).

The unusually large number of episodes in this fugue is the

natural consequence of all the middle entries being isolated. It

will be seen that nearly all the episodes are short, eight of the

eleven being only four bars in length, while the fifth is only onebar. Notice also the symmetry in the arrangement of the middleentries. After B flat major, Bach takes the dominant minor of

the original key, following it by its relative major ; then, after

returning to his tonic, he makes an excursion to the other side of

the key, and we have entries in the subdominant minor, and its

relative major. In its whole construction the fugue is (like

No. 4) one of the most perfect of Bach's works.

52 Fugal Analysis. [Fugue VI.

No. 6.—J. S. Bach. Organ Fugue in D minor ( Dorian).

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Fugue VI.] Fugal Analysis, 53

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62 Fjgal Analysis. [Fugue vi.

We have included this very fine fugue in our collection chiefly

because of its numerous interesting episodes ; but it also serves

to illustrate some other points not seen in any of the preceding.

It has a real answer, and a regular countersubject. Particular

notice must be taken of the short codetta (bars 15 to 17)

preceding the entrance of the tenor. It will be seen that the

soprano imitates the alto in the sixth above at half a bar's

distance. From this little piece of canonic imitation all the

episodes in the fugue, except the last, are constructed.

The order of entry in the exposition is unusual. The secondappearance of the subject is not in the bass (as is mostly the case

when the first is in the alto) but in the tenor. Bach probably

deviated from the general plan for the sake of having the last

entry in an outer part. Before the entry of the bass is a second

codetta, in which at bars 26 to 28 will be seen the inversion in

the octave of the little piece of canon in bars 15 to 17. It wasthere in the sixth above, it is now in the third (tenth) below,

and at the same distance of time as before—half a bar. Thecrossing of the subject and countersubject in bars 31 and 32 is

only apparent, not real. In Bach's organ fugues the lowest part

is always given to the pedals, and sounds an octave lower than

written. We shall have to bear this in mind presently in

examining the episodes.

It will be more convenient to speak of these episodes later bythemselves ; we will first deal with the various entries of the

subject and answer. At bar 43 begins a counter-exposition of anunusual form. Here the answer leads and the subject replies,

as is very often the case ; but the peculiarity here is that each

new entry, instead of following immediately on the last, is

separated from it by an episode. That we really have a counter-

exposition nevertheless, is proved by the fact that answer andsubject are, as before, in the dominant and tonic keys, whichwould not be the case were they middle entries. The answer in

the alto at bar 43 is varied by the substitution of C sharp for Cnatural, and the first part of the countersubject in the bass is

varied and simplified to suit the compass of the pedals. As C is

the lowest note of the pedal board the original form of the

countersubject

mS- -!-

&c.

was evidently impossible. Observe also the varied commence-ment of the subject in bar 57, and that only the last part of the

countersubject accompanies it.

The middle section commences in bar 88, with the fifth

episode ; and the first group of middle entries is found at bar

1 01. Here the soprano has the subject in F major, and the bass

imitates it with a canon in the octave at one bar's distance. The

Fugue VI.] FUGAL ANALYSIS, 63

countersubject is now absent; in fact, it would not fit against both

the voices, though a fragment of it is seen in the tenor of bars

105, 106. When a subject is combined with itself in a close stretto,

a countersubject is seldom available (Fugue, § 176). The next

entry (tenor, bar 115) we have marked as "answer," because it is

in C major, while the preceding was in F. Here there is nocanon ; the countersubject therefore appears in the bass in the

same modified form in which we saw it in bar 44. This is anisolated entry.

At bar 130 we find another group of entries in G minor.

Again we have a canon in the octave; but while the canon at

bar 101 was for soprano and bass, this one is for alto and tenor.

The last middle entry is in B flat, for the tenor (bar 146) ; and,

though there is no canon here, it is accompanied only by a small

part of the countersubject (bars 150, 151).

The final section of the fugue begins at bar 167. Here the

subject is again treated in canon in the octave above (alto andbass). At bar 188 is an entry of the answer, attended by the

countersubject; and the final entries are at bar 203, where weonce more see the canon, but now in the octave below, instead

of (as at bar 167) in the octave above.

We now turn to the episodes. In the first (bars 36 to 42)the subject from the codetta

^Mq-r-^-r-^ &-'— &c.

is treated as a canon in the fifth above at one bar's distance

between bass and soprano, and accompanied by free counterpoint

in the alto and tenor. In the second episode (bars 50 to 56),

the subject is again in the bass, and is imitated by the soprano in

the ninth above at half a bar's, and in the tenor in the fifth above,

at a whole bar's distance. In the third (bars 64 to 70), the canondoes not appear till bar 67, when the subject in the treble is

imitated in the fifth below by the alto, at half a bar's distance,

and in the octave below by the tenor, at a bar's distance. Thefourth episode (bars 78 to 80) shows a canon between tenor

and soprano in the ninth above, at half a bar's distance. Inthe fifth episode there are two canons. At bar 88 the sopranois imitated by the bass in the fourth below at half a bar, and bythe tenor, also in the fourth below at a bar's distance ; and in

bar 95 the soprano is imitated in the seventh below at half abar's distance by the bass, and in the sixth below at a bar's

distance by the alto. In the sixth episode we have at bar noa complicated piece of canon, which, however, is not longcontinued. The subject in the tenor is imitated at half abar's distance by the bass in the sixth below, and at a barand a half's distance by the alto in the second above, and thesoprano in the seventh above. The seventh episode showb

64 Fugal Analysis. iFugue vi.

at bar 125 the subject led by the bass, with a canon in the

fifth above for the tenor, and an octave above for the soprano

;

the former at half a bar's, and the latter at a whole bar's distance.

In the eighth episode (bar 138) the subject in the treble is

imitated by the tenor in the eleventh below at half a bar,

and by the alto in the fourth below at a bar's distance. Likethe fifth episode, the ninth contains two canons. At bar 156is a canon in the tenth below between soprano and tenor, at

half a bar's distance; and at bar 162 the subject in the treble

is imitated by the tenor in the seventh below at half a bar,

and by the alto in the octave below at a bar and a half. Notice

here at bar 164 the quite exceptional introduction of an additional

voice, which is extremely rare with Bach, though not uncommonin Handel's instrumental fugues. The tenth episode also

contains two canons. At bar 178 is a canon in the octave

between alto and tenor at one bar's distance; and at bar 183the subject led by the soprano is imitated by the bass in the

eleventh below, also at one bar's distance. The last episode

(bars 195 to 202) is the only one in which the canon does not

appear; but we see it once more in the coda at bar 211. Herethe subject in the tenor is imitated by the bass in the fourth

below at half a bar's distance, and at a bar's distance by the alto

in the fifth above, and by the soprano in the tenth above. Wesee that from the apparently unimportant codetta in bars 15 to 17

Bach develops no fewer than fifteen canons, no two of which are

identical ! Though less interesting in its subjects than manyother of Bach's fugues, the present is, as regards its construction,

one of the most wonderful works in the whole domain of music.


First Section—Bars 1 to ZZ.


(Order of entry, A S T B.)

(fr) First episode (bars 36 to 42).

(c) Counter-exposition. Answer (A), A minor, bar 43.


(e) Subject (S), D minor, bar 57.


(g) Answer (T), A minor, bar 71.


(/) Subject (B), D minor, bar 81.

Fugue VI.] FUGAL ANALYSIS, 65


(J) Fifth episode (bars 88 to ioo).

(k) First middle group of entries (S B), F major, bar 101.


(m) Entry of answer (T), C major, bar 115.


(0) Entries of subject (AT), G minor, bar 130.

(p) Eighth episode (bars 138 to 145).

(q) Entry of subject (T), B flat, bar 146.

(r) Ninth episode (bars 152 to 166).


(s) Entries of subject (B A), D minor, bar 167.

(/) Tenth episode (bars 175 to 187).

(u) Entry of answer (S), A minor, bar 188.

(v) Eleventh episode (bars 195 to 202).

(w) Final entries of subject (S B), bar 203.

(x) Coda (bars 211 to 222).

F

66 Fugal Analysis. [Fugue vii.

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Fugue VII.] jFUGAL ANALYSIS. Jf

A very interesting fugue, quite clear in its construction,

though somewhat free in its form. It resembles the other fugue

(No. 3) already given from the same mass, in the infrequency of

the appearance of the subject in its complete form.

The answer is tonal ; and there is a regular countersubject,

the end of which is varied on its first appearance, to obtain an"inganno" {Fugue, § 165). In other respects the exposition

is perfectly regular, and includes an additional entry in the bass

(bar 18), to allow the countersubject to be given by the treble.

The middle section begins at bar 22 with the first episode.

We find here a short canon 4 in 2 ; the subject in the bass

(taken from the counterpoint in bars 10, 11) is imitated in the

fifth above by the soprano, at half a bar's distance, and at the

same time the subject in the tenor of bar 22 is imitated at

the same interval and distance of time by the alto. The first

group of middle entries begins at bar 26, with the subject in

the tenor. That this is the subject, and not a real answer (often to

be found in tonal fugues) is clearly shown here by the entry in

the treble of bar 29. The tenor entry is accompanied by afragment only of the countersubject. The treble begins the

answer, in stretto at one bar less than the original distance,

and is followed half a bar later by a small part of the subject

in the alto. The two next succeeding incomplete entries in the

tenor and bass (bars 31 and 32) evidently bear to one another

the relation of subject and answer. By an episode of only twobars (^ and 34) a modulation is made to D minor, in which keythe second group of middle entries (incomplete) is made by the

tenor and bass (bars 34 to 37).

The third episode (bars 37 to 52) is the longest and mostimportant in the fugue. It begins with a sequential treatment in

the soprano of the first bar of the countersubject (bars 37 to 40),

accompanied by a counterpoint in the alto in contrary motion.

The entry of the tenor in bar 40 is clearly a variation of the

commencement of the subject treated sequentially, and imitated

in the fourth above at half a bar's distance by the alto ; while the

bass continues the sequence previously heard in the treble.

The small notes in the soprano part (bars 41 to 45, and later

at bar 57) are additional counterpoints in the orchestra. Avery interesting, and probably accidental, coincidence will benoticed between this canon, and that to be found in the

24th Fugue of the ' Wohltemperirtes Clavier' at bars 17 and 18.

After a passage of free sequential construction (bars 45 to 48),the canon just seen is repeated by soprano and alto ; but the

parts are inverted, the canon now being in the fifth below instead

of the fourth above.

The third group of middle entries begins at bar 53, with apartial entry of the subject in the bass accompanied by the first

notes of the countersubject in the treble, with the alto moving in

sixths below. Sequential repetitions of bar 54 lead in bar 56 to

72 Fugal Analysis. [Fugue vn.

another stretto. The entries of the alto and tenor are both

fragmentary ; the soprano gives the answer complete, thoughwith a slight modification in bar 61. At bar 57 will be seen

in the alto an entry of the subject taking the form of the answer.

(Compare Fugue 1, at bars 49 and 53.)

The fourth episode (bars 62 to 64) needs no explanation.

At the end we see a case not yet met with in this volume—

a

complete half cadence followed by a rest in all the voices, to

introduce a close stretto.

The final section commences at bar 65 with a stretto for

all the voices on the first part only of the subject. Thesequential passage in bars 69 to 72, with its canonic imitations

of fragments of the subject, should here be regarded as continua-

tions of the stretto, rather than as episode. The last real

episode begins at bar 73, and is made by an ingenious com-bination of the counterpoint used in the first episode with afragment of the countersubject. The final stretto is introduced

on a dominant pedal (bars 78 to 83), and is followed by a short

coda founded chiefly on the beginning of the countersubject.

A?ialysis of Fugue 7.


(a) Exposition (Order of entry, BTAS, with additional

entry (B) at bar 18).



(c) First group of middle entries, and first stretto (bars 26to 39).

(d) Second episode (bars 33, 34).

(e) Second stretto (T B), bars 36 to 37.


(g) Third stretto (bars 53 to 62).



(/) Fourth stretto (bars 65 to 72).


(k) Final stretto on dominant pedal (bars 78 to 84).


Fugue VIII.] Fugal Analysis. 73

i

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Fugue VIII.J FUGAL ANALYSIS. 77

As it is desirable to make this volume as far as possible

representative of the different styles of fugal writing, we here

give one of Mendelssohn's organ fugues. Mendelssohn was in

many respects so consummate a master of composition, that it is

surprising to find the part-writing in his instrumental fugues very

loose—we were almost going to say slipshod. Some of the

fugues in the organ sonatas and in the pianoforte works defy all

attempts to put them into score; the parts cross in the mostperplexing way, or appear and disappear suddenly in the middleof a phrase. The present fugue gave far more trouble to putinto score than any other number in this volume; and it wasonly by assuming much crossing of the voices that it was possible

at all. The student need only compare such a passage as bars

68 to 73 of this score with the original, to see where the difficulty

lay.

The first thing to be noticed in this fugue is the very unusual

answer. A subject which begins in the tonic, and goes through

the supertonic to the dominant of the key would, in an over-

whelming majority of cases, take a real answer. In Fugue,

at §§ 6 1 and 280, will be seen two examples of answers to fugue

subjects beginning with the same progression, both of which are

real. Here, however, Mendelssohn prefers to consider the

subject as commencing in the dominant, A minor, and modu-lating at the fourth note to the tonic; he therefore gives it a

tonal answer, the first three notes of which are in D minor, while

the rest is in A minor. The student will see the explanation of

each note of the answer by referring to the table given in Fugue,

§122. We see here an illustration of the important fact that it

is sometimes possible for a fugue subject to take two answers,

both equally correct.

It is doubtful whether we ought not to have included this

fugue in the first section, as having no regular countersubject

;

but as there is a sort of partial countersubject, which appears

from time to time, often in a varied form, we give the fugue to

complete this section, as an example of a partial and irregular

countersubject. Even in the exposition, it does not accompanythe entry of the bass at bar 13, unless the passage in the treble

of that bar be regarded as a very free variation of it, whichrequires some exercise of the imagination.

The exposition ends in bar 16 ; and the middle section begins

in that bar with the first episode. At bar 19 is an entry (tenor)

in A minor. It is curious to notice how in several of these

middle entries Mendelssohn altogether changes the harmonicaspect of his subject. Here there is no modulation in the

harmonies ; the first three notes are not regarded as in E minor

;

and the subject, as we see it here, is what a real answer wouldhave been, had the composer given one. An unusual point is

that the following entry {soprano at bar 25) is in the same key as

the last This is a deviation from the usual rule, which we do

78 Fugal Analysis. [Fugue vm.

not recommend to the imitation of the student Both these

entries are unattended by the countersubject. We cannot con-

sider them as both belonging to one group of middle entries,

because there is a modulation in bars 22 to 24, which we there-

fore regard as episode, and not as codetta.

The group of middle entries commencing at bar 33 is

tolerably regular. The tenor entry is accompanied by the

countersubject in a varied form, while the alto (bar 37) has it

in its original form. At bar 39 is seen a partial stretto, the bass

entering with the subject before the completion of the answer bythe alto. The fourth episode, only two bars (42, 43) in length,

introduces two more entries; tenor (G minor), bar 44, andsoprano (F major), bar 47. The fifth episode (bars 50 to 56) is

sequential in its construction, and more regular in its form than

those that have preceded it. Observe, at bars 52 to 56, that

modulations are made to F minor and C minor—unrelated keys

to D minor. Few modern composers, if any, regard the old rule

as to keeping within, the nearly related keys.

From the point we have now reached, the artistic interest of

the fugue increases. The earlier episodes have been almost too

episodical ; that is, not always clearly enough connected with the

subject-matter of the fugue. At bar 57 is seen a partial entry of

the subject in the bass, with a varied form of the countersubject

in the alto ; and at bar 60 is another entry, begun by the bass

and completed by the tenor. The tenor is imitated by the alto

at half a bar's distance ; and the episode which follows (bars 63to 69) is made from close imitations of the last half of the

subject. We do not consider the entry of the subject in D minor(bass, bar 70) as the commencement of the final section, for tworeasons ; first, that it is varied, being made up of the first half of

the answer and the last half of the subject : and second, that it is

followed by an episode containing modulations to G minor andF major. This episode (bars 73 to 79) is made from close

imitations of the last half of the subject, both direct andinverted.

The final section begins at bar 80, with a stretto at half a bar's

distance for the three upper voices (the tenor entry being perarsin et thesin), while the bass from bar 82 has a dominant pedal,

over which the last episode is seen. A final entry of the answerin the bass (the first note being chromatically altered) and a short

coda conclude the fugue.

Fugue viii.] Fugal Analysis. 79



(a) Exposition (Order of entry, S ATB—compare Fugue 6).



(c) Entry of subject (T), A minor, bar 19.


(e) Entry of subject (S), A minor, bar 25.


(g) Entries of subject (T), G minor, bar 33 ; answer (A);

C major, bar 37 ; subject (B), F major, bar 39.(h) Fourth episode (bars 42, 43).

(1) Entries of answer (T), G minor, bar 44; answer (S),

F major, bar 47.

If) Fifth episode (bars 50 to 56).

{k) Entries of subject (incomplete, B), bar 57 ; subject (B,

completed by T), A minor, bar 60.


(m) Entry of subject, varied (B), bar 70.



(0) Stretto(SAT), bars 80 to 84.

(p) Eighth episode (bars 84 to 87).

(q) Final entry of answer (B), bar SS.

(r) Coda (bars 91 to 95).

As modulations are frequently made in this fugue while the

subject or answer is present, it must be understood that the keygiven in this table for the different entries is that of the commence-

ment of the subject or answer in each case.

This fugue is not given, like most of the others in this

volume, as a masterpiece, but as a fair specimen of Mendelssohn'swork. It was almost the only instrumental fugue of his in whichthe part-writing was clear enough to render it possible to put it

into open score. His choral fugues, on the other hand, wherethey are regular enough to be good models, have nearly always

more or less independent accompaniments. A specimen of these

will be seen later in this volume (Fugue 22).

8o Fugal Analysis, [Fu-ue IX.

Section (c).—Fugues by Inversion, Augmentation, andDiminution.

No. 9.—J. S. Bach. Fugue by Inversion ('Art of Fugue,' No. 5).

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Though inversion is often employed incidentally in fugues

—

we find it, for instance, in thirteen numbers of Bach's 'Forty-

Eight '—it is very rarely used systematically throughout an entire

fugue, as in that now before us. As a matter of fact, there are

so few existing specimens of this form, at least by composers of

eminence, that we have not sufficient material from which to

deduce general rules for the guidance of the student in writing a

fugue of this kind. There are three fugues in the 'Art of

Fugue' (Nos. 5, 6, and 7) in which inversion is employedthroughout ; we find it also in the first chorus in Bach's cantata,

"Siehe zu dass deine Gottesfurcht nicht Heuchelei sei," which

Fugue IX.] FUGAL ANALYSIS. 85

he later used as the " Kyrie " of his Mass in G ; we see it in twowell-known choruses by Handel—" Egypt was glad " in ' Israel/

and " To our great God " in ' Judas Maccabaaus ' ; but in hardly

any two of these pieces is the method of procedure, even in the

exposition, quite identical. All we can do, therefore, in this

section of the volume is, to give two of Bach's fugues in whichinversion is employed throughout, following them by a moremodern example in which it is used incidentally.

In our preliminary remarks to Fugue i we noticed the altera-

tion, by the addition of passing notes, of the original form of the

theme on which the ' Art of Fugue ' is based. We here see that

the inversion of that modified form is taken as the subject. Wehave already seen the inversion of the simple form in Fugue 4.

Obviously the inversion of the subject of the present fugue (as in

bar 4) gives the original subject in its modified form uninverted.

The first thing to notice is that the second voice enters

before the completion of the subject (Fugue, § 61). It will also

be seen that, instead of giving the answer, the bass enters

in bar 4 with the inversion of the subject itself. This is the

practice both of Bach and Handel in their fugues of this kind;

the inversion of the subject does duty as the answer. As Bachintends to use the subject frequently in stretto, there is nocountersubject. Observe that as the subject and its inversion

have very nearly the same compass, the two first voices to enter

do not belong to different pairs (Fugue, § 181).

As we have now had two entries of the subject we mighthave expected that the next two entries would have been the

answer, direct and inverted. This would have been rather moreregular, and is a method not infrequently to be met with, as for

instance in " To our great God " in ' Judas,' above referred

to. Bach, however, makes his third entry (bar 7) with the

inverted form of the subject, and the regular answer appears for

the first time in the tenor (bar 10). In No. 6 of the 'Art of

Fugue ' we also find the first appearance of the answer deferred

till the fourth entry. We may therefore infer that either methodis correct.

The exposition ends in bar 14 ; and the first episode, madefrom the last notes of the subject, direct and inverted, leads to

the counter-exposition, bar 17. Here we see greater regularity.

Two entries of the answer (direct and inverted) are followed

by two entries of the subject, also in both forms. Observe that

in its inversion the answer is real, not tonal. It should also benoticed that the accompanying counterpoints to the entries are

almost entirely formed from the last part of the subject. This

is the case throughout the entire fugue, excepting in two episodes

in canon, to be noticed presently ; and by this means great unity

is given to the composition.

The middle section begins at bar 30, with the second episode.

The first group of middle entries is seen at bar 33. The subject

86 Fugal Analysis, [Fugue ix.

inverted is imitated in stretto at half a bar's distance in contrary

motion—that is, in its direct form. The third episode (bars 38to 40) looks at first sight as if it were but slightly connected with

the subject matter of the fugue. But if we examine the quaverfigure in the bass, we shall see that it consists of repetitions of

the last four notes of the subject, direct and inverted.

The second group of middle entries (bars 41 to 45) is the

exact correlative of the preceding (bars 33 to 37). There wesaw the inverted subject followed in stretto at half a bar's distance

by its direct form ; here the direct answer is followed at half a

bar's distance by its own inversion. The fourth episode, only

two bars in length, leads to the third group of entries. Thesubject is now imitated in stretto (without inversion) at a bar anda half's distance.

The fifth episode (bars 53 to 56) is a very neat canon, 4 in 1,

in the fourth and octave, at one crotchet's distance, made fromthe first notes of the answer. The following group of entries

(bar 57) shows the inverted subject answered by itself at a bar

and a half's distance. Here we see in bar 57 the subject taking

the form of the answer, just as we have already seen at bars 20

and 41 the answer taking the form of the subject. As this

group of entries is in D minor, and there is no subsequent entry

in any other key, it might be supposed that this was the com-mencement of the final section. We have not so considered it,

because of the modulations at bars 62, 63 of the following

episode. (Compare Fugue 8, bar 70.) At bar 65 we see a

modification of the canon in bars 53 to 56; the subject is

inverted, the order and distance of entry are now different, andwe have a second canon, 4 in 1, just as neat as the preceding.

The final section begins at bar 69. The subject is nowimitated in the octave below, at one bar's distance ; and after the

seventh episode (bars 74 to 76) the inverted subject is imitated,

also at one bar's distance, in the octave above.

The eighth episode introduces the final entries (bar 86) on a

tonic pedal. Here the subject and its inversion are introduced

simultaneously—the closest possible stretto ! The pedal is anadditional part, and a second treble part will also be seen in the

last three bars.

One of the most interesting points in this very beautiful fugue

is the symmetry of the entries, all of which, after the counter-

exposition, are in stretto. We first see the subject combinedwith its own inversion, at half a bar's distance (bar 33) ; then the

answer and its inversion, at the same distance (bar 41). Nextcome two groups of entries at a bar and a half's distance

—

Fugue IX.] FUGAL ANALYSIS. 87

subject (bar 47) and inverted subject (bar 57). After this we see

two pairs of entries at one bar's distance (bars 69 and 77); andthus each group of entries has a corresponding group following it.

Analysis of Fugue 9



(Order of entry, ABST.)(b) First episode (bars 14 to 16). . ...

(c) Counter-exposition (bars 17 to 30). "

(Order of entry, S T B A.)



(e) First group of middle entries (B S), F major, bar ^^.


(g) Second group of middle entries (T A), G minor, bar 41,

(h) Fourth episode (bars 45, 46).

(1) Third group of middle entries (B T), B flat, bar 47.

(j) Fifth episode (bars 53 to 56).

(k) Last group of middle entries (S A), D minor, bar 57.



(m) Entries of subject (S T), D minor, bar 69.


(0) Entries of inverted subject (T A), D minor, bar 77.

(J>) Eighth episode (bars 82 to 85).

(q) Final entries (A B) on a tonic pedal (bar 86).

88 Fugal Analysis. [Fugue X:

No. 10.—J, S. Bach. Fugue by Augmentation and Diminution('Art of Fugue, ' No. 7).

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Fugue X.] FUGAL ANALYSIS. 95

Though from a musical point of view the present fugue is

decidedly inferior in interest to several other numbers in the

'Art of Fugue,' it deserves a place in the present volume as

being probably the only specimen existing of its kind. Herethe subject which we saw in the preceding fugue is combinedwith itself by inversion, diminution, and augmentation. HadBach himself not given it the title, " per Augment, et Diminut,"which is found in the autograph, we should naturally haveconsidered the theme which appears in the tenor at the first

bar as the subject—in which case the fugue would have beenone by augmentation and double augmentation. But, from the

composer's own description, we are bound to regard the subject

as being in notes of the same length as in the last-given fugue

;

and we find that, exceptionally, Bach commences with the diminu-

tion of his subject.

As the subject itself is four bars and one crotchet in length

(see the treble entry, bars 2 to 6), it follows that the augmentationwill extend over eight bars and a half. The result is that we find

hardly any episode in this fugue, the subject in one or another of

its three forms being almost continually present.

The exposition (bars 1 to 13) is in stretto ; and we find that

stretto at one distance or another is a special characteristic of

this fugue. As we have marked all the entries, there will be very

little to say about the fugue more than will be contained in our

analysis. One or two points only need be mentioned.

In the preceding fugue we saw that nearly all the accompany-ing counterpoints to the entries were developed from the last

four notes of the subject. Here we see, similarly, that the

counterpoints are formed from the last four notes of the

diminished subject; and we have figures of semiquavers wherebefore we had quavers. Observe that in the exposition we find

two entries of the subject (bars 1, 2), one diminished and oneinverted, followed by two entries of the answer, both inverted—but one diminished and the other augmented. Note also howvarious forms of the diminished subject are combined with the

different parts of the augmented subject (bars 6, 7, and 9).

The middle section begins at bar 13, and, exceptionally, is

not separated from the exposition by an episode. The first pair

of entries (bars 13, 14,) show the inversion in the octave of

bars 1 and 2 ; but inasmuch as the diminished subject begins at

the half bar, and the inverted subject follows at the samedistance as before, it results, that the entry of the latter is

per arsin et thesin. The subject is also modified here, the

notes in the second half of bar 15 being given by diminution;

while the rest of the subject is in notes of the original length.

After the entry of the diminished subject in bar 17, an episode,

only one bar in length, introduces the second group of middleentries (bar 20). These entries are in B flat (bar 20), in F major(bars 23, 24), and in D minor (bars 28, 29). The second episode

96 Fugal Analysis. [Fugue x.

(bars 31 to 34) leads to the third and last group of middleentries. Here are some unusual points to be noticed. In

the first place these entries are mostly in the key of D minor.

We hardly ever find a new group of entries beginning (as here)

in the same key in which the last entry preceding the episode

had been made (alto entry in D minor, bar 29). It must beremembered that in fugues containing much combination of a

subject with itself we generally find far less modulation than in

other fugues. As an instance of this, see the 31st fugue in thei Wohltemperirtes Clavier.' That these entries in D minor donot belong to the final section of the fugue is proved by the

subsequent entries in G minor at bars 45, 46. Observe how the

augmented subject in bar 35 is combined with the original

subject direct and inverted (bars 36 and 38). A most unusual,

and probably unique, point is to be noticed in the alto of this

group of entries. The subject appears three times consecutively

in the same voice, the last note of each entry being also the

first note of the following one. The two entries in G minor(bars 45, 46), spoken of above, are followed by an entry in F(bar 47), leading, without another episode, to the final section of

the fugue (bar 50). Curiously enough, though there are here twoentries of the subject in the alto, there are none in the bass.

From bar 56 to the end of the fugue, an additional voice (a

second soprano) is added.

If we examine the entries in this fugue, we shall find that the

subject is most frequently employed in its diminished form. It

only appears once in each voice in its augmented form (bars 5,

2 3> 35) and 50), and four times in notes of the original length

(bars 2, 14, 36, and 38), while we find it (not counting the in-

complete entry in bar 6), twenty times by diminution. We see

it sixteen times in its direct, and eleven times in its inverted

form. The whole fugue must rather be regarded as a study in

scientific device than as a model for the imitation of the student

;

it is inserted here for the sake of completeness, and as an illus-

tration of what is possible in fugal contrivance in the hands of a

great master like Bach.

Analysis of Fugue 10


(a) Exposition. Subject diminished (T), bar 1 ; subject in-

verted (S), bar 2 ; answer inverted and diminished (A),

bar 3 ; answer inverted and augmented (B), bar 5 ;

Subject (partial entry) diminished (T), bar 6 ; answerdiminished (A), bar 7 ; subject inverted and diminished(T), bar 9.

Fugue X.] FUGAL ANALYSIS. 97


(b) First group of middle entries. Subject diminished (S),

G minor, bar 13 ; subject inverted (A), G minor, bar

14; subject diminished (T), B flat, bar 17.

(c) First episode (bar 19).

(d) Second group of middle entries (bars 20 to 31). Subject

diminished (T), B flat, bar 20 ; subject inverted anddiminished (B), B flat, bar 20 ; subject diminished (A),

F major, bar 23 ; subject augmented (T), F major,

bar 23 ; subject inverted and diminished (S), F major,

bar 24 ; subject diminished (B), D minor, bar 28 ;

subject diminished (A), D minor, bar 29.

(e) Second episode (bars 31 to 34).

(/) Last group of middle entries (bars 35 to 49). Subject in^

verted and augmented (A), D minor, bar 35 ; subject

(T), D minor, bar 36 ; subject (S), D minor, bar 38 ;

subject inverted and diminished (S), D minor, bar 42 ;

subject inverted and diminished (A), D minor, bar 43 ;

subject diminished (A), G minor, bar 45 ; subject in-

verted and diminished (T), G minor, bar 46 ; subject

diminished (B), F major, bar 47.


(g) Final group of entries. Subject augmented (S), D minor,

bar 50 ; answer inverted and diminished (A), bar 51 ;

subject diminished (A), bar 54 ; subject diminished

and varied (T), bar 55.(h) Coda (bars 58 to 61).

9S Fugal Analysis. [Fugue XI.

No. 11.—R. Schumann. No. 5 of ' Six Fugues on the name Bach,' Op. 60.

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104 Fugal Analysis, [Fugue xi.

This fugue is by far the most irregular in its construction of

any that will be found in this volume. It is given, not as a

model for the imitation of the student, but to illustrate the

modern free style of fugal writing. It also shows the incidental

employment of inversion and augmentation, as distinguished

from their systematic use, which has been exemplified in the two

fugues last given. Owing to the extreme freedom of its form, its

analysis has presented more than ordinary difficulties. In ex-

planation of its title—a fugue on the name ' Bach '—we mustremind students that H is the German name for B natural,

and B for B flat. He will then see that the first four notes of

the subject spell the word BACH.The first irregularity to be noticed in this fugue is, that the

bass takes no part in the exposition, which is for three voices

only. We find in the 26th fugue of the ' Wohltemperirtes

Clavier ' what at first sight looks like a similar procedure—an

exposition of a four-part fugue which is for only three voices.

There, however, Bach reserves the entry of the bass for the final

section of the fugue, when it brings in the subject in augmenta-

tion. But here the bass makes its first appearance at bar 16, in

the first episode ; and the complete subject is heard only once in

that voice (bar 56) during the whole fugue. The exposition, as

regards the three voices that take part in it, is quite regular.

The subject, which begins on the subdominant, takes a real

answer, and there is no regular countersubject.

The middle section begins in bar 12 with the first episode,

formed from free imitation of the first part of the subject, which

is sometimes accompanied by its last notes. (See the tenor in

bars 17 and 19.) The first entry of the bass, already referred to,

shows a fragment of the subject.

The first group of middle entries (bar 22)—subject, D minor(alto) ; answer, A minor (soprano) ; subject, D minor (tenor—

a

partial entry only)—leads to the second episode (bars 33 to 36),

founded chiefly on a varied form of the end of the subject. This

is followed by the second group of middle entries, in the original

keys of tonic and dominant.

In this second group the 'Bach' theme comes into pro-

minence; we see it in the tenor at bar 37 by augmentation.

Here we notice a different kind of augmentation from that whichwe have previously met with. If used in triple or in compoundtime, we generally find that augmentation, instead of being in

notes of double length, is in notes of three times the length.

Were we to double the length of the notes in the present subject,

there would be a complete disturbance of the rhythm ; for the

augmented subject would take the following form

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Fugue XL] FUGAL ANALYSIS. I05

augmented, and not the entire subject. This new form of the

theme is used as a counterpoint to the subject itself, which it

accompanies in several of its subsequent entries.

From bars 48 to 52 must be regarded as another episode.

True, the augmented subject is present in the tenor ; but the

imitative passages between soprano and alto have a very

episodical character. Besides this a modulation is effected to

introduce a new group of entries.

If we compare the entry in bar 52 with that in bar 22, it

looks at first as if Schumann had broken one of the fundamentalrules of fugal writing (Fugue, § 325), and introduced two groupsof middle entries in the same key. But an examination of the

following entry, in bar 56, proves that we have here not the

subject, as before, but only the answer preceding the next entry

of the subject in G minor.

A dominant pedal (bar 61) following the bass entry leads to

the final section (bar 62). This is of unusual length, occupying

exactly half of the fugue. It commences with an entry of the

subject in the original key, accompanied by the * Bach ' theme in

augmentation. Note at bar 67 that the pedal is quitted after

a chord of which it forms no part (Harmony, § 546). The episode

which follows (bars 67 to 72) seems at first to suggest modula-tions which should prevent our regarding it as belonging to the

final section of the fugue. As a matter of fact, however, wehave here chromatic harmonies which never really leave the keyof F. The harmonic framework of bars 67, 68 is the funda-

mental chord on the supertonic, of bars 69, 70, the dominanteleventh with a minor ninth, and of bars 71, 72, the minor ninth

on the supertonic. Observe in bars 70 to 72 the little canon in

the octave at half a bar's distance between alto and tenor.

At bar 72 we have a new group of entries. The subject is

now inverted in the alto, and followed in stretto at irregular

intervals by the tenor and soprano. At bar 76 begins a very

long tonic pedal, which continues for 25 bars to bar 101. Themental effect of rests must never be forgotten; in bars 83 and88, for example, the mind carries on the F sounded in the bass

till the next note is heard in the same voice. Over this pedal

point the longest episode in the fugue (bars 80 to 95) is con-

structed from material with which we are already familiar.

At bar 95 we find an entry of the subject (varied) in the tenor,

accompanied by fragments of itself, direct and inverted ; andafter a short episode of only two bars, a last appearance of the

subject (also varied) in the alto at bar 101. The treble at bar 103and the tenor at bar 105 must be particularly noticed. If the

four notes H ^ J===

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theme transposed a fourth lower. Here we have the first instance

106 Fugal Analysis. [Fugue xi.

yet met with of retrograde imitation {Double Counterpoi?it, § 287)In the coda, which concludes the fugue, we see at bars 114 to 116the 'Bach' theme in the treble, and at bars 118 to 120, the

retrograde form in the tenor

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A very curious and most irregular point about this fugue is

the treatment of the dominant and tonic pedals. Of these

there are no fewer than five. In the middle section there is a

tonic pedal (bars 37 to 40); then comes a dominant pedal

(bars 61 to 67) ; next, the very long tonic pedal (bars 76 to 10 1).

This is immediately succeeded by a second dominant pedal

(bars 102 to no); and lastly from bar 114 to the end is anornamented tonic pedal.

In spite of all its irregularities of form, the fugue is a very

charming composition, and fully deserves its place in this

volume.



(a) Exposition (Order of entry, AST).



(c) First group of middle entries (A S T), D minor andA minor, bar 22.

(d) Second episode (bars i>?> to 36).

(e) Second group of middle entries, accompanied by ' Bach p

theme in augmentation, F major and C major, bar 36.


(g) Third group of middle entries (answer, D minor ; subject,

G minor), bar 52.



(/) Entry of subject (S) in tonic key, bar 62.

(j) Fifth episode (bars 67 to 72).

(k) Entries of inverted subject (A TS), bar 72.

(/) Sixth episode (bars 80 to 95).(m) Entry of varied subject (T), bar 95.(n) Seventh episode (bars 99 to 101).

(0) Entry of varied subject (A), accompanied by 'Bachtheme retrograde, bar 101.

(/) Coda (bars 105 to 124).

Fugue XII.] Fugal Analysis. 107

Section (d).—The same Subject treated by

DIFFERENT COMPOSERS.

This section of the present volume is introduced to give

students the opportunity of an instructive comparison of different

styles of fugal writing. It would be difficult to find four fugues

more unlike one another, either in their special detail or in

their general effect, than the lour treatments of what is virtually

the same theme now to be given ; and it is hoped that the

student's insight into the possibilities of fugal composition will

be deepened by observing the very different methods employedby the great masters. It would have been possible to increase

the number of our examples, for there are two fugues byBuxtehude in which the same subject is employed ; but neither

of these is of sufficient importance to render its introduction a

necessity.

No. 12.—J. S. Bach. Fugue in A Minor. ( ' Wohltemperirtes Clavier,' No. 44.)

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This very fine fugue from the ' Wohltemperirtes Clavier ' is so

simple in construction as to need only a very short analysis.

The subject is tonal, and ends on the first quaver of the

third bar, as is proved by comparing it with the alto of bar 5 ;

there is a regular countersubject. The codetta in bar 5, before

the entry of the third voice, should be noticed, because it

furnishes the material for most of the episodes, which in this

fugue are especially interesting.

The middle section begins at bar 8, with the first episode.

The first bar of this is made from the codetta, bar 5, with the

addition of a bass part, while bar 9 shows imitative treatment

of a modified form of the countersubject in the first crotchet

of bar 4. The middle entries are all isolated. The first is in

C major (bar 9), the subject, as is so often the case, taking the

form of the answer. The second episode (bars n to 13) is a

continuation, by imitation, of the last notes of the subject andcountersubject. After another entry of the subject in E minor(bar 13), the third episode shows new treatment of the codetta,

bar 16 being another and somewhat freer variation of the

countersubject. At bar 16 we see a middle entry in the tonic

key—a common procedure with Bach—the subject again taking

the form of the answer. Here (as also at bar 9) the first note of

the subject is shortened. In the fourth episode (bars 19 to 21),

the last notes of the countersubject are treated sequentially in

the bass, and accompanied by a canon in the fifth below, betweentreble and alto, the theme of which is evidently a free variation

of the last notes of the subject.

The last middle entry in D minor (bar 21) leads to the fifth

episode (bars 23 to 25), which the student, after what has beensaid, will have no difficulty in analyzing. The final section is

very short, containing only one entry of the subject (A minor,

bar 25)—the only entry in trie whole fugue which is accompaniedby only a small part of the countersubject. In all the other

entries the countersubject is introduced with the utmost regularity.

Fugue xii.] Fugal Analysis. hi

Analysis of Fugue 12


(a) Exposition (Order of entry, B A S).


(b) First episode (bars 8, 9).

(c) Entry of subject (B), C major, bar 9.


(e) Entry of subject (S), E minor, bar 13.


(g) Entry of subject (A), A minor, bar 17.


(/) Entry of subject (S), D minor, bar 21.

(/) Fifth episode (bars 23 to 25).


(k) Entry of subject (B), A minor, bar 25,

(/) Coda (bars 27, 28).

112 Fugal Analysis. [Fugue XIII.

No. 13.—G. F. Handel. Chorus, "And with his stripes." {'Messiah.')

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Fugue xiii.] Fugal Analysis. 115

The whole style and spirit of this fugue differs widely fromBach's treatment of the same subject. The difference is, nodoubt, partly owing to the fact that this fugue is vocal, while the

other was instrumental ; but it is probably quite as much due to

the difference in the character of the music of the two composers.

The specialty of this fugue is the unusually large number of

codettas found in it. Not only are they seen in the first

exposition (bars 9 to 12, and 16 to 19), but they are interposed

between every pair of entries throughout the fugue till we reach

the final section. After the entry of the bass with the answer

(bar 19) we find in bar 25 an additional entry of the treble, to

allow the bass to give the countersubject ; but there is an irregu-

larity here, as the treble has the answer instead of the subject.

The middle section begins aHraf 29 with an episode of twobars, leading to the first group of middle entries, at bar 31.

Here the tenor gives the subject in B flat minor ; as the next

entry (bass, bar 37) is in F minor, it is evidently the answer to

the subject in the tenor, and we therefore consider it as belonging

to the same group of entries, and consequently regard bars 35to 37, not as episode but as codetta. The second episode

(bars 41 to 48) modulates to E flat, in which key the next

group of entries commences. Here we see a parallel case to

that just met with in the last group. The two next ensuing

entries (alto, E flat, bar 48 ; treble, A flat, bar 55) evidently

stand to one another in the relation of answer and subject,

and form one group, joined to each other by a codetta. Observethat at bars 37 and 48 the answer is real

The third episode (bars 59 to 63) leads to the final section of

the fugue. The subject is now accompanied by a modified formof the countersubject, the second bar of which is transposed a

fifth higher. After two entries (subject, treble—answer, bass)

follows the fourth and last episode, the most artistically con-

structed of the four. It is made from a sequential treatment

of the codetta, bars 35 to 37, and introduces the final group of

entries. Here the order is reversed, the answer now leads andthe subject replies ; but it is a curious point that the entries are

allotted to the same two voices as in the last group, and that

neither the alto nor the tenor enters with subject or answerduring the whole of the final section. A few bars of coda endwith a half cadence ; the reason for this being that in the oratorio,

this chorus (as most of our readers will remember) leads withouta break, into the following number, " All we like sheep."

This interesting fugue shows how large an amount of variation

of detail is possible in a piece, the form of which can hardly becalled irregular. Andre, in his treatise on Fugue, says that the

order of the entries is faulty, and the fugue cannot be consideredas properly treated ; but this only shows how even excellent

musicians may be misled by too blind an adherence to old

and formal rules.

n6 Fugal Analysis. [Fugue xiii.

Analysis of Fugue Ij.


(a) Exposition (Order of entry, SATB), bars 1 to 23.

{b) Codetta, and additional entry (S), bars 23 to 29).


(c) First episode (bars 29 to 31).

(d) First group of middle entries. Subject (T), B flat minor;

answer (B), F minor, bar 31.

(e) Second episode (bars 41 to 48).

(/) Second group of middle entries. Answer (A), E flat

;

subject (S), A flat, bar 48.

(g) Third episode (bars 59 to 63).

Final Section—Bars 6$ to 91.

(h) Entries of subject (S) ; answer (B), bar 63.

(1) Fourth episode (bars 71 to 79).

(j) Entries of answer (S) ; subject (B), bar 79(k) Coda (bars 87 to 91).

Fugue xiv.] Fugal Analysis. 117

No. 14.—J. Haydn. Fugue from the Quartett in F minor, Op. 20, No. 5.

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In this very beautiful fugue the subject of the two precedingis given in a slightly altered form, the tonic being substituted

tor the mediant as the second note. It will be seen also that

what corresponds to the countersubject in the other fugues wehave examined, here appears against the subject instead of against

the answer. Here, therefore, we have a Double Fugue (Fugue,

§ 367), and we mark the first entry in the viola as Subject 2, andnot as Countersubject.

An examination of the exposition of this fugue (bars 1 to 22)leaves little room for doubt that Haydn, when he began it,

intended the two subjects to extend to the first note in bar 7.

Fugue XIV.] FUGAL ANALYSIS. I 25

After making the first two entries in this form, he appears to havechanged his mind—possibly because he thought that such long

subjects would make the developments tedious. From the third

entry, therefore (bar 13), to the end of the fugue, he treats only

the first four bars as his subjects ; we consequently regard

bars 5 and 6, and n and 12, as codetta. These bars are never

referred to subsequently, even in the episodes of the fugue.

The exposition is completed, at bar 22, as soon as both the

subjects have appeared, either as subject or answer, in each of

the voices (Fugue, § 376), and the middle section begins in the

next bar with the first episode (bars 23 to 35). In this, as in

some of the following episodes, canon plays an important part.

At the commencement, the second subject is treated as a canonin the fifth below at one bar's distance between the first andsecond violins. At bar 28 the second violin discontinues the

canon, which is taken up in the fourth below by the viola.

At bar 32 a variation of the last notes of the second subject is

announced by the second violin, and imitated in the sixth above

at half a bar's distance by the first violin.

The first group of middle entries is in A flat (bars 36 to 42).

In this is a fragmentary stretto ; the first notes of the first subject

being heard in the viola (bar 38), two bars after the subject is

given by the violoncello. The more complete stretti are reserved

for a later part of the fugue.

In the second episode (bars 43 to 54) we see some morecanons. At its commencement, the second subject, given bythe viola at bars 41, 42, and continued sequentially, is imitated

in canon in the fourth above, and at one bar's distance bythe first violin. Let the student compare this canon with

that in the first episode, to learn how to combine variety

with unity. The subject of both is the same ; but there Haydngives us a descending sequence with a canon in the fifth below,

while here there is an ascending sequence, with a canon in

the fourth above. At bar 46 is seen in the first violin a partial

entry of the first subject. We regard this as belonging to

the episode, and not to a fresh group of entries, not only

because the subject is not completed, but still more because

it is not accompanied by the second subject. In a doublefugue, both subjects should be heard together in each groupof middle entries (Fugue, § 380). At bar 48 begins a moreelaborate canon—4 in 2. The subject beginning in the first

violin on the second minim of that bar is imitated in canonat the fifth below, one bar later, by the second violin ; at the

same time there is a different canon, also in the fifth belowrbetween the viola and violoncello. The upper canon is a free

modification of part of the first subject, while the lower is

evidently suggested by the last notes of the second subject.

At bars 55 to 58 is an isolated pair of entries in B flat minor,

the close of the first subject being varied ; and the third episode,

126 Fugal Analysis. [Fugue xiv.

of only two bars, leads to a much longer and more important

group of middle entries at bar 61. This group begins with two

entries in stretto in the key of G flat—an unrelated key to

F minor be it noticed in passing. The following entries which

succeed each other continuously are each a fifth above the

preceding—D flat (bar 66), A flat (bar 69), E flat minor (bar 72),

B flat minor (bar 75), F minor (bar 78). As these entries are

not at the regular distances of subject and answer, we have

marked them all as ' S,' though in each case they have the

form of the answer. It ought by this time to be hardly

necessary to remind the student that in the middle and final

sections of a tonal fugue, either form (subject or answer) maybe used indifferently at the discretion of the composer. Theseconstantly modulating entries lead to the final section of the

fugue, which is not here, as usual, preceded by an episode. Wesaw a final section similarly introduced in Fugue 10 of this

volume.

We consider this final section as beginning at bar 81, andnot at bar 78, because the latter entry, though it ends in F minor,

begins in B flat minor, as is proved by bar 77. Here we find

again at bar 83 an entry in stretto of two bars' distance. Atbar 92 the first subject and its inversion are introduced simul-

taneously, and accompanied in the viola by a considerably-

altered form of the second subject. The fourth episode (bars

95 to to 2) is constructed on a sequence in the bass, made fromthe lower of the two canons in bar 48, and it leads to a dominantpedal, on which once more is seen a stretto at two bars' distance.

Both subjects are here present. We do not regard bars 108 to

1 1 1 as episode, as they simply lead up to a pause on the chord of

the dominant minor ninth, and are only a prolongation of the

preceding phrase.

From bars 112 to 124 is another group of entries in closer

stretto than has yet been seen—only one bar. The first entering

part is modified at the close, and therefore unattended by the

second subject, which, however, always accompanies the secondentering voice—see bars 115, 119, and 123.

In the fifth episode (bars 125 to 133) we find another canon,

differing from any of the preceding. A variation of the secondsubject, announced in bar 125 by the viola, is imitated in canonin the second above at one bar's distance by the second violin,

and in the fifth above at two bars' distance by the first violin.

Here, therefore, we see a canon 3 in 1, with a free part for the

violoncello. This episode leads to a second dominant pedal

(bar 134), with stretti above it for the first subject alone, at

one and two bars' distance. A short and not very important

episode (bars 140 to 144) introduces the last and closest stretto

at half a bar's distance. The subject in the first violin is,

therefore, per arsin et thesin. The canon in the octave, at

half a bar's distance, is continued strict to bar 155, and more

Fugue XIV.] FUGAL ANALYSIS. 127

freely to bar 158. Observe how neatly Haydn, in bar 149, brings

in the first subject against the canon in the outer parts.

The coda begins at bar 161 after a full cadence. We regard

this part of the movement as coda, because after this point there

are no more complete entries of the two subjects together;

though at bar 170 we find the end of the first subject in

combination with the second. In this coda, the polyphonic

style is nearly abandoned, the parts mostly moving together.

A final entry of the first subject (bar 179), followed by a full

cadence, concludes this fine fugue, which is an excellent exampleof the free modern style of contrapuntal writing.



(a) Exposition (Order of entry, AT SB) *



(c) First group of middle entries in A flat (bar 36).


(e) Isolated entries in B flat minor (bar 55).


(g) Group of entries, modulating from G flat to F minor(bar 61).


(/i) Entries in C minor and F minor (bar 81).

(/) Fourth episode (bars 95 to 102).

(/) First dominant pedal (bars 103 to 111).

(k) Entries in close stretto (bars 112 to 124).


{in) Second dominant pedal (bar 134).

(n) Sixth episode, on dominant pedal (bars 140 to 144).

(0) Closest stretto and canon (bar 145).

(/) Coda (bars 161 to 184).

* For the sake of uniformity we distinguish the entries by the names of the

four voices, to show their relative positions, though the fugue is for stringedinstruments.

128 Fugal Analysis. [Fugue XV.

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132 Fugal Analysis. [Fugue xv.

This fugue, like our last, is a double fugue, but much moreregular in construction. There is a curious resemblance between

its two subjects and those of the final chorus in Handel's' Joseph,' with which Mozart may possibly have been acquainted.

fp $r$rU\***r*r^^WSwEWS^L •BÊ 2=e:

The treatment of the subjects by the two great composers is

so entirely different that no charge of plagiarism can attach

to Mozart, even if there be something more than an accidental

coincidence here. Not only is Handel's chorus in a majorkey, but it is not even a regular double fugue, as will be seen

by our short extract. The first subject in the bass is only

occasionally employed as a kind of canto fernio, and the wholeconstruction of the fugue is extremely free. Mozart's, on the

other hand, is one of the finest double fugues in existence,

though some pedantic theorists of the old school have foundfault with it because of the modulations to unrelated keys.

The second subject is so written that it will combine with

the first in double counterpoint in both the octave and twelfth.

This is effected by avoiding the interval of the fifth, andemploying the sixth only in such a manner that its inversion

in the twelfth will give a fundamental chord of the seventh

{Double Counterpoint, § 111).

The exposition of the fugue extends to bar 15, and is

completed as soon as both the subjects have appeared in all

the voices. Thus far the only inversions of the two subjects

are in the octave.

The middle section commences in bar 15 with the only

episode in the fugue—only a bar and a half in length. Thisis made from a sequential treatment of a prolongation of

the last notes of the second subject, as will be seen by extract-

ing the passage

—

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proportion of episode than in fugues with only one subject.

We can hardly speak of " groups " of middle entries in this

fugue; because, beginning in bar 16, they follow one another

Fugue xv. ] Fugal Anal ysis. 133

continuously. The first pair are in F major, and at bar 17we see for the first time the two subjects inverted in the twelfth.

This is the only inversion throughout the fugue of the complete

subjects at this interval. At bar 20 the last note of the first

subject is sharpened, inducing a modulation to G minor, in

which key the next pair of entries follows—now in the original

position. This is succeeded at bar 23 by another pair of

entries in the unrelated key of C minor—doubtless one of those

which incurred the condemnation of the old ' Dryasdusts.'

At bar 27 begins the first stretto. The entry of the first

subject in the treble (in B flat) is accompanied by the inversion

in the twelfth of the second subject; and at bar 29 the bass

enters with the first subject in a stretto at two bars' distance,

causing in the following bar the discontinuance by the treble

and tenor of the uncompleted subjects. At bar 30 the tenor

enters again with the second subject. Here is another deviation

from the regular rule : the same subject appears twice in

succession in the same voice.

In bars 32 and 33 we find a partial entry of both subjects in

another unrelated key—F minor; the inversion is again in

the twelfth. A portion of the second subject now appears

with chromatic alterations, and is imitated at one bar's distance

in the fifth above (in bar 37 at the fourth below, the inversion

of the fifth) in all the voices. Here is an interesting exampleof the point mentioned in Fugue (§ 381), that in double fugues

stretti made from one subject alone often take the place of

episodes. Here each new entry at the distance of a fifth

above induces a modulation ; and the music returns from

F minor (bar 34) through C minor (bar 35) and G minor(bar 36) to D minor, the original key (bar 37). Let it benoticed that the counterpoint accompanying these entries, whichis first seen in the treble of bar 34, is developed from the last

notes of the second subject.

The final section begins at bar 39. The two subjects, neither

being quite complete, now appear in their original relative posi-

tions ; but the second subject is now an octave higher than in the

first exposition. The passage which connects this pair of entries

with the following must be regarded as codetta, not episode, as it

does not modulate, nor introduce entries in a new key. In the

last pair of entries the second subject is inverted in the twelfth,

and the same chromatically varied form is used which was seen in

bars 34 to 38. It will be seen that all the later entries in this

fugue are partial; the last complete appearance of the two sub-

jects is in bars 23 to 27. At bar 46 begins the coda, the first bars

of which should be compared with bars 34 to 38. Notice howby altering the intervals of entry Mozart keeps in the keyinstead of modulating as before. The omission of the third in

the final chord was doubtless for the sake of giving an antique,

ecclesiastical character to the close.

134 Fugal Analysis. [Fugue xv



(a) Exposition (Order of entry, B A S T).


(b) Episode (bars 15, 16).

(c) Entry of subjects in F major (bar 16).

(d) Entry in G minor (bar 20).

(e) Entry in C minor (bar 23).

(/) First stretto, B flat (bar 27).

(g) Second stretto, modulating (bar 33).


(h) Pair of entries in D minor (bar 39).

(/) Second pair of entries (bar 43).

(J) Coda (bars 46 to 52).

Fugue XVI.] Fugal Analysis. 135

PART II.

FUGUES WITH MORE THAN ONE SUBJECT \ FUGUES ON A

CHORALE AND CANTO FERMO ; ACCOMPANIED FUGUES.

Section (e). Double and Triple Fugues.

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Fugue XVL] Fugal Analysis. 139

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We have already met with two specimens of double fugues in

Nos. 14 and 15, both of which might have been equally well

included in this section. As they were inserted with a different

object, it was better to put them with the other fugues written onthe same subject. We next give two double fugues, illustrating

several points not shown in our last examples.

In the movement now under notice, we have an interesting

specimen of the rarer kind of double fugue—that in which each

subject has a separate exposition before the two are heard in

combination (Fugue, § 384). It must be remembered that the

form of these fugues differs materially from that of those in which

142 Fugal Analysis. [Fugue xvi.

the two subjects are announced together. Like the others, they

can be divided into three sections ; but of these the first contains

the treatment of the first subject alone ; the second (which we donot now call " middle section") is that in which the secondsubject is treated alone, and the third is that in which they are

both combined. Sometimes, as in Bach's Organ Fugue in

C minor (analyzed in Fugue, §§ 392-394), these three sections

are of approximately equal length \ but frequently, as in the

fugue now under notice, the first two sections are comparatively

quite short, and the greater part of the fugue is occupied with the

combination of the two subjects.

If we examine the first subject, we should be inclined at first

sight to conclude that' it extended to the A at the end of bar 2.

But if we look at the answer, we shall see that this is not so.

A fugue subject never ends on the subdominant. The note Gin the subject, being answered by C instead of by D sharp, showsthat there is here an implied modulation {Fugue, §§ 118-120) to

the key of the dominant \ and the subject, from G in the first

bar to E in the second, is regarded as in the key of E, andanswered accordingly in the key of A. But if the last three

notes of bar 2 were part of the subject, they would certainly showa return to the key of A ; and the answer would have made the

corresponding modulation to E, thus

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that the subject ends, where we have marked it, on E, and that

the three last notes of bar 2 are codetta. As is not infrequently

the case, these notes of codetta are imitated in the exposition byeach succeeding voice.

The exposition of the first subject ends in the ninth bar. Wehave marked the following passage as codetta, and not episode,

because it contains no modulation beyond the tonic and dominantkeys.

At bar 11 begins a counter-exposition of the first subject.

Here the voices which before had the subject now give the

answer, and vice versa. Observe that in the tenor entry the

subject, as so often happens in tonal fugues, takes the form of the

answer. In .such cases its key-relationship to the following or

preceding entry shows which it is. We also see an example of

the employment of stretto in a counter-exposition {Fugue, § 209)

;

the entries are half a bar nearer to one another than before. Wefurther find here additional proof that the subject ends where wehave said ; for the three notes of codetta in bar 2 are not seen at

all in the counter-exposition.

At bar 18, the second section of the fugue commences with

the exposition of the second subject. This is less regular in

treatment than the exposition of the first subject;greater freedom

Fugue XVI.

J

FUGAL ANALYSIS. 1 43

is sometimes taken by composers in such cases, just as with the

middle entries in a simple fugue. In two examples of this formby Handel and Bach, quoted in Fugue, §§ 386 to ^390, will befound other instances of irregularity in the exposition of the

second subject. Here we see in the answer given by the tenor at

bar 19 a striking instance of the disregard of the position of the

semitones, spoken of in Fugue, § 144. The semitone from A to

G sharp in the subject (bar 18) is answered in bar 20 by a tone fromE to D. The result is that, while the second subject is in the keyof A major, the answer is not in the key of E major, but is asimple transposition a fifth higher, without leaving the key.

Though, according to strict rule, this is irregular, it is here, webelieve, capable of justification.

The student will remember that when two subjects of a doublefugue are announced together, both must be in the same key. If

he will look at the first entries of the combined subjects in the

present fugue (bars 28, 31, 33, and 35) he will see that the first

subject is combined with the second answer, and the secondsubject with the first answer. Now though the answer to the first

subject (bar 3) implies a modulation in the subject by answering

the leading note by the third of the tonic—the almost invariable

practice of composers when the leading note does not return at

once to the tonic (Fugue, § 133)—we see from the harmonies with

which Graun accompanies the later entries of his first subject (see

bars 7, 12, and 15) that he regards it as ending in the key of A.

The second subject will obviously not combine with the first at the

point the composer intended; he therefore takes the secondanswer also in the key of A, so that when the two are heardtogether the tonality may not be confused.

Another point in which this second exposition is less regular

than the first is, that the alto entry in bar 20 is half a bar earlier

than its regular place. We see at the end of this exposition a

passage of imitation in the octave between tenor and bass (bars

23, 24), leading to the first episode, bar 26. This consists of a

short canon in the fifth above, founded on the second subject,

with an independent instrumental bass (printed in small notes,

bars 26, 27).

At bar 28 begins the third, and by far the longest section of

the fugue, in which the two subjects are combined. We see first

two entries of the first subject and second answer (bars 28 and

31), and then two of the second subject and first answer (bars 33and 35). In bars 35 to 38, the second subject is treated byitself in stretto, and a modulation is made through D major to

B minor. From this point down to the second episode (bar 49)we have marked all the entries, as usual with ' S,' because of the

irregularities of their distances of interval. Observe in this very

interesting group of middle entries how the various stretti cause

different*parts of the second subject to be combined against the

first (bars 41 and 43).

144 Fugal Analysis. [Fugue xvi.

The second episode (bars 49 to 53) is made by passages of

free imitation between treble and alto, founded upon the secondsubject, direct (bars 49, 50) and inverted (bars 51 to 53). It

leads to the final group of entries (bar 53). Here we find the

first subject treated by itself in stretto at half a bar's distance (bar

53) ; then a similar stretto at bar 56, with which in the following

bar the second answer is combined. At bar 58 is a new com-oination. The first answer, given in the bass by augmentation, is

imitated in the octave above by the tenor, also in augmentation.

Note, in passing, that in the tenor one note, C, is only of the

original length. This piece of irregular canon is accompanied byanother canon in the fifth below (bar 59) for treble and alto at

half a bar's distance, founded upon the first notes of the secondsubject.

The last twenty bars of this fugue (from bar 62) consist of a

free coda. The first subject is heard no more ; but the interest

of the music is fully maintained by canonic and sequential imita-

tions, mostly derived from the second subject. In bar 62 begins

a canon in the fifth above between tenor and alto, and in bar 64a similar canon between bass and treble. After more points of

imitation, hardly continuous enough to be called canon (bars 67,

69), we see an interesting sequence in the bass (bars 70 to 72)leading to a final piece of canon—treble and alto in the fifth

below at half a bar's distance (bars 73 to 75) ; and long-drawn

harmonies of dominant and tonic bring this very fine fugue to a

close. Bars 77 to 81 cannot be properly considered dominantand tonic pedal points, because there are no harmonies above the

dominant and tonic in the bass, of which those notes do not

themselves form a part.

Analysts of Fugue 16.


(a) Exposition of first subject (bars 1 to 9).

(Order of entry, B T A S.)

(V) Codetta (bars 9, 10).

(c) Counter-exposition of first subject (bars 11 to 17).

Second Section—Bars 18 to 27.

(d) Exposition of second subject (bars 18 to 23).

(e) Additional entries (bars 23 to 25).

(/) First episode (bars 26, 27).

Third Section—Bars 28 to 81.

(g) First combinations of the two subjects (bars 28 to 35).

(h) Stretto on second subject (bars 35 to 38).

(/) Middle group of entries, mostly in stretto (bars 39 to 48).

(/) Second episode (bars 49 to 53).

(k) Final group of entries (bars 53 to 61).


Fugue XVII.] Fugal Analysis. 145

No. 17.—L. Cherubini. Double Fugue, "Cum Saneto Spiritu." (2nd Mass.)

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Fugue XVII.] Fugal Analysis, 153

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154 Fugal Analysis, [Fugue xvn.

This extremely interesting, though somewhat free, fugue has

in its general construction more resemblance to the fugue by

Haydn (No. 14 of this collection) than to either of the other

double fugues we have given. It presents, nevertheless, quite

sufficient new points in its treatment to warrant its insertion here.

In its original shape, it has an orchestral accompaniment, which

is mostly in unison or octaves with the voices. A few compar-

atively unimportant ornamentations and fillings up of the harmo-ny

are omitted for the sake of clearness ; but in two places where the

instrumental bass is different from the vocal, this is shown bysmall notes (bars 63 to 74, and 96 to 99).

In the exposition of this fugue, the two subjects are announcedsimultaneously, as in fugues 14 and 15 ; but instead of the

answers being immediately given by the other two voices, as in

the fugue from Mozart's 'Requiem' (No. 15), that method of

exposition is adopted which was described in Fugue, §§ 375-377,and of which we have seen an example in No. 14. Before the

second entry of the two subjects is a codetta (bars 10 to 13). Thisis a canon in the fifth below, founded on a prolongation of the

last notes of the second subject ; we shall find it made much use

of later.

The exposition ends at bar 23, as soon as both the subjects

have appeared in all the voices. The first episode (bars 23 to 29)begins with a neat little canon, 4 in 2, of which the subject in the

treble and bass is formed from the last notes of the first subject

followed by the first notes of the codetta (bar 10). From bars

30 to 39 is a counter-exposition, shorter than the exposition, as it

contains only two pairs of entries. The two answers lead in trie

voices which before led with the subjects, and the other two voices

reply with the two subjects.

The middle section of the fugue begins in bar 39, with the

second episode. This is a modification of the codetta (bars 10

to 13), and is another canon (2 in 1) at the same distance both of

interval and time. The first group of middle entries (bars 42 to

59) contains three pairs of complete entries, in B minor, G major,

and E minor, and one pair of partial entries (in C major, bar 57).

Here the first notes of the first subject are seen, direct in the bass,

and inverted in the treble.

The third episode (bars 59 to 74) presents more than onefeature worthy of notice. From bars 62 to 68, we see in the three

upper parts the first notes of the first subject imitated in the fifth

and octave at two bars' distance, and accompanied by a sequential

figure in the bass. Observe in the alto of bars 67 to 70 the entry

of one of the subjects of the canon at bar 23. From bars 70 to

74 we see the same complete canon, 4 in 2, as in the first episode,

but with a different disposition of the parts, the two upper voices

now having the subject which was before given to the two outer

ones. Besides this, an independent instrumental bass is nowadded as a fifth part.

Fugue XVI I.

]

FUGAL ANALYSIS. 1 55

At bar 75 is the first stretto, made by partial entries of both

subjects (tenor and bass), followed at two bars' distance by treble

and alto. The first part of the fourth episode (bars 80 to 102) is

made by free imitations of the second subject, direct and inverted.

A few chords lead to a half cadence in F sharp minor at bar 95 ;

this is followed by a sequence, the pattern of which consists of

the final notes of the two subjects, omitting the passing note in

the second subject. This will be seen at once if bars 4 and 5

are compared with the tenor and bass of bars 96 and 97.

The following group of entries shows some fresh treatment of

the first subject. At bar 103, it is inverted, the species of inver-

sion chosen being that which is strict as to interval {Double

Counterpoint, § 280). It would have been perfectly feasible here

to invert the second subject in the same way, and use it with the

first, as the student will readily see for himself. Cherubini, how-ever, has preferred to accompany the inverted subject with two

new counterpoints, which are combined with it later, whenever it

appears in its inverted form. We see them again at bars 109, t 17,

and 144. After the entry of the first answer inverted (bar 109),

follows the fifth episode (bar 113). Here we see in the bass the

commencement of the codetta (bar 10), imitated two bars later bythe alto. An isolated entry of the inverted first subject (bar 117)leads to the sixth episode. This commences with the first notes

of the first subject, direct and inverted. At bar 124 begins a

canon, 4 in 1, at half a bar's distance, in the octave and fifth, onone of the subjects of the 4 in 2 canon at bar 23. At bar 132,

the other of these subjects is imitated between alto and treble.

The final section of the fugue begins at bar 136. Here the

first subject, direct, is accompanied by the second subject inverted,

both entries being partial, and followed in stretto two bars later

by the two answers (treble and alto), the second answer inverted,

and placed above the first instead of below. The short codetta

that follows (bars 140 to 143) is the transposition an octave lower

of the last four bars of the sixth episode. At bar 144 is a com-bination of the first subject with its own inversion, and with the

two counterpoints which appeared for the first time at bar 103.

Though we are still more than a hundred bars from the end of

the fugue, it should be noticed that this is the last time that either

of the two subjects is given in a complete shape. In fact, frombar 148 to the end, the fugue becomes extremely free. This is

often found in fugues by modern composers ; we have already metwith similar examples in the two fugues from Haydn's 5th Mass(Nos. 3 and 7). But it does not necessarily follow that, becausethe free style is adopted, the fugue becomes either formless or in-

coherent. In the present case, we shall find the unity of style

strictly preserved" in that part of the fugue to which we are nowcoming ; for, though there are no more complete entries, the

music, at all events down to the coda at bar 208, is constructed

entirely of material already familiar.

156 Fugal Analysis. [Fugue xvii.

The seventh episode (bars 149 to 178) begins with a boldmodulation to the key of B flat. In his treatise on Fugue,Cherubini forbids modulations beyond the nearly related keys,

except a short modulation to the tonic minor, as here in bars 171

to 178. But in this episode we find twenty consecutive bars in

the keys of B flat, G minor, and F major, not one of which is a

nearly related key to D major. The composer's practice wasevidently in advance of his theory ; but surely such an exampleas this shows the absurdity of the antiquated restrictions on whichtoo many theorists still insist

!

The first part of the episode we are now examining (as far as

bar 158) consists of imitative treatment by all the voices of the

alto counterpoint at bar 103 \ this is followed by fragments of the

second subject, direct and inverted (bars 158 to 166). Thecommencement of the codetta (bar 10) is then treated as a canon,

4 in i, at half a bar's distance, each voice entering a fifth belowthe preceding (bars 166 to 170). This little canon has a striking

resemblance to some of the episodes in the 29th fugue of the

* Wohltemperirtes Clavier' (see especially bars 29 to 31, and 35to 37 of that fugue). At bar 170 begins a second canon on the

same subject for all the voices, at half a bar's distance, as before,

but now in the octave instead of the fifth. The episode concludes

with a half cadence in D minor, introducing a dominant pedal

(bars 178 to 191).

On this pedal point is seen a closer stretto than any that havepreceded it. The three upper voices enter, one bar after eachother, with the first notes of the first subject (bars 179 to 183).

Next succeed passages of imitation founded on the second subject.

At bar 191, where the pedal point ends, is a yet closer stretto,

between tenor and bass, at half a bar's distance, the answer in the

tenor being syncopated. Other stretti at various distances—for

three voices (bars 194 to 198), and for four (bars 199 to 204)—in

all of which only the first three notes of the first subject are em-ployed, lead up to a full cadence in the tonic, on which follows

the coda.

Here the time is quickened, and the fugal style is virtually

abandoned. The scale passages of the second subject appearfrom time to time; but after the first few bars, the music canhardly be called polyphonic, and the coda simply serves to bring

the fugue to a brilliant conclusion.



(a) Exposition (Order of entry, TB AS), bars 1 1023.



Fugue XVII.] FiJGAL ANALYSIS. 157



(e) Group of middle entries, in B minor, G major, E minor,

and C major (partial), bars 42 to 59.


(g) First stretto (bars 75 to 79).


(/) Entries by inversion (bars 103 to 113).


(k) Isolated entry by inversion (bars 117 to 121).



(m) Entries with second stretto and inversions (bars 136

to 148).

[n) Seventh episode (bars 149 to 178).

[6) Dominant pedal, with third stretto (bars 178 to 191).

\p) Final and closest stretti (bars 191 to 207).

{q) Coda (bars 208 to 256).

i5* Fugal Analysis. [Fugue XVIII.

No. 18.

—

Leonardo Leo. Triple Fugue, " Tu es Sacerdos," from the' Dixit Dominus,' in C.

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Fugue XVIII.]

Final Section.

Fugal Analysis.

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In speaking of triple fugues, it was remarked (Fugue, § 398)that they were seldom strict. The fine example here given is an

excellent illustration of this point. We have unmistakably a

genuine triple fugue ; the three subjects are announced together,

and are written in triple counterpoint, five of the six possible

positions being made use of in the course of the fugue ; but the

subjects themselves are so varied on their later appearances, andappear so often as fragmentary, or partial entries, that it is impos-

sible to regard this as a specimen of a strict fugue. It may interest

students to know that the work from which this movement is

Fugue. XVIII.]tFUGAL ANALYSIS. 1 63

taken was composed about the year 1740—within a year or two of

Handel's ' Messiah.'

One of the first points that will strike readers of this fugue is

the almost entire absence of modulation. Nearly the whole of

the music is in the tonic and dominant keys ; in the entire fugue,

in fact, there is only one group of entries in any other key.

The exposition of the fugue extends to bar 17, and contains

one entry of each of the subjects, and one of each of the answers.

The exposition is therefore incomplete, as all the subjects are not

heard in each of the voices. (Compare the expositions of the

triple fugues by Albrechtsberger and Mozart, in Fugue, §§ 405,

406, both of which are complete.) In bar 17 the first subject is

given in augmentation by the treble, accompanied, not by the

other two. subjects, but by free counterpoint in the other voices.

Here is another illustration of the point mentioned in Fugue,

§ 379—that m fugues with more than one subject, the place of the

episode is sometimes taken by the treatment of one of the subjects

alone. At this point, we should usually find the first episode, to

connect the preceding 'group of entries with the next, which begins

at bar 32. But in this fugue there is no real episode at all ; andwe have instead, both here and later at bar 53, the introduction of

the augmented first subject. The counterpoint by which this is

accompanied consists of passages of free imitation ; the descending

scales may have been suggested by the first notes of the third

subject. At bar 26 part of the third subject is accompanied by a

fragment of the second.

At bar 32 begins a counter-exposition, the three answers nowleading, and the three subjects replying (bar 40). It will benoticed that in bar 46 the end of the third subject is altered, as it

had already been in the exposition (bar 15). The counter-exposi-

tion ends at bar 48, and the middle section commences, not with

an episode, but with the treatment of the first and second subjects

without the third. Another entry of the subject by augmentation(bar 53), now in the bass, is accompanied, as before, by free

counterpoints, and followed by a fragmentary stretto on the third

subject (alto and bass, bars 62, 64). At bar 69 is a group of

entries (the only middle group) in C major ; all three subjects are

complete, but all are more or less varied. A stretto on the third

subject (bar 77) for all the voices, at one and two bars' distance,

does duty instead of an episode, and brings back the music to the

tonic key, leading to the final section (bar 85).

In this final section none of the subjects appear in their com-plete form. This is not so very unusual ; we have already seen

several instances of it in this volume. What is much moreexceptional is, that the three subjects are never heard together.

We find first three entries of the first and second subjects (bars

85, 89, and 92), all of which are in stretto, as the later entries are

made before the completion of the subject by the voices having

the earlier ones ; and at bar 97 we see the closest stretto in the

164 Fugal Analysis. (Fugue xvin.

whole fugue—part of the first subject by augmentation given byall the voices at half a bar's, and one bar's distance. The entries

of the tenor and alto are very fragmentary. After the appearance

of parts of the second and third subjects in combination (bars

105 to 109), the augmented first subject is heard for the last time

in the treble; but the entry is not completed, and at bar 119 a

free coda, with plain chords, concludes the fugue.

It is interesting to notice that, with all its irregularity, this

fugue in its general construction closely resembles the fugue in Eflat, No. 31 of the * Wohltemperirtes Clavier,' analyzed in Fugue,

§ 294. In both we see a counter-exposition, and a middle section

containing only one group of entries, which is in the subdominantkey. In other respects the fugues differ widely. We have se-

lected a very free triple fugue for insertion here, because the

example we gave of this form in Fugue, § 406 was strict.



(a) Exposition (Order of entry, SATB), bars 1 to 17.

{b) Treatment of subjects separately, in place of episode

(bars 17 to 31).



(d) Treatment of subjects separately (bars 48 to 69).

(e) Group of middle entries in C major (bar 69).

(/) Stretto on third subject (bars 77 to 85).


(g) Stretto on first and second subjects (bars 85 to 96).

(h) Stretto on augmented first subject (bars 97 to 105).

(i) Partial stretto on second and third subjects (bars 105to 109).

(/) Final entry of augmented first subject (bar 112).

(k) Coda (bars 119 to 132).

Fugue XIX.] Fugal Analysis. 165

Section (/).

—

Fugues on a Choral and Canto Fermo.

No. 19.—J. S. Bach. Fugal Treatment of the Choral "Jesu, Leiden, Peinund Tod,'

from the Cantata " Himmelskonig, sei willkommen.

"

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Fugue XIX.J Fugal Analysis, 167

Third Exposition.

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Fugue XIX. Fugal Analysis, 169

From the large number of fugues on a choral to be found in

Bach's Church Cantatas, we have selected the present example,

not only because it is one of the most perfect specimens of its

kind, but also because the choral on which it is founded is the

same of which we have already given three different treatments byBach in Counterpoint, §§ 536-539. It must be remembered that

the form of a fugue on a choral differs materially from that of other

fugues (Fugue, § 424). It generally consists of a series of fugal

expositions of the different lines of the choral ; but when the

choral is long, we often find two lines more or less freely treated

in the same exposition. We shall see illustrations of this in the

present example.

The first exposition comprises the first two lines of the choral.

Of these, the first is easily to be recognized ; the second is moredisguised, the first note being altered. If the student will look at

the first notes of bar 3 in the tenor,

f P dy

and will substitute E for the first note B, he will see that we havehere the second line of the choral (treble, bar 11) in notes of

shorter value, in fact by diminution and double diminution. Asthe subject begins on the mediant and does not modulate, it takes

a real answer. All the entries in this exposition are at the regular

170 Fugal Analysis. [Fugue xix.

distances. The choral as a canto fermo enters in the treble at'

bar 6 ; it thus assumes the form of the subject by augmentation.

On the completion of the second line of the choral by the

treble (bar 14), the second exposition begins. This includes

the third and fourth lines of the choral, the latter being again

much shortened. It will be seen, if we compare the first notes

of the tenor at bar 16

with the treble in bars 23 to 26 \ the melodic progression is ident-

ical. In this second exposition the alto does not enter at the

regular interval ; this group of entries, like some of those that

follow, is treated in the fugato style. (Compare the example byBach in Fugue, § 422.) Observe how variety is obtained by the

incidental modulations—to D minor (bars 16, 17), B minor (bars

20, 21), and E minor (bars 25, 26)

The third exposition begins at bar 27, and gives only the fifth

line of the choral. In this group again the intervals of reply are

regular. The sixth line of the choral is the only one not treated

fugally—probably because in the form Bach has here selected it

consists of only two notes. The more usual form of the melodyis

l 3£r % r 1 r y 1 ^

as will be seen by comparing the versions given in Counterpoint.

The fourth exposition (bar 38) has again the character of afugato, as also has the fifth (bar 46). Each of these, as will beseen, takes only one line of the choral.

It will be noticed that each separate exposition, though com-mencing with a subject taken from the choral, continues with newmatter. This is often, though not always, done. In the examplein Fugue, § 422, nearly all the accompanying counterpoints are

formed from the choral itself. Either plan may be adopted at the

discretion of the composer.

Our analysis of this fugue will be very simple

—


(a) First exposition (bars 1 to 14), lines 1, 2 of choral.

(6) Second exposition (bars 14 to 27), lines 3, 4.

(c) Third exposition (bars 27 to 37), lines 5, 6.

(d) Fourth exposition (bars 38 to 45), line 7.

(e) Fifth exposition (bars 46 to 56), line 8.

Fugue XX.] Fugal Analysis. 171

No. 20.—J. S. Bach. Organ Fugue ('St. Ann's') in E flat, in five parts.

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176 Fugal Analysis,

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Our last number was an example of a fugue upon an entire

choral. The present, one of the finest, best known, and mostpopular of all Bach's organ works, is a specimen of a fuguewritten upon the first line of a choral. The melody is that

known in this country as the ' St. Ann's • tune, commonly said to

be the composition of Dr. Croft. As our great English musicianwas a contemporary of Bach, it is by no means certain that his

tune, if it be his, would have become known in Germany so soonas that Bach should be acquainted with it when he wrote this

fugue. It seems more probable that the melody is that of anold German choral, especially as it is also employed by Handelin his Chandos Anthem, " O praise the Lord with one consent."

Excepting that the order of the first two notes is reversed, the

1 86 Fugal Analysis. [Fugue xx.

theme is the same as that of the first line of the choral "Wasmein Gott will das g'scheh' allzeit "

—

mIn the fugue now before us we see a different form from any

which we have yet met with. The fugue naturally divides into

three parts ; but these do not bear to one another the samerelation as the three sections of the ordinary ternary form. Inthe first movement, the first line of the choral is taken as the

subject, and receives a regular exposition in five parts, whichextends as far as bar 16. The somewhat unusual answer to the

fourth note of the subject was noticed in Fugue, § 102. Thecounterpoint accompanying the answer is varied too much on its

later appearances (compare bars 7, 8, and 14, 15, with bars 3, 4).

to allow us to regard it as a regular countersubject.

The first episode (bars 16 to 21) is made from the counter-

point of bar 4. It is followed at bar 21 by a regular counter-

exposition in stretto, in which the counterpoint of bar 4 is

combined ingeniously with the subject at different points. Wedo not consider the incidental passages at bars 25, 26, and 28 to

30, as episode, but rather as codetta, because they connect

different entries belonging to the same group. A short coda(bars 2>o t0 37) concludes the first movement of the fugue with

a full cadence in the key of the tonic.

The second movement is in four parts only, the organ pedals

being silent throughout. An entirely new subject is nowannounced in the bass, and receives a regular exposition, which

ends at bar 47. To this succeeds a counter-exposition (partial)

of the subject by inversion. Observe that the inversion is not

quite exact, the intervals of a second and third, at the end of bar

45 and the beginning of bar 46, being changed to a third andfourth (bars 47, 48). At bar. 53 begins a partial stretto on the

direct form of the second subject, the continuation of which

leads to a full close in the key of the dominant (bar 59). Thefirst subject now appears in combination with the second, as a

canto fermo, a character which it retains throughout the rest of

the fugue. It is varied rhythmically, to adapt it to the \ time of

this movement. The second subject is also somewhat altered.

After two entries of the two subjects together, is an episode

(bars 64 to 67) made from a sequential treatment of the inversion

of the first part of the second subject. This is followed by two

pairs of entries of the two subjects, the second subject, ex-

ceptionally, appearing twice in succession in the same voice.

The third episode (bars 71 to 73) shows new treatment of the

materials of Episode 2. An isolated pair of entries follows;

the first subject in the tenor (bar 73) being accompanied by a

part of the inversion of the second subject in the treble. It is a

Fugue XX.] FUGAL ANALYSIS. 1 87

curious point to be noticed, that throughout this second move-ment the first subject is never once given to the treble. Thefourth episode (bars 75 to 77) leads to the final pair of entries in

this movement, which, like the first, ends with a short coda,

leading to a full close in the key of C minor.

Though the second movement of this fugue ends in the keyof the relative minor, the third subject does not begin in that

key. If it did, the second quaver would foe B natural and not

B flat, and besides this, it distinctly ends in the key of E flat.

The first note, C, is therefore not a tonic but a submediant.

At first sight, one would be inclined to think that the subject

extended to the B in bar 83 ; but an examination of the later

entries (tenor, bar 93, first bass, bars 101, 113, 114) shows that

this is not the case. The subject ends where we have marked it,

and has a short codetta, which (as often happens) is imitated in

the following entries. A more important codetta is seen in bar

84, before the entry of the third voice ; much use is made later

of this bar. In bar 86 we find another codetta, made from a

sequential imitation of the third subject in the first bass. Wedo not consider this as another entry in the bass ; for it is not in

the right key, neither is the exposition yet completed. It mustbe remarked that it is quite exceptional to find a modulation to

the mediant minor incidentally introduced, as here, in the course

of an exposition. The entry of the third answer in the treble

(bar 87) completes this exposition, in which (as in the secondmovement of the fugue) the second bass takes no part. At bar

88, the first subject (answer) is given by the treble, accompaniedby florid counterpoint developed from the codetta, bar 84. Thesame subject appears in the tenor, in stretto (bar 90), the first

half being accompanied by the third subject in the treble, andthe second half by the same subject in the bass. The following

entries are extremely interesting and ingenious. The last part

of the third subject in the tenor (bar 93) is accompanied by the

commencement of the first subject in the bass. The rest of this

subject is accompanied by the third subject, given twice in

succession by the treble. If we compare the intervals of the

two subjects in bars 91 and 94, we shall see double counterpoint

in the eleventh ; while bar 95 is the inversion in the twelfth of

bar 92.* The fifth episode (bar 96) is made from the counter-

points in bars 89, 90, and is followed by an isolated entry of the

third subject in the first bass, at bar 97. We have marked the

sequential continuation cf the third subject in the bass of bar

98 as the commencement of the sixth episode, though in its

form it precisely resembles the treble of bar 95, which weindicated as a repetition of the third subject. The reason of

the difference is that here the full cadence in F minor at the

beginning of bar 98 clearly shows the commencement of a fresh

* The student can easily verify these inversions by following the instructions

given in Double Counterpoint, §§ 6-9.

i88 Fugal Analysis. [Fugue xx.

section of the music \ while in bar 95 the soprano entry wasused as a counterpoint to the last part of the canto fermo (the

first subject), and therefore could not possibly be regarded as

episode.

The following group of entries, which begins at bar 101, showsmore interesting features. In this bar the third subject is com-bined with the first at an earlier point than has hitherto beenseen, entering on the first note instead of the second. At the

end of bar 102 the treble enters with a variation of the third

subject against the last part of the first subject in the second

bass, at a distance which, compared with that of the same twovoices in bar 95, again gives double counterpoint in the eleventh.

The entry of the alto in bar 103 with the first subject is again (as

in bar 90) in stretto at half a bar less than the original distance.

Another entry in stretto on the first subject (partial and orna-

mented) is seen in the treble at bar 105. At bar 108 we find

the closest stretto in this movement, the first subject being

given by the two outer parts at half a bar's distance. (Comparethe stretti in the first movement at bars 21, 26, and 31.) Herethe third subject is not present ; the student will remember that

in a double fugue we rarely find both the subjects treated

together in a close stretto {Fugue, § 381). Instead of these,

we have here the semiquaver figure in the first bass of bar 89treated by imitation in the three middle voices. After three

entries of the third subject alone (bars 11 1 to 113), the final

entry of the two subjects together is seen in bar 114, and a

bar and a half of coda brings this masterly fugue to a close.

It will be seen that the form of this fugue is quite different

from that of any that we have previously analyzed. Though it

contains three subjects, each of which has a separate exposition,

like the fugue from Bach's ' Art of Fugue,' which is described in

Fugue, §§ 400-402, the present cannot be called a triple fugue,

because the three subjects are never all heard together. In spite

of its sounding like an Irish bull, the most accurate description

of this fugue would be to call it "a double fugue, with three

subjects." In its general form, as Spitta points out in his life of

Bach, the present fugue resembles some of those by Buxtehude,who often wrote fugues in several movements, each in different

time. The rhythmical variations which the first subject under-

goes seem an anticipation of the modern device known as " meta-

morphosis of themes," the most conspicuous examples of whichare to be found in the works of Liszt and Wagner. The moredeeply we study the works of Bach, the more profoundly we are

impressed, not only with his almost miraculous technical skill,

but with that marvellous prophetic instinct which led him to

anticipate nearly every effect known to composers of the present

day.

Fugue XX.] FUGAL ANALYSIS. 1 89


First Movement—Bars 1 to 36.

(a) Exposition (Order of entry, TBi SAB 2), bars 1 to 16.


(^r) Counter-exposition (bars 21 to $2>)-

(d) Coda (bars 33 to 36).

Second Movement—Bars 37 to 81.

(e) Exposition of second subject (bars 37 to 47).

(Order of entry, B 1 T A S).

(/) Counter-exposition (partial) by inversion, bars 47 to 53.

(g) First stretto (partial), bar 53.

(h) Combination of first and second subjects (E flat and B flat),

bars 59 to 64.

(/) Second episode (bars 64 to 67).

(/) Entries of the two subjects (F minor and C minor),

bars 67 to 71.

(k) Third episode (bars 71 to 73).

(/) Entry of the two subjects, the second being inverted

(G minor), bars 73 to 75.

(m) Fourth episode (bars 75 to 77).

(n) Entry of the two subjects (C minor), bars 77 to 79.

(0) Coda (bars 79 to 81).

Third Movement—Bars 82 to 117.

(J>) Exposition of third subject (bars 82 to 2>^>).

(Order of entry, B 1 TAS).(q) Entry of first subject alone (bar ZZ).

(r) First entries of first and third subjects combined (bars 90to 96).

(s) Fifth episode (bars 96, 97).(t) Isolated entry of third subject (bar 97).

(u) Sixth episode (bars 98 to 101).

(v) Entries of first and third subjects together, with stretti onfirst subject (bars 101 to 111).

(w) Treatment of third subject alone (bars in to 113).

(x) Final entry of first and third subjects combined (bar 114).

(y) Coda (bars 116, 117).

190 Fugal Analysis. [Fugue XXI.

Section (g).—Accompanied Fugues.

No. 21.—W. A. Mozart. Choral Fugue, '

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As our first specimen of an accompanied fugue we haveselected one in which the added harmonies are mostly found in

the exposition only (Fugue, §§ 436, 437). These, as will be seen,

are given in small notes on the treble staff. The independentorchestration introduced occasionally in the later parts of the

fugue has mostly been omitted in our score, for the sake of

clearness ; we shall indicate it, where needful, in the courseof our analysis. It would have been a waste of space to give

the accompaniment on two separate staves, as we shall do with

the next fugue ; because in the greater part of this one the

instruments play in unison or in octaves with the voices. .

Fugue XXI.] FUGAL ANALYSIS. 1 99

As the subject, which is unusually long (bars i to 10),

modulates to the key of the dominant, it, of course, takes a

tonal answer. Here we see an interesting example (which wereferred to in Fugue, § 144) of the disregard of semitones. (Com-pare the second exposition of Fugue 16.) As the point is of

some importance, it is worth wrhile to go into it in a little detail.

The answering of A in bar 6 of the subject by D in bar 15,

shows us that Mozart considers the modulation to the dominantkey to be made at this point (Fugue, § 122). Therefore, werethe answer made according to strict rule, the E flat in bars 6 and

7 ought to be regarded as the minor seventh of F, and answeredin bars 15 and 16 by A flat ; or else the E in bars 6 and 7 should

have been natural. We cannot, however, call Mozart's answerincorrect, as it is precisely with these two degrees of the scale

(the fourth and the seventh) that the freedom of treatment

which we are speaking of is most frequently found.

The fugue has no regular countersubject, though unity of style

is obtained by the use, in all the accompanying counterpoints of

the exposition, of the figure (P:=^^r^!^r--j=g=== which we

first see in the bass of bar 10. It will be seen that as additional

voices enter in the exposition, the independent orchestral accom-paniment becomes lighter, and ultimately disappears.

The exposition ends at bar 37; and the middle section begins

in the same bar with the first episode (bars 37 to 43), which

modulates at bar 41 to G minor. In this key we find the first,

group of middle entries—subject (bass), bar 44 ; answer (tenor),

bar 53. It is worthy of notice that though the tenor entry is

here a fifth above the bass, its first notes are not harmonized as

being in the key of D minor ; the note D is here treated as the

dominant of G minor, and not as a tonic. Though, in the first

exposition of a fugue, the dominant key should always answer the

tonic key, there is no necessity to observe the same strictness as

to the harmonic relations of subject and answer in the middle

entries. At bar 53 a quaver passage is introduced in the first

violins, which we have not given in the score. It is this

—

This brilliant figure of accompaniment is continued to the end of

bar 57, after which the violins play in octaves with the voices.

The second episode (bars 62 to 65) modulates to E flat, andintroduces a long and important group of middle entries. First

we have in the treble (bar 66) the subject in E flat, the orchestral

figure of bars 2 and 3 again appearing above the voices. Acodetta (bars 75, 76) leads to another entry in B flat. Let the,

student always remember the distinction between codetta andepisode, of which so many examples have been seen in this

200 Focal Analysis. [Fugue xxi.

volume. A codetta connects two entries of the same group, andcontains no modulation, except occasionally between tonic anddominant ; an episode connects two different groups of entries,

and always contains a modulation, except sometimes the first

episode when it leads either to the counter-exposition or to an

additional entry of the subject, as in Fugues i and 9 of this

volume.

The entry in the alto at bar 77 must be considered as subject

or answer, according as it is looked at in its relation to the

preceding or the following entry in F major, bar 86. We havetherefore marked (S) as well as A for it. Then three entries

are followed by a stretto between bass and alto (bar 95) madefrom the first part of the subject modified like a tonal answer.

The whole passage, bars 95 to 100, is then twice repeated in a

free sequence (bars 101 to in), and is followed by the third

episode, the longest and most important in the fugue (bars ii"

to 132). This begins with imitation between alto and treble of

the sixth bar of the subject. To this succeeds a striking passage

(bar 119) rhythmically connected with the first notes of the

subject. The effect of the bold harmonies is heightened by a

syncopated figure given to the upper string parts

—

(Bars 120, 1

The passage is repeated sequentially at bars 125 to 129, and at

its close the episode modulates back to the key of the tonic.

The final section of the fugue, which commences at bar 133,requires but few remarks. It contains two complete entries

(alto and treble, bars 133 and 142), followed by a partial entry

lor the bass (bar 151); which leads immediately to the rather

long and very interesting coda (bars 155 to 180). Here wesee first a passage of free sequence (bars 155 to 163) foundedupon a fragment of the subject; then, on a dominant pedal

(bars 167 to 172) a different sequence, constructed from the

same material, and lastly at bars 173 to 177 the inversion bytenor and bass of the sequential passage for alto and tenor

just heard above the pedal.

The Litany from which this very fine fugue is taken waswritten in 1772, when Mozart was only sixteen years of age

;

and it would hardly be too much to pronounce the present

movement the most wonderful fugue ever composed by a mereboy. It is not so much the merely technical skill that is

surprising, as the irresistible " go " of the whole . the musicrushes along like a mountain-torrent, carrying away hearer andperformer alike in its headlong course. Its analysis is, never-

theless, very simple.

Fufc'u6 XXL] | FUGAL ANALYSIS. 201



(a) Exposition (Order of entry, BT AS).


(b). First episode (bars 37 to 43).

(c)....':JFirst group of middle entries (bar 44).


(e) Second group of middle entries (bar 66),

(/) Partial stretto (bar 95).

(g) Third episode (bars 112 to 132).


(h) Final group of entries (bar 133).

(/) Coda (bars 155 to 180).

202 Fugal Analysis. [Fugue XXII.

No. 22.—F. Mendelssohn. Final Fugue from the 42nd Psalm.

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218 Fugal Analysis. [Fugue xxn.

The present example is interesting, as showing a fugue whichthroughout its greater part has an independent florid orchestral

accompaniment. It cannot be regarded in any sense as a strict

fugue, and in its form approaches much more nearly to the

fugato style. Its freedom of treatment renders it rather difficult

to analyze with certainty. It is preceded by an introduction of

46 bars, of which we give only the final cadence, introducing the

fugue. We have condensed as much of the orchestral accom-paniment as possible, consistent with clearness, on two staves

;

it will be seen that this transcription is not meant to be played

on the piano; many passages, indeed, would be quite im-

practicable.

The subject of the fugue, announced in bar 3 by the tenor,

is accompanied, in two-part harmony only, by a florid quaverfigure for the basses of the orchestra. As the subject modulatesto, and ends in the key of the dominant, it should take a tonal

answer. The first irregularity to be noticed in this fugue is, that

the answer given by the alto in bar 9 is real, though it ends at

bar 15 with a minor, instead of a major third, to avoid a

modulation to an unrelated key. A similar thing will be seen

in the fugue in Mendelssohn's 95th Psalm, the subject andanswer of which we quoted in Fugue, § 107 (f). Two bars

of codetta (15 and 16) are here necessary to lead back to the

key of F, for the next entry of the subject. The answer given

by the bass at bar 23 is tonal, according to rule, but the last

note is wanting, unless we consider bars 29 and 30 as a pro-

longation of the penultimate note, and regard the answer as

ending at bar 31.

The middle section of the fugue evidently begins with the

modulation to D minor at the 31st bar; and from this point

we have little more than a fugato—or at most an extremely free

fugue. No more entries of the complete subject are to be metwith, though the chief features of the subject are treated separately.

It must be noticed that the subject contains two distinct ideas

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We often find a fugue subject that subdivides in this way ; and it

is not at all uncommon in such a case to see the two sections of

the subject treated by themselves, as here. See, for example, the

episodes of Fugues 2 and 3 of this volume.

The first episode of the present fugue is made by imitation byall the voices of bar 7 of the subject. It leads to an isolated

entry (incomplete) of the subject in the treble. The second

episode (bars 40 to 42) is made from the same material as

the first; but the imitations are now freer, and by inverse as

well as direct movement. This episode modulates to B flat,

Fugue xxii. ] Fugal Analysis, 219

introducing another partial entry in the bass (bar 43), followed bya varied entry (bar 47) in the same voice. At bar 53 begins

the first stretto, made from the first four notes of the subject.

Note how persistently up to this point the florid figure of

accompar 'ment is maintained in the orchestra.

In the third episode (bars 64 to 80) the contrapuntal style is

at first abandoned by the voices, which move together in massive

chords, while the unity of design is preserved by the independentorchestral accompaniment. Observe that on the lower staff the

rhythm of the first four notes of the subject is persistently main-tained by the basses, trombones, and organ, while the upperpart

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gives bar 7 of the subject direct and inverted. At bar 73this same figure is treated by free imitation in the voices, leading

to the second stretto, at bar 81. In this stretto the entries are

more numerous and sometimes closer than in the first. We have

omitted the middle parts in the orchestra, which double the voices

in unison, for the sake of clearness. The fourth episode (bars

89 to 94) is evidently made from bar 7, direct in the bass andinverted in the tenor.

It is difficult to decide with certainty where the final section

of this fugue should be considered to begin. It certainly looks

at first sight as if it began with the pedal point at bar 95,especially as a pedal is very seldom found in the middle section

of a fugue. But to this may be objected, that we seldom find

modulations beyond the tonic and dominant keys in the final

section of a fugue ; while here we have modulations to B flat

(bar 103) and D minor (bar 108). On the whole, considering

that there is no subsequent entry in any other key than F or C, i:

seems best to regard this point (bar 95) as the commencement of

the final section. Observe that there is here a stretto at onebar's distance between the tenor and the violins of the orchestra.

In the choral fugues in Bach's cantatas we often find independent

entries of the subject in the orchestra ; but such are rare with

modern composers. The fifth episode (bars 99 to 117) begins

with a combination of two fragments of the subject ; for the bass

of bar 99 is evidently a variation of the commencement of the

subject, substituting the interval of a second for a third betweenthe first and second notes. Bars 107 to no are clearly con-

nected rhythmically with the commencement of the subject.

After an inverted cadence in D minor (bar 117), a fragment

of the subject is once more introduced. The passage from

bar 118 to 125 is then repeated with fuller orchestration andaugmentation of its last notes ; and in the final coda we see

at bars 134 and 138 the first notes of the subject in the bass

220 Fugal Analysis. [Fugue xxn.

of the orchestra, imitated by an upper part (the trumpets) in the

following bar.

This most effective chorus is a good illustration of the

modern freedom of fugal writing, and in this respect may beregarded as a companion piece to the fugue by Schumann(No. n) in this volume.

Analysis of Fugue 22,


(a) Exposition (Order of entry, T A S B).


(fr) First episode (bars 31 to 34).

(c) Isolated entry (partial) of subject, bar 35.


(e) Group of middle entries (partial) with first stretto, bar 43*


(g) Second stretto (bar 81).



(/) Entry of subject (answer) in tenor, with stretto in the

orchestra, bar 95.


(k) Partial entry of subject, with new continuation (bar 118).

(/) Repetition of the same, with last notes augmented(bar 126).

(m) Coda (bars 134 to 152).

Fugue XXIII.] Fugal Analysis. 221

No. 23.—J. S. Bach—Double Fugue on a Choral, from the Cantata, " Esist nichts gesundes an meinem Leibe."

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Viola.

Soprano.

Alto.

Tenore.

Basso.

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Fugue XXIIL] FUGAL ANALYSIS. 245

For our final specimen of fugue, we have selected the openingchorus from one of Bach's Church Cantatas as a kind of com-pendium of fugal composition. In the same movement we find

here combined an example of close fugue, double fugue with a

separate exposition of each subject, fugue on a choral, andaccompanied fugue. Here, therefore, we have within the limits

of 74 bars, a resume of nearly the entire contents of this volume.

It was quite impossible to transcribe the instrumental parts

of this fugue, as we did in the last number, on two staves ; wehave therefore given the whole in full score. Those who havecarefully studied the fugues in this volume will be by this time

sufficiently accustomed to score-reading to find no insuperable

difficulty in following the developments of this elaborate composi-

tion. It should be mentioned that the " cornetto " seen on the

upper staff of the score is not the modern cornet-a-pistons, whichwas not known in Bach's time, but a now obsolete wind instru-

ment of wood. To the student of instrumentation it will also beinteresting to know that we see here the solitary example in the

whole of Bach's works of the obbligaio employment of the trom-

bones. We frequently find them in other cantatas ; but, except

in this one instance, they always double the voices.

The choral introduced by the wind instruments is that whichis best known in this country by its association with the Passion

Hymn, " O sacred Head, once wounded." To explain its con-

nexion with the present chorus, it must be said that the samechoral also belongs to the German metrical version of the

38th Psalm, " O Lord, rebuke me not in Thy wrath," whichcommences

" Ach, Herr, mich armen Sunder

Straf nicht in deinem Zorn."

The words of the chorus are taken from the third verse of the

same Psalm :—" There is no soundness in my flesh because of

Thine anger; neither is there any rest in my bones because

of my sin." To a German audience, therefore, who would at

once associate the melody of the choral with the words belonging

to it, the appropriateness of its introduction would be at onceevident.

We have thought it best to give some short account of this

wonderful chorus from an aesthetic point of view, that the

student might the more readily appreciate its beauties ; andwe now proceed with our analysis. Being a fugue on a choral,

it does not divide into the three sections of a simple fugue

(Fugue, § 424). The form of such a fugue as the present always

depends upon the manner in which the choral is introduced.

Here we find that two lines of the choral are given at the endof each section ; and the fugue divides into four parts, not

into three.

The first half of the fugue (as far as bar 41) has an inde-

pendent accompaniment for the three upper string parts, the


figure of which is announced in the opening symphony, bars

i to 5. In the bass we see the first line of the choral (comparebar 15) given by augmentation. In the fifth bar the first

subject of the fugue is announced by the alto, while the answer

follows in the treble at half a bar's distance. Here, therefore, wehave a close fugue {Fugue, § 279). In general we determine

the limits of the subject in a close fugue by observing howmuch is imitated by the subsequently entering voices {Fugue,

§ 53) ; but if we do so here, we shall be misled. The imitation

in all the voices is continued three bars further—as far as the

dotted crotchet E of the alto in bar 10. But here we haveguidance from another circumstance. This fugue, as we shall

see directly, is a double fugue, with a separate exposition of

each subject. It must be remembered that the two subjects

of a double fugue should finish together {Fugue, § 374) ; there-

fore to determine the limits of the subject here, we must see

how much of it is combined with the second subject in the

latter part of the fugue. An examination of bars 58 to 61 proves

at once that the subject ends where we have marked it in

bar 7, and that it is continued by a codetta canonically imitated

by the treble. At bar 9, the subject enters in the bass, followed

half a bar later by the answer in the tenor. Before these two

voices have completed the canonic codetta, a third entry of

subject and answer—both incomplete, and the former somewhatvaried—is seen in the alto and treble (bar 14). As the upperstring parts are all independent of the voices, there are from

bar 10 to bar 15 seven real parts. At the end of bar 15 the

first portion of the choral is introduced by the wind instruments,

the cornet, doubled in the octave by three flutes in unison,

playing the melody, and the three trombones completing four-

part harmony for this division of the orchestra. The third

trombone is in unison with the basses, but the other parts are

independent. We have thus, therefore, ten real parts, thoughoccasional unisons may be seen between voices and instruments.

Against the choral, fresh entries of the subject will be seen in the

voices. The first section of the fugue ends at bar 21.

It will be seen that we have here a different kind of fugal

treatment of the choral from that which was found in Fugue 19.

There the different lines of the choral were treated fugally, andwere given in augmentation by the treble. Here there seems at

first sight no connexion between the fugue subjects and the choral;

the fugue appears rather to resemble in its form that from whichwe gave an extract in Fugue, § 427. But, as has been pointed

out by Spitta in his life of Bach, both the subjects of this fugue

are formed from the choral itself. The first notes of the first

subject are a modification of the last line,

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Fugue XXIII.J FUGAL ANALYSIS. 247

while the second subject (see bar 41) is made from the first line

of the choral. This will be seen even more clearly by comparingthe simplified form of the second subject given to the violins at

bar 50 with the melody of the choral at bars 15 to 17. It should

also be noticed, before passing to the second section of the fugue,

that, in the section already examined, the three groups—the

chorus, the strings, and the wind—each make perfectly completeand correct harmony by themselves.

The second section of the fugue, which begins at bar 21,

illustrates Bach's astounding mastery of technical resources.

It is introduced by the same prelude as the first section, with

the first line of the choral by augmentation in the bass. As the

third and fourth lines of the choral, presently to be given bythe wind instruments, are the same as the first and second,

Bach repeats the whole first section of the fugue; but in order

to avoid monotony, he now inverts the parts. We here find that

the treble and alto of the first section are now tenor and bass,

while what were before the tenor and bass have now becometreble and alto. We therefore see, what otherwise we should

probably not have noticed at all—that the voice parts in the

whole of the first section are written in quadruple counterpoint

!

A similar inversion of the two upper and the two lower parts,

though far less elaborate and only a few bars in length, was quotedfrom the ' Wohltemperirtes Clavier ' in Double Counterpoint,

§ 268. With the exception of one or two insignificant alterations

(compare, for instance, the tenor of bar 18 with the treble of bar

38), the inversion is carried out exactly. But it will be obvious

that the conversion of the former alto into the bass changes the

whole harmonic framework of this section, so that the general

effect is quite different from that of the first. The altered

harmonies necessitate numerous changes in the string parts.

The wind instruments enter with the choral at the same point

as before ; but we find that the harmonizing of these four bars is

now entirely different from that at bars 15 to 19.

At bar 41 we reach the third section of the fugue. Herethe second subject is announced by the tenor, and answered(again as a close fugue) by the bass. Another entry of the

answer precedes the second entry of the subject, as in the first

fugue of the 'Wohltemperirtes Clavier.' Notice the alteration

in the first note of the subject, when it appears in the treble.

We see that it begins with a leap from tonic to dominant, whereas

on its first appearance it began on the supertonic. It is not

uncommon in Bach's choral fugues, when a subject is introduced

for the first time in the middle of a movement, as here, to find its

first note altered, to connect it better with what has preceded.

The following entries of the second subject, in bars 45, 46,

show that the entry in the treble is the real form. Later in

the fugue, both forms are used indifferently, as we have so often

seen to be the case with tonal fugues.


This part of the fugue is accompanied only by the basses

and the organ. There is no figured bass to indicate the

harmony ; but this simply arises from the fact that Bach'soriginal part is lost ; we know from the comparison with manysimilar passages in other cantatas that the organ supportedthe voices here. The constantly moving semiquavers of the

bass strikingly depict the sense of the words here sung bythe chorus, " Neither is there any rest in my bones, becauseof my sin."

At bar 47 we see the only episode in this fugue ; and at

bar 50 we find another group of entries of the second subject

in all the four voices at one crotchet's distance. Here the upperstring parts enter, and for the rest of the fugue they play in

unison with the voices, instead of having independent parts,

as hitherto. At bar 53 begins another group of entries, with

a different order of voices to the last; and against this, in

the following bar, the wind instruments give out the fifth andsixth lines of the choral.

We now arrive at the fourth and last section of this wonderful

fugue (bar 58). Here the first and second subjects are combined,the first subject being continued by the codetta in canon already

noticed, first in the alto and tenor (bar 61), and then by treble

and bass, bar 65. Notice that the pairs of voices which nowtake subject and answer together are different from those

which were used in the first and second sections. At bar 69 is

the final combination ; the last two lines of the choral being nowheard together with both the subjects of the fugue; the first

subject being slightly varied. The close of the piece on the

dominant arises from the fact that the melody of the choral

is in the old Phrygian mode ; the note E being the ' final

'

(or, as we should now say, the tonic), it was necessary to finish

with a major chord on that note, to preserve the characteristics

of the melody. Bach harmonizes the end of the choral in

the same way on its last appearance in the c Passion according

to Matthew.'

It is difficult, without indulging in hyperbole, to find words

adequate to describe this marvellous fugue. It is not merely

the astounding cleverness of its construction that impresses

us ; it is the beauty of the expression and the depth of feeling

in the music which raise it far above any mere technical display.

Let the student make himself intimately acquainted with it

;

he will find it grow upon him at each fresh reading, and he

will learn what can be done by a combination of the mostconsummate technical skill with heaven-inspired genius.

Fugue XXIII.] FUGAL ANALYSIS. 249

Analysis of Fugue 2J.


(a) Exposition of first subject ; entry of lines 1 and 2 ofchoral.

Second Section—Bars 21 to 41.

(b) Counter-exposition of first subject, with inversion of parts

;

entry of lines 3 and 4 of choral.

Third Section—Bars 41 to 58.

(c) Exposition of second subject (bars 41 to 47).

(d) Episode (bars 47 to 50).

(e) Further entries of second subject, and combination with

lines 5 and 6 of choral (bars 50 to 58).

Fourth Section—Bars 58 to 74.

(/) Combination of the two subjects (bars 58 to 69).

(g) Combination of both subjects with lines 7 and 8 of choral

(bars 69 to 74).

the end.

Printed by Cassell & Company, Limited, La Belle Sauvage, London, E.C.

R

ORGAN MUSIC.

AUGENER'S EDITION, Nos. 9801-5.

J. S. BACH'S ORGAN WORKS.Edited by W. T. BEST. (Oblong Folio.) Net.

No. s. d.

9801 Vol. I. 6 Preludes and Fugues 30(No. 1 in c, 2 in g minor, 3 in d, 4 in e minor, 5 in f minor, 6 in G.)

9802 Vol. II. 6 Preludes and Fugues 40(No. 7 in c, 8 in a minor, 9 in d minor, 10 in g, 11 in c minor, 12 in E

flat "St. Anne.")

9803 Vol. III. 6 Preludes and Fugues 40(No. 13 in c, 14 in c minor, 15 in a, 16 in b minor, 17 in c minor, 18 in E

minor.)

9804 Vol. IV. 30(Fantasia and Fugue inG minor, Toccata and Fugue in d minor, Toccata

and Fugue in e major, Toccata and Fugue in c major.)

9805 Vol. V 30(Toccata and Fugue in f major, Toccata and Fugue in d minor,

Passacaglia in c minor.)

J S. BACH'S ORGAN WORKS.In Single Numbers. Edited by W. T. Best. (Oblong folio). E. ;—

First Series. The Great Preludes and Fugues. (Singly);— Net.No. s. d.

9821 No. 1, in c major 109822 2, in G minor 109823 3, in d major •. . .109824 4, in e minor 109825 5, in f minor 109826 6, in g major 109827 7, in c major 109828 8, in a minor 109829 9, in d minor 109830 10, in G major . . 109831 11, in c minor 109832 12, in E flat (St. Anne's tune) 109833 13, in c major ..109834 14, in c minor 109835 15, in a major 109836 16, in b minor io9837 17, in c minor 109838 18, in e minor 10

Second Series. The Great Toccatas and Fugues, &c. :

—

9839 Fantasia and Fugue in g minor 109840 Toccata and Fugue in d minor 109841 Toccata and Fugue in e major 109842 Toccata and Fugue in c major 109843 Toccata and Fugue in f major 109844 Toccata and Fugue in d minor 109845 Passacaglia in c minor. 10

I o

I o

I o

I o

I o

I o

I o

I o

Net.J. S. BACH'S ORGAN WORKS {continued):- s. d.

No. Third Series. Fugues, Alia Breve, Canzona, and Fantasias :—

9846 Fugue in g minor

9847 Fugue in c minor

9848 Fugue in b minor

9849 Fugue in c minor

9850 Alia breve in d major

9851 Canzona in d minor

9852 Fantasia in c minor

9853 Fantasia in g major

Fourth Series. 8 Short Preludes and Fugues and 6 Sonatas for two

Claviers and Pedal :

—

9854 Short Preludes and Fugues. No. 1 in c major ; 2 in d minor; 3 in e

minor; 4 in f major

z

9855 Short Preludes and Fugues. No. 5 in g major ; 6 in g minor; 7 in a

minor ; 8 in b flat major

9856 Sonata in e flat major .

9857 Sonata in c minor x

9858 Sonata in d minor • •••••••» ,i9859 Sonata in e minor r

9860 Sonata in c major x

9861 Sonata in g major z

1 o

1 o

o

O

o

o

o

" On opening the volumes of Bach's Organ Works, the first thing to strike the eye is the

size of the note 'heads,' which, as the books lie upon the table, seems unnecessarily large.

But place a copy side by side with ordinary organ music on the desk of a ' three-decker,' andit will be seen that attention has been bestowed upon a point of really great importance,although one too often overlooked. The notes stand out clearly at that distance, so that to aplayer of average eyesight a misreading ought to be an impossibility. Then come indications

oi tempo, both verbal and metronomic ; assistance to the performer in matters of fingering

and pedalling ; elucidations in foot-notes of the old agrements, or Manieren, so little under-

stood, apparently, in the present day ; and, lastly, and even more important than all, from a' past-master ' in the art, a guide as to the proper registering, or combination of stops, to beadopted in each piece."

" Further, the text has been subjected to thorough revision, the editor going to the length

of reducing the whole to manuscript, in order to render the design of each work conspicuously

plain to the student ; and the left-hand part, in particular, has been the object of painstaking

attention, the full extent of which will only be apparent to the practised executant, whoknows but too well how the 'inner parts' are inextricably jumbled together even by com-posers themselves, to say nothing of the doings of untrained copyists and transcribers."

" First come matters of simple notation. Mr. Best clears off redundant notes, accidentals,

double stems, and the like, thus greatly facilitating the work of the student, while nowiseinterfering with the integrity of the text."

—" Record" review, by Stephen S. Stratton.

11 Mr. Best's edition of Bach's 'Organ Works' goes bravely on. We have Nos. 17 and 18

of the great Preludes and Fugues, and Nos. 19 to 24 of the miscellaneous compositions,

including the Toccatas and Fugues in c, e, f, and d minor, and the Fantasia and Fugue in gminor. All these are carefully, though not redundantly, ' fingered ' by the eminent Liverpool

organist, and turned out in excellent style."

—

The Daily Telegraph, January 4, 1890.

"In the matter of clearness to the reader—a detail of greater importance to organists

than to any class of musicians —this edition is undoubtedly the most satisfactory in existence."—The Times, February 15, 1890.

AUGENER & CO., 86, Newgate Street, London, E.C. ; and

i, Foubert's Place, Regent Street, W.

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Fugal analysis : a companion to "Fugue"

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