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AUGENER'S EDITION, No. 9185.

FUGUE.
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,” &c.
NEW YORK:
G. SCHIRMER, 35, UNION SQUARE.
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PREFACE.
Tranepes to
Murle
2194
2
THERE is probably no branch of musical composition in which
theory is more widely, one might almost say hopelessly, at variance
with practice than in that which forms the subject of the present
volume. In Harmony, we are frequently meeting with cases in
which the rules of the old text-books need much modification;
but with regard to Fugue there are few indeed of the old precepts
which are not continually, not to say systematically violated by
the greatest masters. The reason for this is no doubt that the
standard authorities on the subject, Fux and Marpurg, treated it
from the point of view of the seventeenth century, and that most
of their successors, such as Cherubini and Albrechtsberger (to name
two of the most illustrious), have in the main adopted their rules,
taking little or no account of the reformation, amounting almost
to a reconstruction, of the fugue at the hands of J. S. Bach.
Somewhat more liberality of tone will be found in the treatises of
André, Richter, and Lobe; but not one of these, excepting Lobe,
has taken Bach's work as the starting point for his investigations.
Lobe, on the other hand, is too revolutionary; he even abolishes
the names "6 subject" and "answer," using instead the terms
"first imitation," "second imitation," &c.
When we find a distinguished theorist like André saying that
Bach is not a good model because he allows himself too many
exceptions, and are informed that one of the principal German
teachers of counterpoint is in the habit of telling his pupils that
there is not a single correctly written fugue among Bach's "Forty-
Eight," surely it is high time that an earnest protest were entered
against a system of teaching which places in a kind of "Index
Expurgatorius" the works of the greatest fugue writer that the
world has ever seen.
鲁
​i
iv
PREFACE.
}
* * * * * *.*.*
In writing the present treatise, the author has consulted all the
standard authorities, but (as may be inferred from what has just
been said) has followed none. He has proceeded on the same
principles which have guided him in all the preceding volumes of
this series, and has gone to the works of the great composers
themselves, has carefully analyzed and examined them, and from
their practice has deduced his rules, without paying the least
regard to what might be said on the subject by Marpurg or
Cherubini. He has started with the axiom, which few will be
bold enough to dispute, that Bach's fugues are the finest in
existence, and that whatever Bach does systematically, and not
merely exceptionally, is the correct thing for the student to do.
He therefore first put into open score and carefully analyzed the
whole of the forty-eight fugues in the "Wohltemperirtes Clavier."
He next examined every fugue, vocal and instrumental, to be found
in the forty volumes of Bach's works published by the Bach Gesell-
schaft, making notes of all points of importance. But he did not
confine his attention to Bach. He examined probably at least a
thousand fugues, including all those by Handel, Mozart, Beet-
hoven, Mendelssohn, and Schumann, besides a large number by
other writers of more or less eminence, to find out what had been
actually done by the greatest masters of our art. The farther his
researches extended, the deeper became his conviction of the
necessity of placing the laws of fugal construction on an altogether
different basis from that hitherto adopted. The result of his
investigations will be found in the following pages. In the words
of the Psalinist, he may say, "I believed, therefore have I
spoken." A great deal to be found in this book will probably
horrify old-fashioned musical conservatives; but not a single new
rule is propounded for which warrant is not given from the works
of the great composers; and if he shrank from the logical
consequences of the examination of these works, the author
would be untrue to his own convictions.
The general plan of this volume is to some extent the same
as that adopted by Mr. James Higgs in his admirable Primer on
"Fugue," by far the best treatise on the subject in our language.
It would be dishonest of the author not to acknowledge the
à
PREFACE.
V
assistance he has derived from this little work, which indeed it
would be impossible for any later writer on the same subject to
ignore. To Mr. Higgs we owe the clearest exposition yet written
of the important matter of fugal answer; and, though it will be
seen that the rules given in this volume differ in several material
respects from those in the "Primer," the author frankly con-
fesses that it was Mr. Higgs who first put him on the right
track.
It is on this very subject-fugal answer-that the great
composers depart most widely from the old rules. The new and,
it is hoped, very simple rules given in Chapters III. and IV. are
enforced by nearly 150 examples, of which more than sixty are
by Bach. Other composers are also freely drawn upon; but
throughout the volume, in all cases of doubt, Bach is treated as
the final authority.
In order to assist the student, it has been thought best to
take the different portions of a fugue separately, that he may
learn how to construct each part before he proceeds to the
composition of an entire fugue. The chapters on Counter-
subject, Exposition, Episode, and Stretto, contain not only
numerous illustrations from the great masters, but specimens of
each, written expressly for the guidance of the student. While
an endeavour has been made to make them musically interesting,
it must be remembered that they are merely intended as exercises,
and have no claim to be judged as compositions.
The chapter on "The Middle and Final Sections of a Fugue"
will, it is believed, be found new by English readers. The
author cannot, however, claim the credit of the first discovery
that a fugue is written in ternary form. That honour is due
to Dr. H. Riemann, in his analysis of Bach's "Wohltemperirtes
Clavier." It is nevertheless so obvious when once pointed out,
that the author of course availed himself of it, and herewith
acknowledges his obligations to Dr. Riemann for the idea,
though he has developed it in a somewhat different way from that
of the original discoverer.
Of the later chapters of the volume not much need be said
here. The concluding chapter, on "Accompanied Fugue," deals
A*
}
1
!
"
vi
PREFACE.
!
¡
with a branch of the subject not touched on in any book we have
met with; but its importance in modern music rendered it
desirable to say a few words about it.
As belonging to practical composition rather than to mere
theoretical study, fugue is a subject which is best taught by
examples. In the present volume it was impossible to give more
than a very few complete fugues; but this will be followed as
soon as possible by a companion volume on "Fugal Analysis,”
the materials of which are already in great part collected, which
will contain a selection of the finest fugues of the great masters
in various styles and forms. These will be all printed in open
score (like the two fugues by Bach in sections 298, 308), and
fully annotated. It is hoped that they will be found a most.
valuable aid to the student.
With the subject of fugue, the strictly theoretical part of this
series is completed. The remaining volumes will deal with actual
composition, and the next to follow (after "Fugal Analysis") will
be on "Form."
LONDON, December, 1891.
T

TABLE OF CONTENTS.
[N.B.-The numbers refer in every instance to the sections, not to the pages.]
CHAPTER I.-INTRODUCTION
page I
The requisite preliminary knowledge, I-Definition of the term Fugue, 2-
Double, triple, and accompanied fugues, 3-The difference between
fugue and canon, 4-6-General description of a fugue, 7-The Subject, 8
The Answer: real and tonal answers, 9-The Countersubject, 10-The
Exposition, II—Episode, 12-The Counter-exposition, 13-The middle
section of the fugue, 14-The final section: Pedal points, 15-The
Stretto, 16-Close fugue, 17-Strict and free fugues, 18-The Ricercare or
Ricercata, 19-Fugues by inversion, augmentation, or diminution, 20-
The Fughetta, 21-Fugato, 22-The essential nature of fugue, 23.
...
CHAPTER II. THE SUBJECT
page 6
The essentials of a good subject, 24-A Subject defined; fugues with two or
more subjects, 25-The necessity of clear tonality, 26-Implied harmony,
27-Subjects that remain in one key: major, 28-30-Ditto, minor, 31,
32-Subjects in the dominant, 33-Subjects that modulate from tonic to
dominant, 34-Ditto, in a minor key modulate to the dominant minor, 35
-Modulation from dominant to tonic, 36-Ditto, from tonic to dominant
and back, 37-Modulation between tonic and subdominant, 38—A subject
in the subdominant, 39-Incidental modulations, 40, 41-The cadence of
a fugue subject, 42-45-Length, 46-Compass, 47-A subject may begin
on any degree of the scale, 48-49-The subject must be contrapuntal in
character, 50-Adaptability for stretto, 51-Melody and rhythm, 52-
How to determine the limits of a subject, 53-Directions for work, 54.
..
···
CHAPTER III.-THE Answer
page 18
The Answer defined, 55-Key relation of subject and answer, 56-Real and
tonal answers, 57-When a real answer is possible, 58-Examples of real
answers in a major key, 59-65-The answer of a minor subject must be
in the dominant minor, 66-Examples, 67, 68-The last note of a
...


viii
CONTENTS.
↓
Ja
minor subject, 69-Subject in dominant, answer in tonic, 70-The
answer in the subdominant, 71-Ditto, in a minor key, 72-Example by
Bach analyzed, 73-75-Ditto, 76-Ditto, from the "Art of Fugue," 77-
Further examples, 78, 79-When an answer in the subdominant is
possible, 80-Subject in the key of the subdominant, answer in the tonic,
81-Modulation between subdominant and tonic, 82-Treatment of
intermediate modulations, 83-Tonal answer: its origin, 84-The old
rule, 85-Its usual application; modification required, 86—The practice
of the great masters, 87-The leap from tonic to dominant answered
tonally, 88, 89-The rule applies only to the beginning of an answer, 90
-Examples of a real answer in such cases, 91-The dominant approached
through the third of the scale, 92-Subjects beginning with the notes of
the tonic chord: tonal answers, 93-Ditto, with real answers, 94-99—
The principle involved, 100-Rule for our guidance, 101-Subjects that
commence on the dominant, with tonal answers, 102-104-Ditto, with
real answers, 105-107-The reason for real answers here, 108-Fugues
with both tonal and real answers, 109-Tonal answers in the sub-
dominant, 110-Answer in two keys, III-A real answer always possible
when there is no modulation to the dominant, 112-Warning to students,
113.
CHAPTER IV. THE ANSWER (continued)
page 49
Subjects that modulate to the dominant, 114-Only two chief keys used in
exposition, 115-Rule for modulation, 116-Point of modulation, 117—
Expressed and implied modulation, 118-Examples, 119, 120
Modulation to be made as early as possible, 121-Double significance
of each degree of the scale, 122 Its importance, 123 Example
of subject modulating, by Mozart, 124 - Further examples, 125-
Reason for making the tonal change early, 126-Treatment of third and
seventh of scale, 127-Rule for third of scale, 128-Examples, 129, 130—
Treatment of leading note, 131-Examples, 132, 133-Subjects that
modulate from dominant to tonic, 134, 135-One note answered by two,
136, 137-Subjects modulating to dominant and back, 138-Dissonant
intervals generally retained in answer, 139-An important exception, 140
-143-Disregard of semitones, 144, 145-Dominant answered by super-
tonic, 146-148-Treatment of chromatic subjects, 149-151-Answers by
inversion, 152-Ditto, by augmentation and diminution, 153-Change of
an octave in pitch in course of the answer, 154-Irregular answers, 155-
Summary of general principles, 156—Bad subjects, 157-Exercises for the
student, 158.
Wing Madag
...
..
—
CHAPTER V.-THE COUNTERSUBJECT
page 72
Countersubject defined, 159-Must be in double counterpoint with subject, 160
-Need of contrast, 161-Examples, 162, 163-Key of countersubject,
164-The inganno, 165-The material of the countersubject, 166—Often
forms the basis of episodes, 167-Sometimes accompanies only a part of
the subject, 168-Countersubject in tonal fugues, 169-Sometimes needs
modification, 170-Must make correct two-part counterpoint with the
answer, 171-Deferred appearance of countersubject, 172-A fugue with
two countersubjects, 173-Two countersubjects used in succession, 174-
A double fugue, 175-When a countersubject is unnecessary, 176-
Directions for working, 177.


Contents.
ix
1
CHAPTER VI.-THE EXPOSITION AND Counter-expoSITION
page 81
Exposition defined, 178—Order of entry, 179-Relative distance of voices, 180
-How this affects choice of voice for answer, 181-The last entry best in
an outer part, 182-Exposition of a two-part fugue, 183-Order of entry
in a three-part fugue, 184-Place of countersubject, 185-Additional
entry, when advisable, 186-Example, 187-Codetta, 188-When is a
codetta needed before the entry of the answer, 189-191-Codetta between
second and third entries, 192, 193-Example of an exposition in three
parts, 194-197-Exercises, 198-Order of entry in a four-part fugue, 199
-Alternation of subject and answer : exceptions, 200-How a four-part
exposition differs from one in three parts, 201-When an exposition ends
in the tonic key, and when in the dominant, 202-Cases in which all the
voices do not appear in the exposition, 203-Example of a four-part
exposition, 204, 205-Irregular expositions: an "octave fugue," 206-
The Counter-exposition, 207-Often only partial, 208-Frequently intro-
duces the first stretto, 209-Counter-exposition by inversion, 210-
Counter-exposition quite optional, 211-Directions for work, 212.
CHAPTER VII.-EPISODE
page 92
Episode defined, 213-Its use for modulation, 214-Difference between epi-
sode and codetta, 215-The material for episode: sequence, 216-Use of
imitation, 217-Example of episodes developed from subject of fugue,
218, 219-Ditto from countersubject, 220, 221-Ditto from codetta, 222,
223-Various devices used in episodes; example by Handel, 224-226-
Episodes formed from entirely new material, 227, 228-One episode
sometimes the inversion of another, 229-General principles; the im-
portance of sequence, 230-Need of variety in each episode, 231-The
freedom allowed to the composer, 232-The number of episodes variable,
233-Long and short episodes, 234-Fugues without episodes, 235-Ex-
amples to follow the expositions given in the last chapter, 236-Episodes
for the three-part fugue, 237-239-Ditto, for the four-part fugue, 240-242
-The chief essentials of good episodes; directions for work, 243.
··
..
...
CHAPTER VIII.-STRETTO
page 109
Meaning of the word, 244-The old rule, 245-A stretto not indispensable,
246-Subjects should be designed for stretto originally, 247-Examples
of stretto on a subject not so designed, 248-250- Interval of entry, and
number of parts; closest stretti should come last, 251-Incomplete
entries, 252-Varieties of stretto, 253-A subject and answer specially
written for stretto, 254-The various stretti: in two parts, 255-263-
Ditto for three voices, 264, 265-Ditto for four voices, 266, 267-
How to invent a subject suitable for stretto, 268-Stretto in the
counter-exposition of a fugue, 269-Canonic stretto, 270-Regularity
desirable in the entries of a stretto, 271-Subject and countersubject
used together in a stretto; stretto on a pedal, 272-Stretto made
from modified subject, 273-Stretto by inversion, 274 - Ditto_by
augmentation, 275-Ditto by diminution and inversion, 276-The
stretto maestrale, 277, 278-Stretto in the exposition of a fugue; close
jugue, 279, 280-In a close fugue the answer will be in the same key as
the subject, 281-Examples of stretto by Mozart, 282-284-Example by
Mendelssohn, 285-Ditto by Spohr, 286-Ditto by Brahms, 287-
Necessity of analysis by the student, 288-Exercises to be worked, 289.
•


X
Contents.
CHAPTER IX.-THE MIDDLE AND FINAL SECTIONS OF A
FUGUE
..
page 138
Freedom of treatment of middle section, 290-Ternary, or Three-Part Form,
291, 292-Limits of the first section of a fugue, 293-Varied length of the
middle section, 294, 295—Analysis of the 21st fugue of the "Wohltem-
perirtes Clavier," 296-How to distinguish subject and answer in the
middle section, 297-Bach's fugue in E minor analyzed, 298—The first
section, 299-First group of middle entries, 300-Isolated entries, 301-
Return to the tonic key in the middle section, 302-The rest of the
middle section, 303, 304-Final section: the coda; a dominant pedal,
305-Additional voices often introduced in a coda, 306-Summary of
entries, 307-Fugue in D major, by Bach, 308-The subject, 309-
Absence of countersubject, 310-The exposition, 311-Commencement
of middle section, 312-The first stretto, 313-Third episode and second
stretto, 314-A codetta in the middle section, 315-The third stretto,
316-Fourth middle entry, 317-Final section, 318-Advisability of
rests: method of re-entry of voices, 319, 320-The employment of
cadences, 321-Order of modulation; Cherubini's rules, 322-These
rules hardly ever observed by Bach, 323-Modulations beyond the
nearly-related keys, 324-General rules for the treatment of middle
entries, 325-Exceptions, 326-All voices need not take part in a middle
entry, 327-Number of middle entries variable, 328-Treatment of the
pedal point, 329-Need of continuity, 330-The last note before a rest,
331-Individuality of the voices necessary, 332-The composition of a
complete fugue, 333-Should have a definite plan, 334-Specimen fugue
for two voices, 335-Analysis of ditto, 336-339-A fugue for three
voices, 340-The same analyzed, 341, 342-A four-part fugue, 343-
Analysis of ditto, 344-347-Need of practice, 348.
...
...
...
CHAPTER X.-FUGHETTA AND FUGATO
page 171
Definition of Fughetta, 350-Its usual form, 351-Examples by Bach,
352-354-A five-part fughetta by Handel, 355-Example by Mozart,
356-Ditto by Beethoven, 357-The nature of Fugato, 358-Example by
Bach, 359-Ditto from the "Creation," 360-Ditto by Beethoven, 361-
Ditto by Mendelssohn, 362-Ditto by Mackenzie, 363.
CHAPTER XI.-THE FUGUE ON MORE THAN ONE SUBJECT
page 182
Double Fugue, 365-The two kinds of double fugue, 366-How distinguished
from fugues with a countersubject, 367-The two subjects must be
written in double counterpoint, 368-Number of parts requisite, 369-The
exposition of the first kind of double fugue; first method, 370-374-The
second method, 375-377-Need for clearness, 378-The form of this
kind of double fugue, 379-The middle entries, 380-The stretti, 381-
Isolated entries, 382-The second kind of double fugue, 384-How it
differs from the other kind, 385-The two expositions, 386-389-The
combination of the two subjects, 390-Analysis of Organ Fugue in c
minor, by Bach, 391-394-Limits of variation in this form, 395-General
form of this kind of fugue, 396-Small amount of modulation, 397—
Triple Fugue, 398-An unusual form, 399-Fugue from the "Art of
Fugue" analyzed, 400-403-The ordinary form; the exposition, 404—
Example by Albrechtsberger, 405-Triple fugue by Mozart analyzed,
406-409-Freedom of triple fugues, 410-Quadruple Fugue, 411-A
spurious variety, 412-An exposition of a quadruple fugue by Cherubini,
413-Its subsequent treatment, 414.


Contents.
1
}
;
...
xi
CHAPTER XII.-THE FUGUE ON A CHORAL
page 216
The two methods of writing a fugue on a choral, 415—The subjects taken from
the choral itself, 416-Example by Buxtehude analyzed, 417-421—Ex-
ample by Bach, 422, 423—The form of such fugues, 424-The entries of
the canto fermo, 425-Modern examples, 426-The second kind of fugue
on a choral, 427-Example from Bach's Motetts analyzed, 428-Modula-
tions, 429-The choral introduced during the episodes, 430-Example by
Mendelssohn, 431-Why the freer style was adopted, 432-The first line
of a choral taken as the fugue subject; example, 433-The freedom
allowed in this kind of work, 434.
CHAPTER XIII.-ACCOMPANIED FUGUES
page 229
Definition, 435-Accompanied exposition, 436, 437-Filling up thin harmony,
438-Variations of voice parts, 439, 440-Independent counterpoints,
441-444-General principles, 445-448-Importance of good models, 449
Our rules founded on the practice of the great masters, 450.
$


FUGUE.
CHAPTER I.
INTRODUCTION.
1. It is absolutely necessary that any one who begins to study
fugue should have a thorough knowledge not only of Harmony
and Counterpoint, but of Double Counterpoint and Canon.
Without such knowledge any attempt to master fugal composition
is a mere waste of time. A previous acquaintance on the part of
the pupil will therefore be presupposed throughout this work,
either with the preceding volumes of the present series, or with
other books treating of the same subjects.
2. A FUGUE is a composition founded upon one subject,
announced at first in one part alone, and subsequently imitated
by all the other parts in turn, according to certain general
principles to be hereafter explained. The name is derived from
the Latin word fuga, a flight, from the idea that one part starts
on its course alone, and that those which enter later are pursuing
it.
3. Though the definition of Fugue just given may be
accepted as generally correct, it should be mentioned here, to
prevent misapprehension, that fugues may be written on more
than one subject. If there are two subjects, the fugue is said to
be a double fugue; if there are three, it is a triple fugue, and so on.
In such cases the composition will not begin with one part alone ;
the subjects will appear together, although in all probability they
will not all commence exactly at the same time. It must also be
said that we often meet, especially in modern music, with
vocal fugues having an independent instrumental accompaniment.
In such cases what has been said as to the entry of the subject
with one part alone does not apply; a fugue of this kind has
some analogy to an accompanied canon.

4. From the description just given of fugue, it would seem at
first sight to have a considerable resemblance to Canon. The
latter, indeed, was formerly called fuga canonica, and it will
greatly assist the beginner to understand the real nature of a
fugue if we point out the chief differences between it and the
canons which, it may be assumed, he has already studied. One
most important difference is that, whereas in a canon the leading
voice is imitated throughout by all the parts that follow, this
B


FUGUE.
[Chap. I.
+
is never the case in a fugue. The opening theme, known as the
“subject,” is always imitated; frequently also one or more of the
accompanying counterpoints to the various imitations of the
subject are themselves imitated, as will be seen later in this
chapter; but continuous imitation of one part by another
throughout the whole piece is scarcely ever met with in a fugue.*
This is one of the most important distinctions between the
two forms.
5. Another respect in which fugue differs from canon is that
in the latter the imitation by the second voice must always
be exact as to the name of the interval, though in many cases (as
for instance in a canon in the ninth) the quality of the interval
is changed (Double Counterpoint and Canon, $$ 339, 340†).
In a very large number of fugues, on the other hand, the first
imitation is not an exact copy of the subject, but requires more
or less important modification, as will be explained later.
6. A third distinction between the forms which we are now
comparing is that, while in a canon the first imitation may be at
any interval, it must in a fugue be always at the distance of a fourth
or fifth above or below the subject. This, it must be added,
refers only to the commencement of a fugue; in its later develop-
ments the entries may be at other intervals.
7. Before proceeding to treat separately of the various parts
of a fugue, it will be advisable to give a general description of its
form, and an explanation of the names applied to the different
parts. Fugues differ so much in their structural details that it is
impossible to give more than a general outline here; the
numerous variations will be noticed when in later chapters we
treat of the various parts one by one.
8. The SUBJECT of a Fugue is the theme announced in the
first instance by any one part or voice without harmony (except
in the cases mentioned in § 3), on which the whole composition is
founded. By this it is not meant that the subject is to be heard
continuously throughout the fugue; this would probably cause
great monotony, although instances are to be met with (e.g., in
the first fugue of Bach's 'Wohltemperirtes Clavier') in which
the subject is rarely absent. What is intended is that the subject
is to make its appearance, at more or less frequent intervals,
throughout the whole of the fugue.
9. The ANSWER is the transposition of the subject into the
key of the perfect fourth or fifth above or below the key of
the subject. In an enormously large majority of cases the keys
for the subject and answer will be the tonic and dominant;
occasionally we find the answer in the subdominant instead
* As an exceptional instance of a fugue in which two parts are in canon
throughout should be mentioned the 'Fuga canonica in Epidiapente' (¿.e., in the
fifth above) in Bach's 'Musikalisches Opfer.'
+ The references to "Harmony," Counterpoint," and Double Counterpoint
and Canon" throughout this work refer to the preceding volumes of this series.
"
"
3
DENGAN SALA, RUMORS VARY TRAaramp
Chap. I.]
FUGUE.
3
**
of the dominant. (See § 71.) The answer will in the first
instance be given by whatever voice has the second entry,
and the choice of this voice, as will be seen later, will largely
depend on what voice first announces the subject. The
answer is frequently an exact transposition of the subject;
in this case it is called a real answer; and a fugue which
contains a real answer is said to be a "real fugue.” At
other times the answer is a modified transposition of the subject,
alterations being necessitated by the form of the subject itself.
Such an answer is called a tonal answer; and a fugue in which
there is a tonal answer is called a "tonal fugue."
The rules
which enable us to decide whether an answer should be real
or tonal will be fully discussed in Chapters III., IV.
10. The first voice, which announced the subject, should
never be silent while the second voice is giving the answer. It
always accompanies with a counterpoint, which may or may not
be intended for subsequent use. If it be, it must be written
in double counterpoint, so as to be able to accompany the
subject or answer either above or below. A counterpoint which
accompanies subject or answer systematically (though not of
necessity invariably) is called a COUNTERSUBJECT. We sometimes
meet with fugues which have more than one countersubject.
II. A fugue may be in any number of parts, but, whatever
the number, they should all (with very rare exceptions) enter in
turn at the commencement of the fugue with either the subject or
the answer. That portion of the fugue which extends as far
as the conclusion of the subject or answer (as the case may be)
by the voice that last enters is called the EXPOSITION of the
Fugue.
12. The exposition is usually followed by the first EPISODE
An episode is that part of the fugue in which for a while neither
subject nor answer is heard. It is usually founded upon some
material taken either from the subject or from one of the
accompanying counterpoints, in order to give unity to the
composition as a whole. The episode is also employed for
the purposes of modulation, as will be seen when we come
to treat of it later.
13. The close of the first episode is sometimes, though not
always, followed by what is called a COUNTER-EXPOSITION. This
is a second exposition in the same two keys as the first, but with
this difference, that the voices which before had the subject now
usually have the answer, and vice versa. Sometimes the counter-
exposition precedes the first episode, and follows the exposition
immediately. Very frequently also it is only partial; that is to
say, only some of the voices, and not all, take part in it.
To
14. The counter-exposition, if there be one, will generally be
followed by a second episode, different from the first one.
this second episode (or to the first, if there be no counter-
exposition) succeeds the MIDDLE SECTION of the fugue. Here a
\
L
..
4
[Chap. I.
FUGUE.
A
much greater amount of freedom is allowed to the composer; in
fact, there are hardly two fugues the middle sections of which are
identical in their construction. There are no restrictions in this
section as to order, interval, or key of entry, though in the best
models we mostly find that here the two principal keys (tonic and
dominant) of the fugue, which have been almost exclusively
employed during the exposition, are in general avoided, or only
incidentally touched on. The entries of the subject in other than
the chief keys of the movement are here also mostly divided
by episodes.
15. The FINAL SECTION of a fugue is that in which a return
is made to the original key. Here the subject appears once
at least; very frequently the answer is also repeated. It is not
uncommon, especially in vocal fugues, to find a Pedal point
(Harmony, Chapter XX.) introduced toward the close of this
final section. Sometimes there will be two pedal points; in this
case a dominant pedal will come first, and a tonic pedal at the
conclusion of the piece. Pedal points are also occasionally,
though much more rarely, to be met with in the middle section
of a fugue. A good example will be seen in the fugue in
F major, No. 11 of the second book of Bach's 'Wohltemperirtes
Clavier.'
16. An important feature of many, though by no means of all,
fugues, is what is known as a STRETTO. This is an Italian word
meaning "close," and is applied to that part of a fugue in which
the entries of the subject and answer succeed one another more
closely, that is, at a shorter distance of time, than in the first
exposition. For instance, if the subject be four bars in length,
the answer will, in all probability, enter at the fifth bar. If, now,
in the subsequent developments of the fugue the subject is
followed by the answer (or by the subject itself) in another voice
at the fourth, third, or second bar instead of the fifth, so that the
first entry, so to speak, overlaps the second, we have a stretto. A
stretto may be merely for two voices, or all the voices of the
fugue may take part in it in turn. Very frequently we find more
than one stretto in the same fugue. In that case the interest of
the music is not only maintained, but heightened by making each
successive stretto closer than the preceding.
17. We sometimes find fugues in which a stretto is seen in
the first exposition, that is to say, in which the answer enters
before the completion of the subject, not infrequently immediately
after its commencement. A fugue of this kind is called a CLOSE
FUGUE.
18. The old theorists used to draw a distinction between
strict and free fugues. A STRICT FUGUE was one which either
contained no episodes at all, or in which the material of the
episodes was entirely drawn from the subject or countersubject.
Most of the fugues in Bach's 'Wohltemperirtes Clavier' belong
Chap. 1.]
5
FUGUE.
to this class. If the episodes were chiefly constructed on matter
unconnected with the subject or countersubject, the fugue was
said to be a FREE FUGUE. The fugue in Handel's overture to
'Samson' is an excellent example of a free fugue.
19. A strict fugue in which the various scientific devices, such
as canonic imitation, augmentation, diminution, &c., were largely
employed, was formerly known as a RICERCARE, or RICERCATA,
that is a fugue with research. Two elaborate fugues, one for
three and the other for six voices, in Bach's 'Musikalisches Opfer'
are entitled "Ricercare.” The name was also sometimes given
to fugues without episodes.
20. We occasionally find fugues in which the answer, instead
of being, as usual, a transposition of the subject (§ 9), is given by
We shall see
inversion, or by augmentation or diminution.
examples of these as we proceed. Such fugues are called fugues
by inversion, augmentation or diminution, as the case may be.
21. A fugue of only small dimensions, and not developed at
any great length, is called a FUGHETTA—an Italian diminutive,
meaning a little fugue, Many specimens of this kind are to be
found in Bach's organ arrangements of chorals. A good example
will also be seen in Beethoven's Thirty-three Variations on a
waltz by Diabelli,' op. 120, at the twenty-fourth variation.
22. We very frequently meet with passages written in the
fugal style, that is, in which a subject is announced in one part
and imitated by the others, but in which the imitation is not at
Such
the regular intervals of reply of subject and answer.
A whole movement is
passages are called FUGATO passages.
sometimes written in this way; but more often fugato passages
are introduced incidentally. The chorus "Their sound is gone
out" in the Messiah' is an example of fugato.
11
23. It must be clearly understood by the student that what
has been said in this chapter is to be regarded only as a very
general description. There is, probably, hardly any other form
of composition in which there is so much room for variation of
detail as the fugue. Beyond the fact that all fugues contain an
exposition, a middle section, and a final section, there is little or
nothing that they necessarily have in common. The one point
to realize is, that a fugue should be, so to speak, an organic
growth, the materials of which are to be developed mainly from
the subject and its accompanying counterpoints. How this is to
be effected we shall endeavour to show in the following chapters,
in which we shall deal in succession with the various portions of
a fugue.
J
:
6
Chap. II.
FUGUE.
CHAPTER II.
THE SUBJECT.
24. One of the most important points to be considered in the
composition of a fugue is the choice of a good subject. It would
be possible to write a fugue of some kind-or, to speak more
correctly, a piece in fugal form, on almost any subject that might
be selected; but it is by no means every melody that is adapted
for fugal treatment; and it is no more possible to make a really
good fugue on a bad subject than it would be to make a
really good coat out of rotten cloth. In this chapter we shall
endeavour to show what are the essentials of a good subject.
25. A Subject has been already defined (§ 8) as "the theme
announced in the first instance by any one part or voice without
harmony, on which the whole composition is founded." In the
overwhelmingly large majority of cases this definition is correct; it
is only in fugues with more than one subject, or in fugues with
accompaniment, that the subject on its first announcement has
any harmony. Many theorists speak of the countersubject (§ 10)
as a second subject, and call a fugue with a regular counter-
subject "a fugue with two subjects," or "a double fugue." In
this volume we shall restrict the meaning of the word subject'
to that theme which is announced at the very commencement of
the fugue, and speak of a "second" or "third" subject only
when such accompanies the first subject before it has been
answered in another voice. It is possible also for a second
subject to appear later in the fugue, provided it has a separate
"exposition (§ 11) of its own, and is subsequently heard
in combination with the first subject.
(C
"}
"
I
26. The first point to be considered in writing a fugue subject
is clear tonality. This is a matter of the utmost importance,
because if we are in any doubt as to our key, it may be very
difficult, if not impossible, to give a correct answer, as will be
seen in our next chapter. It is quite true that in many of
the older fugues the tonality sounds vague and undecided; but
this is because they were written in the old church modes, about
which, except as a matter of antiquarian curiosity, the student
need not trouble himself. It is not necessary that a subject
remain throughout in the same key; but if a modulation is made
it should be unmistakable, and there should in general be
no difficulty in determining where it takes place.
27. It will greatly facilitate the student's labours in this
respect if he accustoms himself, when inventing a subject, to think
Chap. II.]
7
FUGUE.
of the implied accompanying harmony. Every musical phrase
that has any meaning at all must be capable of being harmonized,
probably in several different ways; and if from the first we think
what harmonic progressions go best with the subject we have
chosen, there will be little fear of our losing the distinct feeling of
a key.
(b)
Cibe
28. To illustrate our meaning we will give a few examples of
simple subjects which remain in one key throughout—
HANDEL. 'Messiah.'
(a)

(c)
fo
HANDEL. 'Judas Maccabæus.'

If the student will examine these subjects, he will see that in
both of them there can be no possible doubt about the key.
Both begin with the notes of the tonic chord (the semiquaver C
in (6) is only an ornamentation of the D); and both end with
the descent from supertonic to tonic. The following example
J. S. BACH. Wohltemperirtes Clavier, Fugue 1.

is somewhat different. Here the progression is by step from
tonic to dominant, and if we look at the first bar alone, the
tonality is a little less decided than in the examples from Handel.
But the prominence given to the dominant in the second bar
fixes the key clearly, and the impression is strengthened by
the subject ending on the mediant (E).
29. Our next example
J. S. BACH. Wohltemperirtes Clavier, Fugue 31.

Cife
is perfectly clear. The key is fixed at once by the leap from
tonic to dominant at the commencement; for although the first
note, E, might be the dominant of A flat, it would be most
unlikely to leap to the supertonic of that key; and if it were the
subdominant in the key of B flat, it would be quite unprecedented
for it to leap to the tonic. Besides this, we must always mentally
supply the most natural harmonies to a subject. In this case, the
first chord must of course be E flat; the second will be either
another position of E flat, or the chord of B flat-in either case
strongly suggesting the key of E flat; and the suggestion is
changed into a certainty by the A flat immediately following. In
general, if a fugue subject begins with an upward leap of a perfect
fifth, or a downward one of a perfect fourth, the first note will be
the tonic of the key, and the second the dominant; if, on the

•
8
FUGUE.
[Chap. II.
other hand, it begins with an upward leap of a fourth, or a
downward of a fifth, the first note will be the dominant and the
second the tonic. There are occasional exceptions to this rule,
as in the following example-
MOZART. Mass in C, No. 12.

NC
Such exceptions are, however, extremely rare, and in these cases,
the close of the subject, or the beginning of the answer, will always
determine the key. In our example, if the subject began in
A minor, it could not end with an implied modulation (§ 118)
to G. This fugue, also, being on three subjects, the key is
defined as C by the other subjects, which accompany the theme
here quoted (see § 406).
30. Similar reasoning will apply to our next example-
J. S. BACH. Wohltemperirtes Clavier, Fugue 21.
(a)


杏
​If we try to think of the simplest and most natural harmonies to
accompany this melody, we shall obtain something like this—
54
(a)
Jobc
CO LO
6
(b)
5
87
Here the A natural and E flat in the second bar prove the key to be
B flat; for there is no other key in which both these notes are
found, unless one be a chromatic note; and there is no suggestion
of chromatic harmony in the subject, which, is diatonic throughout.
Our last example in a major key
(b)
87
requires little explanation. Though the leading note is not used,
the feeling of the whole subject is decidedly that of the key of C,
and not F. Compare the end of the subject with that of
example (c) of § 28.
31. In a minor key we find the tonality equally clear, as will
be seen from the following examples—
J. S. BACH. Wohltemperirtes Clavier, Fugue 2.
BEETHOVEN. Mass in C.



J. S. BACH. Partita in B minor.

Chap. II.]
9
FUGUE.
(c)
for
32. In our next example
(a)
At (a) the juxtaposition of the minor sixth and major seventh of
the scale fixes the key at once. The same result is obtained at
(b) by following the arpeggio of the dominant seventh by that of
the tonic chord (Harmony, § 219). At (c) we are in doubt till
the third bar, though we feel that the key is C, whether the mode
will be major or minor; the A flat settles the question in favour
of the latter.
(c)
Cze
the key is fixed by the arpeggio of the tonic chord (compare
example (b), § 30).
MOZART. Requiem.
(b)
File
Cap
f
J. S. BACH. Organ Fugue in C minor.

Here the interval of the diminished fifth followed by B flat shows
the key to be G minor. In our last example
(6)
(c)
HANDEL. 'Muzio Scevola.'

the first three quavers of the second bar fix the key.
33. Sometimes the subject, instead of being in the key of the
tonic, is in that of the dominant throughout, as in the following
instances-
(a)
MENDELSSOHN. 'Elijah.'
J. S. BACH. Cantata, "Ein ungefärbt Gemüthe."
J. S. BACH. Partita in D major.
HANDEL. 'Samson.
That we have here the key of the dominant is shown, not only by
the signature of the movement, but also (as will be seen in the
next chapter) by the interval at which the answer replies.
•
J






IO
FUGUE.
[Chap. II.
1
L
34. A fugue subject often ends in a different key from that in
which it begins. The case most frequently met with is that
in which it begins in the tonic and ends in the dominant-
J. S. BACH. Cantata, "Ich hatte viel Bekümmerniss."
Key: G.
(a) Key: C.
☺e

Though the leading note
the construction of the
indicates the key of G.
Bach gives to the subject.
(6) Key: D.
*4
(c)
Key: F.
Pl
(d) Key: E2.
2·6-8
of the new key is not introduced here,
melody in the last two bars clearly
This is further proved by the answer
In the following examples
J. S. BACH. Cantata, "Singet dem Herrn.”
Key: A.


Key: C.
(c) Key: F minor.
Dirty &
HANDEL. 'Hercules.'
SCHUMANN. Mass, Op. 147.
Key: Bb.
ま
​
the leading note of the dominant key appears in the subject.
35. If the subject be in a minor key, it is very important to
remember that the modulation must be to the dominant minor,
and not to the dominant major key.
(a) Key: A minor.
J. S. BACH. 'Matthäus Passion.
Key: E minor.

Here, though the dominant chord of A minor is, of course,
E major, the modulation is not made into that key, but into
E minor. Our next example shows a chromatic note in a
subject-
(b) Key: D minor.
SCHUMANN. Fugue, Op. 72, No. 1.
Key: A minor.

In the second bar of this subject the G sharp, though the leading
note of A minor, does not cause a modulation into that key,
because it is preceded by B flat, and immediately afterwards
contradicted by G natural. The modulation does not take place
till the latter half of the fourth bar. Our last example
RUBINSTEIN. 'Paradise Lost.
Key: C minor.

shows a chromatic note (F sharp) as an auxiliary note, and
is therefore similar to the preceding.
Chap. II.]
FUGUE.
II
36. Less commonly we meet with subjects that begin in the
key of the dominant, and end in that of the tonic. Two
examples will suffice-
Key: A.
(a)
##
(b) Key: C.
fre
X
&
In the second of these subjects, the close looks at first as if
it were in the key of C. That it is not so, is proved by the
auxiliary note in the last bar being B flat, and not B natural.
37. It is also possible, though somewhat rare, for a subject to
begin in the tonic, modulate to the dominant and return to the
tonic, as in the following example—
Key: E minor.
•
(b) Key: G.
(a)
Of c
Key: F.
38. Occasionally, instead of tonic and dominant, the two keys
employed for the subject are tonic and subdominant.
following passages
The
(c) Key: E minor.
(d) Key: A minor.
Ceft
J. S. BACH. Mass in B minor.
Key: D.

HANDEL.
Key: G minor.
J. S. BACH. Cantata, "Sehet, welch' eine Liebe.”
Key: B minor.
Key: E minor.
HANDEL. 'Rinaldo.



'Alexander's Feast.
Key: D minor.

Key: D.
begin in the subdominant and end in the tonic.
examples
J. S. BACH. Mass in B minor.

In our next
J. S. BACH. Fugue in E minor.
Key: A minor.

MENDELSSOHN.
Key: E minor.
3rd Organ Sonata.
Key: D minor.

MALL
the subject begins in the tonic and ends in the subdominant. In
example (d) we also find an intermediate modulation to the
dominant.
12
FUGUE.
[Chap. II.
1
39. Quite exceptionally an entire subject is to be found in the
key of the subdominant—
HANDEL. 'Jephtha.'

The key of the piece is D minor; but this subject is decidedly in
G minor, the B natural being, as its subsequent treatment shows,
the chromatic major third of the minor key.
40. In addition to the modulations already spoken of, we
frequently meet with incidental modulations in the course of
a subject which ends, as it began, in the key of the tonic. Of
these the most usual are to the subdominant key for a major
subject, and to the relative major for a minor subject—
J. S. BACH. Cantata, "Wer Dank opfert."

(a)
344
(c)
fot
(b)
O PC
In all these examples will be seen a short modulation to the key
of the subdominant.
藥
​HANDEL. 'Semele.'

41. The same modulation is sometimes found with a subject
in a minor key—
(a)
O
f
MENDELSSOHN. 'St. Paul.'

More frequently, however, the incidental modulation for a minor
key is, as said above, into the key of the relative major--
(b)
BACH. Organ Fugue in G minor.
(c)
HANDEL. 'Messiah.'


HANDEL. Anthem, "In the Lord put I my trust.'
33

Chap. II.1
FUGUE.
13
""
42. A good fugue subject should always (or at least with
extremely rare exceptions) contain a complete musical phrase. By
the word "phrase is here meant a passage containing some
distinct idea, and terminating with a cadence of some kind
(Counterpoint, Chapter XV.). It is not intended by this that
there is actually to be a cadence introduced at the end of the
subject, but only that the final notes of the subject shall be capable
of being harmonized as a cadence-not necessarily a full cadence,
though in a large majority of instances this is the case. If the
student will examine all the subjects already quoted in this
chapter, he will find this condition invariably fulfilled. In almost
every instance the subject ends with either the root or third
of tonic or dominant. In the rare cases where the subject ends
in the subdominant (see § 38, (c), (d), the close will be made
on the root or third of the tonic of that key.
43. In order to obtain a proper cadential effect, it is necessary
in common time that the subject should end on an accented
note—either at the first or third beat of the bar (see for instance
the examples in § 28). In this case, if the cadence is felt as
occurring on the strong beat in the bar, a continuation of the
harmony is sometimes added, as in § 31 (c).
44. The only exception to this rule in common time is, that
the subject may end on an unaccented note, provided that the
preceding accented note has the character of a suspension or an
appoggiatura-
tr
J. S. BACH. Wohltemperirtes Clavier, Fugue 37.
-w
f
Here the end of the third bar suggests the chord of the dominant
seventh; it is resolved at the beginning of the fourth bar, where
the B is clearly an appoggiatura. See also examples § 32 (6)
and § 35 (b).

(a)
45. In triple time this rule does not apply, because here it is
possible for the final chord of the cadence to come on the second
beat (Counterpoint, § 484). As an example of this see § 34 (d).
46. It is impossible to give any definite rules as to the length
of a fugue subject. In the works of the great masters we
sometimes find them quite short, consisting in fact of only a few
notes-
J. S. BACH.
Wohltemperirtes Clavier, Fugue 5.

J. S. BACH.
Wohltemperirtes Clavier, Fugue 22.
(b)
MOZART. Quartett in G, No. 14.
(c)



14
[Chap. II.
FUGUE.
.
At other times they are of very considerable extent—
(d).
fore
&
bb
(e)
☺be
皮
​(f)
J. S. BACH. Toccata in C minor.

MOZART. Litany in B flat.
ま
​

BEETHOVEN. Quartett in C, Op. 59, No. 3.


In long subjects such as these, we very often find sequential
passages introduced. As a general rule, the slower the time, the
fewer should be the bars in a fugue subject. It is important that
the hearer should readily recognize the subject when it reappears,
and this is much more easily done if it be concise than if it be
long and straggling. Many of the finest fugues existing are those
written on short subjects. It should be added that the length of
the subject in vocal fugues will partly depend on the words, as
the cadence should always come where the sense of the text
allows it. Think, for example, how absurd it would be if the
fugue subject at § 28 (a) ended with the words, "and he shall
reign for ever and "— !
47. Another important matter to be considered is the compass
of the subject. In vocal fugues this should rarely exceed an
octave, because if it does, it will be very likely when it appears in
other keys to go beyond the comfortable range of the voices.
Exceptions are occasionally to be met with, as, for instance, in
one example (a) of § 40, which has the compass of a tenth; but
these are rare. In instrumental fugues a larger compass is
possible; but even then it is seldom expedient, because of the
probability of its causing much crossing of the parts, and so
impairing the clearness of the fugue. Many of the best fugue
subjects lie within a small compass. In two of the finest fugues
of Bach's "Forty-Eight" (Nos. 4 and 33) the compass of the
subject does not exceed a fourth. In the examples given above
at § 32 (b) and § 34 (b) the compass is only a fifth; while at
§ 28 (c), § 30 (b), and § 34 (c) it is only a sixth.


Chap. II.]
15
FUGUE.
48. Though there are limitations (§ 42) as to the note of the
scale on which a fugue subject should end, there are none as to
that on which it should begin. In an enormous majority of
cases, the subject begins on either the tonic or dominant; but
numerous examples are to be met with of the employment of the
other degrees of the scale for the initial note. We give a few
instances of each-
J. S. BACH. Cantata, "Der Himmel lacht."

f
(b)
go
(a)

(c)
fur
(d)
Subjects beginning on the supertonic are rather rare. Another
example will be seen in Bach's fugue in B flat, No. 45 of the
'Wohltemperirtes Clavier.' Subjects beginning on the mediant
are also not very often met with-
(6)
yo
(d)
MendelssOHN.
"Surrexit pastor," Op. 39, No. 3.

49. The following subjects begin on the subdominant-
HANDEL. Dettingen Anthem.
(a)
Beethoven. Mass in D.

CHERUBINI. 4th Mass.

S

SCHUMANN. Fugue, Op. 72, No. 3.

In the two next examples the subject begins on the submediant—
BACH. Organ Fugue in E flat ("St. Ann's ").
(c)

HUMMEL. 2nd Mass.

A commencement on the leading note is very rare. We have
given one instance in § 44; we add another—
(e)
HUMMEL.
Ist Mass.

This subject is further interesting from its containing an incidental
modulation to the key of the relative minor, which is somewhat
unusual for a subject in a major key.


16
[Chap. II.
FUGUE.
•
50. There are still two points of importance to be considered
in the selection of a fugue subject. First, it must be contrapuntal
in character, or at least adapted for contrapuntal treatment.
There are many beautiful melodies which would be utterly
unsuitable for fugue; it is difficult to imagine fugues written, for
example, on such subjects as the following—
(a)

f
(b)
tr
BEETHOVEN. Symphony in D.

BEETHOVEN. Sonata, Op. 2, No. 1.

It is impossible to give any precise rules as to what constitutes a
contrapuntal subject; but the student who has properly studied
counterpoint will feel it instinctively. One probable reason why
the melodies just given are unsuitable is that they are too much
cut up by "middle cadences" (Counterpoint, §§ 480, 505).
Sometimes a cadence is met with in the middle of a subject, as in
example (c) of § 41; but in general the subject should flow
continuously, as is the case in the large majority of examples
already quoted.
51. Though not indispensable, it is often advisable that the
subject itself should be adapted for stretto; that is, for imitation
at less than the original distance (§ 16). This question will be
fully dealt with later (Chapter VIII.).
52. The last point of importance to be mentioned is the
necessity of distinct character in a fugue subject. A mere
meaningless collection of notes, resembling a clumsy counter-
point exercise, will never make a good fugue. The chief
essentials in this respect are a clearly defined melody, and a well-
marked rhythm. Such examples as those we have given in
§ 28 (a) (b), § 34 (a), § 46 (a) (b) (c), illustrate the former; while
in § 36 (a), § 41 (6), and § 46 (d) the melody and rhythm are of
equal importance. As the invention of melody is impossible to
teach, we must content ourselves with pointing out what is
required, leaving it to the student's own imagination and skill to
carry the principles here laid down into actual practice.
53. In analyzing a fugue, it is important to be able to deter
mine exactly where the subject ends. In exceptional cases there
may be a doubt about this; for instance, three different text-
books give three different lengths for the subject of the C sharp
major fugue in the second part of Bach's 'Wohltemperirtes
Clavier.' In general, however, there is no difficulty. It has
been already said (§ 42) that the subject should end with a
cadence. If the subject begins with an accented note, the
last note of the subject will usually (though not invariably) be
that on which the answer enters. In other cases, the subject

Chap. II.]
FUGUE.
17
will generally end on a cadential figure either just before or just
after the entrance of the answer. If in doubt we can generally
decide the question by seeing how much of the subject is
imitated in the answer; this will be more clearly seen in the
next chapter. In the case of a close fugue, where the answer
enters before the subject is ended, the length of the subject will
be decided solely by observing how much is imitated in the
subsequently entering voices.
54. The student should now practise the invention of fugue
subjects on the lines indicated in this chapter, bearing in mind
the chief requirements which may be thus summarized:-(1)
clearness of tonality; (2) distinctness of form; (3) moderate
length and compass; (4) good striking melody; (5) contrapuntal
character. He need not trouble himself much about originality;
all the best melodic and harmonic combinations for fugue
subjects have been so frequently employed that novelty in the
subject itself is now hardly possible. In modern fugues,
originality (if it exists at all) is to be looked for in the treatment
of the materials rather than in the materials themselves.
с
7
..
1

18
[Chap. III.
FUGUE.
•
+
M
f
55. In our first chapter (§ 9) we defined the answer as "the
transposition of the subject into the key of the perfect fourth or
fifth above or below the key of the subject." It is most necessary
that the student should know how to find the correct answer to
any given subject; unfortunately there is hardly any point on
which the rules given in the older text-books differ so widely from
the practice of the greatest composers. The rules to be given
in the present chapter will therefore not be taken from existing
treatises, but deduced from the works of the great masters
themselves.
(a)
56. In by far the largest number of cases, the keys in which
the subject and answer are found are the tonic and dominant. If
the subject be in the tonic, the answer will be in the dominant ;
if the subject be in the dominant, the answer will be in the tonic.
If the subject begin in the tonic and modulate to the dominant,
the answer will begin in the dominant and modulate to the
tonic, and vice versa. Occasionally, however, as will be seen
presently, the place of the dominant is taken by the subdominant.
S
CHAPTER III.
57. The answer of a subject may be either real or tonal. It
is said to be real when it is an exact transposition (with one
possible exception, to be noticed in its proper place-see § 69) of
the subject; it is called tonal when certain alterations, the nature
of which we shall explain later, have to be made in transposing it.
J. S. BACH. Wohltemperirtes Clavier, Fugue 33.
A
dddd
(b)
THE ANSWER.

S
"

MOZART. Quartett in G, No. 14.
A
In the above examples the subject is marked S and the answer
A. At (a) the answer is real; at (6) it is tonal, the interval of a
third from G to B being answered by a second from D to E.
Let the student also notice that at (a) the last note of the answer
is longer than the last note of the subject. We shall meet with
Chap. III.]
FUGUE.
19
other instances of this common procedure as we advance; it is
always allowed either to lengthen or shorten the first or last note of
the answer.
58. As being the easier, we shall first speak of real answers.
The rule for knowing when a subject can have a real answer
is very simple, and may be thus stated:-Every subject in which
there is no modulation to the dominant, either expressed or
implied,* may have a real answer, excepting, first, when it begins
on the tonic and leaps to the dominant either direct or with the
third of the scale as an intermediate note; and secondly, when it
begins on the dominant. But even in these two cases a real
answer is always possible (§§ 101, 105-107).
59. We shall first give examples of real answers in the
dominant key to subjects which are in the tonic throughout.
We shall in each case give the counterpoint to the answer, which
is, as will be seen, the continuation of the music by the voice
which has just had the subject; we shall also extend our
quotations beyond the end of the answer, as this will help the
student in determining the limits of the subject. Our first
example illustrates what was said in § 53—that when the subject
commences with an accented note, the answer usually enters on
the last note of the subject—
(
8
A
J. S. BACH. Wohltemperirtes Clavier, Fugue 15.



&c.
That the subject here ends on the F sharp of the fifth bar (the
third of the dominant chord-§ 42) is proved by the fact that the
next note, G, is not imitated in the answer. In this example
the answer is below the subject.
* What is meant by an implied modulation will be seen when we come to speak
of tonal answers (§ 118).
+4
20
[Chap. III.
FUGUE.
60. In our next examples
(a)
#C
seee
4
(b)
S
S
€
J. S. BACH. Wohltemperirtes Clavier, Fugue 29.
A

&c.
J. S. BACH. Wohltemperirtes Clavier, Fugue 43.
A
the answer is above the subject. In both, the subject commences
on an unaccented note, and ends on the accented note (here at
the half bar) immediately preceding the entrance of the answer.
61. The following passage shows some new points-
&c.


&c.
J. S. BACH. Wohltemperirtes Clavier, Fugue 9.
A

answer.
Here the answer enters shortly before the end of the subject,
which terminates at *, the nearest accent to the entry of the
In § 53 it was said that the length of the subject could
mostly be determined by seeing how much was imitated by the
answer. It looks at first sight as if the imitation were here
continued for another half bar; but the subject cannot end on
the D at the beginning of the third bar; because, in that case, as
we shall see later in this chapter, the answer could not possibly
end on A. Besides this, the imitation in the half bar is not
exact, D sharp being imitated by A natural, not by A sharp.
The fact is, we have here a common case, in which part of the
►

Chap. III.]
FUGUE.
21
continuation of the subject is imitated in the answer-sometimes
strictly, at other times (as here) freely.
62. In the example just given, the answer entered before the
end of the subject. In our next
8
A
8
the subject ends (as will be seen by comparing the answer) on the
first note of the third bar, and the answer does not enter till the
fourth. Such cases are of frequent occurrence. Here it would
have been quite possible for Handel to have commenced his
answer in the third bar; thus—
A
HANDEL. 'Riccardo Primo.


G
but if the student will remember what was said in the last
chapter about the implied harmony of a fugue subject, he will see
that at the end of the second bar of this subject there is clearly a
chord of the dominant seventh implied; and the continuation we
have suggested would have been far less satisfactory from a har-
monic point of view. The passage introduced between the end
of the subject and the beginning of the answer, which we have
marked with a, is called a codetta. In many cases some
:such connecting portion is absolutely necessary.
63. The following example
&c.
&c.

&c.
Liet
HAYDN. 4th Mass.


:shows a more chromatic subject than those already given. Here
22
FUGUE.
[Chap. III.
▸
..
the answer enters on the last note of the subject, because it begins.
on an accented beat. Our last example was an exception from
this rule.
64. In our next example
€
ន
12
&c.
S
we see a somewhat rare case. The first voice ceases for some
time to accompany the answer. The quotation is the commence-
ment of a fugue with independent orchestral accompaniment ;
and the tenor, therefore, though the bass is silent, is not left
entirely alone.* Such treatment is, however, exceptional; and
the student is not recommended to imitate it.
65. Our last example in a major key
HUMMEL. Ist Mass.
A


MENDELSSOHN. 2nd Organ Sonata.
A


&c.
bd
shows the leading-note of the dominant treated as the third of
the supertonic chromatic chord, and therefore inducing no modu-
lation. It is consequently answered by C sharp, the third of the
supertonic chromatic chord in the key of G. The last note of
the subject, also, is here slightly altered in the answer, being
delayed by a suspension.
66. We now give some answers to subjects in minor keys.
These will always be in the minor of the dominant-never in the
major. We have seen already (§ 35) that if a minor subject.
* See § 441, where the complete exposition of this fugue is quoted.
"
Chap. III.]
FUGUE.
23
modulates to the dominant, it is always to the dominant minor;
and the same rule holds good when the first modulation that is
made is on the entrance of the answer. This will be seen from
the two following examples—
(6)
se
Ce
(a)
8
A
8
J. S. BACH. Wohltemperirtes Clavier, Fugue 4.
A

X

&c.
J. S. BACH. Wohltemperirtes Clavier, Fugue 20.



&c.
67. If the student will examine the various counterpoints
accompanying the answers we have given, he will see that (like
the answers themselves) they are in the key of the dominant.
Were it otherwise, the feeling of tonality would be obscured, for
the music would be in two keys at once. Occasionally, however,
the harmony of the dominant key is not clearly defined till toward
the end of the answer, as in the following passage—
J. S. BACH. Wohltemperirtes Clavier, Fugue 42.
8
+


24
[Chap. III.
FUGUE.

A

8
3
bb
f
Here the key of D sharp minor, the dominant of G sharp minor,
is not reached till the third bar of the answer.
68. Our next example illustrates a point of considerable
importance-
J. S. BACH. Wohltemperirtes Clavier, Fugue 46.
8
A
&c.


A
Here the last note of the subject is D flat, the minor third of the
tonic; but the last note of the answer is not A flat, the minor
third of the dominant, but A natural, the major third.
69. That this is by no means an isolated case will be seen by
the following examples, taken from a much larger number that
might be given-
(a)
15

&c.
MOZART. Requiem.

&c.
I J
7
Chap. III.]
25
FUGUE.
J
#e
(6) 8
21
HOM
H.MD
H
L
17.
H
A
Further illustrations of this point will be met with when we come
to tonal fugues. The following rule is fully justified by the
practice of the great masters :—
Whenever a subject in a minor key ends on the third of the tonic,
the answer may end on either the major or minor third of the
dominant, as may be preferred.
MUS
#5
70. If the subject be throughout in the key of the dominant,
the answer will be in the key of the tonic-
(a) 8
J. S. BACH. Ouverture (Suite) in F.
Clementi. 'Gradus ad Parnassum,' No. 25.

(b)
S
Codetta.
&c.
A
&c.
&c.

HANDEL.
A

'Samson.


It is important to notice that the answer is now a fourth above,
or a fifth below, instead of being (as in previous cases) a fifth
above, or a fourth below, the subject.
26
[Chap. III.
FUGUE.
I
71. By an extension of this relation of subject and answer,
we sometimes find that when the subject is in the tonic, the
answer is in the subdominant, instead of the dominant-
J. S. BACH. Cantata, "Der Himmel lacht."
(a) S

be
Here the subject is in C, and the answer is no less clearly in F.
The commencement of the answer illustrates what was said in
§ 57, the initial notes being lengthened-
(b) S
A
S
A
boo
A
J. S. BACH. Organ Fugue in C.


Here again the answer is in the subdominant. The alteration of
the semitone near the end (B natural answering F natural) is
frequently to be met with (§ 144)—
(c)
"Surrexit pastor."
MENDELSSOHN.
&c.


&c.
Here the answer is in the fourth above, instead of the fifth below.
This fugue has an independent organ accompaniment (not
quoted), which still more clearly proves the key of the answer
to be C.

72. If we examine the three subjects last given, we shall see
that in all of them prominence is given to the dominant or to
Chap. III.]
FUGUE.
27
notes of the dominant harmony. The same thing will be found
in our examples in a minor key, in which an answer in the
subdominant is much more common than in a major key—
J. S. BACH. Partita in B minor

8
&c.
S
A

Here the subject commences with the arpeggio of the dominant
seventh; then comes tonic harmony, and then dominant harmony
again. The answer is now in the subdominant, in order to carry
out the important principle that dominant harmony should be
answered by tonic.
73. As the possibility of a fugal answer being in the key of
the subdominant has not, so far as we know, been touched upon
in any existing treatise, it will be needful to give a considerable
number of examples by the greatest masters-not only to
establish the fact, but to enable us to deduce the necessary rules
for the student's guidance in deciding when such an answer is
advisable. Our next example deserves close examination—
J. S. BACH. Cantata, "Herr, Deine Augen."
A


&c.
Here the subject does not, like those previously given, begin with
a note of the dominant chord; but the diminished fifth immedi-
ately following clearly indicates the chord of the dominant
seventh. In the next bar is a modulation to the dominant
key, the return to the tonic being made in the third bar.
*
28
FUGUE.
[Chap. III.
74. Now let us examine the answer. The first note is C.
This cannot be regarded as a subdominant, because the tonic at
the commencement of a subject cannot be answered by a
subdominant. We have already seen that it is almost invariably
answered by dominant-that is to say, by the tonic of the key in
which the answer appears.
The C here must therefore be
considered not as the subdominant of G minor, but as the tonic
of C minor. This choice of a key for the answer enables Bach to
carry out the important general principal already mentioned, and
of which we shall have more to say when we come to speak of
tonal answers, that dominant harmony in the subject should be
replied to by tonic harmony in the answer. Here we have the
dominant seventh chord in G at the first bar of the subject,
answered by the notes of the tonic seventh of G in the first bar of
the answer. It would have been quite possible to give a real
answer for this bar, beginning on the dominant; but then the
dominant harmony of the subject would have been answered by
the supertonic harmony, instead of the tonic.
75. It will also be seen that at the second bar of the subject
there is a modulation to the dominant key. Such a modulation
is almost invariably answered by a return to the tonic key. Here,
however, the tonic harmony in the answer is really the harmony of
the dominant key of C minor. Had the answer not been in the key
of the subdominant, a tonal answer would have been necessary.
76. Our next illustrations, containing no modulation,
(a) S
Lifl
(b)
8
foc
A
A
&c.
J. S. BACH. Organ Fugue in D minor.

&c.
J. S. BACH. Toccata in D minor.

ਮੌਤਾਂ
Chap. III.]
29
FUGUE.
further show the answering of dominant harmony at the
commencement of the subject by tonic harmony at the beginning
of the answer. The two subjects are somewhat similar in
character.
77. The same point is exemplified in the following-
Th
S
J. S. BACH. Art of Fugue, No. 10.

&c.
A
We shall see when
The subject here begins on the leading note.
we come to tonal answers that the leading note, excepting when it
is merely an auxiliary note of the tonic, is almost invariably
considered as the third of the dominant, and answered accordingly
by the major third of the tonic (§ 131). This is the case here,
and any other answer than that which Bach has given in the
subdominant key, will either sacrifice this reply of tonic to
dominant, or (if a tonal answer) distort the subject almost
beyond recognition. It should be specially noticed that the
'Art of Fugue' from which this example is taken, was expressly
written by Bach for the purpose of showing the possibilities of
fugal composition; his giving an example of an answer in the sub-
dominant key may therefore be fairly taken as proving, apart from
all the other examples we have given, that he considered such an
answer correct.
78. The last example we shall give from Bach
S
&c.
J. S. BACH. Suite for Orchestra, in D.

A
is similar in character, and even more pronounced. The subject,
except the last note, is formed entirely of dominant harmony,
30
[Chap. III.
FUGUE.
which is therefore answered by corresponding tonic harmony.
The counterpoint accompanying the answer conclusively proves
the key of the answer to be G.
79. We now add a few examples, by other composers, of real
answers in the subdominant key—
(a)
(b) S
(c)
S
S
sf>p
&c.
A
HANDEL. 'Solomon.'

Codetta.
BEETHOVEN. Quartett, Op. 131.
&c.
A
&c.


SCHUMANN. Fughetta, Op. 126, No. 2.
A


After what has been said, these examples require no further
remark.
80. We shall find a few more examples of answers in the
subdominant when we come to treat of tonal answers, but we
have already given enough to enable us to generalize from. The
rule to be deduced from an examination of these and similar
passages is the following:-
Whenever, in a subject which ends in the key of the tonic,
particular prominence is given to dominant harmony, especially near
Chap. III.]
31
FUGUE.
the beginning of the subject, the answer may be in the subdominant
key, in order to conform to the important general principle that
dominant harmony in the subject should be replied to by tonic
harmony in the answer.
81. If the whole subject be in the key of the subdominant,
the answer will be in the key of the tonic-
A
8
8
Re
In this case the relationship of the two keys is evidently the same
as that of tonic and dominant.
A
HANDEL. 'Jephtha.'

82. If the subject begin in the key of the subdominant and
modulate to the tonic, the answer will begin in the key of the
tonic and modulate to the dominant-
8
&c.
HANDEL. 'Alexander's Feast.'
&c.
The subject here ends on the first crotchet of the third bar. It
begins in G minor and modulates in the second bar to D minor.
The answer begins in D minor and modulates to A minor. The
proof that the subject commences in G minor is found in the first
note of the answer. If Handel had regarded A as the dominant
of D minor, instead of the supertonic of G minor, he would have
answered it, according to the laws of tonal fugue, by D and
not E.
83. Intermediate modulations (except to the key of the
dominant) should be imitated exactly in the answer-
(a)
HANDEL. 'Semele.'
A
1



32
[Chap. III.
FUGUE.
(b) S
A
Plagal.
In the second bar of the major subject at (a) is seen a
modulation to the subdominant, imitated at the same point of the
answer; and in the third bar of the minor subject at (b) a
modulation to the relative major, replied to by a similar modula-
tion to the relative major (G major) of the dominant.
84. In order to understand what is meant by a tonal answer,
we must remember that each of the old Ecclesiastical scales, out
of which our modern scales were developed, had two "modes,"
one of which was a fourth below the other, but contained the
same notes. If the scale was from final to final (or, as we
should now say, from tonic to tonic), and the dominant was
in the middle, the mode was said to be authentic; if, on the other
hand, the scale was from dominant to dominant, with the final in
the middle, the mode was called plagal. Each scale was divided
into two unequal halves by the dominant or the final.
us take, for example, the old Dorian mode-
Let
Authentic.
Final
J. S. BACH. Organ Fugue, in A minor.


Dominant
&c.

The dominant in the authentic mode and the final in the plagal
are marked in this example. It will be seen that the lower half
of the authentic scale has the compass of a fifth, and the upper
half the compass of a fourth; while the plagal scale has a fourth
for the lower half, and a fifth for the upper.
85. The old rule for fugal answer was that a subject made in

Chap III.]
33
FUGUE.
3
either half of the authentic scale should be answered in the
corresponding half of the plagal scale, and vice versâ.
For
instance, if the subject began with the leap between tonic and
dominant, in the lower half of the authentic scale,

f
the answer would begin with the leap between dominant and
tonic,

葬
​ē
these being the corresponding lowest and highest notes of the
lower half of the plagal scale; and conversely, if the subject
began in the lower half of the plagal scale, with the leap up from
dominant to tonic, or down from tonic to dominant, the answer
would begin in the lower half of the authentic scale with the leap
up from tonic to dominant, or down from dominant to tonic.
86. The rule to be found in nearly every work on fugue
respecting tonal answer is, that if a subject leaps from tonic
to dominant, either direct or through the third of the tonic,
the answer must be tonal-that is to say, the tonic must be
answered by the dominant, and the dominant by the tonic. This
is a good rule enough, if it were only observed; but, as we shall
proceed to show, the great masters, from Bach and Handel
downwards, "drive a coach and four through it" continually. If
we wish to conform to their practice, we shall have to modify this
rule very considerably.

87. Evidently the first thing to be done is, to find out what
the practice of the great masters really was in this respect. For
this purpose a large number of quotations will be necessary. It
may be at once admitted that in the majority of instances they
conformed to the old rule; but quite enough examples will be found
in which it is broken to show that they did not regard it as one of
the laws of the Medes and Persians. In the examples now to be
given, we shall no longer add the counterpoint that accompanies
the subject, because the student will by this time have learnt how
to find out where the subject ends; instead of this, we shall put
the answer under the subject, in order that the two may be more
easily compared.
88. We first give examples in which the old rule is strictly
followed. Of these there are plenty.
J. S. BACH. Wohltemperirtes Clavier, Fugue 31.

8
A
This specimen of a simple tonal answer illustrates more than one
point of some importance. The subject is here in the tonic; the
D
34
[Chap. III.
FUGUE.
answer will therefore be in the key of the dominant; and, except
the first note of the second bar, every note of the subject be-
longing to the key of E flat must be answered by the corres-
ponding note of the key of B flat. It must be especially noticed
that though the note B flat (the dominant of E flat) is used four
times in the course of the subject, it is answered every time
except the first by F, and not by the tonic, E flat. The rule of
answering tonic by dominant, and dominant by tonic, applies only
to the beginning of a subject and to passages where a modulation to
the dominant occurs. In the present case the claims of the law
are satisfied as soon as E-B at the beginning of a subject has
been answered by B-E; after this, the rest of the subject is
transposed, as if the answer were real, into the key of the
dominant. The following notes of the subject are respectively
the subdominant, mediant, submediant, and dominant of E flat;
and they are answered by the subdominant, mediant, submediant,
and dominant of B flat-and so on, to the end of the answer.
There is no mistake which students are more apt to make in
beginning to write tonal answers than to answer dominant by
tonic every time these notes occur. This is almost invariably
wrong.
89. If we look at the second bar of the above example, we
shall find that an interval of a second in the subject has become
a unison in the answer. Whenever a subject begins with the
leap from tonic to dominant, it always, if answered tonally, causes
a change in the following interval. Here the first and third notes
of the subject are the tonic and subdominant of the tonic key;
the first and third notes of the answer are the tonic and sub-
dominant of the dominant key: but the difference in the size of
the first leap of the subject (a fifth), as compared with the leap of
a fourth in the answer, makes a difference also in the interval
between the second and third notes. We give two more illus-
trations of the same point-
(b) 8
A
J. S. BACH.
Wohltemperirtes Clavier, Fugue 17.
(a) S
S

A
J. S. BACH. Wohltemperirtes Clavier, Fugue 8.

At (a) a third in the subject becomes a second in the answer; at
(b) a second in the subject becomes a third in the answer. Note,
T
Chap. III.]
35
FUGUE.
in passing, the shortening of the last note of the answer at
(b)—(§ 57).
90. That the answering of tonic by dominant, and dominant
by tonic, applies only to the beginning of the subject is clearly
shown by the examples of real answers quoted in § 59 and § 83
(b), both of which contain the leap from tonic to dominant in the
second bar, not answered by the leap from dominant to tonic.
91. Though the general practice of the great masters is, as
has been already said, to answer the leap between tonic and
dominant tonally, a real answer under such circumstances is not
infrequent, especially when the leap is downwards—
(a) 8
J. S. BACH. Organ Fugue in G minor.
(6) 8
J
A
1
A
(c) 8
Sub
A
(d)
(e) 8
A
ن/
€
HANDEL.
?
'Susanna.
HANDEL. 'Saul.
HANDEL. Violin Sonata in A.
&c.
SCHUMANN. Mass in C minor.
&c.
In not one of these examples (and more could be given) is
dominant answered by tonic, but in each instance by the domi-
nant of the dominant key.
•
F
H


-


.
1

4
I
T
-
•
~!
•1
¿
36
Chap. III.]
FUGUE.
4
92. When the tonic goes to the dominant through the third of
the scale, the rule of the old text-books is that the answer should
be tonal. We give two examples by Bach-
J. S. BACH. Four Duets (No. 2).
(b)
(a) S

(b) S
A
A
93. We give first some tonal answers—
J. S. BACH.
Organ Toccata and Fugue in C.
In both these cases the dominant is answered by the tonic. But
these subjects belong to a large class—those that begin with the
notes of the tonic chord taken in succession. In such cases the
great masters give a real answer nearly, if not quite, as often as a
tonal one. We give specimens of both: one example of a tonal
answer to a subject of this kind has been already seen at § 89 (a).
Where the subjects are long we shall quote only the commence-
ment, as the rule is never intended to apply to the middle of an
answer, but only to its beginning.
J. S. BACH.
Cantata, "Ich hatte viel Bekümmerniss."

(a) S
A
&c.

&c.
J. S. BACH. Concerto for Two Claviers.

&c.
In both these cases the D is only an auxiliary or passing-note;
and it is quite evident that the subject commences with tonic
harmony. In our next examples no passing-notes are introduced;
Chap. III.]
37
FUGUE.
both begin with the notes of the tonic chord. Observe at (d)
another instance of the lengthening of the last note of the answer.
HAYDN. 'Seasons.

(d) 8
A
O
(6) 8
A
36
(c) 8
A
94. We now give a number of examples where the leap
between tonic and dominant has a real answer, because the
subject begins with the notes of the tonic chord-
J. S. BACH. Cantata, "Es ist dir gesagt.'
(a) 8
A
y
SEE
(c) S
A
ATHA
HAYDN. 5th Mass.
CLA


J. S. BACH. Cantata, "Bringet dem Herrn Ehre seines Namens.
eagle
J. S. BACH. Sonata in D.
&c.
&c.
"I


In all these instances, taken from the works of Bach, the answers
are real. After what has been said, no further explanation will
be required.
95. In the works of Handel we find a real answer in such
38
[Chap. III.
FUGUE.
✓
cases even more frequently than in the works of Bach. We give
five examples
(6) S
(c) S
A
A
b b
(e) 8
(d) 8
ន
A
A
A
(a)·8
A
HANDEL.
'Theodora.

HANDEL. 'Israel in Egypt.

HANDEL. 9th Organ Concerto.
tr

HANDEL. Ist Grand Concerto.
&c.
tr

96. In the following answer we see that J. Christian Bach, the
youngest son of the great John Sebastian, adopted the same plan
as his father—
HANDEL. 'Tolomeo.

&c.
J. CHRISTIAN BACH.

Chap. III.]
FUGUE.
39
97. Our next examples are more modern—
(a) S
A
(6) S
A
€
8
A
It is only needful to remark that in the latter part of example (a)
there is a modulation. The principle by which this part of the
answer is regulated will be explained in the next chapter.
98. In Cherubini's Treatise on Fugue we find the following
example of a real answer to a subject going to the dominant
through the third of the scale—
MENDELSSOHN. 'Christus.

(a) S
be
(b) 8
SCHUMANN. 'Faust.'

A
Cherubini gives this without a word of explanation; it is clear,
therefore, that he did not regard it as an irregularity.
A
99. Two more passages will complete our illustrations of this
point-
CLEMENTI. Gradus ad Parnassum, No. 45.
CHERUBINI. Treatise on Fugue.
&c.
VERDI. Requiem.
&c.
S
در



40
[Chap. III.
FUGUE.
100. If we examine and compare all the examples we have
given of subjects founded upon the notes of the tonic chord, and
taking real answers, we shall find that there is an important
principle involved in all of them. We have already shown that
the tonal answer is the result of the old modal systems (§§ 84, 85),
which prevailed before modern tonality, as now understood, was
fixed. In all these cases, however, the old rule gives way to a
higher and more important law, to which reference has already
been made, and which has a wider application. This is the
broad principle which is the very basis of fugal answer-that
tonic harmony should be answered by dominant, and dominant
by tonic. If we look at the tonal answers already given-for
instance, § 93 (c), (d)—we shall find that the strong suggestion of
tonic harmony in the first three notes of the subject is not replied
to by an equally strong suggestion of dominant harmony in the
first three notes of the answer. In both these examples the
second note destroys the feeling of the dominant at once.
When
the dominant as the second note of the subject is not followed by
another note of the tonic chord, the feeling of the tonic harmony
is not so pronounced; and here a tonal answer may frequently be
employed with advantage. In this case, however, adherence to
the old rule will sometimes injure the form of the answer. This
will be seen in the following example-
(b) 8
i
A
be
HANDEL. 'Hercules.'

&c.
Here the character of the subject is entirely ruined by the
monotonous repetition of the F's in the answer. A real answer
here would have been far more effective. In example (d) of
§ 91, where Handel has given a real answer, the effect of a tonal
answer would have been even worse-

101. The rule for the guidance of the student to be deduced
from the examples given is as follows :—
If a subject commence with the leap from tonic to dominant, and
the following note is not a note of the tonic chord, a tonal answer is
generally, though not invariably, preferable; but if at least the first
three notes of the subject are all notes of the tonic chord, the answer,
provided that no modulation takes place to the key of the dominant,
may be either real or tonal.
10
Chap. III.]
4I
FUGUE.
102. We now have to consider an important class of sub-
The old rule
jects-those that commence on the dominant.
again was here absolute-that when the subject began on the
dominant the answer must begin on the tonic.* This rule, like
that discussed in §§ 86, 87, is observed by the great masters in
the large majority of instances; but numerous exceptions are to
be found to it. A few examples of its observance will first be
given-
(b) 8
29
f
A
(a) 8
A
(d) 8
A
J. S. BACH. Wohltemperirtes Clavier, Fugue 13.
W

密
​In these answers, which contain no modulation, the first note is
the only one which differs from a real answer. The dominant in
the third bar of (b) is not answered by the tonic. Sometimes,
however (though much more rarely), the dominant is answered by
the tonic on its later appearances, as in the following answers—
A
J. S. BACH. Wohltemperirtes Clavier, Fugue 40.
J. S. BACH. Organ Fugue in E flat (St. Ann's).
(c)
8
&c.


Mendelssohn. 'Elijah,'

&c.
* If, however, the dominant was an unaccented note of small value, a real
answer was sometimes allowed even by the old theorists.
42
FUGUE.
[Chap. III.
103. Our next examples give further illustrations in the last
note of their answers of the rule given in § 69—
tr
(a) 8
A
(b) 8
S
A
A
At the second and third bars of (a) we also see an incidental
modulation into the key of the subdominant, already referred to
in § 41.
It will be observed that the answer here modulates
to the tonic (the subdominant of the dominant key).
104. When the subject begins on the dominant and leaps to
the tonic, the answer usually begins on the tonic and leaps to the
dominant-
HANDEL. 'Messiah.'

A
MOZART. Fugue for Piano, in G minor.

J. S. BACH. Art of Fugue, No. 3.
$

This example illustrates some other points besides that just
mentioned. It will be seen that after the first note, the whole
subject is in the key of the dominant. It is therefore answered
in the key of the tonic (§ 70). The final C sharp of the subject
cannot be considered as the leading note of D minor, for if
it were it would be answered by G sharp, the leading note of
A minor. It is the major third of A, and is answered by F, the
minor third of D, a rare instance of the converse of our examples
in §§ 68, 69, 103.
105. The student will have no difficulty in finding any
number of answers in which the general rule we have given is
adhered to; we now proceed to give examples in which it is not
observed. Our first group will be answers to subjects which
commence with the notes of the tonic chord-
(a) 8
J. S. BACH. Christmas Oratorio.

Chap. III.]
43
FOGUE.
(6) 8
be
f
A
(8
A
H₂
HSH
(c) 8
A
(d) 8
Jones
A
(e) S
A
HANDEL. Anthem, "Let God arise."
ま
​HANDEL. 4th Oboe Concerto.


#sp
eld
PADRE MARTINI.

SCHUMANN. 'Paradise and the Peri.
&c.

&c.
HUMMEL. 3rd Mass.


In all
These are parallel cases to those given in §§ 94-99.
of them the subject begins with tonic harmony and the answer
replies with dominant harmony. Notice in example (f) an
incidental modulation to the key of the supertonic minor.
imitation is here exact (§ 83).
The
44
FUGUE.
[Chap. III.
106. We next give instances in which the leap from dominant
to tonic is not followed by another note of the tonic chord-
HANDEL. Utrecht Te Deum.
(a) 8

(d) 8
(6) S
A
8
(a)
½ c
A
A
(c) 8
A
(e) 8
A
A
HANDEL. Anthem, "O come let us sing.”

BEETHOVEN. Mass in D.

BEETHOVEN. 'Mount of Olives.'

BEETHOVEN. 'Der glorreiche Augenblick.

The answer at (e) looks irregular; but there is here an implied
modulation (§ 118). The subject after the second note is
regarded as being in the dominant key, and therefore answered
by the corresponding notes of the tonic key.
107. Lastly we give examples in which the dominant is
followed by some other note than the tonic-
J. S. BACH. Cantata, "Gottes Zeit ist die allerbeste Zeit."
*
APA
#5
:

Chap. III.]
45
FUGUE.
(f) S
On
71
be
by
A
19
HU
(b) S
(c) 8
A
A
(d) 8
A
(e) 8
Be
A
J. S. BACH. Fugue for Clavier, in A.

J. S. BACH. Fugue (unfinished) in C minor.

be.
CECI
HANDEL.
Anthem, "Have mercy upon me, O God.”
HANDEL. 'Saul.'


&c.

Mendelssohn. 95th Psalm.

We have only to note with regard to these examples that in the first
bar of (b) is a not uncommon case, G sharp being answered not
by D sharp but by D natural. Such disregard of the exact
quality of intervals is not infrequent; we shall meet with more
instances later. At the end of (ƒ) the subject modulates to the
dominant; the answer here is exceptional, and will be discussed
in our next chapter.
·
46
FUGUE.
[Chap. III.
(6
108. We have given quite enough examples to prove that the
rule as to answering dominant by tonic at the commencement of
a subject is by no means so absolute” as it is declared to be by
many theorists.
For this there are two reasons. First there
is the general principle already referred to in § 100, that tonic
harmony in the subject should be replied to by dominant harmony
in the answer. This is illustrated by the examples in §§ 105, 106.
Besides this, the melodic form of the subject should be kept
unchanged as far as possible; and it is quite evident that in
many cases the great composers felt this to be of much more
importance than the keeping of an old rule which was made
before modern tonality was established.
109. A further proof that but little weight was attached to the
necessity for a tonal answer is found in the fact that sometimes in
the first exposition of a fugue the first answer will be tonal and
the second real, as in the following case—
S

pre
FE&C.
A 1.
(a) S
(6) S
Here the first answer is tonal, the first note being shortened
(§ 57); but the second answer (still forming part of the ex-
position, in which strictness is expected) is real. In the later
entries of a subject, we continually meet with real answers where
tonal have been given at first.
110. We saw in § 104 a subject which, except the first note,
was in the key of the dominant, the answer being in the key of
the tonic. We have also seen, in discussing real answers, how an
extension of the same relation of subject and answer rendered
an answer sometimes possible in the subdominant key (§ 71). A
similar answer is also possible where the first note of the subject
is answered tonally, as in the following examples—
J. S. BACH. Cantata, "Es ist euch gut dass ich hingche."
A
J. S. BACH. Organ Fugue in A.
&c.
A
A 2.
&c.

BUXTEHUDE.

Chap. III.]
47
FUGUE.
:.
(c) S
A 1.
A 2.
A
(b) 8
In example (a) we have quoted the counterpoint accompanying
the answer, to prove more clearly that the latter is in the sub-
dominant key. The two examples by Buxtehude are very similar
in the character of their subjects. In all these subjects the
prominence given to dominant harmony, which we have already
mentioned as a feature of all subjects which are answered in the
subdominant, will again be noticed.
III. Sometimes in the exposition of a fugue the first answer
is in the key of the dominant, and the second in that of the
subdominant, as in the following passages—
J. S. BACH. Cantata, "Es wartet Alles auf Dich."
(a) 8
A 1.
£
BUXTEHUDE. Organ Fugue in G minor.

A 2.
4
jd
SCHUMANN.
Neujahrslied.'
112. The proper method of answering subjects that modulate
into the key of the dominant will be treated in the next chapter.
We now sum up our conclusions with regard to the subjects we
have already dealt with. From a careful investigation of the
practice of the greatest composers, we deduce the following
principle:-
Though frequently expedient, and even preferable, a tonal
answer is never absolutely necessary for any subject which does not
modulate between the keys of the tonic and dominant.*
* A merely incidental modulation to the dominant (as in the example to § 73)
does not necessitate a tonal answer.
1


21
t
48
[Chap. III.
FUGUE.
113. In concluding this chapter it is needful to give the
student a most urgent warning with regard to the use of this
book. It is not written as a ""
cram" for examinations; and
although all the rules given in the present chapter are founded
upon the practice of the great masters and enforced by their
example, yet in the present condition of musical examinations,
any student who attempts to carry into practice the principles here
given will almost inevitably be "ploughed." The old theorists
mostly follow one another blindly, like a flock of sheep through a
hedge; and examiners in general adhere to the musty rules of
two hundred years ago, taking little or no account of the progress
made by music since that time. The old rules have therefore
been in all cases given in this chapter, and those who are going
up for examination had better adhere to them until examiners
become more enlightened and liberal. Our object in this, as in
the other volumes of this series, has been to found our teaching
on the practice of the great composers who have brought our art
.to its present state of advancement; but Bach himself breaks far
too many of the antiquated rules to have had much chance of
passing, had he gone up for a Doctor's degree at one of our
universities.
#
1
Chap. IV.]
特色
​FUGUE.
49
CHAPTER IV.
THE ANSWER-CONTINUED.
114. In our last chapter we showed that a tonal answer,
though often advisable, was never absolutely necessary for any
subject which did not modulate to the key of the dominant.
We have now to deal with the treatment of the answer to
subjects in which such a modulation occurs.
115. In order to render intelligible the principles on which
we shall have to proceed, it is needful here to anticipate some-
what, and to say that in the exposition (§ 11) of a fugue, only
two principal keys are employed-mostly tonic and dominant,
occasionally tonic and subdominant. In an enormous majority
of cases the keys will be tonic and dominant. We saw in the
last chapter that if the subject were in the key of the tonic, and
remained in it, the answer would be and remain in the key of
the dominant. The third voice will almost invariably enter with
the subject, and the fourth, if there be four, with the answer. In
such cases the answer will generally be real, or if there be any
tonal alteration, it will only affect the first two or three notes of
the subject.
116. But now suppose that instead of ending, as it begins, in
the tonic key, the subject modulates to and finishes in the
dominant, as in the case given at § 57 (b). It is quite clear
that if we give a real answer in this case, the answer will end in
the dominant of the dominant, that is, in the key of the
supertonic-

fe
Here we have not only introduced a third principal key, where,
as was said in the last paragraph, there ought only to be two;
but (what is still more objectionable) we have modulated to an
unrelated key (Harmony, § 225). To get back to the tonic key
for the entry of the third voice, we shall have to introduce an
awkward and probably clumsy join by means of a codetta. In
order not to wander away into an unrelated key, and to confine
ourselves to the two chief keys already mentioned, which will
always be at a distance of a fifth apart, we require a tonal answer
here, and adhere to the old rule. This is:-If the subject begin
in the tonic, and modulate to the dominant, the answer must begin
in the dominant and modulate to the tonic.
E
50
FUGUE.
[Chap. IV.
117. This important rule needs to be supplemented by
another :-The modulation in the answer from dominant back to
tonic must be made at the same point at which the modulation was
made in the subject from tonic to dominant. This rule will be fully
illustrated as we proceed.
118. The modulation in a fugue subject may be either
expressed or implied. It is expressed when the leading note of
the dominant key appears as a note of the subject, as in example,
$57 (b). It is implied when, although the leading note of the
new key is not actually present, the whole form of the melody,
and especially its last notes, show more or less distinctly that
they are looked at as belonging to the key of the dominant, and
when they produce the mental effect of being in that key.
119. The examples now to be given will show what is meant
by implied modulation-
J. S. BACH. Cantata, "Ich hatte viel Bekümmerniss."

(a)
f
(c)
(6)
56
(d)
8
J. S. BACH. Cantata, "Gott ist mein König.'

It will be seen that in all these passages the mental impression of
the last notes is unmistakably that of a modulation to the
dominant; and it may be stated as a general rule that, whenever
a subject ends with the descent from the submediant to the
dominant of the tonic key, a modulation is implied, and these
two notes are considered to be the supertonic and tonic of the
dominant key.
A
J. S. BACH. Cantata, "Ein' feste Burg."

120. Sometimes the great composers choose to consider a
modulation as implied when there is no absolute necessity for it—
J. S. BACH. Organ Fugue in C.
HANDEL. 'Saul.

Here we see from the answer given by Bach that he implies a
modulation in the second bar, though a real answer would have
been perfectly correct. Had he regarded E as the third of C, he
3

Chap. IV.]
51
FUGUE.
would have answered it by B, the third of G; but he regards it as
the sixth of G, and therefore answers it by A, the sixth of C.
When a subject modulates to the key of the dominant, all that
part which is in the tonic key is transposed in the answer a fifth
higher, or a fourth lower; and that part which is in the key of
the dominant is transposed a fourth higher, or a fifth lower.
121. The next question is, when there is a modulation, at
what point are we to consider it as taking place? The general
practice of the great composers is to regard the modulation as being
made at the earliest possible point, and from that point to consider
every note in its relation to the new key.
122. That the student may quite clearly understand what is
meant by this, we will take all the notes in the scale of C major,
and show how each can be correctly answered in two ways,
according to the point of view from which it is looked at. Sup-
posing our fugue to be in the key of C, and that a modulation to
the dominant occurs in the subject, the answer to each note
will depend on whether that note comes before or after the
modulation :—
C, if regarded as tonic of C, will be answered by G; but if
regarded as the subdominant of G, it will be answered by F,
subdominant of C.
the
D, as the supertonic of C, will be answered by A, the supertonic
of G; but D, as the dominant of G, will be answered by G, the
dominant of C.
Similarly E, as the third of C is answered by B, the third of
G;
but if considered as the sixth of G (as in the example in
§ 120), it will be answered by A, the sixth of C.
F, the subdominant of C, is answered by C; but, as the minor
seventh of G, it will be answered by B flat.
G is answered by D when it appears as a dominant, and by C
when it is treated as a tonic.
A as a submediant is answered by E, and as a supertonic by D.
B, the leading note of C, is answered by F sharp; but if the
context shows it to be the major third of G, it will be answered
by E, the major third of C.
123. If the student clearly understands this possible double
relation of every note it will save him an infinity of trouble in
making a correct tonal answer. We will now analyze a few short
examples illustrating the principle just laid down that the modu
lation should be considered as taking place as early as possible.
124. As an extremely simple example, we will first take the
short passage by Mozart, already quoted in § 57-
MOZART. Quartett in G, No. 14
8
A
•

52
[Chap. IV
FUGUE.
$
Here there is in the subject a distinct modulation to D; the
answer therefore modulates back to G. B, the second note of
the subject, could have been answered either by F sharp or E; but
had Mozart answered it by F sharp, the resemblance of answer to
subject would have been spoilt-

There would, besides, have been another fault of almost more
importance. The subject has a distinct modulation to the
dominant; the last three notes unquestionably suggest the key
of D. The answer therefore should as clearly suggest G; but in
its altered form it does not do so at all, as the first four notes all
belong to the tonic chord of D. Neither shall we improve
matters by putting B for the third note of the answer instead of
A; for then the answer will not distinctly suggest any key at all,
the first three notes now being notes of the tonic chord of
B minor. There is, therefore, no other correct answer than that
which Mozart gives, and, having reached the dominant key at
the second note, he regards all the rest of the subject as being in
that key, and accordingly treats E as supertonic of D-not as
submediant of G-and answers it by A, and not by B. The
last two notes of the subject, of course, admit of only one
answer.
125. After our full analysis of this example, few words will be
needed in explanation of the following, which illustrate the same
point-
(a) S
A
(6) S
☺
A
6
HANDEL. Israel in Egypt.
J. S. BACH. Matthäus Passion.
#
At (a) the C in the subject is regarded as sixth of E minor, and
answered by F; and at (b) G sharp is considered not as the leading
note of A minor, but as the chromatic major third of the
dominant, and it is accordingly answered by the major third of
the tonic.
126. The reason why the tonal change is made as early as
possible is because in this way a closer general resemblance of the
1


Chap. IV.]
53
FUGUE.
answer to the subject is obtained than if the modulation be
regarded as taking place later. Sometimes, however, the form of
the subject does not admit of an early change—
J. S. BACH. Toccata and Fugue for Organ, in C.

(6)
The first notes of this subject were spoken of in § 93. It is
impossible here to regard the modulation as taking place till after
the subdominant harmony at (a). The length and variety of this
subject render it a very suitable illustration of the rules we gave
in § 122. The student will here see nearly every note of the
scale of C in both its relations; we have even at (b) the rare case
of the subdominant considered as the minor seventh of the
dominant.
(a)
127. It is very important to be able to tell when answering a
subject that modulates, in which of its two possible aspects any
note is to be regarded. The only notes with which any difficulty
is likely to be found are the third and the seventh of the tonic,
which are also the sixth and third of the dominant. An examina-
tion of the fugues of the great masters will guide us in laying
down definite rules for the treatment of both these notes.
A
128. As we have to regard every note in its relation to the
new key as early as possible, the third should be considered as
the sixth of the dominant, and answered by the sixth of the tonic,
as in our examples to §§ 120, 124, and 125 (a), excepting, 1st,
when it comes between other notes of the tonic chord, or is
followed immediately by the tonic; and 2nd, when the subsequent
appearance of the subdominant in the subject shows that the
modulation cannot yet have taken place. The following passage
shows the third in both aspects-
J. S. BACH. Cantata, "Lobe den Herren, den mächtigen König."

(a)
The F's in the second bar of the subject prevent our regarding it
as in the key of G; but at (a) the change is made at the earliest
i
54
FUGUE.
Chap. IV
opportunity. The first E, being the resolution of the F in the
preceding bar (the chord being the dominant seventh), must of
course be the third of the tonic, and must be answered by B; the
second E is treated as the submediant of G, and answered by the
submediant of C—viz., A.
129. We give a few more illustrations of the same point.
J. S. BACH. Cantata, "Gott ist mein König."
(a) 8

A
Here the second note of the subject is regarded as the sixth of
the dominant, and all the rest is plain sailing.
(b) 8
b
A
bac
130. In our next example
(a) S
A
Here the presence of the subdominant prevents our regarding
the subject as being in the dominant key till we reach (a), where
the third of the scale is treated as sixth of dominant, and answered
accordingly. There is an implied modulation (§ 118) in the
subject, for it is very rare to find a subject ending on the leading
note. It is almost invariably regarded (as here) as the third of the
dominant key.
MOZART. Mass in F, No. 6.

tr
(a)
HANDEL. Concerto Grosso in C
tr

(a)
the change is not made at the earliest possible moment (in the
first bar), for this would have disfigured the subject too much.

&c.
The mental effect of the music is distinctly that of the key of C,
till we come to (a) where the double significance of the third of
the scale is very clearly shown. The first E, being followed by

Chap. IV.]
55
FUGUE.
C, is the third of the tonic, and is answered by the third of the
dominant; the second E is not followed by a note of the tonic
chord, and is therefore regarded as sixth of the dominant. Our
next example
(b) 8
A
J. S. BACH. Cantata, "Singet dem Herrn ein neues
illustrates a different point. The first F in the third bar cannot
be regarded as belonging to the dominant key, because of the
G natural that follows, neither can the second which resolves the
preceding G; but the F preceding the G sharp is treated as the
submediant of A.
131. The same principles will guide us in dealing with the
leading note. Let the fundamental principle be thoroughly
grasped that the tonal change must be made as soon as possible,
and the whole thing is easy. If a subject modulates, the leading
note must be always treated as the third of the dominant, and
answered by third of tonic, except when it is merely an auxiliary
note of the tonic to which it at once returns, e.g.—
J. S. BACH. Wohltemperirtes Clavier, Fugue 2.
Joht
fire
This subject does not modulate, but it shows the use of the
leading note as an auxiliary note.
132. The following examples
(a) 8
8
Lied."


A
A
J. S. BACH. Organ Fugue in C.

J. S. BACH. Wohltemperirtes Clavier, Fugue 18.


56
[Chap. IV.
FUGUE.
!
(c) 8
bbc
A
show the leading note very early in the subject treated as the
third of the dominant, and answered by third of tonic. The
following notes of the subject are all answered as belonging to
the dominant key.
(a)
133. So strongly is the leading note felt as the third of the
dominant that it is not seldom answered by the third of the tonic,
even when there is no modulation—
J. S. BACH. Wohltemperirtes Clavier, Fugue 19.
(6) 8
Here Bach treats the second and third notes of his subject as
the third and sixth of E, and answers them by third and sixth of
A, though the subject ends in the key of the tonic.
In our
next example
MACFARREN. "The Resurrection.
A
NAUMANN. 1st Mass.



A
the second bar is treated as containing a modulation to the key
of E, the leading note being answered by the third of the tonic.
134. If the subject begin in the dominant, and modulate to
the tonic, the process will be reversed. We shall now, as soon as
possible, consider the sixth of the dominant as the third of the
tonic, and the third of the dominant as the seventh of the tonic.
S
BUXTEHUDE.

T
(a)
y
The first half of this subject is in A; in the second bar it
modulates to D; and F, the sixth of A, is therefore at once
regarded as the third of the tonic.
135. Our next example shows the third of the dominant in
both its aspects.
Chap. IV.]
57
FUGUE.
8
A
SD
Bet
Let it be noticed that this subject might have been considered as
in the key of B flat throughout; it would then have taken a real
answer. Kirnberger has preferred to regard it as in F until the
last two bars. The tonal change might have been made after
the B flat in the fifth bar; but this would have altered the form
of the subject needlessly. The point, to illustrate which this
passage is quoted, is the treatment of the A in the penultimate
bar. It is first regarded as third of dominant, and answered by
D, and then looked at as leading note of B flat, and answered
by E natural. We saw in § 88 how two notes in the subject
were answered by the same note; here is the converse-the
same note in the subject has two different notes in the answer.
A
136. The answering of one note by two is sometimes to be
met with in the case of the dominant and supertonic, as in the
following passage-
J. S. BACH. Fugue for Clavier, in A.
fo
8
A
(6) 8
A
(a)
Here the supertonic at (a) is first answered by the supertonic of
E, and then treated as dominant of E, and answered by dominant
of A. Evidently had it been so regarded the first time, it would
have utterly spoilt the answer.
J
137. Sometimes the dominant is answered first by tonic and
then by supertonic, even when there is no modulation.
(a) 8
HANDEL. Anthem, "I will magnify thee."
KIRNBERGER.

(a)
HANDEL.
}
Belshazzar.'
.
}
F




58
[Chap. IV.
FUGUE.
:
138. If a subject begins in the tonic, modulates to dominant,
and returns to tonic, the answer makes the converse modula-
tions-from dominant to tonic, and back to dominant. No new
principles are involved here; two examples will be sufficient.
J. S. BACH. Cantata, "Sehet, welch 'eine Liebe."
(a) 8

find
(6) S
55b Q
BE
A

A
E. PROUT. 2nd Organ Concerto.


139. In general, any leaps of a dissonant interval, such as a
seventh, especially of an augmented or diminished interval,
should be reproduced exactly in a tonal answer. The student
will find illustrations of this in several of the examples already
given. At § 93 (c) and § 126 will be seen a diminished fifth;
at § 125 (6) a diminished fourth; and at § 132 (6) an augmented
fourth, all of which are retained in the answers. We add one
example of a diminished seventh
J. S. BACH. Wohltemperirtes Clavier, Fugue 44.
S

A

This subject also contains a diminished fifth which is retained in
the answer.
Chap. IV.]
FUGUE.
59
140. There is, however, one important exception to the rule
just given. When one of the two notes forming the dissonant
interval is the tonic or dominant, and the modulation is made at
that point (sometimes even when no modulation is made), a leap
of a dissonant interval in the subject will often become a leap of
a consonance in the answer, and vice versa. We give some
examples-
(a) 8
M
(b) S
A
A
Here both the B and A of the subject are answered by E, on
the principle explained in § 88. Our next example shows the
reverse case—an octave in the subject becoming a seventh in the
answer-
S
A
KIRNBERGER.

(a)
•
&c.
圭
​Here there is an implied modulation, and the change to the
dominant key is assumed as early as possible (§ 121). Obviously
it cannot be before the third bar at (a). The first G is treated as
third of tonic, and the second as sixth of dominant (§ 128).
ALBRECHTSBERGER.

141. In our example (a) of § 110, we see a seventh in the
subject becoming a sixth in the answer. The following interest-
ing passage illustrates both the rule and the exception that we are
now discussing-

KIRNBERGER.
E
The tonal change at the beginning of the answer alters the
seventh into a sixth, but the claims of the tonal answer having
been satisfied in the first bar, the augmented and diminished
intervals in the second and third bars are exactly imitated.
60
FUGUE.
[Chap. IV.
2
:
142. In the following passages we see an augmented fourth in
the subject becoming a major third in the answer.
J. S. BACH. Cantata, " Ihr werdet weinen und heulen."

(a) 8
A
Notice that here the augmented second and the minor seventh in
the second bar are retained in the answer, and the change of
interval comes where the modulation takes place.
(6) 8
A
A
This is a similar instance to the last. The form of the melody
renders it impossible to introduce the modulation earlier.
MOZART. Mass in C, No. 4.
(c) S
This is a curious example, because Mozart by the way he answers
the subject implies three modulations-to the dominant and back
in bar 2, and again to the dominant at the end. It would have
been simpler to treat the first F sharp, which is almost imme-
diately contradicted, as a chromatic note, and to have given the
answer the following form—-
S
ALBRECHTSBERGER.



which would have been equally correct here (compare § 65).
143. Our next example shows the converse case, a major
third in the subject becoming an augmented fourth in the
answer.
A
(a)
ALBRECHTSBERGER.

Chap. IV.]
61
FUGUE.
This passage illustrates the partiality of fugue writers for treating
the third of the tonic as the sixth of the dominant, and the
leading note as the third of the dominant. There is no necessity
for a tonal change till (a), and the answer might have been

$
Here we have another example of what we have already seen
more than once, that it is sometimes possible for a subject to
have two different answers, both correct. The student will learn
by experience, in such cases, which is the better.
144. Though, as a general rule, the transposition of the
subject a perfect fourth or fifth should be strictly carried out,
we often find the position of the semitones disregarded, a semi-
tone being answered by a tone, and a tone by a semitone. This
is especially the case with the subdominant and leading note, as
will be seen by the following passages, selected from a much
larger number we had marked for quotation—
(b) S
(c) S
220
25
A
J. S. BACH. Fughetta on "Allein Gott in der Höh' sei Ehr'."
(a)
S

*
A
* *
*
J. S. BACH. Mass in B minor.

MOZART. Litany in B flat.


62
FUGUE.
[Chap. IV.
1
145. On the same principle-the disregard of semitones—
must be explained the occasional answering of a major by a
minor third, or a minor by a major, in the course of a subject.
This must not be confounded with the regularly allowed substitu-
tion of a major for a minor third, at the end of a subject, spoken
of in § 69.
J. S. BACH. Organ Fugue in B flat.

(c) S
A
(a) S
(b) 8
A
36
A
A
&c.
HANDEL. 'Muzio Scevola.'

N.B.
&c.
In all the above passages the alterations in the answer are
marked with an asterisk. Students are advised not to imitate
such freedoms as these, but in all cases to preserve the position
of the semitones, except, of course, at the moment of modulation.
146. Before leaving the subject of tonal answers, it must be
added that we occasionally (we might also say exceptionally) find
the dominant key answered by the supertonic, instead of by the
tonic. Sometimes this is in an incidental modulation, as in the
following passage—
HANDEL. Dettingen Anthem.
S
P. WINTER. 'Stabat Mater.


&c.
f
Here the answer at the "N.B." is, to say the least of it, unusual.
The subject appears to commence in the dominant, and to
modulate into the tonic; and the regular answer would certainly
have been

&c.
Chap. IV.]
63
FUGUE.
147. Sometimes, though very seldom, we find a final modula-
tion to the dominant answered by one to the supertonic, as in
the example (f) of § 107, where, however, Mendelssohn har-
monizes the last notes of the answer in F minor, instead of F
major, so as not to leave the circle of nearly related keys. In the
following passage there is a distinct modulation to A major in the
answer-
8
8
A
A
148. Our last illustration of this point is instructive.
LEO. "Dixit Dominus."


J. S. BACH. Wohltemperirtes Clavier, Fugue 10.
Notice, in passing, the minor third at the end of the subject
answered by a major third (§ 69). We see here the only example
in all Bach's works of a real answer given to a subject that
closes in the key of the dominant; but here it can be not only
explained but justified. We have already spoken (§ 139) of the
importance of retaining augmented and diminished intervals as
far as possible in the answer. Had Bach given a tonal answer
here,

he would have had to sacrifice the diminished fifth in the second
bar, and the harmonic framework of the bar would have been
We said,
entirely changed. But there is a further reason here.
in § 116, that a tonal answer was required when the subject
modulated to the dominant, in order to get back to the tonic
for the entry of the third voice. But the fugue we are now
discussing is for two parts only; and after the first entry of the
answer, the exposition (§ 11) is complete, and we reach the first
episode, where, as we shall see later, modulation usually begins.
There is, therefore, here no occasion to return to the tonic key.
The same reason may probably explain the putting the second
answer into the key of the subdominant, noticed in § III.
Students should always keep to the regular rule, and answer a
subject modulating to the dominant by a return to the tonic.
64
[Chap. IV
FUGUE.
2
149. Chromatic subjects usually take real answers, unless
there be a modulation expressed or implied.
(c) S
S
(a)
(6) S
A
A
a se
S. BACH. Toccata in F sharp minor.
S

A
fot
At (6) the leap of a fifth is answered tonally, but the chromatic
passage itself is exactly repeated. The answer is in the sub-
dominant (§ 71.) At (c) other notes occur between the chromatic
notes.
J. S. BACH. Fugue for Clavier, in E flat.

150. Sometimes a composer has chosen to consider a modula-
tion implied where there is no real necessity for it.
MOZART. Quartett in D minor, No. 13.
P
Fe
MOZART. Mass in C minor.


Here a real answer, as at § 149 (a), would have been much more
usual, and (with all respect to Mozart, be it said) much better.
The threefold repetition of D spoils the form of the answer.
151. If there be a modulation before the chromatic notes
are introduced, such notes must be considered as belonging to
the new key, and answered accordingly—
HANDEL. 'Jephtha.
(a)

:
1
Chap. IV.]
65
FUGUE.
(6) 8
8
A
A
Kirnberger.

152. Fugue subjects are sometimes answered by inversion.
In this case the answer is not generally in the key of the
dominant; but that species of inversion is used in which
dominant is answered by tonic, and tonic by dominant (Double
Counterpoint, §§ 281, 282). Sometimes the answer by inversion is
given in the first exposition, as in Bach's 'Art of Fugue,' No. 5-
J. S. BACH. Art of Fugue, No. 5.
8

&c.
A

More frequently, however, this device is reserved for the later
developments of the fugue, in order to heighten the interest,
as in Nos. 15, 20, and 46, of the 'Wohltemperirtes Clavier.'
An answer by inversion is much more common with a minor
subject than with a major.
153. We also sometimes find answers by augmentation and
diminution. In these again there is no need that the answer
should be in the dominant key. The object of putting the
answer in the dominant is to prevent its being a mere monotonous
repetition of the subject; and this end is sufficiently attained
either by inversion or by altering the lengths of the notes. In
Nos. 6 and 7 of the Art of Fugue' will be seen examples, too
long to quote here, of answers by augmentation and diminution.
154. Sometimes, especially in vocal fugues, in order to keep
the answer in a more convenient compass, the change of an
octave in pitch is made in the course of the answer, as in the
following passage-
SCHUMANN. Requiem.

777
A similar example, which is familiar to everybody, will be found
in the "Amen" chorus of the 'Messiah.'
F
66
[Chap. IV.
FUGUE.
I
155. It is often said that there are no rules without excep
tions; and in the works of all the great masters we occasionally
find fugue answers which cannot be explained on any of the
principles laid down in this chapter. As our last illustrations, we
give one specimen by each of the greatest composers, of an
irregular fugue answer. If the student has mastered the contents
of this chapter, no notes will be needed; he will see at once
wherein the irregularity consists.
(a) 8
J. S. BACH. Fugue for Clavier, in A minor.

III
H
(e) 8
A
(b) S
€
(ƒ) 8
A
A
A
fo
(c) S
學
​||(α) 8
b
A
A
HANDEL. 'Choice of Hercules.'
Key: C minor.

Key: F major.
HAYDN. 'Creation.

MOZART. Te Deum.

&c.
BEETHOVEN. Mass in C.

WEBER. Mass in E flat.

1
Chap. IV.]
67
FUGUE.
6) 8
€
A
(h) 8
be
A
MENDELSSOHN. Fugue in E minor.

SCHUMANN. Fugue, Op. 72, No. 2.


கீ
The only remarks required by these examples are that (b) has
an independent orchestral accompaniment, the harmony clearly
proving-what does not appear from the quotation itself—that
the subject ends in C minor, and the answer in F major; and
that () may possibly be considered an extreme instance of the
disregard of semitones spoken of in §§ 144, 145.
156. We have now arrived at the end of a very long and
difficult task-that of explaining the principles of fugal answer.
The rules here given differ widely in some respects from those
generally laid down; but not one new rule has been advanced
which we have not justified by the example of the greatest
composers. We shall now, by way of summary, endeavour to
put the general principles into the fewest possible words.
I. The answer to a subject which is in the key of the tonic
should be as a rule in the key of the dominant; but if dominant
harmony is prominent in the subject, the answer may occasionally
be in the subdominant.
II. A real answer is possible for any subject which begins and
ends in the key of the tonic without modulating to the dominant ;
but if the subject begins with a leap between tonic and dominant
commences on the dominant, a tonal answer is mostly
preferable.
or
III. If the subject modulate between the keys of the tonic
and dominant, the answer should make the converse modulations
between dominant and tonic.
IV. A modulation should always be made as early as
possible. In a modulation from tonic to dominant consider the
68
[Chap. IV.
FUGUE.
third and seventh of the tonic as sixth and third of dominant as
soon as the modulation can be considered as having taken place,
and answer them accordingly.
157. These few sentences embody all the fundamental
principles of a fugal answer; the less important details have
been dealt with in this and the preceding chapter. The student
who has thoroughly understood the rules here given will have but
little difficulty in answering any fugue subject that may be set
him, unless (as is sometimes the case in examinations) a bad and
unsuitable subject is given as a "catch." In such cases, he must
trust to his luck; we have seen subjects in examination papers to
which a good answer was absolutely impossible.
158. We conclude this chapter with giving a number of
fugue subjects, original and selected, for the student to answer.
We also, as a useful exercise, give a few answers to which he is to
find the subjects. This will of course be the converse process.
If the answer ends in the key of the tonic, the subject must
have ended in the key of the dominant, and vice versa; if the
answer begins with the dominant, the subject most probably
began with the tonic. First ascertain in what key the answer
ends, and if there has been a modulation, make that modulation
as early as possible in the subject. The rules for the treatment
of the third and seventh of the tonic (§§ 128-133) will be of
considerable assistance in this matter.
EXERCISES.
(1.) Find the answers to the following subjects—
(I.)
efc
(III.)
(IV.)
(V.)
(VI.)
(VII.)
(II.)
Obe







OF
Chap. IV.]
69
FUGUE.
(VIII.)

Ju
O
(IX.) *
(X.)
(XII.)
DI
(XIII.)
5
F
(XIV.) *
4
(XV.)
(XVI.)
(XVII.) *
(XVIII.)
(XIX.)
Ce
(XX.)
(XXII.)
(XXIII.)
•Tele
#
葬
​(XI.)
(XXI.)
Freunde
* Subjects marked with an asterisk can have more than one correct answer.
1















70
[Chap. IV.
FUGUE.
(XXIV.)

(XXV.)

强
​(XXVI.)
(XXVII.)
泰
​(XXVIII.) *
(XXX.)
3
(III)
5
(IV.)
(V.)
(VI.)
tr
(VII.)
(2.) Find the subjects of which the following are the
answers——
(I.)
tr
(XIX.) *
豆漿
​(II.)
鞋
​tr
Jeg











향
​
Chap. IV.]
. 71
FUGUE.

f
(VIII.)
Te
(IX.)
(x.)
f
S




(XI.)
(XII.)

NOTE.-The greater part of these answers are taken from
fugues by Bach. All the more elaborate and difficult ones are
from his works; and the trouble involved in finding the proper
subjects will be well repaid.
72
[Chap. V.
FUGUE.
1
.
13
THE COUNTERSUBJECT.
159. In our first chapter (§ 10), we defined a Countersubject
as "a counterpoint which accompanies answer or subject
systematically, though not of necessity invariably." We have
now to consider the essentials of a good countersubject, and
to endeavour to show when its introduction into a fugue is
advisable.
(a)
be
CHAPTER V.
160. The first and most important requisite for a counter-
subject is, that as it has to accompany either the subject or the
answer in whatever part these may appear, it must be written in
double counterpoint with the answer, as an accompaniment to
which it is first heard. The double counterpoint is, in by far
the largest number of cases, in the octave, but it is also sometimes
in the tenth or twelfth. Sometimes a countersubject which has
been used in the octave at first is subsequently employed in one
of the other intervals. In Double Counterpoint will be seen in
§ 163 an example of a countersubject used both in the octave
and in the tenth; and at § 175 of the same book a similar
instance of the octave and the twelfth.
the
161. A most important point in writing a countersubject is
individuality of melodic character, and contrast of rhythm as
compared with the subject (Double Counterpoint, § 129). This
will be best illustrated by examples, which we shall mostly take
from Bach's 'Wohltemperirtes Clavier,' as being a work accessible
to everybody.
162. In our first examples
CS
!
·
J. S. BACH. Wohltemperirtes Clavier, Fugue 2.



Chap. V.]
73
FUGUE.
(b)
W
tr
tr
S-
CS-
J. S. BACH. Wohltemperirtes Clavier, Fague 37-


te be
the countersubject (CS.) is mostly in longer notes than the
subject, though at the beginning of (a) contrast is secured by
accompanying the quavers of the subject by semiquavers. Let
the student play the countersubjects by themselves, and notice
how different they are from the subjects, and at the same time
how thoroughly suited to them in character.
163. Our next illustration shows the opposite case—
J. S. BACH. Wohltemperirtes Clavier, Fugue 44.
A
傅
​tr

CS

tr
Here the countersubject does not enter with the first note of the
answer; but between it and the subject are a few notes of codetta
(§ 62). This often happens; sometimes, as will be seen presently,
only a part of the subject or answer is accompanied by the
countersubject. In the above passage we see a subject in long
notes accompanied by a countersubject of very short notes.
164. On its first appearance, in company with the answer, the
countersubject should be in the same key as the answer. In
the example last given the answer is in E minor, and the counter-
subject is no less distinctly in the same key. Sometimes, however,
as in our example to § 67, the key of the answer is not clearly
defined by the countersubject until nearly the close.
74
FUGUE.
[Chap. V.
165. It was said in the last chapter (§ 115) that the third
voice in a fugue almost invariably entered with the subject. In
the very common case in which the subject is in the key of the
tonic throughout, the answer will be in the key of the dominant.
In order to return speedily to the tonic key, and to allow the
third voice to enter at once, we often find in such cases that at
the end of the countersubject the leading note of the dominant
key is flattened, becoming the subdominant of the tonic key.
J. S. BACH. Wohltemperirtes Clavier, Fugue 33.

#30
S-
S
CS-
8
A-
CS
X
d

Here the subject ends in E; the answer and countersubject are
in B. To enable the third voice to enter immediately, a return is
made to the key of E at the end of the third bar, by contradicting
the A sharp. Where this is not done, it is mostly necessary (as
will be seen in the next chapter) to introduce a codetta before the
entry of the third voice. The evasion of a full cadence in
the dominant key by the device just explained is frequently called
by its Italian name, inganno, i.e., "deception"-a deceptive
cadence.
&c.
166. Sometimes the countersubject is constructed of material
suggested by the subject itself, as in the following passage.
J. S. BACH. Wohltemperirtes Clavier, Fugue 18.
A-

CS


Here the figure of the subject
furnishes the chief idea
for the countersubject. More frequently, however, the counter-
!
Chap. V.]
75
FUGUE.
subject contains an entirely fresh idea, as in the examples
previously quoted.
167. It is in general desirable that the countersubject should
contain some distinct melodic or rhythmic idea, which may be
used later for codetta or episode. A particularly fine example of
this will be seen in the twelfth fugue of the 'Wohltemperirtes
Clavier.'
J. S. BACH. Wohltemperirtes Clavier, Fugue 12.
12b
S-
8
be the be
3
CS
Notice here the strongly marked contrast between the subject and
the countersubject. This fugue contains altogether six episodes
(bars 16-19, 22-27, 30-34, 37-40, 43-47, and 50-53), all of
which are founded on the first six notes of the countersubject—
3
A


168. Not infrequently the countersubject accompanies only a
part, and not the whole of the subject or answer.
J. S. BACH. Wohltemperirtes Clavier, Fugue 34.
D
W


C8-
A
3
76
[Chap. V.
FUGUE.

1
That the countersubject has only the limited extent here marked
for it, is proved by the fact that the rest of the counterpoint does
not systematically reappear later in the fugue as an accompaniment
to the subject or answer (see § 298, where the whole fugue is
given in score and analyzed).
10
169. In tonal fugues that modulate to the dominant, the entry
of the countersubject is often deferred till after the modulation
has taken place. This allows the countersubject to appear without
alteration against either subject or answer.
J. S. BACH. Wohltemperirtes Clavier, Fugue 24.
tr
**
A-
8-


CS

This subject is quoted in some text-books as a particularly
difficult one to answer. There is, however, no real difficulty
here, if we remember our rule (§ 121), that the modulation must
be regarded as taking place as soon as possible. Here it cannot
be till after the fourth quaver, because G natural does not belong
to the scale of F sharp minor; but from the fifth note of the
subject all is regarded in its relation to F sharp minor, and
answered exactly by the corresponding notes in relation to
B minor, and the whole countersubject is distinctly in the latter
key. Notice the curious, and doubtless accidental, resemblance
of this countersubject to that of the fugue in E minor, quoted in
§ 168.
1
Chap. V.]
77
FUGUE.
170. If, on the other hand, the countersubject begins before
the modulation has taken place, it will often need modification
similar to that of a tonal answer, according to whether it is
accompanying the subject or the answer.
J. S. BACH. Wohltemperirtes Clavier, Fugue 7.
(a)
A-
(b)
8

8-
CS-
CS-
tr

tr

tr
At (a) the countersubject accompanies the answer; at (b) it
accompanies the subject itself, and the third from C to E becomes
a second from A to G. This is because the third in the answer,
between F and D, was only a second (between B and A natural)
in the subject. The change in the countersubject must be made,
like that in the answer, at the point of modulation. Sometimes,
also the countersubject is somewhat altered, even with a real
answer, as in the fugue in E, referred to in § 165 (see the extract
given later in § 269).
171. It may be as well to remind students that, as the
countersubject is first heard against the answer only, it must not
make with the answer any intervals which would not be allowed
in free two-part counterpoint. The laws regulating the employ-
ment of these intervals will be found in Double Counterpoint,
Chapter V.
172. Though, as a general rule, the countersubject makes its
first appearance as an accompaniment to the answer in the
exposition, we not infrequently meet with fugues in which its first
appearance is deferred. The great fugue in C sharp minor
(No. 4 of the 'Wohltemperirtes Clavier') is an example of this
kind. We have already quoted the subject and answer in § 66.
The counterpoint against the answer seen in that example
accompanies also the entry of the third voice, but not those of the
Į
78
[Chap. V.
FUGUE.
=
fourth and fifth, nor is it subsequently used at all. We cannot
therefore consider it a countersubject. But at the 35th bar
a genuine countersubject makes its appearance.
J. S. BACH. Wohltemperirtes Clavier, Fugue 4.

(a) CS
This countersubject accompanies every subsequent entry of
the subject till the coda of the fugue. At the 49th bar a second
countersubject is introduced—
(b) S
Th
S

4
Both countersubjects are worked together with the subject in
triple counterpoint. Another fine example of two countersubjects
introduced late in the fugue will be found in the 38th fugue (in
F sharp minor) of the same work.
CS 2.
173. A remarkable example of a fugue with two regular
countersubjects, both of which appear in the first exposition,
is seen in No. 21 of the 'Wohltemperirtes Clavier.' We quote
the commencement of the fugue, writing it in open score, that the
separate parts may be more clearly followed-
+
J. S. BACH. Wohltemperirtes Clavier, Fugue 21.
S
Codetta.
A-
My


CS 1.
Chap. V.]
79
FUGUE.

b
8.
S
CS 2.
Here the first countersubject accompanies the answer; when the
third voice enters with the subject, the alto, which has just
completed the answer, takes up the first countersubject, while the
treble continues with a second countersubject. Every subsequent
entry of the subject or answer down to the end of the fugue is
accompanied by both the countersubjects.
174. A different method of employing two countersubjects
will be seen in the 47th fugue (in B major) of the same work.
The first appearance of the answer is accompanied by a counter-
subject.
J. S. BACH. Wohltemperirtes Clavier, Fugue 47.
A
C81.-
C81.


This is regularly introduced against subject and answer throughout
Its
the whole of the exposition, after which it is heard no more.
place is taken on the next entry of the subject by an entirely new
countersubject, written in double counterpoint in the twelfth, and
invariably inverted in that interval. We gave it as an illustration
of this species of counterpoint in § 171 of Double Counterpoint,
to which the student is referred. It is very rare to find two
different countersubjects used, not simultaneously, but as here,
successively.
80
[Chap. V.
FUGUE.
=
175. Some theorists speak of a fugue with a regular counter-
subject as "a fugue with two subjects," or "a double fugue." It
is best, however, not to apply this name to fugues such as those
we have been speaking of, unless the countersubject, as is
sometimes the case, does not appear in the first exposition, but
has later an independent exposition of its own, and is not at first
used as an accompaniment to the subject, with which it is not
combined till its own separate exposition is completed. We shall
treat of fugues of this kind, as well as of the other variety of
double fugue, in which the second subject first appears not
against the answer (as in the examples here given), but against
the first subject, later in this volume (Chapter XI.).
C
176. It is by no means necessary that every fugue should
have a regular countersubject. Of the forty-eight fugues in the
Wohltemperirtes Clavier' there are seventeen which have none;
and the question naturally arises, When it is desirable to write a
countersubject to a fugue, and when can it be suitably dispensed
with? It is impossible to lay down a hard and fast rule on the
matter; but a careful examination of those fugues which have no
countersubject shows that, in a large majority of cases, it is
unnecessary, if the subject is intended to be elaborately combined
with itself. The exact meaning of this will be better understood
when we come to speak of the middle section of a fugue, and of
stretto; but one or two illustrations will help to make the matter
clearer. In fugues Nos. 1, 22, 26, 29, and 31, we find no
countersubject, because the subject itself is so largely treated in
stretto (§ 16) that a countersubject would only have been in the
way. In fugues 8 and 20, the subject is treated by inversion and
in canon, and in No. 27 extensive use is made of inversion
and diminution. On the whole it may be said that, when there
is no countersubject, we mostly find the more scientific devices of
fugue writing applied to the subject itself. This, however, must
not be taken for more than an attempt at generalization. There
is no form of composition in which there is so much liberty of
treatment and variety of detail as that of fugue.
177. The student should now compose countersubjects to all
the fugue subjects given at the end of Chapter IV. He should
try to write at least two or three, differing in character, to each
subject. For this purpose he should write the subject on one
staff, following it on a second by the answer, above or below
which, according to its position, he should write his countersubject
as the continuation of the subject. He may always introduce a
short codetta, if necessary, between the end of the subject and the
beginning of the countersubject, but it is best not to leave a rest
between the two. The first voice should go on continuously to
the end of the countersubject.*
C
* We occasionally find exceptions to this sound general principle, e.g., in Nos.
16 and 30 of the Forty-Eight in both of which the entry of the countersubject
is preceded by a rest, probably to call attention to it more strongly. We shall see
later that a rest is generally advisable before the re-entry of the subject.
Chap. VI]
81
FOGUE.
CHAPTER VI.
THE EXPOSITION AND COUNTER-EXPOSITION.
178. If the student clearly understands how to answer a fugue
subject, and how to write a good countersubject against the
answer, he will be ready to commence the next stage of his
work-the composition of a complete exposition of a fugue. By
the exposition, as mentioned in Chapter I. (§ 11), is meant that
part of the fugue during which the voices make their first entries in
succession, and which extends as far as the conclusion of the
subject or answer (as the case may be) by the voice that enters
last. If the student has mastered the preceding chapters of this
volume, and has had sufficient practice in counterpoint to be able
to add free parts to two parts that are in double counterpoint with
one another (Double Counterpoint, Chapter VII.), he will find
that the tasks now before him will offer him but little difficulty.
179. The first question to be considered is the order in which
the different voices should enter in the exposition. The subject
may in the first instance be announced by any voice, but the
order of the subsequent entries will largely depend upon what
voice has led.
180. In order to understand this clearly, it is needful to bear
in mind the fact that the answer should always be at a distance
of a fourth or fifth above or below the subject. It is also
necessary to remember that the compass of the alto voice is about
a fourth below that of the treble; that the tenor is an octave
below the treble, and the bass an octave below the alto. We are
speaking here of vocal music; but the parts in an instrumental
fugue are mostly treated pretty much as if they were voice parts.
For the purposes of fugal answer, we group the voices in pairs,
the higher pair being the treble and tenor, and the lower the alto
and bass. If the student remembers the directions for transposing
a given subject which are given in Counterpoint, § 53, he will be
aware that a subject given in the treble must be transposed
a fourth or fifth lower for the alto, an octave lower for the tenor,
and an eleventh or twelfth lower for the bass.
181. If we apply this principle to the matter now under
consideration, we shall see that a subject announced by one
of the higher pair of voices should be answered by one of
the lower pair, and vice versa.
This is the usual practice of fugue
G
82
[Chap. VI.
FUGUE.
,
writers, though occasional exceptions, with which we need not
now concern ourselves, are to be met with.
182. Our next question is, By which voice of the other pair
(supposing the fugue to be for four voices) should the answer be
given? If, for instance, the treble leads with the subject, should
the alto or the bass have the answer? It is seldom difficult to
decide this point, if we remember that it is generally best for the
last entry in the exposition to be in an outer, rather than in a
middle voice. The reason for this is that it is easier to distinguish
the subject or answer when it is in an outer part, especially
in fugues with four or five voices. In three-part fugues, owing to
the thinner harmony, an entry in a middle part can be more
clearly heard. In the forty-eight fugues of Bach's 'Wohltemperirtes
Clavier,' the last entry is in an outer part in no fewer than forty-
two-seven out of every eight.
183. In a two-part fugue, the exposition will be a very simple
matter. One of the voices (it is indifferent which) leads with the
subject; the other follows with the answer, which the leading
voice accompanies with the counterpoint or countersubject, as the
case may be, and the exposition is complete.
184. In a three-part fugue, the operation is somewhat longer.
If one of the outer parts has the subject, the middle part usually
has the answer, and the remaining outer part has the subject
again. If the middle part commences, the answer may be
equally well in either of the outer parts-it is quite immaterial
which. Occasionally we find one outer part leading, and the other
outer part following, the middle voice being the last to enter.
This, however, is rare; out of twenty-six three-part fugues in the
'Wohltemperirtes Clavier' there are only two (Nos. 27 and 28)
in which this method is adopted.
185. While the second entering voice gives the answer, the
first continues with the countersubject, supposing there to be
one; on the entry of the third voice with the subject, the second
voice, which has just concluded the answer, continues with
the countersubject, as the first voice did before. The counter-
subject, which previously accompanied the answer, must now
be transposed a fourth or a fifth to serve as a counterpoint
to the subject. It may also, in the case of a tonal fugue
require some modification (§ 170). Meanwhile, the leading
voice, having now completed the countersubject, adds a fresh
counterpoint, which may also be a second countersubject;
in this case the subject and the two countersubjects must be
written in triple counterpoint. If the third part be a free part (as
is mostly the case), triple counterpoint is not necessary.
186. Here the exposition of a three-part fugue may end; but,
for a reason now to be shown, it is often continued a little
further. It was said in the last chapter (§ 160) that a counter-
subject should be written in double counterpoint to the subject,
so as to be able to be used both above and below it.
But
嚼
​Chap. VI.]
FUGUE.
83
whenever a subject is announced by an outer part, and the other
voices enter in regular ascending or descending order, a moment's
thought will show the student that the countersubject, if given (as
is best) to the voice which has just completed the subject
or answer, will always occupy the same relative position to the
subject or answer. If the treble leads, the countersubject will
always be above; and if the bass leads, it will always be below.
In such cases, in order to show the countersubject during the
exposition in both its aspects, as an upper and lower counterpoint,
we frequently find one additional entry of subject or answer by
the voice that first led, while the last entering voice has the
countersubject. If the middle voice leads, it is evident that we
shall have the countersubject in both positions without this
additional entry, as it will be below the upper part and above the
lower one.
In such a case, as also when there is no regular
countersubject, the additional entry is not needed. What has
been said in this paragraph applies equally, under the same
circumstances, to fugues with more than three voices.
187. To illustrate the matter now under notice, look at the
example given in § 173. Here is an exposition of a three-part
fugue, which, as it stands, might be considered quite complete.
Before proceeding, however, to the first episode (see Chapter
VII.) Bach introduces the answer in the treble (the voice which
first led) in order to let the first countersubject (which has
hitherto only been heard above the subject) appear below it in
the bass-the voice which has just finished the subject.
188. Very frequently in the exposition of a fugue we meet
with a codetta (§ 62) either before the first entry of the answer,
or between the answer and second entry of the subject. We
must now show when such ɔdetta is expedient, and when it is
A
necessary.
189. Before the first entry of the answer a codetta will be
necessary in the following cases. First, if the subject begin on
the tonic with an accented note (e.g., on the first beat of a bar),
and also end on the tonic, and the answer be below, it is clear
that, as the answer will begin on the dominant, this note being a
fourth below the tonic, cannot be sounded as a harmony note
against it in two-part counterpoint.
(a) S
f
Here it would be very bad to introduce the answer against the
last note of the subject; it will be necessary to add a short
codetta,
(6) 8-
Codetta.
f
thus deferring the entry of the answer till the following bar.
&c.
.


84
[Chap. VI.
FUGUE.
!
•
190. Another case in which a codetta is needed before the
answer enters, is when the subject begins on an unaccented note
near the end of a bar, and ends on an accented note at the begin-
ning of a bar.
f
(a)
S
191. A codetta is also sometimes introduced before the answer
to avoid the collision of tonic and dominant harmony.
S-
55
(6)
J. S. BACH. Wohltemperirtes Clavier, Fugue 36.
Codetta.

09
J. S. BACH. Wohltemperirtes Clavier, Fugue 7.
tr
I
A
Here the implied harmony of the first half of the second bar is
clearly that of a full cadence in the dominant. If we introduce
the answer on the last note of the subject
S
tr
bd
G
the effect, as everyone will feel, is simply atrocious.
&c.

&c.
&c.

192. We much more frequently find a codetta between the
answer and the second entry of the subject. The reason in many
cases is the same as that spoken of in our last paragraph-to
avoid the collision of tonic and dominant harmony. If the subject
begins and ends with a note of the tonic chord, such a codetta
will mostly be desirable.
f
J. S. BACH. Wohltemperirtes Clavier, Fugue 8.
A
•


The student will see at once that if the third voice enters here on
the last note of the answer, there will be the same unpleasant
effect as in example (b) of our last paragraph. Bach therefore
inserts two bars of codetta before the entry of the next voice.
193. If the subject begins with the tonic and ends on the
third or fifth of the tonic, a codetta is generally necessary, as the
Chap. VI.]
FUGUE.
85
last note of the answer will be the third or fifth of the dominant,
against both of which the tonic is a dissonance.
J. S. EACH. Wohltemperirtes Clavier, Fugue 22.
8
李
​
(6) 8
be
S
A
•
CS
In both these examples the answer ends with the tonic chord of
the dominant key; and of this chord the original tonic forms no
part.
194. We will now write an exposition of a fugue in three
parts, taking a very simple and straightforward subject, and
adding a regular countersubject.
S-
CS
A
J. S. BACH. Wohltemperirtes Clavier, Fugue 17.
S-
P

A

(c)
Codetta. CS
H
A
&c.
(3)
1
(a)

We have begun with the upper voice, to let all the parts enter in
regular descending order. Notice first how, by means of
86
Chap. VI.]
FUGUE.
7.
syncopations, we have carefully contrasted the countersubject
with the subject. At (a) will be seen the interval of a perfect
fifth between the two voices. This is generally forbidden in two-
part double counterpoint; it is possible here because its inversion,
the perfect fourth (see (c) in the seventh bar), can be used as an
accented auxiliary note.
195. We have considered the subject as ending on D, in the
second bar. This necessitates a codetta (§ 189), which is
imitated by each of the following voices. This is a case of very
common occurrence. It would have been possible here to
consider the subject as extending to the beginning of the third
bar. In this case, the answer would have been tonal; we regard
the subject as ending on the tonic, so as to illustrate the employ-
ment of the codetta.
196. On the entry of the bass with the subject, the alto, which
had the answer, takes the countersubject, and the counterpoint of
the treble is free. Little difficulty will be experienced in adding
the free parts to the subject and countersubject by any student
who has mastered Chapter VII. of Double Counterpoint.
197. The exposition might end at (6); but we have introduced
the additional entry spoken of in § 186, to show the counter-
subject below as well as above the subject. This entry is made
by the voice that began; but as this is a three-part fugue, it will be
seen that the treble, which before had the subject, now has the
answer. Notice also at (b) the rest before the entry in the treble.
It is generally advisable, though not absolutely necessary, to let a
rest precede the re-entry of the subject or answer.
198. The student should now take the subjects given at the
end of Chapter IV., and write expositions on them in three parts.
He will do well to write two or three expositions at least on the
same subject, with different countersubjects, and altering each
time the order of entry of the voices. He will be surprised to find
how much variety he can obtain by this means in the treatment
of the same subject.
199. In the exposition of a four-part fugue much greater
variety is possible in the order of entry than with only three parts.
But, for reasons already given (§§ 180-182), only a few of the
possible twenty-four changes in the order are in actual use. It is
doubtful whether, except in the cases of the irregular expositions,
to be noticed later in this chapter, any instance can be found of
an answer being given by the tenor to a subject announced in the
treble, or by the alto to a subject announced in the bass. In
consequence of the difference of pitch between the two pairs of
voices, the answer should always be given by a voice of the other
pair from that to which the voice belonged which had the
subject. We said above, that it was generally best, especially in
a four-part fugue, that the last entry be in an outer part.
Chap. VI.]
FUGUE.
87
Consequently the orders of entry most frequently met with, and
best, are the following four :—
(1) Treble, Alto, Tenor, Bass.
2) Bass, Tenor, Alto, Treble.
(3) Alto, Tenor, Bass, Treble.
Tenor, Alto, Treble, Bass.
The following are also possible, and sometimes to be met with,
but are less good :—
(1) Treble, Bass, Tenor, Alto.
Bass, Treble, Alto, Tenor.
3) Alto, Treble, Bass, Tenor.
(4) Tenor, Bass, Treble, Alto.
200. In general, subject and answer should enter alternately
throughout the exposition; and if the student examines the eight
orders of entry just given he will see that in every case one pair
of voices will have the subject, and the other the answer. This
is by far the most common method, but there are occasional
exceptions. In the 41st fugue of the 'Wohltemperirtes Clavier'
the order of entry is Alto, Treble, Tenor, Bass, and the alto and
Some-
tenor have the subject, the treble and bass the answer.
times also another deviation from the regular practice is met with.
In the first fugue of the same work, the order of entry is the same
as that just noted—Alto, Treble, Tenor, Bass; but here the third
voice (the tenor) has the answer, and the fourth (the bass) the
subject. In two other fugues of the same work (Nos. 12 and 14)
the fourth voice, instead of the answer, has an additional entry of
the subject. Here, to avoid two immediate entries of the sub-
ject, the third and fourth entries are separated by a rather long
codetta. We advise the student in his first attempts to adhere to
the usual plan, introducing subject and answer alternately, and
adopting one of the four preferable orders of entry given in the
last paragraph.
201. In other respects an exposition for four voices resembles
one for three, excepting that on the entry of the fourth voice two
free parts must be added to the subject and countersubject,
instead of only one. The additional entry spoken of above may
be used at discretion if an outer part leads.
202. The exposition of a fugue may end in either the tonic or
dominant key. If the subject end in the tonic, the answer will
end in the dominant; in this case, if the number of voices
engaged in the fugue be an even number (two, four, &c.), the
exposition will end in the dominant; if the number be odd (three
or five), the exposition will end in the tonic. If the subject ends
in the dominant, the case will be reversed; with an even number
of voices the exposition will end in the tonic, and with an odd
number in the dominant.
203. Exceptionally, cases are met with in which all the voices
of a fugue do not take part in the exposition. The 26th fugue of
4
2
[Chap. VI.
88
FUGUE
the 'Wohltemperirtes Clavier' is an instance. The exposition,
which occupies the first four bars, is for three voices only, and the
fourth voice does not enter till the 19th bar, when it brings
in the subject by augmentation, and the last ten bars of the fugue
are for four voices. A similar example will be seen in Bach's
Organ Fugue in C major-
J

of which the first 48 bars are a four-part fugue, without pedals.
At the 49th bar the pedals enter with the subject in augmentation
(as in the case last mentioned), and from this point to the end
the fugue is in five parts.
204. We now give an exposition of a four-part fugue, taking
the same subject as before, but adding an entirely different
countersubject and beginning with a middle voice. We choose
the alto, so as to retain the same key.

OL
H
Th
A
CS
8.
CS-
S
Codetta.
CS-
A
&c.
Chap. VI.]
89
FUGUE.
Notice first that though in § 194 we gave the subject to the treble
in the same key, we should have somewhat cramped ourselves in
four parts by beginning so low when there were three other voices
to come underneath it. The number of the parts in which a
fugue is to be written should be taken into account in selecting
the voice and pitch of the subject.
205. The student will by this time know enough of harmony
and counterpoint to need no help in examining the above
exposition. We will only remark that as the countersubject
appears in both positions, the additional entry is here unnecessary;
and that while our three-part exposition ended in the key of the
tonic (not counting the redundant entry), this one ends in
the key of the dominant (§ 202).
206. We sometimes meet with irregular expositions of fugues,
in which the subject appears twice in succession before the
answer is heard at all. The following is an example.
ஆடி
O
لو
d.
لے لے گی
d d d do
P
р
Bo
•
P
HANDEL. 'Solomon.'

d


&c.
d
To save space we have given this passage in "short score."
Here, as the subject is repeated, the two voices of the same pair
follow each other; the alto and bass enter with the answer.
Notice, in passing, that we have here another example of an
answer in the subdominant (§ 71). A fugue beginning in this
way is sometimes described as an "Octave Fugue" to distinguish
it from the ordinary fugue, in which the second entry is at a
distance of a fourth or fifth from the first. In the familiar chorus,
"Fallen is the foe," in Handel's 'Judas,' will be seen a fugue in
which all the four entries are in the octave.
207. In some fugues the exposition is followed, either
immediately or after the first episode (which will be described in
our next chapter), by what is called a Counter-exposition. This is
90
FUGUE.
[Chap. VI.
+
really a second exposition in the same two keys (generally tonic
and dominant) as the first, but with important differences. The
chief of these are that in the counter-exposition the voices which
before had the subject now have the answer, and vice versa; and
that frequently the answer leads and the subject replies. In
fugues I and II of the 'Wohltemperirtes Clavier' will be seen
examples of the former, and in Nos. 26 and 33 of the same work,
illustrations of the latter. Sometimes, as in the first fugue, the
counter-exposition follows immediately on the close of the
exposition; at others (as in Fugue 11) it is separated from it by
an episode. To save space, we simply refer to these pieces
without quoting them; we may fairly suppose that everyone who
wishes to study fugal construction has a copy of the 'Forty-Eight'
by him for reference. If not, the sooner he gets one, the better.
It should be added that in the counter-exposition the entries of
the voices are generally accompanied by free counterpoint in the
other voices; it is seldom that the leading voice in the counter-
exposition is found (as in the exposition) unaccompanied.
208. In many cases, when there is a counter-exposition, it is
only partial; that is to say, not all the voices of the fugue take
part in it. For example, in Fugue 38 of the 'Wohltemperirtes
Clavier,' which is for three voices, the exposition, which ends at
the 11th bar, is followed by the first episode. In bar 14 begins
the counter-exposition. The bass, which before had the subject,
now leads with the answer, which is now real, though it was at
first tonal (§ 109). Before the completion of the answer by the
bass, the treble, which before had the answer, enters with the
subject (bar 16), but the close of the subject in the treble is
followed by the second episode, the alto not entering in the
counter-exposition with either the subject or answer, and having
only free counterpoint throughout.
209. In the passage just referred to, we said that the treble
entered with the subject "before the completion of the answer by
the bass"; and this leads us to notice a feature very often to be
met with when there is a counter-exposition. In many cases this
portion of the work is used to introduce the first stretto,—that is
to say, in the counter-exposition, the entries of the subject are
closer together than in the first exposition. For instance, in the
fugue just noticed, the answer enters in the exposition three bars
later than the subject; but in the counter-exposition it is only two
bars later. In the first fugue of the 'Forty-Eight' the answer in
the counter-exposition follows the subject at only one crochet's
distance, instead of a bar and a half; and in the 31st fugue of the
same work the counter-exposition takes the form of a canon at
one bar's distance first at the fifth below, between tenor and bass,
and then at the fourth above, between alto and treble. Con-
siderably more latitude is allowed as to the entries in the
counter-exposition than in the exposition.
210. Occasionally we find a counter-exposition by inversion.

*
Chap. VI.]
91
FUGUE.
In the fugue in G major, No. 15 of the 'Forty-Eight,' we shall
find an example of this kind between the 20th and the 31st, bars;
and in the 46th fugue we shall find an elaborate counter-
exposition, beginning at bar 42, in which not only the subject but
the countersubject is inverted.
211. It must be clearly understood that the introduction of a.
counter-exposition into a fugue is purely optional. The larger
number of fugues do not contain one at all. We only find one in
thirteen out of the 48 fugues in the 'Wohltemperirtes Clavier';
and this is probably a fair average proportion. The instructions
given in this chapter will sufficiently show the student how to
write a counter-exposition, if he wishes to do so.
212. With the exposition or counter-exposition the first
section of a fugue ends. The construction of the middle and
final sections will be treated of in the following chapters. If the
student can write a really good exposition, he is already well
advanced on the road to fugal composition. Let him now take
the subjects in Chapter IV., and write on them a series of four-
part expositions, as he has presumably already done in three-parts.
He should also write expositions on subjects of his own invention.
He must try to get as much variety as possible both in his
countersubjects, and in the free added parts; he should also vary
his order of entry in many different ways. He must keep his
expositions when he has written them, to furnish him with
material for the exercises he will have to write on the next
chapter.
મ
92
[Chap. VII.
FUGUE.
•
..
S
A
CHAPTER VII.
213. Though we occasionally meet with fugues in which the
subject or answer is almost continuously present, a striking and
well-known example being the first fugue in the 'Wohl-
temperirtes Clavier,' it is generally advisable to give variety
to the composition by the introduction of episodes. An Episode
is that part of a fugue in which for a time neither subject nor
answer is heard. In the majority of cases the reappearance of
the subject attracts more attention and excites more interest, if it
has been absent for a while.
CS
EPISODE.
214. There is another important purpose also served by the
episode. So long as subject and answer continue to enter (as
in the exposition) at the distance of a fourth or fifth from one
another, it is clear that we shall not get away from the tonic and
dominant keys; and although in the middle section of a fugue
we often find entries at other distances than the fourth and fifth,
it is frequently more convenient to effect the modulations by
means of episode than to do so by varying the distances of
entry, which would sometimes necessitate more or less important
changes in the form of the subject itself. How modulations can
be made during an episode will be seen presently.
215. The student must be careful to distinguish between an
episode and the codetta spoken of in the last chapter. When a
codetta appears between the second and third entries in the
exposition, it often has much the same character as an episode;
the difference is, that the former appears in the course of the
exposition, and the first episode never till its close. This will be
clearly seen from the following example, in which the codetta
and the first episode are composed of nearly the same material.
J. S. BACH. Wohltemperirtes Clavier, Fugue 2.
fore



•
Chap. VII.]
93
FUGUE.

姦
​Codetta.
CS
어
​
S

Episode.
bom
&
Here the answer ends on the third of the dominant; a codetta
is therefore introduced (§ 193) to lead back naturally to the key
The codetta is
of the tonic, in which the subject reappears.
made from a modified form of the first notes of the subject
treated sequentially, and accompanied (also sequentially) by the
This is
first notes of the countersubject in inverse movement.
not an episode, because the exposition is not yet complete. The
subject then enters in the bass, with the countersubject above it.
No additional entry being here required, as the subject was
announced by the middle voice (§ 186); the exposition ends
here, and is followed at once by the first episode.
216. If we examine this episode, we shall see that it is made
from the same material as the codetta, but with different treat-
ment. The two upper voices have a theme founded on the
first notes of the subject, the alto imitating the treble as a canon
in the fifth below. The bass gives the commencement of the
countersubject, not (as in the codetta) by inverse movement,
but in its direct form. Observe also how, by means of sequence,
a modulation is effected to the key of the relative major, in which
key the subject follows in the treble voice immediately on the
conclusion of the above extract.
217. We said in Double Counterpoint (§ 307) that imitation
was a most important ingredient in fugue, and the quotation
just given will show how it is to be used. Except in a stretto,
the construction of which will be explained in our next chapter,
imitation is seldom found during the entries of the subject itself;
but it is almost constantly employed in the episodes. By this
means unity of character is given to this part of the work, and
anything like patchwork is avoided.
..
.
·
94
FUGUE.
[Chap. VII.
..
218. It is for the same reason that we mostly find the
episodes of a fugue formed, either wholly or in part, from
material already met with, either in the subject, countersubject,
or codetta. We give examples of each. In the sixteenth fugue
of the 'Wohltemperirtes Clavier,' the following is the subject.

The fugue contains two episodes, both founded on the second
bar of this subject.
J. S. BACH. Wohltemperirtes Clavier, Fugue 16.

25
+
In this episode the figure marked with a
is seen in the
different voices in turn, by direct, and once by inverse movement.
In the last bar, where a modulation is made to the relative major,
the imitation is merely rhythmic.
219. The second episode is rather more elaborate.

Here the bass treats the last part of the subject sequentially,
while the figure of counterpoint propounded by the alto is
Chap. VII.]
95
FUGUE.
freely imitated by the treble in contrary motion. It must be
noticed that, though the fugue is for four voices, both the
episodes are in three parts. This is very common in four-part
fugues; it would be bad for all the voices to be continually at
work throughout. Three-part, and even two-part, harmony is
often met with, especially in the episodes, furnishing relief and
contrast. In the four-part fugue in F minor (No. 12 of the same
work), five out of the six episodes are for three voices only.
220. In our next example the episodes are formed from the
countersubject. The subject and countersubject of the fugue are
the following—
J. S. BACH. Wohltemperirtes Clavier, Fugue 14.

8

A
CS

Codetta.
8
&c.
We have quoted the codetta preceding the entry of the third
voice, because (as we shall see directly) it is used at the beginning
of the first episode, though it does not appear in the others.
221. This fugue contains three short episodes.
(a)

96
[Chap. VII.
FUGUE.
.
..
(c)

55
(a)
=
The first bar of (a) consists of the codetta, with the addition of
a middle part; the rest of it, as will be seen, is made out of the
first notes of the countersubject. At (b) the same theme is seen
in the bass, with free upper parts; while at (c) it is treated
sequentially, the outer parts which move in tenths imitating
the inner parts moving in thirds. Here again, though the fugue
is for four voices, two out of the three episodes are in only three
parts.
222. In § 191 we gave the subject of the seventh fugue in
the 'Wohltemperirtes Clavier.' In the second bar was seen a
codetta before the entry of the answer, the reason for which we
showed. From this codetta the episodes of the fugue are chiefly
developed.
(b)
P
J. S. BACH. Wohltemperirtes Clavier, Fugue 7.


Ez
In this episode the codetta is treated by sequential imitation
between the outer parts with a middle part, made from the
augmentation of the semiquaver figure of the bass. The first
part of the next episode

Chap. VII.]
97
FUGUE.

་
DEED!
Q
t
is an inversion of the preceding, the augmentation being now
in the bass. By the substitution in the third bar of B natural
for the B flat of our preceding quotation, a modulation is effected
to the key of the relative minor. The figure of the codetta is
maintained in the upper part till the end of the episode, the last
two bars of which are in two-part harmony only.
223. In another episode in the same fugue, of which we give
only the beginning,
(c)

&c.
the codetta has only a subordinate part; it evidently suggested
the arpeggio figure which is seen in the bass in the second half
of each bar. The chief figure here is the sequence, the theme of
the upper voice being a modification of the subject of the fugue.
In our last example from this fugue,
(d)

the same material is used as in our quotations (a) and (b). In
its general character this episode much resembles (a); but the
H
98
[Chap. VII.
FUGUE.
figure taken from the codetta is now allotted to the two lower
voices, and is seen in the alto by free inversion, and in the treble
by augmentation.
224. As all our examples hitherto have been from Bach, we
will now give one by Handel. The second of his 'Six Fugues
for Organ or Harpsichord' is particularly rich in interesting
episodes. We first give the subject and countersubject.
(a)
G
Codetta.
8-
A
CS
IJI
In the first episode that we shall quote,
(6)
8
HANDEL. Six Fugues, No. 2.




the first notes of the subject in the bass are imitated at half a
bar's distance by the treble, and also accompanied by the
countersubject in the middle voice in double counterpoint in
the tenth; the passage is twice sequentially repeated, after which
an inverted cadence brings back the subject.
Chap. VII.]
99
FUGUE.
225. The following episode
(c)


OF
A
begins with repetitions of the first four notes of the subject
(or answer), after which the same material is employed as in
episode (b); but the notes of the countersubject are now used
against a different part of the subject. The episode from which
we shall next quote is too long to be given entire.
(d)

&c.
Here the last notes of the subject and countersubject (instead of
the first, as hitherto) are developed. The first four bars of our
extract show a sequential treatment of a one-bar theme; at
the fifth bar, the subject is in the bass, and is accompanied
by the countersubject in inverse movement. At the ninth bar,
the close of the subject is in the middle voice, and is
accompanied by the countersubject, in direct movement above,
and in inverse movement below.
•


100
FUGUE.
[Chap. VII.
226. Two more short passages will conclude our examples
from this fugue.
(e)
4


(ƒ)
&c.
Here we see two inversions of the subjects of episode (b).
Though the second one, in which the original countersubject
is in the bass, is not developed at any length, enough is given
to show that the passage is written in triple counterpoint.


[[
In the first bars of this passage we see the second and third bars
of (b) treated by inverse contrary movement (Double Counter-
point, § 454). In the fourth bar we see the inverted subject
in sixths accompanied by the inverted countersubject in thirds.
227. Occasionally the episodes of a fugue are formed from
entirely fresh material. In this case care must be taken that
the new matter is in keeping with what has preceded.
example of episodes of this kind will be found in Bach's Organ
Fugue in D minor, arranged from one of his violin fugues-
An
fse

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Chap. VII.]
IOI
FUGUE.
4
.
We give extracts from two of the episodes.
(a)
(6)
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Dolce e cantabile.
J. S. BACH. Organ Fugue in D minor.

&c.

Another good example of the same kind will be seen in Bach's
great Organ Fugue in E minor,
fu
&c.

228. In both the cases just referred to, the episode is of a
more florid character than the subject of the fugue. In the
great fugue which forms the finale of Beethoven's Sonata,
Op. 106, the theme of which commences thus-
tmun

&c.
Here is an episode in
we find an example of a different kind.
the key of D major, which itself begins like the exposition of a
fugue-
(a)
BEETHOVEN. Sonata, Op. 106.

&c.
After this episode has been developed for 29 bars, Beethoven
•
102
FUGUE.
[Chap. VII.
combines it with the first part of the subject of the fugue in the
following manner—
(6)

p
&c.
It looks at first sight as if there were here a double fugue (§ 175),
with an independent exposition of its second subject. That this
is not really so, is shown by the fact that the episodical theme
does not subsequently appear regularly as a counterpoint to the
subject.
229. Sometimes in the same fugue some of the episodes
will be made from material already used, while others will be
constructed of entirely new matter. An excellent example of this
will be met with in the 37th fugue of the 'Wohltemperirtes Clavier.'
We have already quoted the subject and countersubject of this
fugue at § 162 (6). There are altogether four episodes. Of these
the first and third were quoted in § 256 of Double Counterpoint, as
an example of triple counterpoint in all its possible positions.
The second episode is made from a sequential treatment of
the countersubject, and the fourth is a transposition of the
second, with inversion of the upper parts. This is often met
with for instance, in the two-part fugue in E minor (No. 10 of
the 'Wohltemperirtes Clavier') there are four episodes, of which
the third is an inversion of the first, and the fourth of the second.
230. We could multiply examples to any extent, and have, in
fact, noted far more for quotation than we have room to insert;
but we have already given enough to allow us to deduce general
principles from them as to the construction of episodes. The
first, and one of the most important inferences to be drawn
from our illustrations, is the essential part played by sequence
in nearly all the episodes. If we were forced to restrict ourselves
to giving the student only one rule in this matter, we should
select, as the most valuable we could give him, Construct
your episodes sequentially." Sequences not only furnish a very
easy and simple means of modulation, but they combine variety
of detail with unity of design in a degree which perhaps no other
artistic device can attain. It is not necessary that the sequential
(C
*

Chap. VII.]
103
FUGUE.
S
imitations be at any regular distance. Sometimes they are so, as
in our examples to §§ 222, 223; at other times, as in the second
part of our quotation in § 225 (d), the distances of imitation are
irregular.
231. Sequential treatment, important as it unquestionably is,
is by no means the only point to consider with regard to episodes.
A no less necessary requisite is variety. Each episode must have
some feature which has not been seen in any of the preceding
episodes. A mere transposition of one episode into a different
key will be invariably weak and bad if no modification be made.
On the other hand, some of the best episodes are made by
This
repetition of an earlier episode with inversion of parts.
gives the requisite variety, and at the same time preserves the
artistic unity.
232. Beyond these general principles, it is impossible to
teach the student how to write episodes for his fugues, excepting
by showing him how the great masters have written them. It is
here (just as with the "free fantasia" of a sonata or symphony)
that the composer's imagination has the fullest scope. So long
as he keeps within the bounds of the artistic and beautiful,
he may in this part of the fugue do whatever seems good in
his own eyes; and it will be in this part of the work, more
than in any other, that his originality (if he have any) will be
likely to assert itself.
233. Besides its use for the purposes of modulation, the
episode serves, as already said, to separate the different groups
of entries, or isolated entries, of the subject. We shall see, when
we come to treat of the middle section of a fugue (Chap. IX.),
that there is no restriction as to the number of these middle
entries. Sometimes they are very few, at other times they are
numerous. Consequently we find great differences as to the
number of episodes in different fugues. For example, in the
'Wohltemperirtes Clavier' the 31st fugue has only one episode,
and the 16th only two; but the 3rd, 12th, and 15th have six
each. The number will depend entirely on the number of
middle entries.
234. The length of the episodes is as variable as their
number. In the majority of fugues they are comparatively
short—often only two or three bars each; and in many cases
it is better not to have too long an interval between the different
entries of the subject. But they are occasionally found of
considerable length. For instance, of the six episodes in the
fugue in C sharp major (No. 3 of the 'Wohltemperirtes Clavier'),
the first four and the last do not exceed four bars in length,
but the fifth extends to fourteen bars. In the F major fugue
(No. 35 of the same work) is seen a very unusually long episode
The
of 28 bars. This, however, is quite an exceptional case.
composer's feeling of proportion and balance must be his guide
in deciding both on the number and length of his episodes.
104
FUGUE.
[Chap. VII.
235. Occasionally, though very rarely in modern music, we
find fugues without episodes. Such fugues were more frequently
written, and more highly esteemed, by the old contrapuntists
than they are at the present day. There is always danger of
monotony if there are no episodes; even the first fugue of the
'Wohltemperirtes Clavier'-perhaps the finest fugue without
episodes ever written-is from a purely musical point of view
somewhat inferior in interest and charm to many others in the
same collection.
236. As it is only by actual working, and not by any amount
of mere verbal instruction that fugal composition can be learned,
we shall now practically illustrate the directions given in this
chapter by writing a series of episodes suitable to follow the
expositions given in the last chapter-in three parts in § 194,
and in four parts in § 204. They are both in the key of
D major; and we will assume that the next appearance of
the subject is to be in B minor, which is one of the most
probable keys for the next entry. Our exposition ended in
A major, from which key a modulation to B minor is perfectly
easy, either direct or touching on D major first. In each of the
episodes we give, we shall make use of material found in the
exposition. We shall write all our examples in open score,
that the student may be able to follow more easily the progression
of the different voices; and we strongly advise him to follow the
same plan in all his fugal exercises.
237. We first write some episodes to follow the three-part
exposition in § 194, and in each case begin by completing the
unfinished bar at the end.


CS
S
W
&c.
In this passage, the last half of the subject is treated sequentially
in the treble, and accompanied by imitative counterpoint in the
other two voices.
Chap. VII.]
105
FUGUE.
HE.
H
238. For our next episode

1}.
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C8
8
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we take the codetta in the second bar, which precedes the
entrance of the answer, treat it sequentially, with imitation
in the fifth above between the two upper parts, and accompany
it in the bass with a semiquaver figure, developed from the
figure
in the second crotchet of the first bar of the
alto part.
CS
239. In both the above episodes we have returned from A to
D, before going into B minor. In our last example in three parts
we will make the modulation direct.
S
&c.


&c.
This episode is made from the first part of the countersubject,
which is accompanied by a new semiquaver figure in the alto,
freely imitated in the tenth below by the bass.
106
FUGUE.
[Chap. VII.
240. We now give some episodes suitable for our four-part
exposition. Although in actual practice, it is neither necessary
nor expedient that all the episodes of a four-part fugue should
be in four-part harmony, yet, as the episodes we are now
writing are simply meant as illustrations of the method of
composition, and as our previous examples have been in three
parts, we will write these in four. As before, we begin by com-
pleting the last bar of the exposition.


ន
11.
TH
CS
&c.
This episode is founded on the first three notes of the subject,
treated sequentially in the bass, imitated by inverse movement
in the tenor, and accompanied by a semiquaver figure in the
upper voices, which is an imitation, partly inverted and partly
direct, of the tenor part in the first half bar of the passage.
241. We not infrequently find in fugues that an episode
founded, not on subject or countersubject, but on one of
the incidental counterpoints. To illustrate this, we construct
our next episode in this way.


Chap. VII.]
107
FUGUE.

PE.
CS
O
8
The sequence here seen in the treble is founded on the figure
employed in the tenor in the second half of the seventh bar
of the exposition in § 204. It is accompanied by a sequence in
the tenor, formed from the beginning of the countersubject, and
imitated in the second above, and at one crotchet's distance by
the alto.
242. Our last episode is more elaborate, and is given to
illustrate the incidental employment of canon in fugal writing.
w
8
37%
&c.
CS
In the second bar of this passage the first bar of the counter-
subject is introduced in the alto, and treated sequentially in
the following bar. It is also accompanied by a sequential
counterpoint. Both these parts are imitated by the tenor and
bass, making a 4 in 2 canon; but the inversion of the
voices, instead of being, as usual, in the octave, is in the tenth,
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*
·


108
FUGUE.
[Chap. VII.
2
1
thus giving a somewhat rare combination of canon and double
counterpoint in the tenth. In the last bar of the episode, the
canon is abandoned, and we have merely ordinary imitation,
direct and inverted, of a fragment of the countersubject.
243. These examples will show the student how much variety
of episode is possible, even with such commonplace subjects
as we have been treating here. He will now see clearly what
we meant when in Double Counterpoint (§ 307) we spoke of
Imitation as "a most important ingredient" in fugues. In
fact, imitation and sequence are the chief essentials of good
episodes. Let the student now turn back to the expositions
he has written as exercises on the last chapter, and utilize
his material (subjects, countersubjects, codettas, and incidental
counterpoints) for the construction of many different episodes,
after the manner which we have shown him in this chapter.
He should write five or six episodes for each fugue, varying
the keys to which he modulates. For the present he should not
go beyond the nearly related keys.
Chap. VIII.]
109
FUGUE.
CHAPTER VIII.
STRETTO.
244. The word "STRETTO" is the past participle of the
Italian verb, "stringere," to draw close. It is occasionally
used in music other than fugues as equivalent to the present
participle of the same verb, "stringendo," in the sense of
pressing on, or hurrying up the time; but when employed,
as it mostly is, in connection with fugue, it is the name for
that part of a fugue in which the entries of the subject or
answer follow one another at a shorter distance of time than
in the first exposition.
245. Most theorists name the stretto as a necessary part of
every good fugue. Cherubini speaks of it as an "indispensable
condition" and an "essential requisite"; and he adds that
"a good fugal subject should always give scope for an easy
and harmonious stretto." But this rule, like most others given
in the old text-books, will not stand the test of applying it to
Bach's practice. Out of the forty-eight fugues in the Wohl-
temperirtes Clavier,' more than half have no stretto at all;
and of the remainder some have only a fragmentary, or partial
one. If a stretto is really an essential part of a fugue, then
it is evident that more than half Bach's fugues must be badly
written. The simple truth is, that it is not Bach's workmanship,
but the rule that requires to be altered. Any rules regarding
fugue, which will not fit the works of the greatest fugue-writer
that the world has ever seen, carry their own condemnation on
their face.
246. Instead, therefore, of laying down a law that every
good fugue must contain a stretto, we maintain that, though
often a most valuable ingredient of fugue writing, it is never
absolutely indispensable. In the 'Wohltemperirtes Clavier'
some of the fugues which have no stretto (e.g., Nos. 2, 12, 21,
and 40) are among the finest and most perfect works of art of
the whole collection.
247. It is by no means every fugue subject that adapts
itself easily and naturally to the purposes of stretto. A subject
intended for this should be expressly designed for it in the first
instance; otherwise there will most likely be a certain stiffness
or harshness about some of the imitations. For example, in
writing the fugue subject of which we gave expositions in
IIO
FUGUE.
[Chap. VIII.
§§ 194, 204, it did not happen to occur to us to make one
which would be suitable for stretto afterwards. Consequently,
though it is quite possible to introduce later entries at a shorter
distance than two bars, these will not be so effective, nor flow so
naturally as if the subject had been written with this object in
view. We give a few stretti as illustrations.
(a)
(b)

(c)
&c.
(d)
&c.

248. These examples, which must not be regarded as models
of a good stretto, but are written to show that a stretto of
some kind is mostly possible even for a subject not at first
designed for it, illustrate several points relating to its construction.
We see at (a) a case of common occurrence. Here the imitation
is not in the fourth or fifth, but in the octave. As a matter of
fact, the imitation in a stretto may be at any interval, though
in general those in the fourth, fifth, and octave will be found
the best. At (b), as at (a), the imitation is at one bar's distance;
but it is here in the fifth below; the answer leads, and the subject
replies. The imitation of the answer by the subject often gives a
different set of combinations.
249. At (c) the subject leads and the answer replies at half a
bar's distance. The consecutive fourths between the first and
second bars are bad, as they stand; but a stretto for two voices,
like a two-part double counterpoint, is mostly accompanied by
free parts.
Here we have left the bass staff empty, instead of
putting rests, to show that a bass is meant to be added, which
will make the fourths right. Observe that the last note of
the subject has to be changed here, to avoid consecutive octaves.
250. Our last stretto, at (d), is also the closest. It is for three
voices at one crotchet's distance. It is evident that now the
bass cannot possibly complete the subject; it will therefore
have to continue with a free counterpoint, which we have
purposely not filled in, so as to show only the close imitations.
The middle voice now has the subject, per arsin et thesin, and, as
at (c), the last note requires to be altered.
251. Before writing a subject specially to show the different
possibilities of stretto, it will be well to give a few general hints
."
'.

Chap. VIII.]
FUGUE.
III
for the guidance of the student. We said in § 248 that a stretto
might be at any interval; to this we now add that it may be in
any number of parts. If a stretto is employed in a fugue at all,
we generally find more than one; and in that case, in order that
the interest of the music may gradually increase, we mostly
find the later stretti either in more parts or at a shorter distance
of entry, or both, than the earlier ones.
252. It is not always possible for the voices which enter
first in a stretto to continue the subject after another voice
has entered. This was shown in § 247 at (d), where the bass
had to discontinue the subject on the entry of the treble.
Though it is best to carry on the imitation as far as possible,
it is always allowed to break off the subject, or to modify
it after another voice has taken it up. But it should be
remembered that the last entering voice in a stretto should have
the subject complete. We of course use the words " subject
and "answer indifferently here, as the entry may be at any
interval.
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در
253. From the same consideration—that of freedom of
interval in the entries-we are allowed in a stretto of a tonal
fugue to employ either subject or answer, as may be more
convenient. The imitations in a stretto may also be by
augmentation, diminution, or inversion, or (as we saw at (a)
§ 247) per arsin et thesin.
254. We will now write a subject and answer adapted for
stretto, and then show some of the numerous stretti of which
it is capable.
J Z


As there is here in the subject an implied modulation to the
dominant, the answer will be tonal. In accordance with the
rule given in § 121, we regard the modulation as being made
as early as possible-here, after the first note of the subject.
The answer enters at the beginning of the fifth bar.
255. We will first try to bring in the answer as near the
end of the subject as we can. Clearly if we keep the tonal
answer, we cannot introduce it in the fourth bar of the subject.

This is manifestly impossible, though the addition of thirds
below the answer would render it practicable. But we said
in § 253 that it was allowed to use either form of the subject
II2
FUGUE.
[Chap. VIII.
in the stretto of a tonal fugue. It would therefore be quite
feasible to introduce the answer against the last bar of the
subject thus-
(a)

&
As this passage is written in double counterpoint in the octave,
the answer could also be introduced above the subject.
(b)
&c.

256. We will now reduce the distance of entry by half a
bar, bringing in the answer, per arsin et thesin, on the second
half of the third bar.
&c.

娄
​The student will see that at this distance of entry, it is impossible
to complete the subject. Note also that in consequence of the
bare fifth at the end of the third bar this stretto cannot well be
inverted as the last one could.
P PP
PT
This stretto, like that in § 255, will also invert in the octave.
(c)
257. If we next try to make a stretto with the answer at two
bars' distance, we shall have either to discontinue or to modify
the subject on the entry of the answer.
(a)
j
&c.

It would, however, be possible here to continue the subject
unchanged to the end, if we make the imitation in the octave
instead of the fourth. We shall have to shorten the first note of
the imitation (§ 57).
(b)
&c.

&c.

&c.
Chap. VIII.]
113
FUGUE.
258. At one bar's distance we can get a stretto in the fifth
below.
(a)

We might here also have preserved the tonal form of the answer
by treating the A in the second bar as an accented passing note.

In the fourth bar we have varied the rhythm of the imitating
voice, to retain the subject in the leading voice for half a bar
longer. Obviously we could not write
Such slight modifications, either of rhythm or melody, are very
common, and always permissible in a stretto. We now give
the inversion of the above.
(b).
259. Lastly, we can make a stretto with this subject at only
half a bar's distance.
(a)
$
&c.



Like most of the preceding, this stretto can be inverted in the
octave.
(b)
I
*
&c.

260. If now we begin with the answer instead of the subject,
we shall obtain a different series of stretti, though resembling
those already given in their general character.
(a)
his me
•
&c.

&c.
·
114
FUGUE.
[Chap VIII.
TE

Here the subject enters three bars after the answer. We give the
inversion.
HAJJAR

(b)
泰
​261. We next show the answer followed by the subject at two
bars' distance.
(a)
The above will also invert—
&c.

A
It will be seen that the leading voice cannot here continue the
subject to the end. This imitation inverts as follows—
(8)
(b)
&c.
&c.

262. At one bar's distance the answer cannot be comfortably
imitated by the subject. Here, therefore, we make the imitation
in the octave; and even at this interval we cannot continue it
long.
&c

263. At half a bar's distance, it is possible to reply with the
subject, and the imitation can be continued somewhat farther
than in the last example.
(a)

&c.

&c.
264. Hitherto we have only given stretti in two parts;
but the subject we have chosen will also work in stretto in
Chap. VIII.]
FUGUE.
115
three or four parts in many different ways. We give two
specimens in three, and two in four parts.
#ZI
¡

Here is a simple example, in which each part follows at a
distance of one bar. The intervals of entry are irregular;
the alto being a fifth below the treble, and the bass a seventh
below the alto.
265. In our next example,
#
15
&c.
#
the intervals of entry are the same as in the last; but a quite
different effect is produced, because now the answer leads and
the subject replies; and, besides this, the distance of time in
the entries is irregular, the second voice being two bars later
than the first, and the third voice only one bar later than the
second.
266. In our first four-part example,
3
&c.
&c.
the entries are regular as regards distance of time (one bar),
but irregular as to interval. In this stretto it is not possible
in any of the voices (except, of course, the bass which is the
last to enter, and in which it should be complete-§ 252) to
continue the subject to any great length.
:


116
[Chap. VIII.
FUGUE.
"
267. We lastly give the closest possible stretto in four parts.

Here the entries are regular both as regards time and interval,
each succeeding voice being introduced half a bar later, and
a fourth below the preceding one. It will be noticed that in
each voice the subject is carried down to the same point.
268. We have now given more than twenty stretti on the
same subject, of which we have by no means exhausted the
possibilities. It is probable that, by using all the combinations
in three and four parts at the various distances of time and
entry, we might make at least forty or fifty stretti on this
subject. The student may not unnaturally be inclined to ask,
What is the difference in character between this subject and
the one worked in § 247; and how is it that so few good
stretti could be obtained from the one, and so many from
the other? The explanation is very simple. We said in § 247
that a subject intended for stretto should be expressly designed
for that purpose. The best and easiest way of so designing it
is, to write it in the first instance as a canon in the fourth or fifth
at the shortest distance at which it is intended ultimately to
be introduced. In the present instance we began by composing
the little canon seen at § 259 (a), as far as the first note of the
fourth bar. We then completed the subject by the addition of
the notes-

A
The entries at longer distances were then found by experiment—
trying to fit the answer against the subject, or the subject against
itself, at all possible intervals and distances of entry. It will
nearly always be found that subjects which, like this one, work:
in close stretto, can also be employed at longer distances.
¿
+
269. The stretto is mostly met with in the middle and
final sections of a fugue, of which we shall speak in the next
chapter; but when the fugue has a counter-exposition, the
first stretto (as already mentioned in § 209) is frequently intro-
duced at that point. A good illustration of this is seen in
the 33rd fugue of the 'Wohltemperirtes Clavier.' We quote
the exposition and the counter-exposition.
Chap. VIII.]
117
FUGUE.
H
H
@
1
8
4
7
8
CS-
A-
2
S-
5
11
8
J. S. BACH. Wohltemperirtes Clavier, Fugue 33.

A-
CS
HIGH
A
C8
CS-
3

CS-
6

9
A-
8-

&c.
10
12
The bars are numbered for convenience of reference. Note
the altered forms of the countersubject spoken of in § 170.
1

118
[Chap. VIII.
FUGUE.
+
The exposition ends at the beginning of the seventh bar. The
two bars that follow have hardly enough distinct character to
constitute an episode; they are rather a kind of codetta—a
prolongation of the exposition, leading up to a half close, to
introduce the counter-exposition. Here we see (§ 207) that
the voices which before had the subject (the bass and alto)
now have the answer, while the tenor and treble have the
subject; we also see the entries in a rather close stretto. It
looks at first as if the introduction of a close stretto so early
in the fugue were premature; but Bach has other devices in
reserve for the later part of this fugue, as we shall see presently.
270. In the 31st fugue of the same work, the counter-
exposition contains a canonic imitation in stretto, first between
tenor and bass, and then between alto and treble. We quote the
passage; the subject and answer of the fugue were given in § 88.
J. S. BACH. Wohltemperirtes Clavier, Fugue 31.
Wyb
I
HO
Het
El.
bė
€
om
A
¡

S-

A-
S

&c
Chap. VIII.]
119
FUGUE.
Here, as in our last example, the answer leads and the subject
replies; but a deviation is made from the usual practice,
inasmuch as the tenor, which had the answer in the first
exposition, has it again here, and the bass (as before) has the
subject; but with the other pair of voices, the usual plan is
followed, the alto now giving the answer instead of the subject,
and the treble giving the subject instead of the answer. The
irregularity is probably due to the fact that Bach intended to
invert the canon on its repetition by the upper pair of voices.
Canonic imitation in stretto is not uncommon in a fugue; the
student will see other instances of it in Nos. 20 and 46 of
the 'Wohltemperirtes Clavier'; but it is seldom met with so
early as in the counter-exposition; more frequently we find it
in the middle or final section of the fugue.
271. Though, as has been already said, the imitations in a
stretto may be at any interval, it is generally advisable to
observe some kind of order in the entry of the different voices.
Our next example will illustrate this point, as also that mentioned
in § 252, that one voice in a stretto may discontinue the subject
as soon as another voice enters with it, but that the last voice
that enters should complete the subject. The student will find
the subject, answer, and countersubject of this fugue in § 169.
HI
S-
8.
incomplete.
¿
J. S. BACH. Wohltemperirtes Clavier, Fugue 24.
incomplete.

S-

S-
7
incomplete.
1-
}
1
V
¡
1
120
i
·
He to
S-
FUGUE.
Here the entries are at a regular distance of one bar after
each other; the alto is a fifth below the treble, the bass a fifth
(twelfth) below the alto, and the tenor the fourth above the
bass, which is the inversion of the fifth below. Each voice,
except the tenor, which is the last to enter, discontinues the
subject when the next voice enters with it. In the fifth bar of
the extract is seen a fragment of the countersubject in the
alto, which, in the following bar, is continued by the treble.
It is not uncommon in the middle section of a fugue to find a
countersubject begun by one voice and completed by another..
It should be noticed that the counterpoint of semiquavers,
seen first in the bass and then in the treble, is developed
from the codetta in the fourth bar of the example in § 169,
before the entry of the countersubject.
CS 2-
272. Sometimes not only the subject, but the countersubject
of a fugue is used in a stretto. A remarkably fine example
of this is seen in the great five-part fugue in C sharp minor
of the 'Wohltemperirtes Clavier.' It will be remembered that
this fugue has two countersubjects, both of which we quoted in:
§ 172. Only the second one, shown at (b) is employed with the
subject in the stretto. Though the passage is rather long, it is so
interesting, and deserves such careful examination that no apology
is needed for quoting it in full.
[Chap. VIII.
++
&c.
CS 2
CS 1-
!
1


Chap. VIII.]
121
FUGUE.
It
CS 2
CS 2
8-
8

CS 2
C8 2
incomplete. CS2-
CS 2-
CS2
CS 2
CS2-
8-
He
S-
CS 2
CS2-
CS 2
8

"A

122
[Chap. VIII.
FUGUE.

+
WEBSTA -
CS 2-
8-
-
C82-
CS 2-
8
C82-

CS 2-
| M M Ma
———
It would occupy too much space to analyze this passage fully.
The student, with the aid we have given him by marking all
the entries, will have no difficulty in doing it for himself. But
this extract illustrates a point we have not yet had occasion
to notice. It contains two pedal points, first dominant and
then tonic. These, the former especially, are not seldom to
be met with toward the close of a fugue, more particularly
with vocal fugues; and when they are found, it is very common
also to find close stretti built above them.
273. A stretto may be made from only a part of the subject
of a fugue, with a new continuation. The "Amen" chorus of
the 'Messiah' furnishes a familiar illustration of this; the subject
of the fugue is too well known to need quotation.
1.
1
Chap. VIII.]
123
FUGUE.
Here the first five notes only of the subject are taken for the
stretto, the continuation of the passage being new. The stretto
is at one crotchet's distance in all the voices, and is in reality a
canon 4 in 1, at the octave and fourth below.
Q
HIN
274. A fugue subject may also in a stretto be taken by
inversion, augmentation, or diminution, or any combination of
these, instead of in its original form. No rules can be given as
to when these devices should be employed; this must be left
to the judgment of the composer. We give a few examples.
The subject of the 6th fugue in the 'Wohltemperirtes Clavier'
is the following—
(a)
(c)
Jos
Ꮗ .
Zo
The answer enters in the third bar. In the course of the fugue
we meet with the subject slightly altered in form (a major third
being substituted for a minor), and imitated at one bar's distance
by its own inversion.
(b) 8-
J. S. BACH. Wohltemperirtes Clavier, Fugue 6.
tr
HANDEL. 'Messiah.'

tr
S (inverted)-
H
Later still all three voices of the fugue take part in the stretto,
the inverted subject now leading.
8 (inverted) -
&c.


8.
8 (inverted)
&c.
i
#5

"
124
[Chap. VIII.
FUGUE.

S
S
275. Our next example, also in three parts, shows augmenta-
tion of the subject, as well as inversion.
J. S. BACH. Wohltemperirtes Clavier, Fugue 8.
8 (augmented)
S (inverted)
S (augmented}
&c.
Ger
自
​¡



S-

Chap. VIII.]
125
FUGUE.
**
The student will find the subject and answer of the fugue in
§ 192.
In our extract the subject in the middle voice is imitated
in the fifth below and by augmentation, at half a bar's distance,
therefore in a close stretto. On the completion of the subject by
the alto, the treble gives it by inversion. Thus the augmented
subject is accompanied in the first half by the subject in direct,
and in the second half in inverted form. The bass then takes
the subject in its direct form, and is followed (again at half a
bar's distance) by the alto with the augmented subject. A
comparison of the two voices here with their appearance at the
beginning of our quotation shows us that the subject and its
augmentation are here inverted in double counterpoint in the
twelfth. The treble now accompanies the augmentation at a
different point from before, and with the direct instead of the
inverted form of the subject.
276. In speaking of the first stretto of Bach's fugue in E, in
§ 269, we said that Bach had other devices in reserve for the
later part of the fugue. The following extract will show what
was meant.
H.
ť
4
8 (diminished)-
J. S. BACH. Wohltemperirtes Clavier, Fugue 33.
8 (dimd.).
S-
8 (dimd.)
S (dimd.)
8 (dimd.)—
S (invd. & dimd.).
8 (invd, & dimd.)-
S (invd
•
.


*
126
[Chap. VIII.
FUGUE.

}
1
!
8 (invd. & dimd.)
& dimd.).
S
S-
ន
S (invd, & dimd.)
The first half of this passage shows us the subject treated by
diminution, and imitated mostly at half a bar's distance. In the
second half, the subject is both diminished and inverted, the first
note being varied, and in this form it is used as a counterpoint
against the subject in its original shape.
277. We said above (§ 252) that one voice was allowed
to discontinue the subject in a stretto when the next voice
entered with it. It is, however, sometimes possible for each
voice to continue the subject to the end, so that the stretto is
a canon at short distances of time for all the voices. A close
stretto of this kind was called by the old theorists a stretto
maestrale--that is, a ،،
masterly stretto." The following is a fine
example-
J. S. BACH. Wohltemperirtes Clavier, Fugue 1.
S-
3*
S-
&c.
4


Chap. VIII.]
127
FUGUE.
·
Here, though the interval of entry is irregular, there is a certain
symmetry observable; the alto is a fourth below the treble, and
the tenor a fifth above (the inversion of a fourth below) the bass.
Such slight modifications of the subject as are seen in the tenor
here are always permissible in a close stretto. The first notes of
the bass are the conclusion of an entry of the subject in that
voice.
278. Another interesting example of the stretto maestrale is
seen in the following-
$
B
MA
O
Here the distances of entry are regular, both as regards time and
interval, each voice entering a third (or tenth) below, and a
crotchet after the preceding. The entries of alto and bass are
consequently per arsin et thesin. Even a finer example may be
seen in the fugue which forms the finale of Mozart's "Jupiter'
symphony. The passage was quoted in Double Counterpoint,
§ 305, as an illustration of close imitation.
""
(a)
H l b
Ha A
#ME
#I
8
279. There is still one variety of stretto to be mentioned.
Sometimes, though comparatively seldom, the first exposition of
the fugue is in stretto, the answer entering before the completion
of the subject, and very often immediately after its commence-
ment. In such cases the second pair of voices will mostly follow
the first pair with subject and answer at the same distance of
interval and time.
$
8-
S-
8
8.
J. S. BACH. Wohltemperirtes Clavier, Fugue 29.
A
J. S. BACH. Motett, "Der Geist hilft uns're Schwachheit auf."
.
$


128
[Chap. VIII.
FUGUE.
K.
1
↓
(b)
(c)
8-
S
8-
A-
be
A fugue of this kind is generally called a "close fugue." We give
two specimens of the beginning of a close fugue by other composers.
HANDEL. 'Israel in Egypt.
1

A-
A

S-
A-
S-
$e
&c.

MendelssoHN. 'St. Paul.'
A-
·་
&c.

Chap. VIII.]
129
FUGUE.
}

II
H
H
蕃​藝
​8
280. The second pair of entries in a close fugue is sometimes
at a different distance of time from the first.
A
A
&c.
8
HANDEL. 'Jubilate.'
&c.
Here the tenor follows the alto at one bar's distance; but
the treble does not enter till three bars after the bass. Notice
that here, as the first entries are by the middle voices, the
second pair of entries give the inversion of the first pair-
the answer being now above the subject instead of below it.
If the student will examine the various entries of the subject
here, he will see that they differ so much towards the close
as to render it impossible to decide with absolute certainty
where the subject ends. For this reason we have not marked
its limits as in our other examples.
J
¿


D

130
FUGUE.
[Chap. VIII.
-1
車
​1
281. In speaking of the answer of a fugue, we pointed out
that a subject in the key of the tonic must have an answer
in the key of the dominant. But if this is done with a close
fugue, we shall have the music in two keys at the same time.
In this case, therefore, to keep a clear tonality, we do not
put the answer in the key of the dominant, but simply transpose
the subject a fourth or fifth without leaving the key. In example
(a) of § 279, the answer is just as much in the key of B flat as
the subject.
282. As all our examples till now have been from Bach
and Handel, we will conclude this chapter with some extracts
from the works of more modern composers. Next to Bach,
the greatest master of all kinds of scientific writing is un-
questionably Mozart. We saw this in the specimens of canon
by him given in our last volume; and he is no less great in
fugal writing. One of the best, though one of the least known,
of his masses, is No. 12 in C. This work contains three fine
fugues, in one of which, the "Et vitam," we meet with a
peculiarity of form, deserving mention. A partial stretto occurs
on the first entry of the answer, and this is seen against each
succeeding entry. We quote the exposition.
VANES
S-
A
1
MOZART. Mass in C, No. 12.
1
·


Chap. VIII.]
音
​FUGUE.
i31

S-
A-
8-
CS-

C S-

CS-
&c.
•
It will be seen that when the tenor has the answer, the bass
imitates it in stretto. When the alto enters with the subject,
the imitation is given to the tenor, and then for the first time
appears the countersubject in the bass; it thus accompanies
the second entry of the subject instead of the first entry of
the answer as usual. There is an additional entry (§ 186)
of the subject in the bass, to allow both the countersubject
and the imitation in stretto to appear above it.
132
FUGUE.
[Chap. VIII.
1
283. From the numerous stretti found in this fugue, we select
two for quotation.
Th
H.
(a)
8
CS
A
S
S
be
į
MOZART. Mass in C, No. 12.

8
WI
8


&c.
Here not more than three of the voices are engaged with the
subject at the same time. It will be seen that the entries in
the bass and treble are per arsin et thesin, and that the last
↓
Chap. VIII.]
133
FUGUE.
i
1
voice to enter (the tenor) gives the subject complete, the other
entries being mostly fragmentary. Our second extract
(b)
A
8
VIOLINO Imo.
VIOLINO 2do.
A
VIOLA.
is the last and closest stretto, and is founded only on the first part
of the subject. In this all the voices take part.
VIOLONCELLO.
284. The fugue in Mozart's quartett in D minor (No. 13), of
which we gave the subject in § 150, is particularly rich in good
stretti. We give some of the closest.
8
HUH
Mi
5
HH
[J
*T.

(a)
&c.
&c.
(b)
MOZART. Quartett in D minor, No. 13.
ded
4
I


··

134
[Chap. VIII.
FUGUE.
i
Dip
Gib
H
H
ESTE
I
(c)
4
he be
¿


(d)
•


Chap. VIII.]
135
FUGUE.

H.
After the full explanations given of previous examples, but few
words are needed with regard to these. Observe that at (ỏ)
both subject and answer are employed by inversion, as well
as in their direct form; and that at (d) all the imitations are in
the unison and octave.
HSH
285. It is not uncommon in a stretto to find the last notes
of the subject slightly altered. In the fugue occurring in the
course of the second chorus of Mendelssohn's 95th Psalm, we
find a stretto so continuous that if the original subject
8
had been retained unaltered, we should have had a stretto
· maestrale. It will be seen that the modification is in the
melody, not in the rhythm.
S-
8-
8-
be
be
+ bu

8
S-
ន
MendelssohN. 95th Psalm.

S-
Creep
2
·
i

136
[Chap. VII.
FUGUE.
286. Our next illustration is by Spohr. The original subject
of the fugue is
In the last and closest stretto of this fugue, only the first notes
of the subject are imitated by the alto and tenor; but the treble,
which enters last, gives the entire subject, though with some
modifications of detail.
#N
Ee
(a)
bo
&
287. Our last examples, by a living composer, will illustrate
the modern freedom of treatment in a stretto.
BRAHMS. Deutsches Requiem.
bo.
ddddd
bo
1

•
لو
be
SPOHR. 'Fall of Babylon.



be
d
&c.
Chap. VIII.]
FUGUE.
137
The lower notes on the bass staff are the real bass of the
harmony, given to the orchestra; the upper notes show the
voice part. Here is an example of a close stretto, modulating
freely from C through F and B flat to E flat. This is distinctly
modern in character; the old masters rarely go beyond tonic and
dominant keys in a very close stretto.
(b)

Call
H.
$3
&c.
In this passage from the same fugue, the imitation is closer
and more continuous than in the preceding. There are in all
nine entries of the fragment of the subject, the last being a
sequential repetition of the preceding.
288. The stretto is capable, as will be seen from our examples,
of so much variety that it is impossible to deal exhaustively
with the subject in such a book as this. It is hoped that
enough has been said in this chapter to enable the student
to analyze for himself, and to understand any stretti that he
may meet with in the fugues he may be playing. He will
learn far more by such analysis than in any other way; and
it is for this reason that we have dissected and explained so
many passages in this and the preceding chapters.
289. As practical exercises on the stretto, let the student
take the fugue subjects given at the end of Chapter IV., and
try to make as many stretti as he can from them. He will
find that some of them will work quite easily in this way,
while others will be less pliable. He should try them at various
distances, both of time and interval. For his two-part stretti he
should also write free parts, making three or four-part harmony.
4
138
Chap. IX.
FUGUE.
CHAPTER IX.
THE MIDDLE AND FINAL SECTIONS OF A FUGUE.
Ist Section.
Chief subject.
(Tonic key.)
290. Hitherto our task has been comparatively easy. It is
possible to give very definite rules as to the correct answering of
a fugue subject, the treatment of the exposition and episodes, and
the construction of stretto. But in dealing with those parts of a
fugue which we are now approaching, we are met by far greater
difficulties than any we have as yet encountered. These arise
from the fact that as soon as in composing a fugue we get
beyond the exposition (or counter-exposition, if there be one), we
are left to a very great extent free to do what we please; and it
is quite impossible here to give more than very general principles
for the guidance of the student.
DAROGA OMERTULISANE MAR
(Manda
*** #0 {
291. The first great fact which must be clearly grasped is,
that every fugue, however much variety there may be in the
details, is in its main outlines constructed in the same general
form. This is the form which is commonly known by the name
of Ternary or Three-part form.* A movement in ternary form can
always be divided into three principal sections. In a piece other
than a fugue (for instance, in the slow movement of a sonata, in
which this form is frequently used), the first section will be mostly
in the key of the tonic, and will close either in that key, or in
one of the most nearly related keys-probably the dominant if
the movement be in a major key, and the relative major if it be
in a minor key. The second part of such a movement generally
consists of an episodical subject, but is invariably in a different
key from the first part; while the third section usually repeats
the subject of the first in the tonic key.
292. We can best show the ternary form by a diagram—
2nd Section.
1
Episode.
(Related key.)

3rd Section.
Chief subject.
(Tonic key.)
This skeleton form can be filled up in an almost infinite number
of different ways, as regards variety of detail; but the broad.
outline given above can always be distinctly traced.
* The subject of Form as a whole will be dealt with in a later volume of this
series; but a short account of ternary form is needful here to render the subsequent
explanations intelligible.
1
+
Chap. IX.]
FUGUE.
139
293. The same form, though with some modifications, which
we shall proceed to point out, is clearly to be seen in every
well-written fugue. Its first section comprises the exposition and
counter-exposition, when there is one, or (if there be no counter-
exposition) it may also include an entry of subject or answer after
the first episode, provided such entry be in either of the keys of
the exposition. It will be remembered that the whole of the
exposition oscillates, if we may so speak, between the keys of the
tonic and dominant. If at the end of the exposition, the first
episode modulates, so as to introduce an entry of the subject or
answer in a new key, then the first section of the fugue ends with
the exposition itself. For an illustration of this, see the passage
from Bach's fugue in C minor, quoted in § 215. Here the
exposition ends on the first note of the ninth bar, and the follow-
ing episode, which modulates to E flat, to introduce the next
entry of the subject, is the beginning of the middle section of the
fugue. But if the first episode does not modulate away from
the tonic or dominant key, but leads either to the counter-
exposition, or to an isolated entry of subject or answer in the
original key (as in our example (a) § 222) this episode and the
following entry belong to the first section. To put it in general
terms- The first section of a fugue extends as far as the end of the
last entry of the subject or answer in the original keys of tonic and
dominant. As a natural corollary of this, the second section
begins with the commencement of the first episode which
modulates to any other key than that of tonic or dominant.
294. The length of the middle section varies greatly in
different fugues. In some it is very short, containing only one
or two entries of the subject, connected by episodes of only a
few bars' length. For instance, in the 31st fugue of the 'Wohl-
temperirtes Clavier,' a somewhat long exposition is followed by
the counter-exposition in stretto which we quoted in § 270.
Thus far all belongs to the first section of the fugue, because
we never get away from the tonic and dominant keys. If the
student will examine this piece he will see that, out of 70 bars
which it contains, the exposition and counter-exposition extend
to bar 44, or nearly two-thirds of the whole. There is only one
episode in this fugue (bars 44 to 53), followed by an entry of the
tenor in the key of the subdominant (bars 53 to 58), after which
the reintroduction of the subject and answer in the tonic key
(bars 59 to 70) form the final section of the fugue. The whole
will therefore be analyzed thus-
First Section-Exposition and Counter-exposition (bars 1-44).
Middle Section-Episode and entry of subject in subdominant
(bars 44-58).
Final Section-Return of subject and answer in tonic key:
Coda (bars 59-70).
295. The disproportion in the length of the middle and final
sections of this fugue, as compared with the first section, is
+
T
i
140
[Chap. IX.
FUGUE.
i
very unusual, and we have purposely given it as an extreme
instance. More frequently the exposition will be comparatively
short, and the middle section will contain at least two or three
entries, or groups of entries, of the subject. We will take
the 21st fugue of the 'Wohltemperirtes Clavier' as
a fair
average specimen of the relative lengths of the three sections.
The opening bars of this fugue were quoted in § 173.
296. If the student will take his copy of the fugue, and
number each bar for reference, he will find the following analysis
of its form perfectly easy to follow.
First Section (Bars 1 to 17)-Exposition, including an addi-
tional entry in the treble (§ 187).
Middle Section (Bars 17 to, 41)-This section contains four
distinct features :-(a) First episode (bars 17 to 22); a sequential
extension of the last part of the subject, modulating to G minor ;
(b) First group of middle entries (bars 22 to 30), viz. : subject
(alto) in G minor; answer (bass) in C minor, both entries being
accompanied by the two countersubjects; (c) Second episode
(bars 30 to 35); a modification of the first, in the first bars
of which we see a free inversion of bars 19, 20, the change in
the quaver figure of a fifth to a third, causing the double counter-
point to be partly in the octave and partly in the thirteenth;
(d) Second group of middle entries (bars 35-41). This com-
mences with a fragmentary entry of the answer in the alto,
followed by a complete entry of the subject in E flat.
Final Section (Bars 41 to 48)-Return of subject (alto) in
the tonic key, the first notes being altered to connect better with
the key of E flat (bars 41 to 45); coda (bars 45 to 48).
297. The analysis of another fugue from the same work
will assist us in understanding the construction of the middle
section. We select No. 34 in E minor. This fugue, of which
we quoted the subject and countersubject in § 168, has a real
answer. In such a case, it is impossible to distinguish between
subject and answer, excepting by observing the distance of
entry. If a second entry is a fifth above or fourth below
the first, we know that the first was the subject and the second
the answer; if the second were the fourth above or fifth below
the first, then the first would be the answer and the second
the subject. But with single entries, or entries at other distances,
there is no means of distinguishing; we therefore shall always
speak of the theme as the subject in doubtful cases. If the
answer be tonal, as in the fugue last analyzed, the difference
in its form shows at once which it is; though even in this
case we often find a real instead of a tonal answer in the later
sections of a tonal fugue.
298. The fugue in E minor is so instructive that we give it in
full, writing it in open score. We most strongly recommend to
the student the putting fugues into score; he will get a far deeper
Chap. IX.]
FUGUE.
141
and more accurate insight into their construction by this means
than by any amount of mere reading or playing them.
J. S. BACH. Wohltemperirtes Clavier, Fugue 34-
H
O
H
4
7
10
S-
13
1
5
11
14
8
2
6
12
CS-
15
3
CS
9
te
A
te
8-
1
1
·
1

*

.
C


·

142
[Chap. IX.
FUGUE.
16
19
22
25
17
23
20
26
CS-
A
Sel
S-
18
24
30
27
21
Middle
Section.

Episode 1.





28
29
Chap. IX.]
143
FUGUE.
11.
O
H.
31
H
INH
FLH
IFR
34
37
IOS
40
43
es
fe
C8-
32
35
38
41
CS-
44
#ego
33
Episode 2.
S
36
39
42
45
I

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&


↑
↓
·
144
Th
H.
MM
HE
H
HTH
HI
49
CS-
52
55
58
3.
は
​8-
Episode 4.
47
50
56
53
FUGUE.
Jed. J
Episode 3.
8
48
51
54
57
[Chap. IX.






59
60
Chap. IX.]
145
FUGUE.

H
II.
H.
TO
61
64
67
70
73
#d
Final Section.
K
Pre
71
65
CS
62
68
CS-
Episode 5.
8
66
69
72
63

?
Ι
*



74
75
146
[Chap. IX.
FUGUE.
4

1
:
❤
76
79
82
85
77
<
83
80
AM
86
Coda.
78

81

84

299. The first section of this fugue contains only the exposi-
tion. Though the subject is announced in an outer part, we do
not find here the additional entry spoken of in § 186; perhaps
because of the extent of the subject, which is the longest of any
in the Forty-Eight.' The exposition ends in the 18th bar, and
is immediately followed by the first episode (bars 18 to 23). As
this episode does not introduce a new entry in either tonic or
dominant key, but modulates to the relative major, we see
Chap. IX.]
HUGUE.
147
that it belongs to the middle section of the fugue, and not
to the first (§ 293). This first episode is formed from the last
bar of the subject, continued sequentially in the bass as far as
bar 20, and accompanied by a figure, evidently founded, as
regards its rhythm, on the third and fourth bars of the subject,
and treated by free imitation between treble and alto. The
second half of the episode contains a new sequence in the
bass-a modified form of the treble of bar 7-accompanied by
the last notes of the subject, given alternately by inverse motion
in the treble and direct motion in the alto.
300. The first episode, ending, as we have seen, in G major,
leads to an entry of the subject in that key (bar 23). It is
accompanied by the countersubject, which enters in the alto at
bar 26, and which here for the first time appears below the subject.
At bar 29 the answer enters in the alto. That it is to be looked
at as an answer here, is shown by the fact that it is a fourth below
the preceding entry in the treble. The countersubject is given,
as usual, to the voice which last had the subject. The bass
accompanies with a free part, the material of which is taken
partly from the treble of bars 7 and 8, and partly from the last
notes of the subject. These two appearances of subject and
answer form the first group of middle entries, which extends from
bar 23 to bar 35.
301. The second episode (bars 35 to 41) is made of the same
material as the first-mainly the last notes of the subject, but
with different combinations from the previous ones, and modu-
lates to B minor. In this key, the next middle entry is made
by the bass (bar 41), the countersubject now being in the alto,
and the treble supplying a counterpoint mostly made from the
last notes of the subject, direct and inverted. It must be
noticed that all the middle entries after the first are isolated
entries—that is, each one is divided from the following by an
episode.
302. The third episode is the shortest of any (bars 47 to 49).
It is a transposition a fourth lower (with a slight modification at
the end) of bars 18 to 20 of the first episode, and leads to an
entry of the subject (alto) in the original key (bars 49 to 55).
In a large number of fugues a return to the tonic key is not
found till we reach the final section of the fugue; but we
sometimes, as here, meet with a middle entry in the tonic.
We see another instance in the third fugue (C sharp major) of
this work. When an entry of the subject in the tonic is not
followed by any entry in another key (except possibly the
dominant), this tonic entry indicates the beginning of the final
section of the fugue; if, as here, another subsequent modulation
is made, the tonic entry forms part of the middle section. In
the entry now under notice, the countersubject appears for the
first and only time in the bass. Though this entry and the
preceding (in bar 41) bear to one another the relation of tonic
1
=
148
[Chap. IX.
FUGUE.
:
{
and dominant, we have not described the B minor entry as an
answer, because it is separated from the next by a short episode.
303. The fourth episode (bars 55 to 59) presents us with the
old material—the last notes of the subject sequentially treated in
the treble—with new counterpoints for alto and bass. It modu-
lates to A minor, in which key the last middle entry is made by
the treble (bars 59 to 65), the alto having the countersubject.
304. The fifth, and last episode (bars 65 to 70), like all the
others, shows the last part of the subject in fresh combinations.
It leads back to E minor, to introduce the final section of the
fugue, which will always be in the key of the tonic. The pause
after the half cadence in bar 70 is rather rare in an instrumental
fugue, but somewhat more common in a vocal one.
305. One introductory bar after the pause leads to the final
entry of the subject (bass) in the tonic key (bars 71 to 77). In
some fugues all the voices enter with either subject or answer in
the final section. This is especially the case in fugues which
have a stretto, a feature which, it will be seen, is wanting in the
one now under notice. But in many of the fugues of Bach, the
final section contains, as here, only one entry. This is followed
by the coda (bars 77 to 86). A coda (Italian = tail) is a passage
added at the end of a piece of music to bring it to a satisfactory
conclusion. Sometimes, as here, it will consist of only a few
bars; sometimes, as in many symphonies and sonatas, it will be
of considerable length and importance. The chief feature of the
present coda is the ornamented dominant pedal (bars 78 to 81);
we also, quite exceptionally, find a second pause (bar 83), here on
the last inversion of a dominant minor ninth.
306. Another point of importance is illustrated in this coda.
In the 83rd and last bars will be seen the introduction of an
additional voice. This is often met with at the conclusion
of a fugue. Out of the 48 fugues in the 'Wohltemperirtes
Clavier' we find such additional parts in sixteen, mostly in
approaching the final cadence, but occasionally (e.g., in fugues
35 and 39) earlier in the coda. Let the student examine, as
striking examples of this procedure, the last bars of the fugues in
A minor (No. 20) and C sharp major (No. 27).
307. We will now tabulate, for future use, the entries of the
subject in the fugue just analyzed, noting the succession of keys,
and the voice to which each entry is given.
I. Exposition.
1. Subject (treble)—bar 1.
2. Answer (alto)-bar 6.
3. Subject (bass)—bar 12.
II. Middle Section.
E minor.
B minor.
E minor.
4. Subject (treble)-bar 23. G major.
5. Answer (alto)-bar 29. D major.
Chap. IX.]
149
FUGUE.
1
1.
IH
III. Final Section.
5
It will be seen that no two consecutive entries are for the same
voice, or in the same key.
loo
6. Subject (bass)-bar 42.
B minor.
E minor.
7. Subject (alto)—bar 49.
8. Subject (treble)-bar 59. A minor.
308. Before proceeding to lay down any general principles, we
will analyze another fugue from the same work, constructed on a
different plan, and illustrating several points not shown in the
fugue in E minor.
1
8
9. Subject (bass)-bar 71. E minor.
S-
6
2
A-
Middle
Section.
S-
10
J. S. BACH. Wohltemperirtes Clavier, Fugue 29.
A-
7
3
11
Episode 1.
A-
8
4
12
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-
-


J

150
[Chap. IX.
FUGUE.

·
H
HINH
Episode 2.
OH
13
17
21
24
8-
that
14
18
A
22
A
25
A-
8-
15
19
S
23
26
16
20
Episode 3.



1
Chap. IX.]
151
FUGUE.
3

Fin
HN
#
14.
741
O
27
31
Episode 5.
35
39
A-
28
32
A?
36
Final Section.
8-
29
33
37
41
S-
Episode 4.
8-
Ha`H.
UI.MH
.
8-
30

34

38

et
40
42
152
[Chap. IX.
FUGUE.
i
43
A-
47
Coda.
S
44
48
4
S-
?
F
8.
S-
45
49
77
8-
46
50
This splendid fugue-one of the most perfect of the Forty-
Eight' is a remarkable example of Bach's power of letting
art conceal art. There is not one which flows more naturally
and unconstrainedly, and yet there is not one which is fuller of
scientific device. This will appear from our analysis.
C
309. Let us first look at the subject. We see here an
exception to the general rule given in § 29, that with a downward
leap of a fifth the first note will be dominant, and the second
tonic. The subject begins with a leap from tonic to sub-
dominant, and consequently takes a real answer. Had D been
a dominant, the key of the fugue would have been G, and the
answer
As C sharp is not used in the subject, the key is doubtful at first;
in such cases the answer always decides the point.
310. As Bach intends the fugue to contain a large amount of
close imitation and stretto, there is no regular countersubject
(§ 176); but instead of this, the last half of the subject is
ingeniously made to serve as a counterpoint to the first half,
-;




Chap. IX.]
FUGUE.
153
■
against which it is mostly employed in double counterpoint in the
tenth (compare bar 3 with bars 6, 10, 21, etc.). The figure
cannot be called a countersubject because it is not contrasted
with, but derived from the subject. We shall see that it forms
the germ of all the episodes. In the fourth bar it is already used
in imitation to make a codetta.
311. The exposition foreshadows the treatment by stretto
which Bach intends; for the entry of the bass in bar 6 is
half a bar sooner than its regular place. The exposition ends
at the 7th bar, and the first episode is made from the figure just
quoted, by close imitation, in all the voices at one crotchet's
distance.
•
312. As the following entry of the subject (bar 10) is in
E minor, we should expect the episode to modulate to that.
key. Bach, however, does not do this, but makes his modulation
on the first notes of the subject itself. As the original keys of
tonic and dominant are not quitted till after the episode, we
include this in the first section of the fugue, and consider the
middle section to begin in bar 10.
313. The first group of middle entries, bars 10 to 13-
subject (alto), answer (treble)—is followed by the second episode,
only one bar in length. We count this as an episode because it
effects a modulation from B minor to A. At bar 14 the first
stretto is introduced. It is for two voices only, in the fourth
above, and at a distance of half a bar. It is seldom that so early
a return is made to the tonic key; but it may be said here, that
in fugues containing much stretto, we often find a much greater
prevalence of the original keys, and less modulation, than in
fugues in which there is no close imitation. Nos. I and 4 of the
'Wohltemperirtes Clavier' are illustrations of this.
314. In the third episode (bars 16-21) we see the figure of
the second, a sequential prolongation of the first, treated by close
imitation in all the voices. It leads to the second stretto (bars 21
to 23). We said in § 251 that when there were several stretti,
their interest should gradually increase. We see this illustrated
here. Three voices now take part in it; the treble enters one bar
after the tenor, and the alto half a bar after the treble. The
intervals of entry (fifth and octave) are again regular.
315. Bar 24, though not containing subject or answer, cannot
be considered as episode, because it does not modulate to a fresh
key, but introduces an entry which clearly belongs to the preceding
group, being the regular answer to the last preceding entry-the
subject in bar 22. We therefore regard bar 24 as a codetta,
similar to that so often seen in an exposition.
+
/
154
FUGUE.
[Chap. IX
t
:
}
1
LA
}
+
•
316. At bar 27 the third stretto is introduced. The interest
is here heightened by bringing in the imitations at a closer
distance-one crotchet instead of half a bar. Variety is also
obtained by introducing all the voices in the octave. We have
marked the entries with 'A' instead of 'S,' because the G natural
of the tenor in the 28th bar proves the key of the music to be D.
The 'A-?' in the alto of the same bar indicates an incomplete
entry. Another, similarly marked, will be seen in bar 44.
317. Another series of close imitations will be found in
the fourth episode (bars 29 to 33). This leads to the fourth
middle entry-another stretto for three voices, each a sixth
above the preceding, and at a crotchet's distance. This stretto
is an advance upon the preceding, inasmuch as now all the
three voices complete the subject.
318. The fifth and last episode leads to the final section
of the fugue, in which the subject is once more introduced
in the tonic key (bar 40). It is now accompanied with simul-
taneous double counterpoint in the tenth and octave (compare
bar 40 with bar 3). The entry of the answer at bar 43, with
chromatic alterations, leads to the last and closest stretto. This
is the stretto maestrale, already quoted and described in § 278,
and it is followed by a short coda, in which the figure of imitation,
so often referred to, is maintained to the very last note.
319. It will be seen that this fugue differs in many important
respects from the fugue in E minor, and nearly every leading
feature of a fugue which is not shown in the one is illustrated by
the other. One point of difference is that in the former there
are scarcely any rests; all the voices are almost continuously
occupied. In the fugue in D, on the other hand, we find not
only one, but in bar 16 two voices resting at once. It is
generally better to give occasional rests to some of the voices.
After such a rest, the voice that has been silent should enter with
the subject, or with some decided feature of the counterpoint (see
the entries in bars 17 and 18), and not drop in, as it were, inci-
dentally, and without anything particular to say.
320. Another point to notice in this fugue is that nearly all
the entries of the subject are preceded by a rest. That this is
not absolutely necessary was seen from the fugue in E minor, in
which very few of the entries are so approached; but it is
nevertheless preferable as marking the entrance of the subject
more clearly. Where this cannot well be managed, the next
best thing is to approach the entry by a leap, as in the fugue
in D, bars 27, 33, and 43.

321. In bars 16, 20, and 27 of the fugue in D will be seen full
cadences, and at bars 10, 33, and 44, inverted cadences. The
latter are very common, the former are rarer. It must be
remembered that when a full cadence is employed in a fugue,
the music must never come to a standstill; the last note of
the cadence must always be a starting point for a new entry,
}
Chap. IX.]
155
FUGUE.
l
either of the subject (as at bar 27) or of some important figure of
counterpoint (as at bars 16 and 20). Occasionally in old fugues,
we meet with a full close in some related key just before the final
stretto; but this is not to be recommended.
322. To what keys, and in what order, is it advisable to
modulate in the middle section of a fugue? To this important
question it is not possible to give more than a general answer.
The rule given by the old theorists was that the modulations in a
fugue should be confined to the nearly related keys. We quote
Cherubini's remarks on this subject :-
"When a fugue is in a major key, the key into which we should modulate
first is that of the dominant with its major third; then into the sixth-the
relative minor key of the principal key; after that into the major key of the
subdominant, to the minor key of the second, and to the mediant, also minor;
and then return to the key of the dominant, in order to proceed to the
conclusion, which should be in the principal key.
"It is permitted in the course of a fugue in a major key to change the
principal key into the minor; but this permutation should be employed
only for a few moments, and merely to bring in a suspension on the dominant,
in order afterwards to attack the principal major key.
"When a fugue is in a minor key, the first modulation is into the mediant
major key, which is the relative major of the principal key; then we modulate
in turn into the dominant minor key, into the sixth major key, into the
subdominant minor key, and into the seventh major key; and lastly from
one of these keys return to the principal key."
323. We have quoted Cherubini somewhat fully, because it is
well that students who are working for an examination should
know what the old rules are; but when we come to apply to
them the test of Bach's practice, we find that they will not hold
water for a moment. In the whole of the 'Forty-Eight,' there is
not one single fugue in which the order of modulation prescribed
by Cherubini is observed. What is even more to the point-in
the Art of Fugue,' a work written by Bach, to show the proper
method of fugal construction, we also find no fugue written on
Cherubini's plan.
،
324. Besides this, we find that Bach, though he generally
keeps within the circle of nearly-related keys, has no hesitation
about going into unrelated keys when he has a mind to. No. 4
of the Art of Fugue,' the key of which is D minor, contains a
modulation to B minor. In the fugue in E minor (No. 10 of the
'Forty-Eight') there is at bar 30 an entry of the subject in
D minor; and in the fugue in A flat (No. 41 of the same work),
we see at bar 32 an entry in E flat minor. The great organ fugue
in D contains entries in C sharp minor and E major, and the
organ fugue in B minor has an entry in C sharp minor. It is
quite clear, either that Bach did not know how to write fugues
properly, or that the old rules need altering. Of course we choose
the latter alternative.
325. The rules as to the course of modulation and the
middle entries in fugues which we deduce from Bach's works,
are as follows:-
I. It is best in general to keep within the circle of nearly-
.
156
[Chap. IX.
FUGUE.
!
related keys, but an entry in an unrelated key is occasionally
possible, if such key be naturally introduced, and not (to use
Mozart's immortal phrase) "pulled in by the hair of its head."
II. A middle entry may either be isolated-that is a single
appearance of subject or answer in one voice; or there may be a
group of entries, two or more voices in succession giving subject
or answer. In the latter case it is best, except in a close stretto
(see bars 44, 45, of the fugue in § 308), that the entries should be
at the distance of a fourth, fifth, or octave.
III. No two successive groups of entries should have the
same order of voices.
IV. No two groups of middle entries should be in the same
key, nor should the same voice have subject or answer twice in
succession.
A
326. This last rule is not always strictly observed.
remarkable exception will be seen in the 19th fugue of the
'Wohltemperirtes Clavier,' where the bass gives the subject in
bar 4, and the answer immediately after in bar 6. Another
example will be seen in the fourth fugue of the same work,
where at bars 19 and 22 there are two consecutive entries of
the subject in the tenor. The rule is, nevertheless, a good one,
and the student will do well to adhere to it carefully.
327. It is not necessary that all the voices should take part in
a group of middle entries. In a two-part fugue it will of course
be needful, but in one with more than two voices, one at least
may rest, if desired. This, in fact, is often expedient, for the
sake of obtaining the contrast of thinner and fuller harmony.
For an example, see No. 15 of the 'Forty-Eight,' bars 34 to 46,
and 51 to 55.
In the final section of a fugue, which always
begins with the last return of the original key, it is imperative
that all the voices be engaged, though it is not necessary that all
should have subject or answer. If, however, the fugue contains
stretti, it is best that all the voices take part in the final stretto,
which should also be the closest.
328. We have already seen that there is no fixed number of
groups of middle entries, which may vary from one or two to five
or six, or even more. Neither is there any rule as to the order of
voices for these middle entries, except in so far as concerns the
point referred to in Rule III., § 325. It must not be forgotten
that if stretti are used, their interest should always be cumulative.
329. When a pedal point (either dominant or tonic) is met
with in a fugue, it is almost always in the final section.
Occasionally we find a pedal earlier in a fugue, as, for instance,
m No. 35 of the 'Wohltemperirtes Clavier,' and in the choral
fugue, "For holy blood must be" in Schumann's 'Paradise and
the Peri.' Such cases are, however, exceptional, and the student,
if he wishes to use a pedal point, had better reserve it for the
final section, as it is seen in the fugue in E minor in § 298. In
a fugue containing stretti, the last is often made upon a pedal,
Chap. IX.]
157
FUGUE.
which sometimes in this case is an additional voice, as in fugue 20
of the 'Forty-Eight,' bars 83 to 87.
330. A few general principles will conclude this part of our
subject. We have already ($ 321) spoken of the necessity of
continuity in fugal writing. This necessity will be best shown
by quoting a passage from Mozart's Musical Joke,' written as a
burlesque of unskilful composers. This work is full of the most
ludicrous mistakes in composition, intentionally introduced.
Consecutives, passing notes quitted by leap, and similar atrocities,
abound in it, but treated so skilfully that the joke is always
perceptible. In the finale, Mozart introduces a little bit of
fugue, thus-
MOZART. 'Ein Musikalischer Spass.

VIOLINO Imo.
VIOLINO 2do.
VIOLA.
Basso.

tr

The student will see that there is here a subject, a counter-
subject, and a regular exposition; and yet how ludicrous the
158
[Chap. IX.
FUGUE.
?
effect of the whole is! This is because of the want of
continuity; the piece is chopped up by the full cadences into
lengths of four bars each. A full cadence in a fugue (which
should in all cases be sparingly used) must always be a point
of departure for some new entry, if not of the subject, at all
events for some important feature of counterpoint. We have
referred to this above, but we repeat it as a point of vital
importance in fugal writing, which will be enforced by the
example just given.
331. We saw in the fugue in D (§ 308) the expediency of
occasional rests in the voices (§ 319). After a rest, the voice
which has been silent may enter on any part of the bar; but it
should always end before a rest, on an accented beat.
332. One final point remains to be noticed. It has several
times been incidentally said that a fugue is essentially a polyphonic
composition. It is therefore of great importance that each voice
should preserve its individuality. Passages for two parts in thirds
or sixths, though not absolutely prohibited, should be sparingly
used, and, in any case, not for long together. Passages in which
a subject is accompanied by plain chords are also seldom
advisable, though they are occasionally to be used, even with
good effect, as in the following example-
J. S. BACH. Wohltemperirtes Clavier, Fugue 18.

th
LEA
The student will do well in his attempts at fugue to keep to the
strictly contrapuntal style.
333. The student may now begin the composition of a
complete fugue. To show him how to set to work, we shall
write three fugues for him, one in two parts, one in three, and
one in four.
We will take the subject we wrote in § 254 to
illustrate stretto, as this will give us the opportunity of intro-
ducing several stretti at different intervals and distances. The
student had better begin by writing a few two-part fugues, as
these are easier than those with three or four voices. He
must remember not to introduce any progressions between the
voices which would not be allowed in free two-part counterpoint.
He should also always bear in mind the harmonic progressions
indicated by the outline harmony.
A
4
FUGUE.
159
334. The first thing to do is to lay out clearly in the mind the
general plan of the fugue. We know that the first and the final
sections will be in the keys of the tonic and dominant; but we
ought also to decide on the keys and order of the middle entries,
and not start on our journey like Abraham, not knowing whither
we go, and trusting to luck to come out somewhere. As we do
not intend any of our specimen fugues to be very long, we will
content ourselves for the one in two parts with two groups of
middle entries—one in A minor and the other in F major. The
outline of the fugue will therefore take the following form :-
Chap. IX.]
(1) Exposition, to which, as there are only two voices, we shall
add a counter-exposition.
(2) First episode, modulating to A minor.
(3) First middle group of entries in A minor, with first stretto.
4) Second episode, modulating to F.
(5) Second middle group of entries in F, with closer stretto.
(6) Third episode, modulating back to C.
(7) Final section of fugue; entries in C, with closest stretto.
335. Some such outline as this ought to be clearly in the
student's mind before he begins to write. We now give the
complete fugue.
5
Allegro.
A
8-
1
13
CB
2
A-
10
14
CS
CS-
3
11
15
4
12
8
16
L
3
.
ف


•

J

160
[Chap. IX.
FUGUE.

C-
17
21
25
29
33
37
41
$7
?
26
18
42
A
22
S-
34
30
thats
38
Middle Section.
Episode 1.
43
19
23
27
31
?
A
Episode 3.
35
39
36
44
20

A-
24

28
Episode 2.

32

Final Section.
S

40
rall.
A

45
Chap. IX.]
FUGUE.
161
The rule given in § 325 that two successive entries should not be
in the same voice does not apply to two-part fugues; for if it did,
the same voice would have either subject or answer mostly all
through a fugue. We shall therefore modify the rule in this case,
and say that in two-part fugue "the same voice should not have
subject or answer twice in succession, unless separated by an
episode."
336. We have written a countersubject against the answer
(bars 5 to 9), but shall be unable to make much use of it in
the middle and final entries, because of the stretti; for the
countersubject must evidently be discontinued when the voice
that is giving it has to take up the subject or answer.
fragments of it will be seen in bars 26 and 34.
But
337. In the counter-exposition (bars 10 to 18) the treble
which first had the subject leads with the answer, and the
bass replies with the subject. The first episode (bars 18 to 21)
is made from the inversion of the last three notes of the subject,
treated sequentially by the treble, and imitated in the fourth below
by the bass.
338. The first group of middle entries (bars 22 to 28) is led
by the answer, and imitated in the octave, also by the answer, at
two bars' distance. The leading voice is here able to complete
the answer. The second episode is founded on the fourth
bar of the subject, imitated in the fourth above; it will be
remembered that the imitation in the first episode was in the
fourth below. This second episode is only two bars in length.
339. In the next group of middle entries (bars 30 to 35), the
subject in the bass is followed in the regular interval by the
answer at one bar's distance. The third episode is a sequential
treatment by the treble of an ornamented form of the counter-
subject in bar 8, imitated in the fifth below by the bass. The
final section of the fugue contains the closest stretto (bars 40 to
45) at half a bar's distance, the answer being lengthened by the
repetition in bar 43 of half a bar, to bring the piece to a
satisfactory close.
340. We will now write a three-part fugue, and for the sake of
variety will take the answer of the last fugue as our subject. As
this answer was in the key of the tonic, it follows that the present
answer will be in the key of the dominant, and will consequently
be identical with the subject of the last fugue. We will write an
entirely new countersubject-this time, for a change, in double
counterpoint in the twelfth, and will begin the fugue with the
middle voice, so as to show the countersubject in both positions
in the exposition. Our plan of modulation shall be the same as
in the last fugue, with middle entries in A minor and F, and each
group of entries after the exposition shall contain a stretto.
L
162
[Chap. IX.
FUGUE.

THE
Allegro.
S
5
1
A-
S
9
CS-
13
CS-
Episode 1.
S-
17
Middle Section.
2
C8-
6
10
14
18
3
?
7
11
15
A-
19
4

8

12

16

20
?
Chap. IX.]
163
FUGUE.
AD
H
HNI
A-
21
25
28
8.
32
Episode 3.
36.
C 8-

Episode 2.
22
29
33
37
?
?
26
b
CS-
?
38
23
S-
30
34
27
39
24


8
31

35

1
164
[Chap. IX.
FUGUE.
S
40
Final Section.
44
A-
-
S-
41
8-
45
42
46
1

43
?

47
341. After the explanations given of the last fugue, this will
need but few remarks. Note that in all the stretti the last voice
to enter always has the subject or answer complete (§ 252).
Observe also, as showing how much variety is possible in a
subject well adapted for the purpose, that none of the stretti
here given are identical with those in three parts made from
the same subject in §§ 264, 265. The incomplete entries are, as
before, indicated by S--? Where the entries are at irregular
distances, they are marked with S, whether they resemble subject
or answer.
342. Now let us look at the episodes. The first is made
from the sequential inversion in the bass (bars 13 to 16) of the
last notes of the subject, accompanied by sequential imitations in
treble and alto of a variation of bar 4 of the subject, by direct
motion. The second (bars 25 to 30) is a canon in the fourth
below between treble and bass, founded on the first part of
the countersubject, and accompanied by a florid counterpoint
in quavers for the alto. The third (bars 36 to 40) is another
piece of canonic imitation between treble and bass, now at
half a bar's distance, made from the beginning of the answer
in a varied form, while the alto has partial imitation (mostly
rhythmic) of the first notes of the subject. . Note in bar 43 the
transient modulation to the subdominant, to avoid the awkward
progression of a tritone in the alto and bass.
343. For our last illustration we write a four-part fugue. We
take the first half only of our subject, so as to make the piece
Chap. IX.]
FUGUE.
165
more concise. A short subject is frequently advisable with a
larger number of parts; with a longer subject there is often
danger of the fugue becoming straggling and tedious. As we
intend to combine the theme with itself in stretto as much
as we can, we will write no countersubject (§ 176). We will
also introduce some points not illustrated in the preceding fugues.
We will make a larger number of modulations, giving middle
entries in G, A minor, D minor, F, and E minor (all the nearly
related keys) before we reach the final section of the fugue.
H.
H.
11.
IM
KUH
MCH
H
Allegro.
8

1
5
Codetta.
2
6
A-
10
7
A-
Speed
3
4

8
8

Middle Section.
Episode 1.
11
12
166
[Chap. IX.
FUGUE.

13
S-
17
21
A
25
TH
18
A
Ee
14
22.
26
Episode 2.
15
A
23
19
A-
16

20
24
S-
?
S (inverted.)


1
27
28
Chap. IX.]
167
FUGUE.

1.
TH
LIKED
11
That
JEN
IH
11
29
33
8-
36
40
b
b
Episode 3.
30
8-
41
37
S
34
8-
31
42
8.
38
8-
35
32


b
39

43
Episode 4.
168
[Chap. IX
FUGUE.

*
44
48
S-
52
56
S-
53
45
49
57
54
S
46 ·
50
Final Section.
S
-8
Coda.
S
58
·
55
S-
47
S
Pedal.
51
S-
S-
59
•
S-

S-


Chap. IX.]
169
FUGUE.

The
60
61
62
63
344. In bars 5 to 7 we have introduced a codetta. There
was no necessity for this, as the tenor could perfectly well enter
with the subject in bar 5; but, as Bach frequently has such
a codetta in his fugues, we have written this to show how to
manage it, if it is desired. The first episode (bars 12 to 16)
is made by inverting the codetta in the tenor and bass, and
adding a sequential counterpoint in quavers for the treble.
The first group of middle entries (bars 17 to 22) shows the
first (partial) stretto, the bass entering half a bar before the
regular time with the inverted subject. Here a modulation from
G to A minor is made during the entries, instead of (as is more
usual) during the episode.
345. The second and shortest episode is made from the
beginning of the inverted subject in the treble, with a continuation
freely imitated by direct and inverse motion in the alto and bass.
Both first and second episodes are for three voices only.
346. The second group of middle entries, in the keys of A
minor and D minor, gives a stretto at one bar's distance in all the
parts—the alto entry being incomplete. It leads to the third
episode, the most elaborate of the three (bars 30 to 35). It is
a short canon 4 in 2, at one bar's distance, by contrary motion,
and with inversion of the voices, founded on the first notes
of the subject with a counterpoint of quavers. The third group
of middle entries (bars 35 to 43) is again a stretto at one bar's
distance; but it differs from the last, inasmuch as now all the
voices have the subject complete. At bar 41 is a modulation
to E minor, in which key a partial stretto, for alto and tenor only,
at half a bar's distance is seen. The last short episode (bars 43
to 46) founded on a sequential continuation of the last notes
of the subject, leads to the final section of the fugue.
347. This final section (bars 46 to 63) is far more extended
than in the other two fugues. It begins with a stretto maestrale
(§ 277), led by the treble, each succeeding voice entering at
half a bar's distance, and a fourth below the preceding. At bars
51 to 57 a pedal point is introduced, with four voices above it
(§ 329). Here there is a second stretto maestrale, the order of
170
[Chap. IX.
FUGUE.
entry of the voices being now reversed, and the bass leading. The
pedal is continued over a passage of free imitation founded on
the treble of bar 35; and at bar 58 is a coda, with a final entry of
the subject in tenths for treble and tenor, imitated by alto and
bass in tenths in the following bar.
348. From the full analysis of the way in which we have
written these three fugues, the student will probably learn as much
as is possible to teach in a book as to fugal construction. More
can be learned by analysis than in any other way. For this
reason we shall follow this book by a companion volume on
Fugal Analysis, which will contain a collection of some of the
finest fugues ever written put into score and fully annotated.
There is not room in this volume for a sufficient number of
examples to illustrate the matter thoroughly. But mere analysis
will not of itself suffice: the student must practise for himself,
writing each separate part of a fugue (exposition, episode, stretto,
&c.) till he has acquired fluency. Nothing but natural aptitude,
aided by a great deal of study and hard work, will ever make
a good fugue writer.
.
¿
Chap. X.]
171
FUGUE.
CHAPTER X.
FUGHETTA AND FUGATO
349. In the preceding chapters of this volume we have
explained the construction of the most common kind of fugue—
that with only one subject. Before proceeding to treat of
fugues with more than one subject, fugues on a choral, or
fugues with free accompaniment, there are two other varieties
of fugal writing with which this is the most suitable place to deal.
These are the FUGHETTA and the FUGATO.
"
350. The word Fughetta" is the Italian diminutive of
"Fuga," and merely means "a little fugue." It is a term of
somewhat vague application; and it is impossible to lay down a
hard and fast line of distinction between fughetta and fugue. For
example, among Bach's works for the Clavier, we find a so-called
'Fughetta' in E minor, beginning

§ 4
which is a regularly developed fugue, extending to 105 bars, with
a long middle section. In its number of bars it exceeds 46 of
the 48 fugues in the 'Wohltemperirtes Clavier.' This is an
exceptional case; but we refer to it to show the vagueness with
which the term is sometimes applied.
1
351. In the form most frequently met with, a fughetta is an
abridged fugue, and is almost always a complete movement in
itself. It contains a regular exposition; but the middle section
will have at most not more than one group of middle entries, and
in many instances it is omitted altogether. In such cases the
exposition is followed either by an episode leading to the final
entry of the subject in the tonic key, or this final entry may
follow the exposition immediately, without any episode whatever.
2
352. These variations in fughetta form will be most clearly
shown by examples. We first give an illustration by Bach of
the longer fughetta, containing the regular three sections of a
fugue, though all are on a small scale.
J. S. BACH. Fughetta in D minor.
3
4
5
6
&c.

7
8
3
172
[Chap. X.
FUGUE.

¡
9
14
19
24
29
34
!
10
15
Middle Entries.
20
25
30
35
11
for
26
31
16
21
36
12
22
27
32
17
3.7
33
Middle Section.
13
المشعل
18
28
Episode.


23


38
។

i
Chap. X.]
173
FUGUE.
39
D.
43
.66
471
51 |
40
44
48
52
Final Section.

41
45
49
53
b
ままま​.
54
42

46

50

55i
As the fugue is for only three voices, and contains no crossing of
parts which might render it difficult to follow, we give it, to save
space, on two staves. The student will by this time be sufficiently
accustomed to analysis of fugues to render it superfluous for us to
mark, as hitherto, the entries of the subject.
353. An unusual point in the exposition of this fughetta is,
that the third voice enters with the answer instead of the subject.
The group of middle entries appears to commence with the
subject in the tonic key; but the following reply at bar 25
shows that the entry in bar 20 is really the answer to the
subject in the key of G minor. Further entries in the same
key, now at the octave, are seen at bars 33 and 37, after which,
without a second episode, the final section, containing two entries
of the subject succeeded by a coda, follows immediately. This
fughetta is really a complete fugue, much condensed-a sort of
Liebig's extract" of fugue.
174
[Chap. X.
FUGUE.
354. An interesting fughetta of a different kind, also by Bach,
is that in F.

Au
It will be seen that the subject is identical with that of the fugue
in A flat, No. 41 of the 'Forty-Eight'; and if the two pieces
are compared, it will be found that, except as regards key, they
are exactly the same down to the 24th bar, where the
fughetta ends. The latter is the earlier version, and it contains
a complete exposition, an episode of four bars-no middle section
at all—but a large final section with entries for all the voices,
which, when Bach rewrote the fugue for the 'Wohltemperirtes
Clavier,' was made to do duty as a counter-exposition. If the
student will read the first half of the A flat fugue, he will see the
fughetta complete; there is therefore no occasion to quote it.
be
355. Our next example, by Handel, is different in form.
HANDEL. Utrecht Te Deum.

7
1
e
2
8
3
9
H
4
F
10
LO
5
11
6

Chap. X.]
175
FUGUE.

#21
b
12
**
H
#
18
13
15
This fughetta is for five voices. It begins like a close fugue
(§ 279); and it will be seen that at the entry of the fifth voice
(tenor), in bar 5, the subject is varied. Handel's fugues are
usually freer than Bach's. There is no episode at all, but there
is a fragmentary group of middle entries (bars 7 to 10). This
embryo middle section, if we may so term it, is followed by a
final entry of the subject in the tonic key (bar 12), and a short
coda completes the movement.
#INIMA
1
14
2
356. Another variety of the fughetta form is that which
consists merely of a complete exposition, followed by one final
entry of the subject by the voice that first led. A very neat
specimen of this variety is the following, taken from one of
Mozart's Masses.
5
16
efo
6
17
3
MOZART. Mass in F, No. 6.


176
[Chap. X.
FUGUE.

.
Off
7
HA
HO
10
8
1
2
11
9

It will be seen that here the final entry is in stretto at close
distance of time for all the voices; but in this form it is not
necessary to observe the rule (§ 252) that the last voice that
enters must complete the subject. Here the tenor in bars 10
and II gives the subject in an abridged and slightly varied form.
357. Sometimes, after a complete exposition, the final entry
will only be fragmentary, and will be followed by a coda.
d
3
12
4
BEETHOVEN. Mass in C.

ged!
Chap. X.J
FUGUE.
H.
It
#1
H
HINH
H
5
13
14
6
M
10
त
HH
15
7
11
16
8
12
177
It is somewhat unusual for the first voice to leave off on the
entry of the third, as here at bar 5; generally (and preferably)
it continues, as in our other examples, with a free counterpoint.
The final entry (bar 10) is only partial, not more than the first
half of the subject being given by the treble; from the eleventh
bar, the polyphonic style is abandoned, and in the coda all the
voices move together in plain chords.
358. The word Fugato simply means "fugued," and is
applied to passages written in the fugal style-that is to say,
in which the same subject is introduced successively in the
different voices-but in which the entries are not at the regular
!



178
[Chap. X.
FUGUE.
interval of subject and answer, or, if they are, their employment
is only incidental. Passages of imitation, provided that all the
voices take part in them, will very often be also fugato passages;
but in general in such cases the voices will enter in succession,
the first voice being either unaccompanied by any harmony at all,
or only accompanied by instruments, and not by any other voices.
Such passages are often found in pieces not otherwise in fugal
form:
359. In consequence of the freedom allowed in fugato, it is
quite impossible to give any fixed rules for its construction. Its
nåture will be best understood by the examination of specimens
by different composers, and in various styles. Our first example
will be by Bach.
J. S. BACH. Matthäus Passion.'

Et
H:
11.
U:D)


&c.

In this passage we omit the semiquaver accompaniment in the
}
Chap. X.]
179
bass, which is to some extent independent of the voices; the
bare fourths in the sixth and seventh bars are filled up by
the instrumental part. We see here that, though the interval of
entry of the voices is quite regular, it is not that of fugue
subject and answer as regards the third and fourth voices;
we have here therefore a passage of fugato.
3
360. The following well-known extract from the 'Creation' is
given in short score to save space, and the independent orchestral
accompaniment is omitted.
HAYDN. 'Creation.'
Z
FUGUE.



ממן
This example is somewhat similar to our last; but while the first
three entries are at regular distances-each a fifth above the
preceding the treble is only a fourth above the alto.
&c.
361. Similar passages to these are of frequent occurrence.
As fine examples may be mentioned, the passage in the
Offertorium of Mozart's 'Requiem' to the words “ ne absorbeat
eas tartarus, ne cadant in obscurum," and the beginning of the
allegro of the chorus, "Praise ye Jehovah's goodness" in
Beethoven's Mount of Olives.'
.
We merely refer to these,
and prefer to quote for our next illustration a fugato of a
totally different style-the opening bars of the slow movement
of Beethoven's first symphony. We condense the orchestral
score on two staves.
BEETHOVEN. Ist Symphony.
1

180
[Chap. X.
FUGUE.

11
Obe C
Although the commencement of this passage looks at first like
the subject and answer of a fugue, a moment's examination of
the counterpoint accompanying the answer will show that we have
here only fugato. The rhythm of subject and counterpoint are
identical, and the style of the whole passage is distinctly homo-
phonic rather than polyphonic. After the end of our extract,
every attempt at imitation is abandoned.
362. We conclude this chapter with two more modern
examples.
MENDELSSOHN. 'Elijah.'
CHORUS.
Basses of orchestra.
In this passage the small notes on the bass staff indicate the real
bass of the harmony, which is given to the orchestra. It will be
seen that here no two consecutive entries are at the same distance
of interval.
363. In our last illustration,
Spe
&c.


¡
MACKENZIE. 'The Rose of Sharon.'


Chap. X.]
181
FUGUE.

= &c.
the basses of the orchestra have so independent a part that it is
needful to write it on a separate staff. Here we have an example
of the modern free treatment of the contrapuntal style. Not only
the interval of entry, but the form of the subject itself varies on
nearly every repetition.
364. It is hoped that these examples will sufficiently show the
nature of the fugato. It is, of course, far easier to write than a
strict fugue, or even a fughetta, and is not of sufficient importance
to require a lengthy notice; but as this volume might perhaps
have been considered incomplete without it, we have devoted a
few pages to its consideration.
•
I
:
1
¿

F
in
·
J
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•
1
182
;
FUGUE.
CHAPTER XI.
THE FUGUE ON MORE THAN ONE SUBJECT.
[Chap. XI.
365. Having in the preceding chapters of this book fully
explained the construction of those fugues which, being founded
on only one subject, are sometimes termed "simple" fugues,
we have in this chapter to speak of the important class which
contains two, three, and occasionally even more subjects. We
shall first deal with the DOUBLE FUGUE, in which, as its name
indicates, there are two subjects.
366. In speaking of the countersubject, we incidentally men-
tioned (§ 175) that some theorists speak of a fugue in which the
subject is regularly accompanied by the same countersubject as a
"double fugue." If, however, we adopt this nomenclature, we
have no means of distinguishing between fugues with one subject
and fugues with two or more. It is very much better and clearer
to restrict the name of double fugue to two classes of fugue now
to be described :-First, those in which the two subjects are
announced simultaneously; and, secondly, those in which each
subject has a separate and complete exposition before the two
are heard in combination. Of these, the first kind is by far the
more common and the more important; we therefore deal with
it first.
367. A fundamental distinction between the kind of double
fugue we are now noticing, and the fugue with a regular counter-
subject (with which the student is already familiar) is, that in the
latter the countersubject never appears before the first entry of
the answer, and, as we have seen (§ 172), not always then. But
in a double fugue the second subject, which is really a counter-
subject of the first, accompanies the leading subject on its first
entry. This, as we shall see presently, makes a difference (some-
times a very considerable difference) in the form of the ex-
position.
368. It ought to be hardly necessary to remind students
that the two subjects of a double fugue must be written in
some kind of double counterpoint with one another. In the
enormous majority of cases, this will be double counterpoint
in the octave. In the Kyrie' of Mozart's 'Requiem," the
two subjects (which we quoted in § 175 of Double Counterpoint)
are so written as to be capable of inversion both in the octave
"
•

Chap. XI.
HUGUE.
183
and in the twelfth. It is also necessary that there should be
contrast, both melodic and rhythmic, between the two subjects,
so that each may be easily recognized whenever it appears.
369. It is best that a double fugue should be written for at
least four voices, and in vocal music this is almost invariably the
case. It is nevertheless possible, though less advisable, to write
a double fugue with only three parts. In any case, the student
will do well to attend to Albrechtsberger's recommendation that a
fugue should always have at least one more voice than it has
subjects. Thus, a double fugue ought to be in at least three
parts, and a triple fugue (with three subjects) in at least four.
But in fugues with more than three subjects (which are very rare),
this rule is not always observed, probably because in a fugue with
four subjects it is seldom that all four are present at once. The
object of the extra voice is, to be able to add a free part when all
the subjects are going on at the same time.
370. The exposition of a double fugue can be managed in
more than one way. In a four-part fugue, the best arrangement
is to let two of the voices announce the two subjects, which the
other two follow with the two answers by inversion-that is to
say, the upper of the two subjects will appear as the lower of the
two answers, and vice versa. A few examples will make this quite
clear.
J. S. BACH. Cantata, "Aus der Tiefe rufe ich.”
H
H
$1.
KOB
6+
ஆகும்
A 2.
$ 2.
A 1.
&c.
The small notes on the bass staff here show the instrumental
bass; the bass voices have only the second subject, which is
•
•
•
1



184
[Chap. XI.
FUGUE.
-
printed in large notes. Here the two subjects are announced
by the outer voices; when the middle parts bring in the answers,
the two themes are inverted in the octave. Notice that the two
subjects do not begin simultaneously. It is extremely rare for
this to happen. Frequently the second commences only a
crotchet, or even a quaver, after the first; but it is undesirable
that they should start together, as it would make it more difficult
to distinguish them. The counterpoint in the treble of the last
two bars is, as will be seen, a free part.
371. In our next example,
Dibe
81.
--
A 1.
tr
HANDEL. Six Fugues for Harpischord, No. 1.

$ 2.

tr
&c.
A 2.

the order of entry of the preceding is reversed. Here the two
middle voices have the subjects and the outer ones the answers.
Note in the answer in the treble the change of an octave in pitch
(§ 154) to keep the music within the reach of the hands. The
alteration at the end of both the answers is an illustration of what
has been more than once mentioned-that Handel's fugue writing
is usually much more free than Bach's.
372. It is not always necessary that the two voices which
enter with the answers should be in the opposite relative
positions to those which announce the subjects. Sometimes
the part which was the higher at first is still the higher, as in
the following example.

Chap. XI.]
185
FUGUE.
81.
H MEN
IND.
HCH
II L
JULK
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81.
5
402
9
AL
A 2.
3
6
81.
8 2.
10
HAYDN. Ist Mass.

82.
&c.
11
12
We have here a subject taking a tonal answer; the second
subject (which corresponds to the countersubject of a simple
-




186
[Chap. XI.
FUGUE.
fugue) also needs modification (§ 170). We have quoted the
whole exposition, as it shows a very frequent manner of com-
mencing a double fugue.
373. After the first entries of the two subjects and answers,
we see other entries in the same keys as before, but differently
distributed between the voices. At bar 5, the tenor has the first
subject, and the alto the second; in the seventh bar the bass has
the first answer, and the alto a modified form of part of the
second. Lastly, at bar ro, the first subject is seen again in
the treble, while bass and tenor both have the second subject,
the tenor being written in double counterpoint in the tenth.
When an exposition contains only one entry each of the subjects
and answers, it will be very brief. This is the case with the
example in § 371, where our extract is immediately followed by
the first episode; more frequently, as here, additional entries
precede the introduction of any episodical matter.
374. Occasionally after two voices have announced the
subjects, the other pair, instead of giving the answers, repeat
the subjects, but inverted in their relative positions.
be
81.
82.
1
6
2
81.
3
8 2.
HANDEL. 'Judas Maccabæus.'

4


8
Chap. XI.]
187
FUGUE.

***
11.
14.
H
Th
SI
21
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9b6
It looks at first sight as if the first subject extended to the
sixth bar. That this is not the case is proved by the second
subject. If bars 4 and 10 are compared, it will be seen that
they are quite different. Now it is an important rule in writing a
double fugue that, though the two subjects had better begin one
after the other, they must always finish together. Bar 10 proves
that the second subject ends on the first note of bar 4;
consequently the first subject must end at the same point, and
bars 5 and 6 must be regarded as codetta.
be
H
EL PANTU
INDA
Hau
375. The exposition of a double fugue is sometimes arranged
in quite a different manner, which will be best understood by an
example.
6
1
81.
A 2.
2
10
S 2.
3
..
11
4
12
&c.

5
HUMMEL. 2nd Mass.
A 1.

81.
2
7
9
8
188
[Chap. XI.
FUGUE.
:
C
10
14
82.
A 2.
11
15
12
16
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13
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A 1.

As in the preceding examples, the two subjects are announced
together, here by the tenor and bass voices; but instead of
the two answers being given by the other two voices, the tenor,
which has just completed the second subject, continues with
the first answer, the alto entering with the second answer. The
bass continues as far as bar 7 with a free counterpoint, and is
then silent till it re-enters with the second answer in bar 14.
376. The alto, having completed the second answer, continues
with the first subject, while the treble enters with the second
subject, going on in its turn with the first answer. This gives the
bass the opportunity of bringing in the second answer below the
first (as in the additional entry of a simple fugue), and the
exposition is completed when both the subjects (or answers)
have been heard in each voice.
377. In the above example, each new voice entered first with
the second subject. In the following we see the reverse case, all
the fresh entries being with the first subject.
1


Chap. XI.]
189
FUGUE.
C
1.
81.
8
82.
1
15
21
1
2
A 2.
9
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A 2.
190
[Chap. XI.
FUGUE.
1
f
✔
28
#

29
31
30
34
After the explanations of the preceding exposition, few words are
needful concerning this one. If the student will examine it, he
will see that a codetta is introduced before each new pair of
entries. The treble, which ied with the second subject, makes its
final appearance at bar 27 with the first, showing the inversion of
the two subjects, just as they were shown at bar 14 of the example
by Hummel.
32
33
&c.
378. Another important point is illustrated by the two ex-
positions just quoted. It will be seen that though both are
for four voices, only three are present at any one time, while
a considerable part of the exposition in § 375 is for two voices
only. We often find this in the exposition of a double fugue;
the reason is that it is absolutely necessary that both the subjects
shall be clearly and easily distinguished, and this end is attained
by leaving them either without any other counterpoint, or with
only one added part. Clearness is, if possible, of even more
importance in a double fugue than in a fugue with only one
subject.
379. The general form of such double fugues as those we are
now describing mostly follows the plan shown in Chapter IX.
But there are some differences of detail often to be met with that
must be mentioned. In the first place we sometimes find less
episode in a double than in a simple fugue. For instance, the
'Kyrie' of Mozart's 'Requiem,' one of the finest double fugues
ever written, contains only one episode, and that is but a bar
and a half in length. When there is so little episode, its place is
usually taken by developments of one of the two subjects without
the other.
380. In general, both subjects should be heard together in
each group of middle entries. Occasionally, we find such an
entry for one subject alone; but this is far more exceptional
than the entry of a subject in a simple fugue without its counter-
subject.
381. It is seldom practicable in a double fugue to write a
stretto in which both the subjects shall take part. We have
already seen with simple fugues that if there is much stretto,
there is generally either no countersubject, or, if there be one,
it is omitted in the stretti. The obvious reason for this is, that
*
Chap. XI.]
191
FUGUE.
=
¿
that part of the countersubject which is written against the latter
part of the subject can seldom be also made to fit the first part
which, in a stretto, will be appearing in another voice; while, if all
the voices are joining in the stretto, there will evidently be none
left to give the countersubject. As the second subject in a double
fugue is virtually a countersubject to the first, it is clear that the
same reasoning will apply to it. Consequently the stretti, when
there are any, in a double fugue are mostly made from one subject
alone, and very often take the place of the episodes.
382. The general rules as to the order of entries, etc., given in
§ 325, apply also to double fugues, excepting that in the latter
there should be no isolated entry for one of the subjects un-
accompanied by the other. One entry of the two subjects
together may, however, be divided by episodes from the preceding
and following.
383. Our space will not allow us to give complete examples
here of double fugues, as we did of simple fugues in Chapter IX.
In the volume on Fugal Analysis, which will follow the present
one, we shall insert some fine specimens of this kind. Meanwhile
it is hoped that the explanations given in this chapter will enable
the student to understand the construction of a double fugue, and,
if necessary, to write one for himself.
384. We have now to speak of the second variety of double
fugue—that in which each of the two subjects has its own
separate exposition, and it is only in the latter part of the
fugue that they appear together. Though some very fine
examples of such fugues are to be found, they are far rarer
than the kind of which we have been hitherto speaking, and
they are constructed after a different plan.
385. It is, of course, just as necessary in this kind of fugue as
in the other that the two subjects must be composed together in the
first instance, and that they must be in double counterpoint with
one another; otherwise it is in the highest degree improbable
that it will be possible to combine them. The essential difference
between this and the other class of double fugues is, that here the
combination, instead of being shown at first, is reserved for the
climax, whereby its effect is frequently much increased.
386. There is considerable difference in various fugues of
this class as to the amount of separate treatment which each
subject receives before they are brought together. Sometimes
the first subject will have a regular exposition, and the second
only a partial one, as in the following passage, which, to save
space, we give in short score.
DEC
HANDEL. 'Dettingen Anthem.

戸
​192
[Chap. XI.
FUGUE.

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PPP

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Symphony.
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Chap. XI.]
193
FUGUE.

136.
Ind

ē
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Pi

&c.
Here the first exposition is separated from the second by a short
symphony for the orchestra. In the second exposition, the
subject in the alto is answered by the treble; but the bass
and tenor have only free imitations of its first notes, and there
is no complete exposition of the second subject. After the
cadence in G major, the two subjects are combined; but the
freer style is soon resumed, as will be seen from the last bars of
our quotation.
387. Our next illustration is somewhat more regular in
treatment.
J. S. BACH. Cantata, "Lobe den Herrn, meine Seele."
4
3

*

1
T
:
194
3
',
FUGUE.
i
&c.
1.
[Chap. XI.


The subject here (as will be seen later when the two are
combined) extends to the D at the beginning of the fifth bar.
We have here therefore a "close fugue
"close fugue" (§ 279), though the
answer does not enter so immediately after the commencement
of the subject as in the examples of this kind of fugue previously
given. The small notes on the bass staff show, as in other cases,
the real (instrumental) bass of the harmony. We have here a
quite regular exposition, of which (to save space) we have
omitted the last two bars of the bass entry. In the continuation
of the passage there are two instrumental entries-subject
(2nd violins), answer (1st violins), making in all an exposition
of a six-part fugue.
388. After three bars of interlude for the orchestra, there is a
counter-exposition of the first subject. Here the bass leads with
the answer and the tenor replies with the subject, all the entries
being in the reverse order of that of the first exposition. We
exceptionally find here that it is only the order of entry that is
reversed; usually a voice that had the answer in the exposition
will have the subject in the counter-exposition, and vice versa.
389. The counter-exposition is followed at once by the
exposition of the second subject.



,
Chap. XI.]
195
FUGUE.
}

(a)
&c.
This subject, like the other, is four bars in length; it is also
treated in six parts by the addition of entries for two violins;
but the irregularity of the intervals of reply show that this
exposition belongs to the fugato (§ 358) rather than to strict
fugue.
។
390. To the counter-exposition succeeds immediately the
combination of the two subjects, of which we quote the first
bars. For the sake of clearness, we here give them in open
score.
&c.
•


i

196
FUGUE.
[Chap. XI.
L
{
It will be seen that modifications are made in the second pair of
entries; in bar 7 of our extract the close of the first subject is
transferred from the bass to the treble. We have already seen
the same thing (§ 271) in the case of a countersubject. A little
later we find the two subjects combined in a different manner.
(b)
Here the first half of the first subject serves as a counterpoint to
the second half of the second subject—a combination which we
just now remarked (§ 381) was very seldom possible. But
The
almost anything seems to have been possible to Bach.
whole fugue which we have been describing is a marvel of
scientific contrivance, though we do not recommend students
to imitate the consecutive seconds seen in the last bar but
one of our last example.
391. One of the most perfect examples, as regards its form, of
this kind of double fugue is an organ fugue by Bach in C minor.
The piece is too long to quote here; it will be found in the
Peter's Edition of Bach's Organ Works, Vol. IV., p. 36, to which
we refer the student, confining ourselves here to a short analysis
of the piece.
It will be seen to differ considerably from the
examples already described.
(a)
foot
;

392. The first subject of the fugue, which is in four parts, is
J. S. BACH. Organ Fugue in C minor.
tr
fo
&c.

(b)
This subject receives a regular exposition (bars 1-14) followed by
an episode of four bars. To this succeed four isolated entries in
the keys of G minor (bar 18), E flat major (bar 23), and
C minor (bars 29 and 34). After a full close in G minor, with
"Tierce de Picardie," the second subject is announced
(bar 37):
the

This subject, like the first, has a complete exposition, the second
and third entries of which are divided by a codetta (bars 42, 43).
This second exposition ends in bar 49, and is followed by entries
of subject or answer in G minor (bar 49), C minor (bar 52),
F minor (bar 55), C minor (bar 57); then, after an episode
Chap. XI.]
FUGUE.
197
(bars 60 to 63), C minor again (bar 63), and an altered entry
(bars 66 to 69), partly in F minor, and partly in C minor.
393. At bar 70 the two subjects appear together for the first
time. We quote the first two entries.
J. S. BACH. Organ Fugue, in C minor.
MANUAL.
PEDAL.
bb
X
bb
Abbr
مل
&c.
The modifications in the tonal answers will be easily understood
if Chapter IV. of this volume has been thoroughly mastered.
It will be seen that the figures of semiquavers have been
simplified for the pedals. This is probably less because of
their technical difficulty than because of the very practical
reason that the lower notes of the pedal organ cannot be depended
on to speak with sufficient rapidity. When the second subject
(the more florid of the two) is given to the pedals, as at bars 77
and 88, it is even more simplified than the first subject.
394. The fugue we are now examining contains five entries
subsequent to those last quoted. All of them are either in the
tonic or dominant key, and in all both the subjects appear in
their complete shape. A coda of six bars (bars 99 to 104)
concludes the movement.
395. By comparing this fugue with those we have previously
spoken of, we see what may be approximately described as the
$



[+
198
[Chap. XI.
FUGUE.
i
+
limits of variation in the form now under notice. In both
our earlier examples, the second exposition followed immediately
on the first,—in the case of the fugue in "Lobe den Herrn, meine
Seele," after the counter-exposition. In the C minor fugue, on
the contrary, each subject has a considerable amount of working
out before the next is introduced. In the fugues in §§ 386, 387,
the combination of the two subjects followed close after the
second exposition; here it is not so. In fact, it is left entirely
to the judgment of the composer in a fugue of this kind, how
much development he will give to each of his subjects separately
before he proceeds to treat them in combination.
396. A double fugue of this class, like a simple fugue, is in
ternary form; but its three sections are different from those of a
simple fugue which we showed in Chap. IX. A fugue of the
kind now under notice will contain the three following sections :-
(1) Treatment of first subject separately.
(2) Treatment of second subject separately.
(3) Treatment of both subjects combined.
We have already said that it is optional how much each section
contains.
397. There is one more point to be noticed with respect to
this variety of fugue. Owing to the fact that both the subjects
will have their expositions in the original keys of tonic and
dominant, we usually find very little modulation in a fugue of
this sort. As a striking illustration of this, take the fugue in
C minor which we have just analyzed. Not counting the
expositions, it contains in all fifteen entries, either of the single
subjects or of the two together. Of these, twelve are either
in C minor or in G minor. Only three (one fifth of the whole)
are in any other key. It is quite possible, as Bach conclusively
proves in this masterly fugue, to obtain variety by other means
than incessant modulation.
1
398. A Triple Fugue, that is, a fugue with three subjects, is
very much rarer than a fugue with two, and when we find one, it
is seldom strict. The first requisite for such a composition is,
that the three subjects must be written in triple counterpoint,
as each will in turn have to do duty as a bass. It is also needful
that all the subjects be well contrasted in character, as we have
already seen that they should be in the case of a double fugue.
399. It is possible to write a triple fugue after the second of
the two methods above shown for a double fugue, that is to say,
to give each of the three subjects a separate exposition before
combining them. But this plan is seldom adopted, probably
owing to the length to which it will cause the composition
to extend. A striking illustration of this is seen in the final
fugue in Bach's Art of Fugue,' of which we will here give
a short account before proceeding to speak of the more common
kind of triple fugue.
Chap. XI.]
FUGUE.
199
400. The fugue now to be noticed, one of Bach's latest
compositions, was unfortunately never completed, being inter-
rupted by the composer's blindness, which shortly preceded
his death. Enough, however, exists to show the scope of the
whole work. We first give the exposition of the first subject.
J. S. BACH. 'Art of Fugue.
be
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[Chap. XI.
FUGUE.
3
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20
25
+
21
112
26
81 (inverted).
113
22
27
23
114
28
S2-
St
24
115
29
After the entry of the answer in the treble (bar 16), we have in
bar 21 the inverted subject in the bass, imitated in stretto and
in direct motion by the tenor in bar 24. This subject is
henceforth treated both by direct and inverse motion, and
mostly in stretto at two or one bar's distance till bar 114,
at which point a full close is made in the tonic key. We have
thus far a fugue on one subject complete in itself, and the
whole piece might end here. Bach, however, makes his cadence
the starting point for a new departure.
id
401. We give the cadence closing the first part of the fugue,
and the commencement of the second exposition, which is too
long to quote in its entirety.
(a)
81-
&c.
bd
.
•



Chap. XI.]
201
FUGUE.

116
120
124
128
82-
121
117
A 2
125
T
129
118
122
126
&c.
119
123
127
L
K
}


.

I
202
FUGUE.
[Chap. XI.
-
1
This exposition ends at bar 141. and, after an episode of five
bars, the first and second subjects are combined thus :-
(b)
147
151
82-

148
152
S1-
149
#f
153
150

154
&c.
Later in the fugue (bars 167 to 173) the two subjects are
combined in a different manner, the first subject being now
introduced, not against the second, but against the third bar
of the second subject. The end of the second section of the
fugue shows another ingenious device. Above the second
subject (in the bass) the first is introduced by treble and alto
in stretto at one bar's distance, one entry being on the third and
the other on the fourth bar of the second subject.
402. The second section of the fugue closes in G minor, and
at bar 193 the third subject, made from the composer's name, is
introduced. For the sake of those who do not understand
German, it will be well to say that in Germany the note B flat
is simply called B, and B natural is named H. We now give
the third exposition.
Chap. XI.]
203
FUGUE.
CON
(a)
192
196
200
204
197
201
193
83-
205
83-
B A C H
198
202
194
206
195
199
203
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​A 3-
A 3-
207
་
&c.
#
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+


204
•
FUGUE.
[Chap. XI.
!
1
This third subject is then treated both by direct motion and by
inversion (see bars 213 and 222); and at bar 232 a half close in
D minor is made which leads to the final section of the fugue, in
which all three subjects are combined. Of this section Bach only
lived to write seven bars, which we give exactly as they are found
in his autograph.
(b)

232
235
238
S3
233
236
239
S2
Free Part.
234
237
S1-

R

403. A triple fugue, constructed on this plan, will clearly
contain four sections, instead of the three with which we are
familiar in other fugues; for there will be one for each separate
exposition, and a fourth for the final combination of the three
}
Chap. XI.]
205
FUGUE.
subjects. But the length to which the composition will extend
will necessarily be so great that this kind of triple fugue is
extremely rare. We have met with no other example of it
than that which we have been analyzing, though Albrechtsberger
mentions a similarly constructed fugue in G minor by Mattheson,
from which he quotes a few short passages.
404. In the ordinary triple fugue, the three subjects are
announced simultaneously, like the two subjects in the double
fugues seen in §§ 370 to 377. But in a four-part fugue, it is
evident that the method of exposition in the examples of
$$ 370 to 374 will be impossible. After three of the voices
have announced the three subjects (which, it must be remembered,
should not begin exactly together, though they must all finish
together), the fourth voice should enter with the answer to the
first subject, two of the other voices giving the other two answers,
while the remaining voice may either be silent or add a free part.
The three subjects are then heard again, differently distributed
between the voices, and then the three answers once more. The
exposition is complete as soon as all the subjects have been
heard (either as subject or answer) in each of the voices. It is
important to remember that the same subject should not be
heard twice in succession in the same voice.
405. The instructions given in the last paragraph will be now
illustrated by the exposition of a triple fugue by Albrechtsberger.
ALBRECHTSberger.
81-
6
1
A1
82-
A 2
2
7
83-
3
A 3-
8
4
9
5
tr
1


206
[Chap. XI.
FUGUE.
+
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+
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10
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14
18
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19
11
15
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20
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It will be seen that each voice has all three subjects in turn, but
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&c.
406. The form of this kind of triple fugue is the same ternary
form as that of a simple fugue, and the construction of a complete
piece of this character will be best shown by the analysis of a fine
example from Mozart's Twelfth Mass, a work from which we have
already had more than one occasion to quote.
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FUGUE.
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&c.
The small notes in the bass of bars 14, 21, 25, and 26, and in
the treble of bars 34 to 36, are additional parts for the orchestra.
We have omitted a few notes for the violins, which merely fill up
the harmony, so as to show the fugal construction more clearly;
and we have not given the last nine bars of the movement,
because these are merely a free coda, and not a part of the fugue
itself.
407. The exposition of this fugue extends to the first note of
bar II; it will be seen that each subject has then been heard in
all the voices. An additional entry of all the subjects leads to
the key of A minor, the last note of the first subject being
sharpened in the tenor, to induce the modulation. The middle
section of the fugue therefore commences at bar 13, with an
episode only one bar in length. At bar 14 is the first group
of middle entries, the three subjects appearing in A minor.
These are at once followed by incomplete entries of the three
answers in E minor, shown, as in our preceding examples, by
A-? Fragments of the subjects are then treated sequentially in
the second episode (bars 19 to 21), bringing the music to the key
of F. In this key the second group of middle entries, incomplete
in all the voices, is made at bar 21. The third and last episode
(bars 23 to 26) leads back to the key of C, and to the final
section of the fugue, which begins in bar 26.
408. This final section contains three groups of entries, all
of which are in stretto. In the first and second, the answer
enters at a bar and a half's distance after the subject, and all
three subjects are present, though, as will be seen, some are
incomplete. In the third and closest stretto (bar 34), a part of
the first subject is treated by itself in imitation in the octave at
one bar's distance in all four voices. It will be seen that at bars
34 to 36, a fragment of the second subject is given by the violins
as a counterpoint to the first subject in the voices.
409. It will be noticed that as the subjects modulate to the
dominant, they require tonal answers. The subdominant in the
second subject prevents the modulation from taking place till
M
Chap. XI.]
211
FUGUE.
1
the third bar, and we see that all three subjects need modification
in the answers. Of the six possible combinations of a triple
counterpoint, Mozart has only employed three; but it must be
noticed that each of the subjects appears in the bass (Double
Counterpoint, § 253). One more point remains to be noticed
about this fugue-the almost entire absence of free parts. For
the sake, no doubt, of that clearness which is so essential in
double and triple fugues, the three subjects always appear without
any additions, which might prevent their being easily distinguished.
It is not till bar 38 of our extract, and the coda which we have
not quoted, that we find any continuous four-part harmony.
410. It is seldom that we find a triple fugue so strictly treated
as that by Mozart which we have just been analyzing. Composers
usually allow themselves considerable freedom in such cases.
For example, the very interesting 'Fuga à 3 soggetti in Haydn's
quartett in A, Op. 20, No. 6, the three subjects of which are
quoted in Double Counterpoint, § 262, is, strictly speaking, not a
triple fugue at all, but a double fugue, with one regular counter-
subject; for the third subject appears for the first time as an
accompaniment to the answer, and not to the other two subjects,
and in some of the middle entries only two of the three subjects
are employed together.
"
411. A Quadruple Fugue, or a fugue on four subjects, is so
extremely rare that it will not be needful to say much about it.
The four subjects will now evidently have to be written in quad-
ruple counterpoint; but it is very seldom that they will be all
announced at once. In Haydn's Fuga à 4 soggetti,' in his
quartett in C, Op. 20, No. 2, only two of the subjects are
announced at first, the third and fourth subjects entering as
countersubjects to accompany respectively the first and second
appearances of the answers. The four subjects of this fugue, with
their various inversions, were quoted as examples of quadruple
counterpoint in Double Counterpoint, § 270.
412. In Handel's 'Alexander's Feast,' the final chorus, "Let
old Timotheus yield the prize," is sometimes spoken of as a fugue
on four subjects. So, in one sense, it is; but it cannot be
regarded as a specimen of a true quadruple fugue, because
seldom more than two, and never more than three of the four
subjects are employed simultaneously. The fugal writing, as is
mostly the case with Handel, is far from strict throughout.
413 In Cherubini's 'Counterpoint and Fugue' will be seen a
good example of a strict fugue on four subjects, the opening bars
of which we gave in § 269 of Double Counterpoint; but probably
the finest specimen of a quadruple fugue ever written is the final
movement of Cherubini's great 'Credo' for a double choir, which
has not only four subjects, but two countersubjects in addition,
which make their first appearances against the answers.
We have
only space to quote the opening bars of this movement.
*
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[Chap. XI.
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FUGUE.
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SECOND CHOIR.
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215
As the last notes of this extract are the commencement of the
first episode, we have here the complete exposition of the fugue.
With the indications we have given of the entries of the subjects,
&c., the student will easily understand it. In a fugue for so many
voices and with so many subjects, it is not needful that each subject
should be heard in every voice in the course of the exposition.
Were it so, the fugue would be protracted to an inordinate length.
Let it be also noted that, with so many subjects, the rule that all
shall end together is relaxed. Here the second subject ends in
the third bar, and the other three not till the fourth.
modifications will also be seen in the two countersubjects.
Slight
414. In the later developments of such a fugue as this, it is
not necessary that all the four subjects should be invariably
present together. It will give more variety if sometimes only
two or three are treated and developed at once. We advise the
student to obtain the score of this "Credo,' by Cherubini, which
is published for a mere trifle in the well-known 'Peters Edition,'
and to analyze the whole piece carefully for himself, as we have
done the opening bars for him. He will thus probably learn
more about the construction of a quadruple fugue than we could
tell him in twenty pages of this volume.
.
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216
[Chap. XII.
FUGUE.
>
Manual.
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415. In addition to the different varieties of fugues treated of
in the preceding chapters, we not infrequently find fugues written
upon a choral.
As with a canon on a choral (Double Counter-
point, § 391), there are two ways in which this can be done. We
can either take the melodies of the choral itself as the subjects of
our fugue, or we can write a fugue on an entirely independent
subject, introducing the choral in longer notes in one of the
voices as a kind of canto fermo. Owing to the much greater
freedom of its form, it is far easier to write a fugue on a choral
than a canon.
PEDAL.
CHAPTER XII.
416. We will first speak of that form in which the choral itself
furnishes the subjects of the fugue. The plan most often followed
is to write a separate fugal exposition for each line of the choral,
the last entering voice, which, for the sake of clearness, is generally
one of the outer parts, introducing the melody, in most cases,
though not invariably, by augmentation.
1
THE FUGUE ON A CHORAL.
417. As this method will be best taught by examples, we give
two entire fugues of this kind, one very simple, the other rather
more elaborate. The first is by one of Bach's great predecessors,
the Danish organist Buxtehude. It is on the choral "Erhalt uns,
Herr, bei deinem Wort." In the original there is only one flat in
the signature, according to the custom of the time, though the
key of the piece is G minor; for the convenience of students, we
adopt the modern key-signature.

2
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BUXTEHUDE.
•
Chap. XII.]
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Chap. XII.]
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FUGUE.

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418. The first line of the choral is announced as a fugue
subject in the tenor, and answered by the alto in bar 3. The
treble gives the subject again in bar 6, and the bass (pedals) joins
in with the subject at bar 8. The subject, and not the answer, is
given to the bass, because, as we see from the rest of the fugue,
this part has the character of a canto fermo, and gives nothing but
the simple choral, line by line, throughout the piece. We there-
fore find the subject here instead of the answer, as in an ordinary
fugal exposition. It will be seen that the canto fermo is here only
in notes of the same length as the other parts. More usually, as
in our next example, the plain choral is given in longer notes.
419. At bar 10 begins the exposition of the second line of the
choral. Here we see a little irregularity of treatment. The
theme in an ornamented form appears in the tenor, and is
imitated in stretto in the next bar by the treble. At bar 13,
the answer is repeated, not by the alto (which had not had it),
220
>
FUGUE.
[Chap. XII.
but by the tenor which gave the subject just before. The entry
of the subject in the bass (bar 16) concludes the second section
of the fugue.
420. The third section is longer. The subject is first heard
in the alto (bars 18 to 20), the answer in the treble (bar 21), and
again in the tenor (bar 23), followed by an additional entry of the
subject in the alto (bar 26), and completed by the canto fermo on
the pedals (bars 28 to 30). The treatment of the last line is on a
similar plan, as the student will easily see for himself.
421. It will be noticed that this fugue really consists of four
short expositions of different subjects, but that the first entries in
all the lines of the choral, except the first, are accompanied by
independent counterpoint. It is not necessary that all the inter-
mediate expositions in a fugue on a choral should begin with one
voice alone, though our next example will show that this may
sometimes be done.
422. The above fugue is given not as a perfect model for
imitation, but as showing one of the earlier and simpler ways of
treating a choral in the fugued style. The following example by
Bach is a much more finished and artistic piece of work.
H
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Chap. XII.]
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Chap. XII.]
FUGUE.
223
423. Here the canto fermo is in the treble, in minims against
the crotchets and quavers of the other voices, and the fugue is a
close fugue (§ 279). It will be seen that the second and third
lines of the choral (bars 6 and 12) are treated in fugato style, the
entries not being at the regular intervals, while the first and fourth
(bars 1 and 20) are in the intervals of subject and answer. The
close imitations, and the treatment of fragments of the subjects
deserve careful examination.
424. If we observe the form of these two fugues, we shall
find that they both differ considerably from the general fugal form
described in Chapter IX. This will always be the case with a
fugue on a choral; and it is quite impossible to lay down any
fixed rules for its form, because this will in all cases depend on
the course of modulations of the choral itself. A certain amount
of variety is always obtainable by varying the harmonies of the
different lines of the choral, as Bach has done in the above
example, by harmonizing the end of the second line of the choral
(bars 11 and 12), not as a full cadence in E flat, but as a half
cadence in C minor. But in the case of short and simple chorals,
such as the two given in our last examples, there will generally
be comparatively little modulation, and only to nearly related
keys.
425. Another point illustrated by these two fugues is, that the
entries of the lines of the choral as a canto fermo need not be at
any regular intervals of time. In Buxtehude's fugue, the first line
enters at the eighth bar, there are five bars' rest between the
first and second lines, nine between the second and third, and
nine between the third and fourth. With Bach, there is a bar
and a half before the entry of the first line, two bars between the
first and second, three between the second and third, and three
again between the third and fourth. The points at which the
various entries should be made is a matter that is entirely within
the composer's discretion; he may introduce his canto fermo
exactly where he finds it most convenient.
426. This form of fugue on a choral is less common in modern
music than it was in the last century. Two effective examples
may be seen in the late Sir George Macfarren's oratorios. The
chorus, "My soul, praise the Lord," in 'St. John the Baptist,' is
founded on Dr. Croft's hymn-tune 'Hanover'; and the 'Old
Hundredth' is treated fugally in the final chorus of 'The
Resurrection.' Both these fugues, however, differ from the
models here given, inasmuch as, although the whole of the choral
is heard as a canto fermo, the actual subject of the fugue itself is
in each case only the first line. These pieces, therefore, form a
kind of connecting link between the variety already treated of and
that now to be described.
427. The second method of writing a fugue upon a choral is
to take an entirely independent subject—that is, one not suggested
by any part of the choral itself—and against this to introduce the
!
224
[Chap. XII.
FUGUE.
}
..
=
"
lines of the choral as a canto fermo at such points as may be found
most convenient. A fugue of this kind is very seldom strict as to
the intervals of entry. Of the numerous specimens to be found
in Bach's 190 Church Cantatas, there is not a single one which
would not be more accurately described as a fugato with a choral.
As these have nearly always an independent orchestral accom-
paniment, we prefer to select as an illustration the first twenty
bars of a fugue on a choral taken from one of the motetts. The
movement is too long to be quoted in full.
4
7
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J. S. BACH. Motett, "Fürchte dich nicht."

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Chap. XII.]
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FUGUE.

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[Chap. XII.
FUGUE.
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428. Here the key of the piece is A major; the subject,
therefore, being throughout in the dominant, the answer is in
the tonic (§ 70). The first answer is at the regular interval
but the next entry of the subject (bar 4) is in the key of D
instead of E; and from this point the entries, though each is
generally at a fourth or fifth above or below the preceding, are so
irregular that it is impossible to say which are subjects, and which
are answers. We have therefore marked them all with 'S.'
429. It must be remembered that it is not allowed to trans-
pose any phrases of the canto fermo into other keys; consequently
only such modulations are available as can be introduced without
doing violence to the original form of the choral. The same rule,
of course, applies to the variety of fugue noticed in the earlier
part of this chapter. Any other modulations, if used at all, can
only be employed in what may be termed the interludes between
the different lines of the choral. For instance, in our last
example is a transient modulation at bar 9 to the key of E minor,
introduced between the first and second lines of the choral.
430. Though it is advisable, where practicable, to employ the
theme of the fugue as a counterpoint against the choral, it is also
allowed to introduce the latter during the episodes. This consider-
ably lightens the composer's labours; for (as we have already seen
in Chapter VII.), though the materials of the episodes should have
some connection with the subject or countersubject of the fugue,
considerable liberty of treatment is allowed; and it will be much
easier to introduce the choral than if we are bound to make it
combine with a given theme.
431. A fine example of this method of treatment is seen in
Mendelssohn's third Organ Sonata. There is here a double
fugue, each subject having a separate exposition before they are
combined. We quoted the first subject in § 38 (d). After a
regular four-voice exposition, Mendelssohn at the 17th bar of
the fugue introduces on the pedals the first line of the choral
"Aus tiefer Noth schrei 'ich zu Dir," as a fifth part. The
subject is only suggested above the choral, a new entry taking
place on the last notes of the line. The entries of the second
and third lines of the choral (bars 22 and 28) are similarly
treated. At bar 35 the exposition of the second subject (a
figure of semiquavers) begins. After it has been carried through
all the voices there is an episode (bars 43 to 47) against the
latter half of which (from bar 45) the next line of the choral is
heard. At bar 57 the two subjects are combined, and the
choral is introduced in the pedals from time to time; but in no
one place throughout the fugue is either of the subjects in its
entirety ever combined with the choral.
432. Mendelssohn's organ sonatas are so well known and so
accessible that we have contented ourselves with merely referring
to this fugue instead of quoting from it, because no short extracts
from it would have been of much assistance to the student.
It
мен
Chap. XII.]
FUGUE.
227
shows that it is not necessary actually to combine the fugue
subjects with the choral. This fugue is a very fine specimen of
its class, and it is no disparagement to Mendelssohn's genius that
he has here preferred the freer style. It would have been very
difficult (perhaps impossible for anyone except Bach, to whom
nothing seems to have been impossible) to combine the choral
with either of the themes he had selected for his fugue. He
therefore wisely chose rather to write an effective composition
than to attempt elaborate and difficult combinations, which, had
he succeeded in effecting them, would probably have smelt
strongly of the lamp. An over-display of technical cleverness is
very likely to be dry.
433. Sometimes only the first line of a choral, instead of the
whole, is selected for fugal treatment. A well-known example of
this is Bach's organ fugue in E flat, known in England as the
'St. Ann's Fugue.' This is a double fugue of a somewhat
unusual form, in three movements. The first is a simple fugue
in five parts, the theme of which we quoted at § 102 (c), and
which is the same as the first line of the hymn-tune, 'St. Ann's.'
This movement ends with a full cadence in the tonic, introducing
the second subject.
(a) 8 2.
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(b)
This second movement is in four parts only, without pedals.
After a regular exposition, the new subject is treated by inversion,
and then combined with the first subject, of which the rhythm is
now altered, and which assumes the character of a canto fermo.
8 1.
8 2.
(c)
J. S. BACH. Organ Fugue in E flat, ('St. Ann's.')
S3
&c.
82.
Subsequently the canto is also heard against the inversion of the
second subject. A full close in C minor leads to the third move-
ment, which, like the first, is in five parts. The theme will be
seen at § 49 (c). We now have a third exposition, followed by
combinations of the third subject with the canto fermo in various
ways, of which one will serve as a sample.
81
&c.
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FUGUE.
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subjects and three expositions, like the great fugue analyzed in
Chapter XI., §§ 400-402, yet it is not really a triple fugue, as
the three subjects are never all heard together. It more nearly
resembles a fugue with two countersubjects heard in succession
(§ 174).
434. The fugue on a choral affords an illustration of the
general principle so often referred to in these volumes, that
in proportion as the difficulty of the task increases, greater
freedom is allowed to the composer. This has been amply
shown in our examples. By the time that the student is so
far advanced as to be able to attempt a composition of this
class, he ought also to have acquired sufficient experience not
to permit his liberty to degenerate into license.
Chap. XIII.]
229
FUGUE.
•
FIRST CHOIR.
SECOND CHOIR.
CHAPTER XIII.
ACCOMPANIED FUGUES.
435. We not seldom find in fugues written for voices with
instrumental accompaniment, that the instrumental parts are, to
a greater or less extent, independent of the voice parts, by which
iatter the fugue is carried on. We are not now speaking of the
doubling of voices in the octave above by violins, or other
instruments, because mere doubling adds no new parts to the
harmony, but of those cases in which either the harmony sug-
gested by the voices is filled up by the instruments, or the latter
have independent figures of counterpoint. Such fugues may be
described as Accompanied Fugues.
436. In Bach's vocal works, especially in the great Church
Cantatas, which deserve to be far better known than they are,
we frequently find the first exposition of a fugue accompanied by
the basses and organ, the latter filling up the harmony, as in the
opening choruses of the cantatas, “Es ist dir gesagt,” and “Sehet
welch 'eine Liebe" (Nos. 45 and 64 of the Bach Society's edition).
Sometimes, as in one or two of the motetts for a double choir,
the exposition of a fugue by one choir is accompanied by full
harmony for the other.
J. S. BACH. Motett, "Singet dem Herrn.

230
[Chap. XIII.
FUGUE.





I


Chap. XIII.]
231
FUGUE.
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CHORUS.
ORCHESTRA.
Here the harmonic outline implied in the fugue subject is filled
up by the chords of the second choir.
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from one of Bach's cantatas.
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CHORUS.
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​It is difficult to condense Bach's very polyphonic orchestra on
two staves without sacrificing clearness. At the sixth and seventh
bars of our example, where the parts on the lower staff appear to
cross, it must be remembered that the bass is still really the
lowest part, because it is doubled in the lower octave by the
double basses and the pedals of the organ. The figured bass is
in Bach's own score, though we have in one or two details
modernized his notation, as, for instance, where he writes b7
instead of 7, according to the custom of his day. The
passages in which there is nothing but a figured bass were accom-
panied on the organ. The independent accompaniment of the
orchestra, with the contrasted tones of the strings and oboes,
is continued through the greater part of the fugue.
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7
438. The following passages from Cherubini's first mass,
which is for three voices only, show how thin harmony in the
voice parts can be filled up.
LET
5
&c.
CHERUBINI. Ist Mass.
i
P
↓
▪;
મ

i
.
:
:
!
7

.
234
[Chap. XIII.
FUGUE.

I
..
J
VIOLINO IMO.
VIOLINO 2do.
The accompaniment here is for the full orchestra; we give it in
the condensed form in which it appears in the published vocal
score.
VIOLA.
439. A little further on, in the stretto of the same fugue, we
find a different kind of independent orchestral accompaniment.
As only a few instruments are employed, we quote the passage
from the full score.
SOPRANO.
TENOR.
BASS.
Mu
DICH
tto
H
SENT
Th
Cze
pp stac.
&c.
pp stac.
CHERUBINI. Ist Mass.


Chap. XIII.]
235
FUGUE.

Pi
E
M
pp stac.
J

&c.
It will be seen that the string parts here are partly a free variation
of the voice parts, and partly a filling up of the harmony by new
and independent figures of accompaniment
236
[Chap. XIII.
FUGUE.
440. In Haydn's masses we find some excellent examples of
florid accompaniments for the violins, generally as variations
of the voice parts. As an especially good illustration of this
method of accompanying a fugue, we quote the opening of the
"Et vitam" of his first mass. We give only the voice parts with
the accompaniment of the violins and the basses; the other
instruments double the voices, except in a few unimportant notes.
HAYDN.
VIOLINI I & 2.
SOPRANO.
ALTO.
TENOR.
BASS.
VIOLONCELLO &
Contrabasso.
25
IKS
DEL
S
404+
f
'Celli.
1st Mass.

;

Bassi.
Chap. XIII.]
237
FUGUE.

W
20
Cob
·
"
f

238
[Chap. XIII.
FUGUE.

יין
1
VIOLINI 1 & 2.
I
SOPRANO.
ALTO.
It looks at first sight as if this were a double fugue; that it is not
so in reality is shown by the fact that the second subject,
announced at first in the tenor, is only occasionally introduced
in the remainder of the fugue, and does not even accompany all
the entries in the exposition.
1
441. At other times we find an orchestral counterpoint which
is quite independent of the voice parts.
TENOR.
BASS.
CON
'Celli.
Ob
&c.
HUMMEL.
Ist Mass.


•
239
Chap. XIII.]
FUGUE.
!
Ob
O
C
bo
Ed
w
&c
The subject and answer of this fugue were quoted in § 64, when
we remarked on the rarity of the first voice being silent during
the answer. We have selected this extract to explain what we
said before, and also because it is a very good illustration of an
independent accompaniment to a fugue; but considered merely
as a fugal exposition the counterpoint of the voices is pitiably
weak.
i

•
i


•

•
1
1
·
FUGUE.
442. Our next example is much better.
240
VIOLINO IMo.
VIOLINO 2do.
SOPRANO.
ALTO.
Tenor.
BASS.
Spony
f
f
fl
d
SCHUBERT.
[Chap. XIII.
Mass in F.
A




Chap. XIII.]
.
}
J
FUGUE.
Pē
C
P
&c.
241
1
}
$
.




··
242
FUGUE.
[Chap. XIII.
The instruments not quoted in the above extract simply double
the voice parts. These are written rather injudiciously low-the
result, probably of the composer's inexperience, as he was only
seventeen years of age when he wrote the mass; but the counter-
point is very good, and the moving figure for the violins gives
great animation to the fugue.
443. Among modern composers, Mendelssohn has been con-
spicuously successful in his treatment of the accompanied fugue.
It is needless to quote examples, which would only be further
illustrations of the points shown in passages already given; but
we may refer students to the fugue on the words, "Behold now
total darkness covereth the nations," in the chorus,
"Rise up,
arise!" of 'St. Paul,' and the final chorus of the 42nd Psalm, as
excellent specimens of this class of composition.
444. We have several times referred to Mozart's wonderful
mastery of every scientific device. Our final example will give
one more illustration of this.
VIOLINO IMo.
VIOLINO 2do.
SOPRANO.
ALTO.
Tenor.
BASS & BASSI.
be
,
MOZART. Mass in F, No. 6.

2

Chap. XIII.]
243
FUGUE.
J
tr
tr
1.
&c.
M>



244
FUGUE.
[Chap. XIII.
·
...
This passage deserves close examination. It will be seen that in
the voice parts we find not only a regular fugal exposition, but an
almost strict canon, 4 in 1, in the fourth and octave below, the
slight deviations being those necessitated by the tonal answer.
At the same time the violin parts, for the sake of which the
extract is quoted, have a different canon, 2 in 1, also very nearly
strict, and these close imitations are carried on in as easy and
natural a manner as possible. The passage is worthy of old Bach
himself.
445. It will be seen that this chapter consists almost entirely
of examples. It is only in this way that assistance can be given
to the student; for in every branch of practical composition the
invention of the melodies and the counterpoints must be left to
the composer himself. By seeing what others have done before
him, the student will be stimulated to go and do likewise. A few
general inferences may, however, be drawn from the examples we
have given.
446. First and foremost is the necessity of clearness, on which
we have already so often insisted, the importance of which
increases as we add to the number of parts. As an illustration
of this, look at the passage by Bach in § 437, and note how the
orchestral accompaniments are written in such a way as never to
obscure the progression of the voice parts by which the fugue is
carried on. The same thing will be observed in the fugue by
Haydn quoted in § 440.
447. If the accompaniment to a fugue is anything more than
a mere filling up of the harmony-that is, if it has independent
features of its own, as in the examples to §§ 441, 442, 444, it is
very desirable that it should be well contrasted with the subject
and counterpoint of the fugue itself.
448. It is seldom advisable to have more than one, or at
most two, free instrumental parts in the accompaniment to a
fugue, because not only is the difficulty of composing much
increased, but each added part renders it less easy to preserve
clearness. It is quite true that we often find more than two free
parts added in Bach's vocal fugues; but it must not be forgotten
that it seems to have been about as easy to Bach to write in ten
or twelve real parts as it is to the average composer to write in
four. The student will do well not to overtax his strength by
attempting feats too difficult for him. Unless he can write florid
counterpoint fluently in at least five or six parts, he had better not
try to compose an accompanied fugue at all.
449. Beyond these general hints, it is not possible for us to
go. The farther we advance in this series of theoretical works,
the more we are compelled to leave the student to his own
resources. In our earlier volumes on Harmony and Counter-
point, it was possible, at all events in most cases, to give very
definite rules as to what to do, and what not to do. These
subjects bear the same relation to composition that grammar
་
Chap. XIII.]
FUGUE.
245
does to poetry. The old Latin proverb, Poeta nascitur, non fit,
applies equally to music. Just as a man may have a thorough
knowledge of the grammar of a language, and yet not have an
idea of poetry in his head, a musician inay have perfectly
mastered Harmony and Counterpoint, and yet be no composer.
Anyone who, like the author, has ever acted as an examiner for
musical degrees at one of our universities, will need no further
proof of the correctness of this statement than the recollection of
some of the candidates' exercises that have passed through his
hands-quite correct, perhaps grammatically, but as dry as the
bones in Ezekiel's vision, and without the faintest spark of
musical life. As soon as the teacher approaches the higher
branches of composition, his relations to his pupil become to
some extent modified. From a pedagogue, whose word is
"You must," or "You must not," he now becomes an adviser
who can only generally indicate the direction which the student's
work should take, by setting before him the best models, and
showing him how to imitate them. It must not be forgotten
that every great composer has begun by being an imitator.
Even Bach was no exception to this; his earlier works were
modelled after those of Froberger, Pachelbel, Buxtehude, and
others of his predecessors. In order that the student may have
a sufficiency of good models to guide him, we shall, as we
have already incidentally mentioned, follow this volume by a
companion work on Fugal Analysis,' which will contain a
selection of the finest fugues by the great composers, in various
styles, put into score and fully analyzed. From an examination
of these, the student who has mastered the present volume will
probably learn all that is possible to be learned from books.
450. One word in conclusion. Many of the rules laid down
in this volume differ materially from those given in most other
treatises on fugue. The reason of this is that this work, like all
the others of the series, is founded, not upon any other theoretical
works whatever, but solely upon the practice of the great masters
themselves. Not one rule is given which is not enforced by the
example of distinguished composers. Where theory and the
practice of Bach, Handel, or Mozart come into collision, theory
must give way; and the student who writes fugues according to
the directions given in this book may at all events comfort himself
that if he is wrong, he is in exceedingly good company.
C
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Nach den Originalwerken für Violine und Bass (oder den vorhandenen
Orchesterpartituren) bearbeitet und mit Vortragszeichen versehen von
GUSTAV JENSEN.
CLASSISCHE
Francesco Geminiani. Sonate I. (a dur).
II. (H moll).
""
99
G. B. Somis. Adagio and Allegro
7403 Pietro Nardini. Adagio.
J. B. Senaillé. · Aria
7404 G. Pugnani. Sonate (E dur)
7405 J. B. Senaillé. Sonate (G dur).
7406 Arcangelo Corelli.
E dur)
7407 Giuseppe Tartini.
7408
""
""
""
""
7409
7410 Henry Purcell.
""
7414
7415 Antonio Veracini.
Sonate (c dur); Giga (G dur)
The Golden Sonata (for two
Violins and Piano)
7410a The same for two Violins, Piano, and Vio-
loncello
Francesco Geminiani.
""
""
3 Sonaten (A dur, E moll,
7411
7412
""
""
7413 L. Borghi. Sonate II. (a dur).
Sonate IV. (G moll)
·
·
•
Sonate (2 Violins, Piano,
and Violoncello ad lib.)
Sonate (A moll)
99
7416
7417 G. Torelli. Concerto (for 2 Violins and Piano)
7418
W. A. Mozart. Andante, Menuetto, and Rondo
7419 Arcangelo Corelli. Folia con Variazioni (D moll)
7420
W. A. Mozart. Adagio (E dur); Rondo (c dur)
7421 F. H. Barthélemon.
7422 G. F. Handel.
7423 Antonio Vivaldi.
7424 F. M. Veracini.
7425 J. M. Leclair. Sonate IV. (D)
Sonate (E moll)
Sonate (A dur)
•
Sonate (A dur)
Concert-Sonate (E moll)
··
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net, I
net, I
net, I
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