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B ^ Eia 75ti





D.Mus. (London)











Preliminary ...


The Countersuujegt —

(i) Style


The Countersubject —

(ii) luvertibility ...


The Answer (I)


The Exposition (I) ...


The Answer (II)


The Answer (III) ...


The Exposition (II) ...


The Answer (IV) ...


The Middle Section


Episodes (1)


» (2)


„ (3)




The Final Section


The Coda


The Fugue as a Whole


The Vocal Fugue ...






















This is a purely utilitarian book, designed entirely to help the candidate over
some of the pitfalls he will encounter in dealing with the examination Fugue, and to
give him some idea of appropriate style and construction. My only apology for
adding to the existing number of books on Fugue is the fact that I have felt the
need for some such compilation in my own teaching. The historical and traditional
aspects of Fugue may be (and should be) studied in many other books ; I am not
herein concerned with anything but the kind of Fugue which has to be produced,
under conditions which generally involve a certain amount of nervous strain, in a
maximum time of three hours ; a Fugue which is likely to present problems which
were rarely, if ever, envisaged by Bach who, despite the speed at which he obviously
had to work, was not labouring under the handicap of a rigid time-limit.

I make no apology for my strictures on the kind of trap subject sometimes set
— strictures which might be construed as being uncomplimentary to the devisers of
such subjects. While I am in no way opposed to the setting of problems of legitimate
difficulty, I feel that it should be a sine qua non that such problems be capable of a
really musical solution. This, unfortunately, is not always the case, and one could
quote numerous examples of subjects which seem to be designed to find out what
sort of a second-rate best the harassed candidate can make of what is in any case
bound to be a musically bad job.

My thanks are due to Dr. B. Burrows for much invaluable criticism and advice.

W. L.




1. It is taken for granted that the student using this book is already conversant
with the general principles of fijgal construction, and has also an adequate under-
standing of what constitutes good style in two-, three- and four-part contrapuntal
writing, both vocal and instrumental. It is necessary to realize from the very start
that a sound and logical harmonic structure is always essential, whatever the
number of voices (or parts) involved at any given point. Full appreciation of this
is especially to be stressed in writing for two voices only, e.g. in adding a counter-
subject to a subject,* and in view of the harmonically feeble kind of two-part
writing, whether in Fugue or anything else, which is not infrequently submitted by
students and examinees, no apology is offered for drawing attention to it, even in a
book which deals with quite advanced technique, f So many students seem to
think that because they have managed to scrape through some relatively elementary
examination they can go straight ahead to such a complex matter as Fugue, even
though their harmonic foundations may be far from strong. The student — and
there are far too many — who cannot harmonize a moderately difficult melody or
bass with certainty and effectiveness, should put aside any thought of tackling fugal
work until he is properly competent. All too often the teacher is faced with the
problem of trying to prepare a student for an examination which involves some
such advanced work as Fugue or Canon, and simultaneously patching up harmonic
foundations ; this is a hopeless task.

2. As stated in the Foreword, this book is designed merely to elucidate some
of the problems which frequently face the candidate who has to write an exposition,
or a complete Fugue, in the examination room, and to help him to solve these
problems in a way which will be reasonably certain to satisfy the examiner. The
final authority in all matters fugal is, of course, J. S. Bach, but to discuss all
possibilities by reference to his practice would increase the size of the book far
beyond what is intended. In any case, the historical aspect has already been amply
dealt with by other writers, and it may here be remarked that the student is urged
to extend his study of Fugue to include that aspect.

3. The rather unusual plan of dealing first with the Countersubject has been
adopted since the principles are the same whether the answerj be real or tonal, and
the main difficulties attendajit on the construction of an invertible C.S. can be
cleared up once and for all. Moreover, harmonic basis is always of prime import-
ance, whatever the kind of answer, and the ability to evolve a harmonically
satisfactory invertible C.S. is a prerequisite when dealing with the more recondite
and complicated types of S. and A. The Exposition has not been left until all the
problems of tonal answers have been considered, as is usually the case, since it is
felt desirable that the student should gain experience as early as possible in the
laying out of complete expositions. This enables the harmonic aspect to be more
clearly grasped.

* These terms will in future be abbreviated to " C.S." and " S." respectively,
t For a full discussion of two-part writing, see my " Free Counterpoint,"
Part I (Hammond & Co.).

X Normally abbreviated to " A."

4. The problems of the tonal answer are treated in four separate sections,
each with its own exercises, in order that the student may not have too much to
digest at once. There are so many possible complications that to deal with them
all in one chapter is felt to be asking too much. It is necessary thoroughly to under-
stand the approach to, and the solution of, one particular problem before tackling
another. Even so, it is not suggested that the four chapters on the tonal answer
cover every single possibihty ; everj' subject has to be considered individually and
all that can be done in a book of the size of the present one is to deal with as
representative a selection of cases as is possible. It would be quite easy to add
another four chapters dealing with further specific examples. In any case, there is
only one thing which ultimately matters — that the answer should be musical.

5. The procedures suggested for the middle and final sections of a fugue do
not pretend to be exhaustive ; they merely show some useful possibilities which
experience has proved to be workable by the average student within the allotted
time. If it be suggested that they are rigid and lacking flexibility, the answer is
that little more can be expected of an average student, while the more gifted should
be able to introduce any desired degree of flexibility into the various proposed
schemes. And in any case the discipline of working to a set scheme is beneficial.
Some such scheme is essential when working to a time-limit ; it is useless to
leave the question of design to the inspiration (if any) of the moment. The writer
remembers asking a fellow-candidate for D.Mus. what kind of a plan he used for
the fugue. The answer was: " Oh, I don't have a plan. I just write as I feel."
He failed to complete his fugue ; he also failed the examination.

6. The most realistic attitude to adopt is to decide on one set plan for the
fugue and to practise working to it. This may appear to be unmusical advice —
maybe it is ; but it does lead to success, as any competent examination coach knows.


(i) Style

1. In adding a C.S. to a given S. two prime essentials must always be borne
in mind: —

(a) The harmonic basis must be entirely satisfactory ;

(6) The C.S. should be rhythmically contrasted with the S.

2. Adequate stress has already been laid on (a) in Chapter I. With regard
to (b), it should be realized that while contrast is essential (otherwise the significance
of the prefix " counter " is largely negated), the general rhythmic style of the C.S.
should not be too far removed from that of the S. ; the contrast should be within
reasonable limits, or there may be an inartistic mixture of styles. A vigorous S.
needs a vigorous C.S., a flowing S. a flowing C.S., and so on. But the rhythmic
details will be contrasted.

3. Broadly speaking, running passages in the S. should be countered by more
steadily moving ones in the C.S. and vice versa, but this advice must not be inter-
preted too literally ; everything depends on the style of the S. and every S. has its
own individuality. The style of the S. in Ex. 1 is obviously quiet and flowing —
pastorale. Ex. 1 (a) shows an inappropriate C.S. ; (6) is better, being consistent
in style though contrasted in detail.

Ex.1. Andante piacevole

UlJ P ''

(a) is fussy and monotonous ; (&) flows easily. Moreover, allowing for the limited
time available in the examination room, there are far too many notes to be written
in (a) ; and in any examination the time-factor has always to be considered.

4. As indicated above, contrast of movement between S. and C.S. should not
be overdone. Consider the following vigorous type of S. : —

Ex.2. Allegro

■TO/^ PT3i.n n mrij ip=


The C.S. at Ex. 3 [a] forms a good basis, but lacks the rhythmic drive to back up
the S. Ex. 3 (6) shows this basis elaborated into something more apt.





i^u'^'o^y -




The points to be noted are: —

(i) the ornamental resolution which breaks up the long minim ;
(ii) the shake on the leading note. In instrumental writing it is often most
useful, from the rhythmic point of view, to put a shake over a leading
note which is of any length ;

(iii) the extra vigour obtained by the rhythmic and melodic modifications as
compared with {a).

Note also the type of bowing, especially the use of staccato. In instrumental
writing, details of phrasing as expressed by the contrasts of legato and staccato
must* always be carefully considered, both as to their appropriateness and their
rhythmic effect.* The snappy, crisp style of phrasing in the S. must be matched
by that in the C.S. Refer back to Ex. 1 (6) on this point, and note the style.

5. The following examples further illustrate the above points and should be
carefully studied.



-^'*^ Allegro Qs

Note the vigour of the staccato bowing and the " punch " given by the repeated
notes in bars 4 and 5.

* Phrasing should always be inserted as the notes themselves are written. It
is a thoroughly bad habit to evolve a C.S., or any other part, merely as a series of
notes and then to add the phrasing as a kind of afterthought. Phrasing is such a
vital matter that it must be considered as an integral part of every voice, not as
something to be stuck on afterwards.

Sturdy and forceful.

Mod era to



5 ij J


I V I iv • y, -.

The cross-rhythm bowing at the beginning is effective


(c) Andante





Kj J -J | J

r' r^irr n^ K^'c^ r r


1^ n / 1

The use of the figure r— i is a good point, giving consistency. The rest in bar 4
makes a neat " breathing place."

Quiet and flowing.

'^ ^urm

IJ^ ' "L^ f

6. The use of rests in the C.S. depends on appropriateness to the style indicated.
If the S. itself contains no rests, it is well to consider the possibility of introducing
some into the C.S., always allowing for the risk of implied harmonic clashes. The
fact that a note followed by a rest within the bar lasts in effect to the next accent
must never be overlooked. Occasionally a S. will be encountered which definitely
seems to suggest some riests in the C.S., but care must always be taken that such
rests do not induce an inappropriate " chopped up " effect. Ex. 4 (a) shows
effective use of short, pointed phrases in the C.S., separated by short rests. Ex. 5
is another instance.




^.i^Lj ' - ^p ^^


J' '^^^^IJl

7. Where rests occur in both S. and C.S., the end of a phrase in one should
always overlap the beginning of a phrase in the other ; gaps involving complete
silence, however momentary, must be avoided. The following is bad: —


At (a) there is no overlap of phrases — the C.S. ends on the 3rd quaver of the bar
and the S. resumes on the 4th. " Butting up " may be part of the art of paper-
hanging, but it is not conducive to good part-writing.
At (fc) there is a complete hiatus on the 3rd quaver of the bar.

8. While uninterrupted contrary motion between S. and C.S. is neither possible
nor desirable, too much parallel motion — and too much parallel rhythm — is a
weakness. Ex. 7 shows overmuch melodic and rhythmic parallelism ; the C.S. is
not so much " against " the S. as with it.

9. Imitation of the S. by the C.S. is undesirable even if the S. is such that it
seems almost to be invited. Compare the following : —




At (a) the C.S. is practically in free canon with the S. ; there is no real contrast, and
a good stretto possibility is used up. (6) shows good contrast, and its value is
enhanced by the rhythmic imitation indicated by the brackets. This example also
shows a good style of phrasing when writing for organ or piano.

10. A subject such as that in Ex. 9 seems almost to demand imitation by the
C.S. (Ex. 9 (a)) ; but such imitation is to be avoided (Ex. 9. (b)).

> •»' q

i'. •> H

ti^r ^ '^^Lj l y-


(a), like Ex. 8 (a), is too nearly in stretto to be desirable.

11. As a general rule a sequence in the S. should be harmonized sequentially
in the C.S., but this is not to be considered absolutely essential except in the case
of a modulating sequence. It is necessary to be guided by what seems most effective
in each individual case. To try to treat Ex. 9 sequentially would be useless.

12. In vocal writing tne compass of each voice must be kept in mind.
Students quite frequently expect, e.g., a soprano to take a top B or C. Vocal
fugues are taken to be for a normal chorus, not one composed of virtuosi. The
general basic principles are similar to those explained above in connection with
instrumental work, but care must be taken to achieve a truly vocal style.
Naturally, a S. set for vocal treatment will be in a vocal style, and the C.S. must
match it.

13. When words are given (as, obviously, they always should be) especial
care is needed

(a) that any necessary word-repetitions make sense, and

(b) that the accentuation is correct.

Mention of these two points might seem. superfluous, but it is surprising, not to say
distressing, how many quite well-educated students produce utterly ridiculous results
when handling words, whether in fugal writing or anything else. Even such non-
sense as Ex. 10 is hardly beyond the bounds of possibility.





Sing ye to the, to

the Lord.

14. The introduction of rests into a vocal C.S. needs special care in order that
the sense of the words be not destroyed. No exact guidance is possible here, though
the reminder in para. 6 must never be overlooked. It is simply a case of common-
sense and an elementary appreciation of the meaning of the words. Ex. 11 shows
two contrasting cases. At {a) the introduction of rests into the C.S. is effective,
while at (6) the words cannot be satisfactorily split up and the rests are avoided
laithin the sentence " I shall not want." In order to make these words " spin out "
against the S., the whole sentence is repeated and there is obviously no objection
to the breathing-place before the repetition.

the Lord.

C.s.Sing ye

(bj The Lord

Sing- ye t?v — ^ the Lord,

is my shep - - herd

j~7Tj J J U^^ H 11^




I shall not want

shall not -Want.

Note how the phrasing and shape of the C.S. help to enforce the spirit of the words.
Note also that if the lower part were given as the S., the upper (as C.S.) would
perforce need to be continuous, since the lower is already sufficiently broken up.

15. Whether writing for voices or instruments, it is not by any means essential
that the C.S. begin at exactly the same point as the S. ; this has already been shown
in many of the examples. In many cases, as will be seen later, it is simplest to
start tne C.S. proper after the beginning of the S., but where words are concerned
it is sometimes necessary to start C.S. before S. This point will be fully considered
in Chapter 5.



1. Add a C.S. below each of the foUowing:-


f '' 1 .^)! r p c ^ i [^ r } ^ 1 ^ c ^ r ^-^'^i^ ^


Alleifro vi^oroso




i'.rr_rir- n i" ' ^


f i if . ^ j- i J ^^^-^ ;j : 7T^-J^


^M^^ rjrp

^ff - ^


Ky-ri - e e - le
Use the same words for C.S.


1 - son



pi J irnrr J i rjr r


My soul — dothmag-nify the Lord, dothmag^-ni-fy the Lord.
C.S. to the words -

'And my spirit hath rejoiced in God my Saviour'


2. Add a CS. above each of the foUowing:-


Mode ra to

li t I II , -n^. . ^



Modern to





9\,\>'ii J JT^

X)o - - na, do - - aa no - bis pa - cem

Use the same >\'ords for C.S.

Mode ra to


f p fHr M r r

Glo - ri - a

in-cx-cel - si De - o,

in -

ex - eel


Use the same words for C.S. Keep some movement (mainly in
quavers) against the penultimate long note.


(ii) Invertibility

1. For the purposes of the examination fugue the S. and C.S. should always
be in invertible counterpoint, i.e.. they should be so combined that each forms a
good bass to the other, with satisfactory harmonic implications either way up.
Invertibility may be at either the octave or the fifteenth, though for reasons which
will appear later the former, where practicable, is in many cases to be preferred.

2. Invertibility at the octave means that the original lower part on being
transposed up an octave shall lie entirely above the other part ; or that the higher
part transposed down an octave shall lie entirely below the other. This involves
attention to two points: —

(a) S. and C.S. may not cross ;

(6) S. and C.S. should at no point be more than one octave apart.
Ex. 12 shows what happens if these points are disregarded.

At (i) —1 in Ex. 12 (a) the C.S. is crossed above the S. At the same place
in the inversion, Ex. 12 (b), the C.S. is again above the S., i.e. the relative positions
of the two voices remain unchanged and there is no inversion.

At (ii) in Ex. 12 {a) S. and C.S. are more than an octave apart, S. being above
C.S. At (ii) in Ex. 12 (6) the S. is again above the C.S. and no inversion has

y. Invertibility at the 15th implies that S. and C.S. may be anything up to
two octaves apart (but not more) at any given point, and that to show the inversion
one of the voices must be transposed two octaves. Ex. 13 shows two countersubjects
applied to the same subject, (a) is invertible at the octave, {b) at the 15th.


Inversion C.S-



C.S. 1

J^. ^OT^f^',^





!Hiii' I m n



4. The main difficulties in connection with invertibility arise from the \ . If
at any given point the 5th of the impHed chord is in the upper part, the inversion
will naturally imply a 4. If such a 4 is a legitimate one, i.e., a properly managed
cadential, passing or arpeggio 1 , there is nothing to be criticized ; but unfortunately
this is not always the case, and it is necessary to examine the possibilities in some

5. Root and 5th of a chord should only occur together off the accent, the 5th
being taken in arpeggio as a short-value note.

Ex.14. ^.




» ^






rj-if r ' I'. M l

#— ♦


The 5th above the bass at {a) inverts satisfactorily as at (6) ; the 4th, F — B t? ,
is momentary. That at (c), however, is not good. Owing to the slower speed the
bareness of the 4th is unduly noticeable.

Ex. 15 shows the undesirability of root and 5th taken in any other way.

ix.lS. ^, Cii)

The 5th at (a) implies VI — quite acceptable harmony ; but its inversion at (6)
produces a 4th which is harmonically meaningless.


6. If the lower note of an accented bare 5th is a suspension or appoggiatura,
the progression is, of course, satisfactory.


.>i r,^f|Lffr nrf if fff i f


The bass at (a) is a suspension and inverts at (6) into a good 4-3. The small
notes are inserted to make the harmony clear.

7. The diminished 5th above the leading note is always safe provided it
resolves inwards, implying Vb — I (Ex. 17 (a)). The inversion implies VM — lb (6).








p ' ^ "ML?

Vd lb

The diminished 5th above the supertonic of the minor key, and its inversion,
are to be avoided.

8. The 5th of a chord taken in arpeggio against the 3rd, off the accent,
is both satisfactory and useful.



r^j-] „ fi jS

7 rt ^ ^ u u ^ U^ w

1 1^'^ IV V lb IVb V Vb 1 (OlV V

9. To the student who has been well grounded in ideas of harmonic progres-
sion, all the above should be merely commonsense. The biggest difficulty in
connection with invertibility arises over the implied cadential \ on the dominant
(Ic). In two-part writing this involves the sounding together of the 3rd and 5th
degrees of the scale. These two notes are bound to imply one of two chords, viz.
I or III. Ill, to quote the apt phrase of the late Prof. Kitson, is an edged tool,
and the student who has reached the stage of tackling fugal problems should be
quite well aware of its possibilities and limitations.


Ex. 19 shows what happens when an apparently safe implied \ I is inverted.

Ex.19. ^^ ^

j- O i j ;

r^ ' r "^^^


The 4th at * is impossible.

10. From this we deduce an important prohibition: —

An implied I I progression is never possible if the supertonic occurs in S. or C.S.
as a factor of the second chord.

The only safe solution is to make 3rd and 5th of the scale fall simultaneously to 2nd
and 4th respectively, implying Ic — V^d.



:^j— r^.j-'j


F »

rTfr-f i rLf i r


IV IVb Ic V'd


11. Another point arises from Ex. 20. At (a) the Ic — Vd progression is the
only really satisfactory solution ; but the inversion might equally well be har-
monized thus: —


J— n.j-j

■■ ^'i ^ r - ^


n Lffff f tr li

This shows that the actual chords in the inversion need not necessarily be on the
same roots as those at corresponding points in the original. The S. and C.S.,
melodically speaking, remain unchanged, but the harmonic implications may be
varied as seems desirable.


12. Ex. 22 covers the points dealt with in paras. 4 to 11, an inner part being
added for harmonic clarity. No account has been taken of whether invertibihty is
to be at octave or fifteenth.

Ex.22. (i) "^ ^^ I "> ■

r r





IV V''b I

IV lb.



(b) C.S

I IV IV b Ic V'd lb

^iv) ^ — ^ (vi;

r , 'f I I


r r

r r fr r r-


I * I



I Vb_ Vd lb iVb Ic V''d lb IVb IV lb Vllb I

Note : — (i) 4ths, upper notes unessential, inverting at (ii) into 6ths, lower notes

(iii) The E and C sharp in S. and C.S. respectively treated as passing notes.

At (iv) they must be factors of VM in order to resolve correctly the preced-
ing Ic. Compare Ex. 20.

(v) The Ic — VM progression inverts into lb — Vllb at (vi), Vllb being
merely an incomplete dominant 7th.

13. Particularly at cadences, passages are apt to occur where it is easy to fall
into a 4 trap. Consider the following: —


1 3 4 5 6 7

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