# Fugue (Prout)/Chapter 2

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 countersubject "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.
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 ​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.
28. To illustrate our meaning we will give a few examples of simple subjects which remain in one key throughout—
Handel. 'Messiah.'
Handel. 'Judas Maccabaeus.'
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 (b) 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.
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 ​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.
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.
If we try to think of the simplest and most natural harmonies to accompany this melody, we shall obtain something like this—
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
Beethoven. Mass in C.
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.
J. S. Bach. Partita in B minor.
J. S. Bach. Organ Fugue in C minor.
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.
32. In our next example
Handel. 'Muzio Scevola.'
the key is fixed by the arpeggio of the tonic chord (compare example (b), § 30).
Mozart. Requiem.
Here the interval of the diminished fifth followed by B flat shows the key to be G minor. In our last example
Mendelssohn. 'Elijah.'
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—
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.
​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."
Though the leading note of the new key is not introduced here, the construction of the melody in the last two bars clearly indicates the key of G. This is further proved by the answer Bach gives to the subject. In the following examples
J. S. Bach. Cantata, "Singet dem Herrn."
Handel. 'Hercules.'
Schumann. Mass, Op. 147.
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.
J. S. Bach. 'Matthäus Passion.
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—
Schumann. Fugue, Op. 72, No. 1.
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.
shows a chromatic note (F sharp) as an auxiliary note, and is therefore similar to the preceding.
​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—
J. S. Bach. Mass in B minor.
Handel 'Rinaldo.
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—
J. S. Bach. Cantata, "Sehet, welch' eine Liebe."
38. Occasionally, instead of tonic and dominant, the two keys employed for the subject are tonic and subdominant. The following passages
Handel. 'Alexander's Feast.
J. S. Bach. Mass in B minor.
begin in the subdominant and end in the tonic. In our next examples
J. S. Bach. Fugue in E minor.
Mendelssohn. 3rd Organ Sonata.
the subject begins in the tonic and ends in the subdominant. In example (d) we also find an intermediate modulation to the dominant.
​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."
Handel. 'Semele.'
Mendelssohn. 'St. Paul.'
In all these examples will be seen a short modulation to the key of the subdominant.
41. The same modulation is sometimes found with a subject in a minor key—
Handel. 'Messiah.'
More frequently, however, the incidental modulation for a minor key is, as said above, into the key of the relative major—
Bach. Organ Fugue in G minor.
Handel. Anthem, "In the Lord put I my trust."
​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 on 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—
J. S. Bach. Wohltemperirtes Clavier, Fugue 37.
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 (b) and § 35 (b).
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.
Mozart. Quartett in G, No. 14.
J. S. Bach. Toccata in C minor.
Mozart. Litany in B flat.
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.
​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."
Mendelssohn. "Surrexit pastor," Op. 39, No. 3.
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—
Beethoven. Mass in D.
Cherubini. 4th Mass.
49. The following subjects begin on the subdominant—
Handel. Dettingen Anthem.
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").
Hummel. 2nd Mass.
A commencement on the leading note is very rare. We have given one instance in § 44; we add another—
Hummel. 1st 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.
​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—
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 counterpoint 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 (b), 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 determine 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 ​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.