Fugue

Front matter

AUGENER'S EDITION, No. 9185.

FUGUE.

BY

Chapter 1

Fugue.

CHAPTER I.

INTRODUCTION.

s11. 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.

s22. 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.

s33. 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.

s44. 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 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.

s55. 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.

s66. 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 developments the entries may be at other intervals.

s77. 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.

s88. 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.

s99. 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 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.

s1010. 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.

s1111. 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.

s1212. 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.

s1313. 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.

s1414. The counter-exposition, if there be one, will generally be followed by a second episode, different from the first one. To this second episode (or to the first, if there be no counter-exposition) succeeds the Middle Section of the fugue. Here 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.

s1515. 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.'

s1616. 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.

s1717. 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.

s1818. 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 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.

s1919. 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.

s2020. We occasionally find fugues in which the answer, instead of being, as usual, a transposition of the subject (§ 9), is given by inversion, or by augmentation or diminution. We shall see examples of these as we proceed. Such fugues are called fugues by inversion, augmentation or diminution, as the case may be.

s2121. 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.

s2222. 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 the regular intervals of reply of subject and answer. Such passages are called Fugato passages. A whole movement is 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.

s2323. 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.

Chapter 2

Chapter II.

THE SUBJECT.

s2424. 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.

s2525. 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.

s2626. 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.

s2727. 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.

s2828. 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).

s2929. 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).

s3030. 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.

s3131. 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.

s3232. 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.

s3333. 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.

s3434. 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.

s3535. 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.

s3636. 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.

s3737. 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."

s3838. 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.

s3939. 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.

s4040. 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.

s4141. 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."

s4242. 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.

s4343. 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).

s4444. 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).

s4545. 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).

s4646. 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. At other times they are of very considerable extent —

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"—!

s4747. 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.