EXAMPLE FOR ANALYSIS, No. 2.

Bach: Fugue No. 2, C-minor, in three voices. "Well-Tempered Clavichord." Book 1. [7]

Like all the fugues in Bach's "Well-Tempered Clavichord," this fugue is preceded by a prelude, in free style, like a series of embroideries on chords, intended to prepare the nearer for the more active musical enjoyment of the fugue to come. Parry, in the "Oxford History of Music," says of the Prelude of Bach and Handel: "It might be a simple series of harmonies such as a player might extemporize before beginning the Suite or the Fugue, [such is the case in the present prelude]; or, its theme might be treated in a continuous consistently homogeneous movement unrestricted as to length, but never losing sight of the subject" ... etc.

A fugal subject is usually longer and more pretentious than an invention subject, and more nearly approaches what we should call a complete melody. It may contain several motives. Moreover, while the second voice is "answering" the subject, the first voice continues with further melody, and if this is of definite, individual character it may easily assume almost as great importance as the subject itself, in which case we may give it the name of "counter-subject." In Figure XI the subject and counter-subject of this fugue are shown. The long brackets show subject and counter-subject; the short brackets show the three chief motives, marked a, b, and c. The simplicity of the melodic material is noticeable. Motive a, which, with its three repetitions, forms most of the subject, consists of five tones, in a charming and unforgettable rhythm of two shorts and three longs. Motive b is simply a descending scale, in equal short notes. Motive c is four equal long notes. Play the subject and counter-subject through separately, several times, and get them well "by heart" before going farther.

This fugue is a wonderful example of what a master-composer can make out of simple materials; the whole piece is built from these three motives. Our analysis may conveniently be made in tabular form, the student being expected to trace out the development for himself, measure by measure.

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FIGURE XI. SUBJECT AND COUNTER-SUBJECT OF BACH'S FUGUE IN C-MINOR
(WELL-TEMPERED CLAVICHORD)

TABLE OF THEMATIC TREATMENT OF FUGUE IN C-MINOR

Measures.
1-2	Subject in Alto.
3-4	Subject "answered" in Soprano ("imitation"), counter-subject in Alto.
5-6	Episode 1: Motive a prominent in Soprano.
7-8	Subject in Bass, counter-subject in Soprano, fragments of motive c in Alto.
9-10	Episode 2: Motive a tossed between Soprano and Alto, motive b in Bass.
11-12	Subject, in key of E-flat major, in Soprano, counter-subject in Bass.
13-14	Episode 3: Motive b in Soprano, motive c in other two voices.
15-16	Subject in Alto, counter-subject in Soprano, motive c in Bass.
17-19	Episode 4: Motives a and b variously distributed between all three voices.
20-21	Subject in Soprano, in tonic key again, counter-subject in Alto, motive c in Bass,
22-25	Episode 5: Motives a and b in all voices.
26-28	Climax: Subject in Bass, motives b and c in other voices.
29-31	Coda: Subject in Soprano.

Note that all the episodes take the form of sequences, as, for example, in the following instance (measures 9-10):

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FIGURE XIa. A SEQUENCE FROM BACH'S FUGUE IN C-MINOR.

The general form of this fugue illustrates the same principles of modulation, and of restatement of subject after contrast, that we noticed in the folk-songs and in the invention. This may be tabulated thus:

TABLE SHOWING STRUCTURE OF FUGUE IN C-MINOR.

A.	B.	A.
STATEMENT.	CONTRAST.	RESTATEMENT.
Measures 1-10 in key of	Measures 11-19 in various keys,	Measures 20-31 in
C-minor.	beginning with E-flat.	C-minor.

The modulation in this case, however, is not to the "dominant" key, but to what is called the "relative major" key, as is usual in pieces written in minor keys, (see the folk-song, "Sister Fair," in Chapter II), the reason being that the relative major affords the most natural contrast to a minor key, just as the dominant affords the most natural contrast to a major key.

The conclusion is emphasized by the finely rugged statement of the subject in Bass at measure 26.

The treatment of this fugue, for all its consummate skill, is comparatively simple. It does not employ the more subtle devices often employed in fugues, of which may be mentioned the following:

1. "Inversion:" The subject turned upside down, while retaining its identity by means of its rhythm.

Original Subject.

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Inversion.

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FIGURE XII. THE DEVICE OF "INVERSION."

Original Subject.

Augmentation.

Original Subject.

Diminution.

FIGURE XIII. THE DEVICES OF "AUGMENTATION" AND "DIMINUTION."

2. "Augmentation and Diminution:" The length of the notes doubled or halved, while their relative length, or rhythm, is carefully maintained. (Figure XIII.)

3. "Shifted rhythm:"[8] The subject shifted as regards its position in the measure, so that all the accents fall differently.

Original Subject.

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Shifted.

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FIGURE XIV. DEVICE OF "SHIFTED RHYTHM."

4. "Stretto:" The imitation of the subject by a second voice occurring prematurely, before the first voice has completed the subject, frequently with highly dramatic effect. (b) in Figure IX is an example of stretto.

These devices are mentioned here not only because they occur in many fugues, but because they are used in the symphonic music of Mozart and Beethoven, as we shall later have occasion to see.