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.
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.
