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365. Having in the preceding chapters of this book fully explained the construction of those fugues which, being founded on only one subject, are sometimes termed "simple" fugues, we have in this chapter to speak of the important class which contains two, three, and occasionally even more subjects. We shall first deal with the, in which, as its name indicates, there are two subjects.

366. In speaking of the countersubject, we incidentally mentioned (§ 175) that some theorists speak of a fugue in which the subject is regularly accompanied by the same countersubject as a "double fugue." If, however, we adopt this nomenclature, we have no means of distinguishing between fugues with one subject and fugues with two or more. It is very much better and clearer to restrict the name of double fugue to two classes of fugue now to be described:—First, those in which the two subjects are announced simultaneously; and, secondly, those in which each subject has a separate and complete exposition before the two are heard in combination. Of these, the first kind is by far the more common and the more important; we therefore deal with it first.

367. A fundamental distinction between the kind of double fugue we are now noticing, and the fugue with a regular countersubject (with which the student is already familiar) is, that in the latter the countersubject never appears before the first entry of the answer, and, as we have seen (§ 172), not always then. But in a double fugue the second subject, which is really a countersubject of the first, accompanies the leading subject on its first entry. This, as we shall see presently, makes a difference (sometimes a very considerable difference) in the form of the exposition.

368. It ought to be hardly necessary to remind students that the two subjects of a double fugue must be written in some kind of double counterpoint with one another. In the enormous majority of cases, this will be double counterpoint in the octave. In the 'Kyrie' of Mozart's 'Requiem,' the two subjects (which we quoted in § 175 of Double Counterpoint) are so written as to be capable of inversion both in the octave