the third bar, and we see that all three subjects need modification in the answers. Of the six possible combinations of a triple counterpoint, Mozart has only employed three; but it must be noticed that each of the subjects appears in the bass (Double Counterpoint, § 253). One more point remains to be noticed about this fugue—the almost entire absence of free parts. For the sake, no doubt, of that clearness which is so essential in double and triple fugues, the three subjects always appear without any additions, which might prevent their being easily distinguished. It is not till bar 38 of our extract, and the coda which we have not quoted, that we find any continuous four-part harmony.
410. It is seldom that we find a triple fugue so strictly treated as that by Mozart which we have just been analyzing. Composers usually allow themselves considerable freedom in such cases. For example, the very interesting 'Fuga à 3 soggetti.' in Haydn's quartett in A, Op. 20, No. 6, the three subjects of which are quoted in Double Counterpoint § 262, is, strictly speaking, not a triple fugue at all, but a double fugue, with one regular countersubject; for the third subject appears for the first time as an accompaniment to the answer, and not to the other two subjects, and in some of the middle entries only two of the three subjects are employed together.
411. A Quadruple Fugue, or a fugue on four subjects, is so extremely rare that it will not be needful to say much about it. The four subjects will now evidently have to be written in quadruple counterpoint; but it is very seldom that they will be all announced at once. In Haydn's 'Fuga à 4 soggetti,' in his quartett in C, Op. 20, No. 2, only two of the subjects are announced at first, the third and fourth subjects entering as countersubjects to accompany respectively the first and second appearances of the answers. The four subjects of this fugue, with their various inversions, were quoted as examples of quadruple counterpoint in Double Counterpoint, § 270.
412. In Handel's 'Alexander's Feast,' the final chorus, "Let old Timotheus yield the prize," is sometimes spoken of as a fugue on four subjects. So, in one sense, it is; but it cannot be regarded as a specimen of a true quadruple fugue, because seldom more than two, and never more than three of the four subjects are employed simultaneously. The fugal writing, as is mostly the case with Handel, is far from strict throughout.
413. In Cherubini's 'Counterpoint and Fugue' will be seen a good example of a strict fugue on four subjects, the opening bars of which we gave in § 269 of Double Counterpoint; but probably the finest specimen of a quadruple fugue ever written is the final movement of Cherubini's great 'Credo' for a double choir, which has not only four subjects, but two countersubjects in addition, which make their first appearances against the answers. We have only space to quote the opening bars of this movement.
