either of the subject (as at bar 27) or of some important figure of counterpoint (as at bars 16 and 20). Occasionally in old fugues, we meet with a full close in some related key just before the final stretto; but this is not to be recommended.
322. To what keys, and in what order, is it advisable to modulate in the middle section of a fugue? To this important question it is not possible to give more than a general answer. The rule given by the old theorists was that the modulations in a fugue should be confined to the nearly related keys. We quote Cherubini's remarks on this subject:—
"When a fugue is in a major key, the key into which we should modulate first is that of the dominant with its major third; then into the sixth—the relative minor key of the principal key; after that into the major key of the subdominant, to the minor key of the second, and to the mediant, also minor; and then return to the key of the dominant, in order to proceed to the conclusion, which should be in the principal key.
"It is permitted in the course of a fugue in a major key to change the principal key into the minor; but this permutation should be employed only for a few moments, and merely to bring in a suspension on the dominant, in order afterwards to attack the principal major key.
"When a fugue is in a minor key, the first modulation is into the mediant major key, which is the relative major of the principal key; then we modulate in turn into the dominant minor key, into the sixth major key, into the subdominant minor key, and into the seventh major key; and lastly from one of these keys return to the principal key."
323. We have quoted Cherubini somewhat fully, because it is well that students who are working for an examination should know what the old rules are; but when we come to apply to them the test of Bach's practice, we find that they will not hold water for a moment. In the whole of the 'Forty-Eight,' there is not one single fugue in which the order of modulation prescribed by Cherubini is observed. What is even more to the point—in the 'Art of Fugue,' a work written by Bach, to show the proper method of fugal construction, we also find no fugue written on Cherubini's plan.
324. Besides this, we find that Bach, though he generally keeps within the circle of nearly-related keys, has no hesitation about going into unrelated keys when he has a mind to. No. 4 of the 'Art of Fugue,' the key of which is D minor, contains a modulation to B minor. In the fugue in E minor (No. 10 of the 'Forty-Eight') there is at bar 30 an entry of the subject in D minor; and in the fugue in A flat (No. 41 of the same work), we see at bar 32 an entry in E flat minor. The great organ fugue in D contains entries in C sharp minor and E major, and the organ fugue in B minor has an entry in C sharp minor. It is quite clear, either that Bach did not know how to write fugues properly, or that the old rules need altering. Of course we choose the latter alternative.
325. The rules as to the course of modulation and the middle entries in fugues which we deduce from Bach's works, are as follows:—
I. It is best in general to keep within the circle of nearly-
