Kirnberger.
152. Fugue subjects are sometimes answered by inversion. In this case the answer is not generally in the key of the dominant; but that species of inversion is used in which dominant is answered by tonic, and tonic by dominant (Double Counterpoint, §§ 281, 282). Sometimes the answer by inversion is given in the first exposition, as in Bach's 'Art of Fugue,' No. 5—
J. S. Bach. Art of Fugue, No. 5.
More frequently, however, this device is reserved for the later developments of the fugue, in order to heighten the interest, as in Nos. 15, 20, and 46, of the 'Wohltemperirtes Clavier.' An answer by inversion is much more common with a minor subject than with a major.
153. We also sometimes find answers by augmentation and diminution. In these again there is no need that the answer should be in the dominant key. The object of putting the answer in the dominant is to prevent its being a mere monotonous repetition of the subject; and this end is sufficiently attained either by inversion or by altering the lengths of the notes. In Nos. 6 and 7 of the 'Art of Fugue' will be seen examples, too long to quote here, of answers by augmentation and diminution.
154. Sometimes, especially in vocal fugues, in order to keep the answer in a more convenient compass, the change of an octave in pitch is made in the course of the answer, as in the following passage—
Schumann. Requiem.
A similar example, which is familiar to everybody, will be found in the "Amen" chorus of the 'Messiah.'
