Counter-fugue
Fugue with inversion of the subject in the answer.
What it means
A counter-fugue (German Gegenfuge) is a fugue in which the answer brings the subject not in its original shape but in inversion: what goes upward in the subject goes downward in the answer, and vice versa. The subject thus appears from the start in two shapes, the direct and the mirrored one, which alternate or are combined with one another.
Musical use
In an ordinary fugue the answer is a transposition of the subject to the dominant level. The counter-fugue replaces this transposition with inversion and thereby includes one of the techniques of transformation of counterpoint in the layout of the exposition. In the further course both shapes appear together, often in stretto, in which the direct and the inverted form overlap one another.
The prerequisite is a subject that also sounds convincing in inversion and can be combined with its mirror shape. Not every subject is suited to this; especially favourable are subjects with a clear contour whose inversion differs distinctly from the original and yet is recognized as the same.
The counter-fugue is to be distinguished from the mirror fugue, in which not only the subject but the whole piece is mirrored, so that a second complete version arises, and from the double fugue, which rests on two different subjects. The designations are not always used uniformly in older literature; occasionally “counter-fugue” also designates fugues in general in which inversion plays a significant role.
The counter-fugue is a special form in which the answer brings the subject not in the original shape but mirrored. Well-known examples are found in Bach's Art of Fugue, where several Contrapuncti are laid out in this way. In the teaching of the eighteenth century it is also called fuga contraria.
Performance practice
Mark the direct and the inverted subject entries differently before you practise. Shape both forms equally distinctly — the inversion is no afterthought but of equal rank. And, in stretti, listen to the meeting of both shapes; the appeal of the form lies there.