Mirror fugue
A fugue in retrograde or inverted shape.
What it means
A mirror fugue is a fugue built so that a second, complete version can be obtained from it by mirroring. Not only the theme is inverted, but the whole texture: every voice is mirrored in all its intervals, and the voices simultaneously exchange their position, so that the topmost becomes the lowest. The result is a second fugue that is just as correct as the first.
Musical use
The demand is extraordinarily high. Every combined sound must remain permissible in the mirroring as well — what was a consonance must remain a consonance, every dissonance must also be treatable correctly when mirrored. Because, upon inversion, fifths become fourths, and the fourth above the bass counts as a dissonance in strict writing, the texture must be laid out from the outset so that this transformation produces no errors.
The best-known example is found in Bach's Art of Fugue, where mirrored fugues are notated in both shapes — in the direct and in the inverted form. Alongside inversion mirroring, a retrograde mirroring is in principle also conceivable, in which the texture is read backward; the designation “mirror fugue,” however, usually refers to inversion.
The mirror fugue is to be distinguished from the counter-fugue: there the theme appears inverted in the answer, but the texture as a whole is not mirrored. And it differs from the double fugue, because that rests on two different themes.
Among these belong Contrapuncti 12 and 13, each existing in rectus and inversus form. A precondition is a texture that remains harmonically coherent in both shapes, which demands high contrapuntal art.
Performance practice
If you play a mirror fugue, compare both versions in the notation — the correspondences explain the construction. Shape each version as music in its own right, not as a calculation problem. And mark the thematic entries in both versions; their position changes with the mirroring.