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Art of Fugue: Mirror Fugues and
Canon in Augmentation & Contrary Motion



What In the World is a "Mirror Fugue?"

Mirror fugues are a pair in which, whatever one does, its mirror does the opposite. Bach called the original fugue the Rectus, and its opposite the Inversus. The two were said to be playable alio Modo, "in either fashion." In the following fugues, Bach employs not one, but six mirrors at the same time! That Bach was able to accomplish this without deviation of a single pitch is astounding, and accords the mirror fugues of die Kunst a unique place in the puzzle music of the western tradition.

  1. Melodies Are Mirrored: Each melody of the mirror fugue moves in the opposite direction. Where a melody ascends, the mirror fugue descends. This is called melodic inversion, and it applies to every voice of the fugue. Click the "mirror man" on the right to see how the subjects of these mirror fugues are melodically inverted.

    Technical Note: While they do invoke melodic inversion, Bach's mirror fugues are not true mirror inversions because they do not preserve interval qualities. The "mirror" designation applies, here, to the fugue itself, not to the specific type of melodic inversion.

  2. Voice Entries Are Mirrored: In Contrapunctus XII, each voice of the mirror enters in the opposite order of the original. Where a voice entered first, the mirror enters it last. Where a motive is stated by the soprano, the mirror states it in the bass. Click the exposition icon (top right) to see how vocal entries are mirrored in Contrapunctus XII.

  3. Tonal Functions Are Mirrored: Tonic pitches are replaced by dominants and dominants by tonics. While this reversal can be heard in the subjects, it is especially audible in pedal tones. Where there is a pedal on "do," the mirror fugue pedals "sol" (and vice versa). Click the following examples to hear the difference. (Pedal tones are in yellow, subjects in green.)


  4. Keys Are Mirrored: Modulations move in the opposite direction. Where there is a modulation to the dominant or mediant, the mirror fugue modulates to the SUB-dominant or SUB-mediant. (Click the noteheads below to compare tonal regions at analogous points.)

  5. Sequences Are Mirrored: Sequences move in the opposite direction. Where a sequence went up, in the mirror it goes down. Listen to analogous sequences at the following points:

      Contrapunctus XII, mm. 46-49
      • Rectus (ascending sequence)
      • Inversus (descending sequence)

      Contrapunctus XIII, mm. 52-57
      • Rectus (ascending sequence)
      • Inversus (descending sequence)

  6. Cadences Are Mirrored: The cadence chord is approached from the opposite direction. Where there is an authentic (V-i) cadence, the mirror fugue has a plagal (iv-i) cadence.



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