What In the World is a "Mirror Fugue?"

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.
   

• Contrapunctus XII a 4
  
  
  • Rectus

• Inversus

• Contrapunctus XIII a 3
  Whereas Johann Sebastian did not specify instrumentation for his Art of Fugue, Carl Philipp Emanuel included transcriptions of Contrapunctus XIII for duo harpsichords. While we do not know who transcribed them, these arrangements represent the practice of the Bach household where improvisation was clearly the order of the day.
  
  
  • Rectus
    Coming Soon
    
    

• Inversus
  Coming Soon
  
  

• Canon per Augmentationem in contrario Motu
  The "Canon in Augmentation and Contrary Motion" comes after the mirror fugues and before the "Great" Fugue which concludes the cycle. This canon is one of the best examples in music literature of not only proportional canon, but also canon in contrary motion, and double counterpoint at the octave. Please refer to the Canons of the Art of Fugue study for an analysis of this canon.