The Art of Fugue, BWV 1080, by Johann Sebastian Bach

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"Über dieser Fuge..."
Structure of The Art of Fugue
The "unfinished" fugue
About the realization
How to listen to The Art of Fugue
About the narratives below


The Art of Fugue

Simple Fugues
Contrapunctus I  (3:52)
Contrapunctus II  (3:12)
Contrapunctus III  (3:49)
Contrapunctus IV  (3:18)

Canon alla Ottava  (4:12)

Stretto Fugues
Contrapunctus V  (2:24)
Contrapunctus VI  (4:20)
Contrapunctus VII  (2:49)

Canon alla Decima  (4:44)

Double and Triple Fugues
Contrapunctus VIII  (5:17)
Contrapunctus IX  (2:46)
Contrapunctus X  (3:29)
Contrapunctus XI  (6:58)

Canon alla Duodecima  (3:33)

Mirror Fugues
Contrapunctus XII + inversus  (3:36)
Contrapunctus XIII + inversus  (4:23)

Canon per Augmentationem  (4:16)

Quadruple Fugue
Contrapunctus XIV  (11:52)

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Contrapunctus XII: mirror fugue, 56 bars, 3:36   

Here's the first of AOF's mirror fugues. These are among AOF's most engaging and enjoyable music, and the fact that Bach achieved such an effect within the constraints of the severest technical rigor is amazing.

The first thing to realize is that when you play the clip above, you will hear two fugues or, more correctly, the same fugue twice. In the graphic below, I'll show you both the start of the fugue, and its mirror.

The measures above the blue line are what you'll hear at the start of the audio clip. The measures below the blue line begin the mirror fugue, at 1:47. As you can see from the graphic, this is exactly the same fugue, except everything is perfectly inverted. All parts are turned upside down with the intervals preserved. Moreover, the parts are switched...the bass from the first fugue becomes the soprano in the mirror, tenor becomes alto, alto becomes tenor, soprano becomes bass. It's as if you took the top part of the graphic and flipped it over the blue line, and a whole new fugue results. Amazing, eh?

Player image: This beautiful sight is the Egg Nebula, a region of gas and dust brilliantly illuminated by a dying star. The concentric rings are shock fronts excited by emission from the star, which is swathed in thick dust which, through poorly understood processes, permits brilliant beams of starlight to emerge only in preferred directions (as with the four brilliant beams in the image). As much as Nature abhors a vacuum, she loves symmetry. Image credit: Hubble Space Telescope.