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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Canon per augmentationem: 4:16   

The last canon of AOF is its most complex. Bach calls it Canon per augmentationem in contrario motu, and the idea is shown in the figure below.

At top is the leader, an elaborate variant of the AOF theme. Below is the follower, and you'll see that not only is it the augmentation of the leader (all note values multiplied by 2), but also its inversion (the "contario motu"). And -- you guessed it! -- like the Canon alla decima and the Canon alla duodecima, Bach plays this canon twice, exploring double counterpoint, once starting a fourth down from the leader, and then again at the octave. The result is an extraordinarily complicated and difficult canon, but one with a sense of content timelessness, a lovely conclusion to the AOF canons.

Player image: The Rotten Egg Nebula glows in multicolored hues of gas and dust ejected from a dying star. At the center of the symmetric -- though lopsided by about a factor of two -- lobes of gas is a white dwarf, the dead remnant of a star like the Sun. This is a precursor to the images shown with the mirror fugues; a few thousand years hence, it will have evolved into one of the beautifully symmetric shapes shown in those pictures. Image credit: Hubble Space Telescope.