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

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Introduction

"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 VII: stretto fugue, 61 bars, 2:49   

We've seen how we can take the subject from Contrapunctus V:

and divide its note values by two to get a diminished copy of the subject in Contrapunctus VI:

If we can divide, why not multiply by 2, to get an augmented version of the subject? That's just what Bach does here, to get this.

You can see that this is a 2X copy of the top subject, and 4X of the diminished subject, as you'd expect. And -- incredibly -- Bach manages to superpose all three of these and their inversions in a magnificent fugue in which the augmented subject marches inexorably up through the voices. You'll hear its long, sonorous notes singing forth at 0:10, 0:58, 1:29, and 2:07 in the bass, tenor, alto, and soprano, respectively, and by the time the alto entrance arrives, this formerly lighthearted fugue is rolling along like a juggernaut, leading to a splendid five-voice finale that wraps up the set of stretto fugues in fine style.

Player image: This image shows a beautiful "gravitational lens." The bright yellow area is a massive galaxy. Light from distant galaxies behind it is bent by the massive galaxy's gravity, in accordance with the canons of general relativity set forth by Albert Einstein. The galaxies hidden behind the main one appear bent into graceful arcs, some short, some quite long. You can see them in the picture forming a roughly circular pattern around the lensing galaxy. Image credit: Hubble Space Telescope / NASA.