Canon per Augmentationem – Jeffrey C. Hall

AOF home page

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

The Art of Fugue

Simple Fugues
Contrapunctus I
Contrapunctus II
Contrapunctus III
Contrapunctus IV

Canon alla Ottava

Stretto Fugues
Contrapunctus V
Contrapunctus VI
Contrapunctus VII

Canon alla Decima

Double and Triple Fugues
Contrapunctus VIII
Contrapunctus IX
Contrapunctus X
Contrapunctus XI

Canon alla Duodecima

Mirror Fugues
Contrapunctus XII + inversus
Contrapunctus XIII + inversus

Canon per Augmentationem

Quadruple Fugue
Contrapunctus XIV

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.

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 timelessness, a lovely conclusion to the AOF canons.