J.S. Bach, Canon at the Fifth in Contrary Motion - Goldberg Variation No. 15

Fourteen infinite canons over the first eight notes of the Goldberg Variations bass, jotted on a scrap of paper tucked away at the back of his own copy of the said work, are as close as Bach gets to handing us the keys to his canonical art. He spells out nothing explicitly, but a close study of these canons reveals a pedagogical gift of the highest order, and that he is secretly conveying how to design a canon in contrary motion effortlessly. (In all the mind-numbing contrapuntal tours de force his music offers us it is obvious he is hardly breaking sweat working out his conceptions.) He first brings to our attention, in a simple crab canon, that the first eight notes of the Goldberg bass are contrapuntally compatible with their own retrograde. He then uses this to teach us, step by step, the mechanics of a canon in contrary motion—with an independent third voice, no less—culminating in a six-voice triple canon—the same one he is seen holding in the 1748 portrait of him by E.G. Haussmann.

There are two canons in contrary motion in the Goldberg Variations. This, one of the greatest andantes ever written, is the second.