"Achilles: You mean, the composer was Bach, and these were the so-called "Goldberg
Variations"?
Tortoise: Do I ever! Actually, the work was entitled Aria with Diverse Variations, of
which there are thirty. Do you know how Bach structured these thirty magnificent
variations?
Achilles: Do tell.
Tortoise: All the pieces - except the final one - are based on a single theme, which he called an "aria". Actually, what binds them all together is not a common melody, but a
common harmonic ground. The melodies may vary, but underneath, there is a
constant theme. Only in the last variation did Bach take liberties. It is a sort of "postending ending". It contains extraneous musical ideas having little to do with the
original Theme - in fact, two German folk tunes. That variation is called a
"quodlibet".
Achilles: What else is unusual about the Goldberg Variations?
Tortoise: Well, every third variation is a canon. First a canon in two canonizing voices
enter on the SAME note. Second, a canon in which one of the canonizing voices
enters ONE NOTE HIGHER than the first. Third, one voice enters Two notes higher
than the other. And so on, until the final canon has entries just exactly one ninth
apart. Ten canons, all told."
- - - -
Douglas R. Hofstadter (1979), Gödel, Escher, Bach: An Eternal Golden Braid. A Metaphorical Fugue on Minds and Machines in the Spirit of Lewis Carroll
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