play one or another of these thirty variations. Consequently (and
somewhat ironically) the variations became attached to the name of
young Goldberg, rather than to the distinguished Count's name.
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 Varia-
tions, 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 to-
gether 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 "post-ending
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 which the
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. And-
Achilles: Wait a minute. Don't I recall reading somewhere or other about
fourteen recently discovered Goldberg canons ...?
Tortoise: Didn't that appear in the same journal where they recently re-
ported the discovery of fourteen previously unknown days in
November?
Achilles: No, it's true. A fellow named Wolff-a musicologist-heard
about a special copy of the Goldberg Variations in Strasbourg. He went
there to examine it, and to his surprise, on the back page, as a sort of
"post-ending ending", he found these fourteen new canons, all based
on the first eight notes of the theme of the Goldberg Variations. So
now it is known that there are in reality forty-four Goldberg Varia-
tions, not thirty.
Tortoise: That is, there are forty-four of them, unless some other
musicologist discovers yet another batch of them in some unlikely spot.
And although it seems improbable, it is still possible, even if unlikely,
that still another batch will be discovered, and then another one, and
on and on and on ... Why, it might never stop! We may never know if
or when we have the full complement of Goldberg Variations.
Achilles: That is a peculiar idea. Presumably, everybody thinks that this
latest discovery was just a fluke, and that we now really do have all the
Goldberg Variations. But just supposing that you are right, and some
more turn up sometime, we shall start to expect this kind of thing. At
(^392) Aria with Diverse Variations