Wednesday, March 4, 2009

Cage's square root form

Thinking about square root day, yesterday, I remembered John Cage's square root form.

It works like this:

The overall form is the short form (phrase level) squared. So, to use today's canon as an example. Five measure opening phrase -- 25 measure overall form.

But the real key is that the features that are present in the short form are also exemplified by the large form and each of the other parts of that form.

Again, this canon is 5 squared or 25 measures long. The overall form divides 10 + 10 + 5.

Each 5 measure section divides 2 + 2 + 1 -- This structural rhythm is also stated twice at the beginning by the dux and then, of course by each comes.

(click on image to enlarge)

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