[microsound] category theory and composition

[Justin Glenn Smith]

I have heard the claim that Bach wrote out the entirety of possible music composition - that every possible variation was present in his music, and nothing could be new after him.

This, of course, is laughably false.

But I was thinking about a context in which this could be made a true statement. In category theory there is the concept of a functor, which is a structure-preserving mapping from one category to another. If we treated two genres of composition as categories, we could define a functor to take a composition in one of these genres and get a composition in the other, without losing structural information (ie. analogous patterns would exist).

Did I make this up? Am I remembering it from somewhere? Has someone tried it already? I am imagining mapping the sequence of pitches in a bach piece to spectral densities, and the durations to amplitude, and amplitude to pitch center, and timbre to duration. For example. With enough of a clinamen, of course, to keep things interesting (or maybe just keeping the clinamen of the original figured bass for example, but mapping it to a different part of the composition?).