[microsound] category theory and composition

[Justin Glenn Smith]

Andrew Salch wrote:
> On Tue, 22 Dec 2009, Justin Glenn Smith wrote:
>> 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).
> 
> 
> How do we regard a genre of composition as a category? What are the
> objects and the morphisms of a genre of composition?
> 

I was imagining that the objects of a genre of composition would be the individual compositions. And the morphisms would be whatever transformations are appropriate to that genre (arrangements, orchestrations, samplings, remixs, covers, each of these having sub variations remix->chop and screw, etc.). Each of these objects would be its own category, with key signatures, samples, instrumentation etc. etc. as its objects.

Thus what I was imagining was a Functor allowing the usage of the material in another genre without losing structure, by remapping to a new category (thus in one mapping of categories for example the point in time in which a sound occurs may be mapped to the timbre in another domain). I was imagining I would allow myself the freedom to potentially invent a new genre (or if I was lucky, happen upon an existing one), by just letting the new genre be whichever one my deterministic mappings created. And reinventing those mappings until I get a result that somehow pleases me.

It could be that my reasoning is sloppy about some of this, or that I am misusing some of these concepts. If so I do welcome correction. In the worst case I guess one could say that some guy probably wrote a song while looking at a sunset and on the other hand I wrote a song while thinking about math.