The April 18 edition of Science has an interesting article on representing musical
characteristics as orbifolds (singular quotients of Euclidean space).
is the summary article, and it has a link to the full text of the paper, which itself is short.
It was written by music professors, so the math is a bit imprecisely stated and one might have to read some things multiple times to figure out what is meant (vice what is said). Some of the references at the end are interesting too.