Mathematics itself is music. See [Mathematics, the Music of Reason][1].
The point I am making here is that to "define (aspects of) music" is *not* a mathematician's goal. That is perhaps the task of someone who is more interested in music and has little interest in mathematics, or perhaps someone who needs to find credibility in what he does by resorting to popular culture, in order to *show* others that mathematics is useful and can *even* define aspects of music. What is special about *music* in this question other than it is a popular form of art that can be enjoyed more easily by more people? Asking "if mathematics can define (aspects of) music" is similar to asking if mathematics can define (aspects) of cinema, which may be a good question but not for MO.

  [1]: http://www.amazon.com/Mathematics-Music-Reason-Jean-Dieudonne/dp/3642080987/ref=sr_1_1?ie=UTF8&qid=1341535160&sr=8-1&keywords=Mathematics+the+music+of+reason