I would no more expect a mathematical answer to the question "What is music" than I would to "What is fire" or "What is an electron".

Which is to say, I would expect those questions to be primarily addressed by other branches of inquiry, but perhaps with a healthy serving of mathematics in the answer.

There certainly are a lot of applications of physics, biology, and psychology to Music, and underlying those there is certainly a lot of mathematics. One of my favorite old books on this topic is by Juan Roederer, Introduction to the physics and psychophysics of music.