Music was taught as part of the quadrivium (alongside arithmetic, geometry, and astronomy), so it has a long history of being thought about in mathematical terms. There's nothing wrong with looking at music that way. What is so interesting about music is its ability to turn mathematical beauty into aesthetic, artistic beauty.

Sometimes the math is just there in the background: "This chord progression is based on certain physical facts related to the harmonic series. That makes it sound good, and I like it". Sometimes it is brought to the forefront: "All of this music appears to be generated from a short pattern of notes which is recognizable even as it is subjected to rotations, elongations, truncations, etc. That is beautiful."

Certain types of music play up the lovely-pattern-ness of music, and some don't. Neither is better than the other (denigrate the art of Justin Bieber who dare), but you can probably guess which I prefer :)

Consciousness, pattern-recognition, spatial rotation of abstract objects, natural mathematical beauty, poetry, drama, acting/performance, nonverbal collaboration, shared rhythm: music is a nexus for all of these things. Music is nothing short of awesome, in the truest sense of that word.