This is quite a nice coincidence, as I studied and did research with both Dr. Gary Don and Dr. James Walker back in my undergraduate for mathematics and music, authors of one of the math and music articles in the AMS website. These two professors created a textbook Mathematics and Music: Composition, Perception, and Performance published in 2013. (My name is in the Acknowledgements, and I have an autographed copy from Dr. Don!) My impression is that Dr. Walker specialized mainly on harmonic analysis before he wrote this book, so there's some mention of FFTs, for example.

In addition, there is a website for this textbook.