In the Summer of 2012, I supervised Kalin Ellison on a project on Music and Mathematics. At that point, Kalin had finished her freshman year at LaGuardia High School. We focused on how Mathematics can be a language to describe Music. As such, we studied number systems with different bases, Fourier analysis and concepts from abstract algebra such as equivalence classes.
In addition, we discussed relations to Physics and Computer Science. In particular, we wrote some small music programs in the visual programming language PureData.
I gathered some of the materials in online lecture notes.
Part of the project was practical, as the eventual goal is to make improvising and playing music easier and more fun. We tried out different ways of representing music, different notations, and actually played using those.
For the final project, Kalin devised her own alternative music notation and described it in a nice paper. The notation uses numbered notes in base twelve. The final report can be accessed here: Thinking Outside the Staff. It contains two examples of songs in her notation.