Should I talk to my supervisor about including a new field in my PhD?
First, this makes perfect sense. What you are describing is a project in the digital humanities, and there are others in music using computational methods to analyze music and its social context. The place I would suggest starting is to look at the Music Encoding Initiative, which has developed an xml mark-up language for music. The community there can lead you to many other possibilities for integrating music and computation at various levels of computational complexity. The focus remains on the music as the object of study but applies new research methods to it.