Music can exhibit fractality in many ways, from rigid self-similarity of the composition to a psychological superposition of patterns on different scales. Because of its ephemeral nature, it presents challenges when one attempts to assess it from a fractal perspective. Beware of books or webpages about fractal music: many of these are the worst kind of nonsense.
Given the general lack of clarity associated with the subject, Benoit Mandelbrot suggested to Harlan Brothers that he undertake a rigorous treatment of fractal music. Brothers began exploring the specific ways in which compositions can exhibit power-law relations. He found that Western composers have been composing a form of fractal music for over six centuries with the development of the mensuration or prolation canon. Here is a discussion and example.
Descriptions and audio files of other types of musical scaling can be found at his page on fractal music.