Is music fractal? Yes!
Fractal dimension is a way of talking about things that seem to break the normal rules of geometry. The dimension of music audio is between 1 and 2: between a flat line and a two dimensional space. According to this paper, it is more specifically between 1.7 and 1.9. Different genres have different values, with rock having a higher value than classical, for instance.
Paper: “Fractal dimension and classification of music”, Bigarelle and Alain, 2000, available here.