We investigate the fractal nature of classical music networks considering their node degree distributions, skeletons, and assortativity coefficients. The musical networks represent the relationship between musical notes (Do, Re, Mi, Fa, Sol, La, Si, and their sharp), chords, and duration. We show that classical music networks present disassortativity, that scale-invariance happens often (either in the original network or its skeleton) and that a significant part of the networks present self-similarity.