This is the reason for measurements of intermodulation distortion and THD+N by frequency. A proper evaluation of, say, a power amplifier will look at a dozen, maybe a couple dozen different measurements; taken all together, these provide a reasonably complete picture of how the amp performs.

But - from an engineering perspective, music can in fact be decomposed into a series of sine waves - and effectively all digitally recorded music goes through this process as part of a/d conversion (sort of; it's complicated) or FFT-based digital equalization. See: https://en.wikipedia.org/wiki/Fourier_analysis