Sinewaves are not magically simpler in this sense. Complex musical signals are just as combination of sinewaves so if something works for one sinewave, it works for a million sinewaves. To proof this I did the same for music, now in STEREO! Look and be amazed!What you are showing here works with a simple sinewave. However, it is not relevant because an actual musical waveform is much more complicated than a sinewave.
Fourier demonstrated that it can be represented with sinewaves, but this series of sinewaves must generally be infinite.
Band-limited signals have a finite/limited series of sinewaves.