Timbre and acoustics
A string does everything at once
A plucked string does not vibrate at one frequency. It vibrates at all the whole-number multiples of one frequency simultaneously, and nearly everything in music theory is downstream of that fact.
The ear hears the list, not the shape
Two sounds with the same partials and different phases have completely different waveforms and sound identical. What the ear extracts is a list of frequencies and strengths, and everything else is discarded.
The shape of a note, which is most of what an instrument is
Cut the first fifty milliseconds off a recorded piano and listeners stop calling it a piano. The attack carries more identity than the steady tone it leads into, and it is the part every spectrum plot leaves out.
The room is part of the instrument
A room has frequencies it supports and frequencies it will not. In a small one those frequencies are far apart, so some bass notes are loud in one corner and absent in another — and no equipment fixes it.