What stuck out to me was that there are brief, sub-harmonic sounds that musical instruments make that we hear as uniquely identifying to the instrument.
Are those the "overtones"(harmonics)?
I don't understand why it's not possible to capture and replay them. Maybe I just never had good enough hifi gear. But there is something about live music, some little tinge it has, that's instantly recognizable. Some people in my experience are indifferent to it, but i'd wager this community is keenly sensitive. I once walked a city block to investigate what turned out to be a guy on the sidewalk playing Beethoven's 9th on a Disston D23 handsaw. (He had good taste in saws.)
The ear does sort of a fourier transform - the nerve endings inside are each sensitive to a specific frequency. So I guess our brain receives the fundamental note and all the overtones as a simultaneous and rich pattern of impulses. I don't know why it likes a chord and dislikes discord, but sure it seems to be aware when the mathematical relation between the pure tones it hears is not an orderly one...
As an aside, it's overtones that are behind the "tube vs solid state" amplifier debate in the rock world. Modern solid state amplifiers, when overdriven into distortion as guitar guys are wont to do, add odd numbered harmonics to the signal. That's because they sharply clip both the top and bottom of the wave in a sharp and similar fashion, resulting in symmetric distortion, and symmetrical distortion of a sinewave adds odd harmonics - third, fifth, etc.
Tube circuits on the other hand drive into their upper and lower limits in a soggy and dissimilar fashion, clipping the wave tops and bottoms unequally with non-sharp and non-symmetric distortion... Non symmetric distortion of a sinewave makes even numbered harmonics - second, fourth etc. Non-sharp distortion favors the lower ones.
Apparently the ears of rock musicians have no trouble discerning the difference. And there's some psychological preference.
Cogito ergo doleo.