[Oren-T]

Vocal cords have even more pronounced overtones than strings. To a first approximation, they produce a series of pulses. And we are exposed to these harmonic-rich sounds from the womb.

It would be an interesting (and perhaps cruel) experiment to expose babies to synthesized sounds that have a harmonic structure with different mathematics. For example, sounds with lots of sqrt(2) frequency ratios.

[clarry]

The ear itself produces some harmonic distortion, at moderate levels. I don't know if that's important enough to play a role in our pitch perception though.