Where is the choice of orthogonal basis being made in the human auditory system?

Question

I have a vague question which I have trouble googling an answer to.

Let $X$ be a circle. I want to think of $L^2(X)$ as embedded into the space of periodic functions on the real line, with period 1, and as such each element of $L^2(X)$ gives rise to a "sound" (to define what sound precisely we have to fix units on x and y axes for time and pressure respectively).

Now, characters form a basis of $L^2(X)$, and the corresponding sounds are perceived as pure by humans. Obviously there are other bases of $L^2(X)$, for example all elements of a basis might correspond to some square waves.

But the corresponding sounds are not perceived as as pure. More extremely, in triangle waves I can distinctly hear several different tones, although it might be just my poor laptop speakers.

Thus human auditory system seems to have a preference for one specific orthogonal basis. I've had a look at the wikipedia's description of the human auditory system but it's quite complicated.

Question: Is it possible to pinpoint where does this preference for characters emerge in the human auditory system?

Answer 1

I don't know the mechanism, but it takes place in the cochlea. Check out this image from this article.

Answer 2

It is my understanding that different frequency components resonate in different parts of the cochlea, and the activity is picked up by the hairs in the different locations and passed along to the brain. Basically, it's performing a spectral decomposition. But my understanding could be wrong.

Update (from Wikipedia): The basilar membrane of the inner ear spreads out different frequencies: high frequencies produce a large vibration at the end near the middle ear (the "base"), and low frequencies a large vibration at the distant end (the "apex"). Thus the ear performs a sort of frequency analysis, roughly similar to a Fourier transform. However, the nerve pulses delivered to the brain contain both rate-versus-place and fine temporal structure information, so the similarity is not strong.