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If they do a Fourier transform, how can they know the formula to find coefficients?

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In general you shouldn't put any weight on formulas, as they are merely human inventions for describing nature, not laws that nature has to look up and obey. Your ears no more understand Fourier transforms than the Earth understands Kepler's laws for planetary motion. – Chris White Jul 17 '13 at 5:26
related:… . In their broad outlines, I think pitch perception and color perception are pretty similar. You have a hardware-based frequency filter followed by multiple stages of neurological processing. In those stages, as much information may be flowing out (backwards) as in (forwards), i.e., the higher-level parts of the nervous system influence the operation of the lower-level parts. – Ben Crowell Jul 17 '13 at 17:30

Cochleae, the little spiralling tubes in our inner ears, separate the frequencies of incoming mechanical wave.

Human cochlea is equipped with thousands of hair cells attached to organ of Corti that runs along the length of the tube. Hair cells vibrate with the surrounding liquid. Each of the hair cells have different resonant frequencies. That way the ear get the 'coefficients' (more precisely, spectral power distribution)

(Imagine having thousands of radios tuned to different frequencies to get a really fast Fourier Transform of an incoming radio wave!)

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Obviously ears don't "know" a formula. But, the process of trial and error and keeping all the little incremental improvements we call evolution can result in some pretty sophisticated (although often kludgy) solutions.

In the case of our ears, there is a mechanical structure that sortof separates frequencies spacially, or at least produces different frequency filtering of the input signal as a function of distance. Different nerves sense vibrations at different points along this filter structure, and the rest is signal processing to produce the perception of a frequency spread.

More details belong elsewhere, possibly on the biology site.

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Link that might answer your question in part:

Definition of the phon scale and what loudness means. This lecture note is very comprehensive, the only problem is in german:

General biophysical explanation on the ear and the various topics concerning hearing like chromatics etc.

This one is in english:

The same topics are covered but in english.

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In general we discourage link-only answers (see the faq and this meta post). Could you summarize some of what is mentioned at those links? – Chris White Jul 17 '13 at 5:29

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