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I'm learning about pitch perception, and learned about the case of the missing fundamental.

In the main image in that wikipedia page, it seems like the bottom graph, with the fundamental frequency and its second harmonic removed, that the wave is still very periodic at 100 Hz. Since the Organ of Corti has some area which should be excited when there's a sound wave of frequency 100 Hz, why does this sound wave, which seems periodic at 100 Hz, not directly excite that region of the organ?

Can someone explain the workings of the inner ear and detail on why the missing fundamental does not activate the cochlea? Reversely, how can 100 Hz be heard when the cochlea is not even activated at that frequency?

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  • $\begingroup$ Also tried asking on the DSP community. $\endgroup$
    – Kevin Wang
    Apr 16, 2018 at 23:36
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    $\begingroup$ I just saw you cross-posted. That's strongly discouraged at SE. I changed the pitch of your question (pun unintended) to make the questions sufficiently different. It's a good question. $\endgroup$
    – AliceD ♦
    Nov 22, 2018 at 21:01

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The basilar membrane in the inner ear (cochlea) is a place-dependent Fourier transformer (Fig. 1). This means that there is an orderly tonotopic map projected on the basilar membrane (BM). Traveling waves imposed on the BM via the ossicle chain and the oval window start of at the base and travel all the way to the apex. Along the way the resonance frequency of the BM gradually decreases, as the BM gets wider and more flexible (like piano strings).

Now, if a certain frequency is missing, the BM is not moving at that frequency location, and hence the hair cells do not become activated, and the neurons with that specific characteristic are not activated either. How on earth can you still hear that frequency?

It is the harmonic structure that determines our perception of pitch, rather than the lowest harmonic alone. Our brains are sensitive to the frequency difference from one harmonic to the next and base the "real" pitch of the tone on that difference. This is referred to as the "difference tone". When you hear two pure tones, the ear and brain subtract one frequency from the other, and you "hear" a tone with a frequency of this difference (source: National Taiwan University).

Cochlea Fig. 1. Frequency tuning in the cochlea. source: New York University

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