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Quora answer by Mr. Kennan Hye BS (Engineering), MEng. (Acoustics):

Pitch is sometimes defined as the fundamental frequency of a sound wave (i.e. generally, the lowest frequency in a given sound wave). For most practical purposes, this is fine, and pitch and frequency can be thought of as equivalent. On the other hand, for most practical purposes, amplitude can be thought of as volume.

However, technically, pitch (and volume) are human perceptions. Thus, our perception of pitch and volume are not solely based on frequency and amplitude respectively, but are based on a combination of both (and even other factors). Frequency overwhelming dictates perceived pitch, but amplitude also does have some small, small effect on our pitch perception, especially when it is very large. For example, a very loud sound can have a different perceived pitch than you would predict from its frequency alone.

That all being said, usually these effects are negligible, and pitch can be thought of as equivalent to fundamental frequency.

Please explain elementarily; I'm never studied natural sciences.

I still don't accept intuitively how Amplitude can affect pitch. Can the bold sentences be exemplified by anything simple? The example in my mind is opera singers: a competent one's loud singing, shouldn't affect the frequency, because then (s)he'll sound off-tune.

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The section you've highlighted is concerned with psychoacoustics, a branch of psychophysics. So, the problem doesn't involve amplitude causing the frequency of the wave to change. It involves amplitude causing our mind's perception of pitch to change (Typically we perceive lower pitches.)

Note that this change is quite small! In Brian C.J. Moore's 5th Edition of Introduction to the Psychology of Hearing he reviews existing literature to suggest that this change in pitch perception for tones between 1kHz and 2kHz is less than 1% (i.e., 10 - 20 Hz).

Consider this in terms of your Opera Singer: singing a C at 1047 Hz. Even with a decrease to 1037 Hz she'd still be quite far from the B below it at 987.8 Hz, and it'd probably be difficult for her to tell that much has changed.

Overall he concludes "at present there is no generally accepted explanation for the shifts in pitch with level". Both the rejected theories have to do with hair cells in the cochlea. The more promising has to do with auditory fatigue due to being exposed to a loud sound, which might cause a shift in excitation of the cochlea's tiny hairs towards lower-pitched (basal) side of the organ. These basal hairs vibrate with lower incoming frequencies. Thus a proposed mechanism for the perceived shift in pitch.

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    $\begingroup$ A 1% miss in a note can easily be heard above 1kHz, particularly in a chord. That's an interesting figure, because often deliberate detuning is used both by singers and by piano tuners to set up beats with other notes in chords or with the other strings in the same note (notes above 1kHz have three strings each on a piano). Presumably, however, amplitude induced pitch shift would sound quite different, because it wouldn't induce beats (which are physical, rather than psychophysical). $\endgroup$ – WetSavannaAnimal Nov 10 '17 at 4:04

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