[chrisshroba]

Could you elaborate a bit more? It seems to me like the note being played would always correspond to the fundamental frequency observed. When is this not the case? Maybe as the note rings out, the fundamental frequency and first few overtones lose power, and all that's still audible are the higher overtones?

[isoprophlex]

There is a nice little rabbit hole to go in to: psychoacoustics of church bells.

https://www.hibberts.co.uk/what-note-do-we-hear-when-a-bell-...

Almost all musical instruments (such as pianos, organs, orchestral instruments and the human voice) have sounds that contain a range of frequencies f, 2f, 3f, 4f and so on where f is the lowest frequency in the sound. The pitch or note we asssign to the sound corresponds to the frequency f. Frequencies with this regular arrangement are called harmonic. The frequencies in the sound of bells, on the other hand, are not harmonic, and the pitch we assign to the sound of a bell is roughly an octave below the fifth partial up ordered by frequency. This partial is called the nominal, because it provides the note name of the bell. There often isn’t a frequency in the bell’s sound corresponding to the pitch we hear.

[gexaha]

That's actually not true, perceived pitch can be different from fundamental frequency, because of psychoacoustics. E. g. you can have "missing fundamental" - https://en.wikipedia.org/wiki/Missing_fundamental - or other effects like "sum and difference tones", which are quite popular in spectralism / spectral music

[xavriley]

Simple techniques like autocorrelation can still recover a missing fundamental. To answer the GP post, using neural networks for this task is overkill for simple, clean signals but it can be desirable if you need a) extremely high accuracy or b) robust results when there are signal degradations like background noise

[miningape]

We may perceive the same pitch (perhaps with a different timbre) even if the fundamental frequency is missing from a tone [1].

It seems to me like wikipedia agrees that even if the fundamental frequency is missing we could still use some kind of FFT to find the fundamental frequency being played (and therefore the perceived pitch). I might be missing something this is very far from my area of expertise :P

1 - https://en.wikipedia.org/wiki/Missing_fundamental