The waveform produced by sounding a note on most physical instruments will often not exhibit a peak, or will not exhibit the strongest peak, on the note being sounded. Rather, most instruments will instead produce harmonic overtones and our brains fill in the gap of the pitch that’s intended to be sounded.
You can still absolutely deduce the fundamental with great accuracy via an FFT, but the approach is a bit more involved. The relevant research area here is called ‘fundamental frequency estimation’.
For an example of this, you can see this app I built that lets you give keyboard and mouse inputs via playing notes on a bass guitar, which are recognized over the microphone: https://github.com/codyd51/offkeyboard
Hi, author of axle here - thank you for the shout out! It’s been a wonderfully fun and enriching project to work on over the years. I’m now working on XNU at Apple, so won’t be working further on axle for the foreseeable future.