I've re-done the sim using as input a wav file of a nylon-stringed acoustic guitar playing E3 (165Hz).
Interestingly, it looks like the thing that would screw up the frequency counter is more likely to be the initial transients as the string is plucked, rather than any harmonic content. So the counter reading during the first ~200ms of the note should be ignored.
Although the harmonics affect the wave shape they seem to have little effect on the interval between zero-crossings of the waveform (which is what the counter would measure).
Interestingly, it looks like the thing that would screw up the frequency counter is more likely to be the initial transients as the string is plucked, rather than any harmonic content. So the counter reading during the first ~200ms of the note should be ignored.
Although the harmonics affect the wave shape they seem to have little effect on the interval between zero-crossings of the waveform (which is what the counter would measure).
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