Modern music uses the ‘equal tempered scale’. This means that all octaves are exact, while all other intervals are a bit ‘out’ from the harmonic series. The scale is listed here:

https://pages.mtu.edu/~suits/notefreqs.html

For example, E2 is 82.41 Hz and its 3rd harmonic is 247.23 while the nearest note on the scale is a B which is 246.94. Obviously, that is pretty close. But for higher harmonics the situation gets worse, e.g. the 5th harmonic is 412.05 while the G# on the scale is 415.3

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