# First harmonic above fundamental in piano recording?

I am currently working on a project, the final aim of which is to see if one can classify which instrument a sound recording is coming from, by looking at the fourier transform of a note and comparing the intensities of the fundamental frequency to the first several harmonics. While I am aware that in general how humans perceive sound is much more complicated than just the spectrum of frequencies, in the data collection there were some somewhat strange results. Specifically, in two recorded samples of a piano note, which sound indistinguishable when listening by ear, produced these two very different fourier transforms.

Looking closer at the actual waveforms, there is some clue as to why in the second case we see a dominant second harmonic:

It looks like in the second case, the first harmonic is almost "separated out" as an independent wave, whereas in the first case it is almost completely "absorbed" into the fundamental. Both cases were recorded on the same instrument with the same microphone, and as mentioned before, sound identical. I was wondering if anyone had any ideas about what causes this kind of behavior, or potentially how to mitigate it in recording/processing.

• You can experiment with the effect of phase changes yourself. Taking the amplitudes from the first graph, plot the functions $1.6\sin t + 0.5\sin 2t$ and $1.6\sin t + 0.5\cos 2t$ for example. (Then try changing the $+$ signs to $-$ to get two more plots...) Commented Apr 28, 2021 at 17:40
• @Theo If you analyze a human singer, depending on the vowel sound being sung, you will see the $2f_1$ analyzer peak stronger than the fundamental, but the "note" you hear matches a sine generator tone of the fundamental ($f_1$). Psychoacoustics (brain+ear) is a fascinating topic. Commented Apr 28, 2021 at 20:35