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I would like to say something about the method I was thinking of when trying this. If you look at the harmonic content of a piano, you see a lot of additional harmonics to the main frequency. Some of them might be an octave above it, but some may be a fifth, forth or others for example, thus I tried to mix in one that is 07 semitones above and ended up modulating it in through fm. And then through pure luck, I found a sweetspot, enhanced a resonant frequency a bit and that was it. Unfortunately the high end is really not great in this and loses the timbre quickly.

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