Now, I think I finally did it, and I am enjoying it a lot ¡¡¡ I insert an image, since I am sure the boxes would be a mess as code: But when I compare the result of shifting E2 by 2x (1 octave) and E3, they are not the same pitch. I could indeed shift the frequencies of a 5 sec guitar note (E2). Of course this is just about getting the characteristic - I could record a guitar and analyze the result. I tried to use Periodogram, but it was not clear that the partition option could be used to get the spectral component values at a set of time-delayed windows, for fitting to exponential decays. I saw no way to just get a simple list of sample amplitudes.
But I found that many of the tools would not work. I tried to do this for the midi sound for a guitar as produced by Mathematica by first analyzing the sound for the harmonics. Then a sampled sound list could be constructed from the fundamental. However, for struck or plucked instruments, such as guitar or piano, we would want in addition to know a decay rate for the fundamental and each harmonic. That would not include non-continuous components, for example the sound of the trumpet note being initiated. For a continuous note, such as made by a violin or trumpet, it may be sufficient to know the harmonics and their amplitudes relative to the fundamental.
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