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If possible, I would like to write a little script that can identify different musical instruments from just a recording. Apart from variations of amplitude and frequency over time (which can be shown by time-dependant and spectrogram, respectively), what other variables are there?

Furthermore, how would one do the classification? Fingerprinting is an option, but that would only work if a single piece at a time is played.

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I think this is a bigger task than "a little script", but could be done with some determination. I've had the same idea over the years, and this is how I'd go about it:

You'd be working with individual tracks of reference instruments, and would build an 'overtone array' of the relative power of the overtones as compared to the fundamental frequency. You would also need to write a script to detect the fundamental frequency, of course. Other features would also be of interest like attack and sustain characteristics.

Once you had that information for all of your reference instruments, you would take the same measurements of a new recording and compare it to your reference overtone arrays and other characteristics, and output whichever one it is most similar to.

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What you want to do is timbre recognition.

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