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As you can see from the spectrograph, there are two melodic lines in this excerpt. These two voices are played by different instruments. Is there a tool (preferably free) that will allow me to extract one instrument out of this mix?

A basic approach would be to extract just the peak frequencies as circled, but I don't even know where to start on that. To also get the timbre of the instrument would require extraction of the overtones as well.

This piece was probably mostly computer generated and contains very pure tones, so I imagine this task would be at least somewhat feasible.

Spectrograph of music excerpt

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Rather than extracting one instrument, you would try to remove the other one. There are dedicated tools for exactly this task (like this one), but you can also do it manually, with notch- and/or comb filters. You can use a simple EQ plugin for this, for instance you can split up the track into overlapping regions so that each note is contained in one such region. You then use a narrow band boost to find the note you'd like removed and switch the EQ node to notch or a strong narrow band cut once you've found the frequency. Repeat (if necessary, also with harmonics: you can avoid this by using a comb filter, but this will more heavily affect the overall spectrum) until it sounds as desired.

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