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> Maybe it’s a stretch to apply this to audio. If you play a flat on piano, and IMD3 falls on a sharp, then that sounds bad.

Do the math, your distorted spectrum will contain sum and difference frequencies. (For me, what makes the math easy is breaking a real sine wave into a sum of its complex components, which are easier to work with.)

This is, as you say, what makes 3rd order bad in RF, because if I have two frequencies F1 and F2, F1+F2 or F1-F2 can be filtered out no problem, but 2F1-F2 or 2F2-F1 is a problem. But this intuition about distortion does not extend to music.

In music, it is not so much the individual frequencies that are relevant, but the harmonic spectra, and the spectrum is within spitting distance of baseband, so filtering won’t do you any good (at least not in eliminating distortion).

And since music contains harmonic spectra to begin with, for a given F in the signal, you probably already have 2F, 3F, 4F. So when you calculate the spectrum for 2nd order or 3rd order distortion, you get the SAME frequencies in the output either way, just in different quantities.

As a result, as electric guitarists know, you have to be very careful about what harmonic content you feed into distortion. If you feed in a note, you get the same note out with different texture. If you feed an octave, it sounds good. Perfect fifth, great, the distortion adds overtones of the octave below the root. A major third is iffy and something you’d use with less distortion. As you get farther away from simple intervals, like octave 2:1, fifth 3:2, fourth 4:3, or major third 5:4, it gets worse and worse. (Eddie Van Halen reportedly retuned his guitar, tuning the second string down 14 cents, to get the major third closer to a harmonic third.)

And this is why distortion for a single instrument sounds good, but distortion for an entire song with multiple instruments (some of which are usually inharmonic) sounds bad. Even with 2nd order distortion, do you really want sum and difference frequencies between overtones of the guitar and overtones of the snare drum? No.




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