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https://www.steinberg.net/fr/spectralayers/

This might help you?

That synth is extremely distorted post summing of the voices. (That whole album has so much distortion, it's lovely).

So not only is timbre not independent of frequency, summing multiple notes is also non-linear. The "beating" this causes is most obvious on the second chord to play. This beating is not consistent as the notes change, it's based on the difference in frequencies between the two notes being played.

Maybe 2nd-order spectral relationships would get you a bit closer, e.g. bispectrum / bicepstrum