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@phiofx - "do these constraints reflect some generic feature of our neural network topology?"

I don't think it's our neural network topology: I think the common features of music between culture traces its way back to the math of vibrations, overtones and resonance. The octave and perfect fifth having the simplest frequency ratios, namely 2 and 3/2, gives them special physical properties. The major third, with frequency 5/4, is also important.

It surprised me at first how similar western music is, in its basics, to Carnatic and Hindustani music. All of them prominently feature 7-tone scales contained in the 12-tone chromatic scale, and the favorite 7-tone scale is always the one that contains a frequency, the frequencies 3/2 and 2/3 times that, and the frequencies 1, 5/4 and 3/2 times all those. This forms 3 "triads" shown below in the key of C in western music notation.

@skarthik