it is my understanding that, in western theory, the belief is that those intervals and tunings sound best, that fit to the overtones that are in the sounds of the instruments used. this always seemed a bit nonsensical to me. a sine has no overtones yet is one of the most harmonic soundsources one can use, with the usual intervals. i read that in psychoaccoustic, a sine is perceived as having 1, 2 overtones. yet, sine's also great with complex intervals that don't run along the basic overtones.
also, most importantly, when doing music myself, i noted, that when a melody or harmonic structure sounds great, it also sounds great when you use a different waveform with completely different overtones. for example, a melody based on a (very harmonic) sawtooth-wavshape also sounds great with a waveform of completely complex overtones. if the "overtone harmony" theory would hold true, it must sound horrible if you exchange waveforms with those of completely different overtones.
in my album "crystalline derivates" i took the same track, the same melody, and used completey different wave sources for it - completely harmonic sines and saws, completely strange ones, even some that are not a based on a short looped sequence at all. listen to it for yourself, if you are interested. if you can appreciate the original track, i think all variations sound "correct" in their way, not one of them is detroyed by the use of complete different overtones.
http://lowentropy.bandcamp.com/album/crystalline-derivates
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