I think the hypothesis described here is pretty much refuted by the work of William Sethares (http://sethares.engr.wisc.edu/ http://sethares.engr.wisc.edu/), wh

I think the hypothesis described here is pretty much refuted by the work of William Sethares (http://sethares.engr.wisc.edu/ http://sethares.engr.wisc.edu/), who finds that severely non-harmonic intervals can sound just fine when played with (synthetic) instruments whose overtones are suitably non-harmonic, and that using such instruments can make nice harmonic intervals sound just as nasty as severely non-harmonic ones do on conventional instruments with harmonic spectra. There's a slightly convincing example at http://sethares.engr.wisc.edu/mp3s/challoct.mp3 http://sethares.engr.wisc.edu/mp3s/challoct.mp3 -- what you hear there is two successive sequences of (note A, note B, chord A+B) where B is an octave above A in the first case and about 1.07 octaves -- an octave and 0.8 of a semitone -- in the second. The instrument has a weird spectrum that makes the second A+B sound better than the first -- but it's weird enough that, to me at least, even the individual notes sound really odd. A better example: http://eceserv0.ece.wisc.edu/%7Esethares/mp3s/tenfingersX.mp3 http://eceserv0.ece.wisc.edu/%7Esethares/mp3s/tenfingersX.mp... is a piece in "10-tone equal temperament", in which notoriously almost all chords sound dreadful with normal instruments. http://sethares.engr.wisc.edu/mp3s/Ten_Fingers.mp3 http://sethares.engr.wisc.edu/mp3s/Ten_Fingers.mp3 is the exact same notes, but played on an instrument with a spectrum designed not to sound horrible in 10-tet.