Fascinating paper! Somehow, this escaped my attention when I was researching this topic. I was interested in the question of how the heck we evolved such a craz

Fascinating paper! Somehow, this escaped my attention when I was researching this topic. I was interested in the question of how the heck we evolved such a crazy system of 7 white notes + 5 black notes (i.e. the diatonic (and pentatonic) scale overlaid on the 12-tone equal temperament), as well as the origin of the Western concepts of major and minor scales and chords. Long story short, it seems the answer is that our scales and chords derive from a combination of what makes for interesting voice leading and what notes sound good together in a given timbre. The choice of approximating ideal chords and scales using 12 equally spaced notes derives from a instrumental playability concerns and the desire to be able to freely transpose and to modulate between distant keys. It's a deep topic, but if anyone's interested, I recommend two books: - Timbre, Tuning, Spectrum, Scale by William Sethares - A Geometry of Music by Dmitri Tymoczko