The major scale is just the most straightforward way to be able to construct the most usable 4:5:6 ratios and 10:12:15 ratios (i.e. major and minor chords) from

The major scale is just the most straightforward way to be able to construct the most usable 4:5:6 ratios and 10:12:15 ratios (i.e. major and minor chords) from the fewest possible notes. In equal temperament, those ratios are approximated rather than exact, but those are the mathematical relationships implied by the chords. The desirability of "simple ratios" is based on the idea that if we play two pure sine waves at the same time, they sound good if they're exactly the same frequency and if they're some distance apart, but they sound bad if the two notes are close but don't line up. (This creates a beat frequency, which make the music sound unstable and noisy.) Notes played on real instruments have harmonics, and so if you play two notes at once all those harmonics either need to be a long way from each other or they need to line up. Notes with frequencies that correspond to simple ratios are the ones where the harmonics also line up in the cleanest way. Simple ratios like 2:1 or 3:2 are very stable and consonant. Larger ratios like 5:4 make modern music a bit more interesting. Still larger ratios like 7:4 and 11:8 can start to sound pretty alien and sort of dissonant and more complex. Basically, the most consonant music, which is easy to play (imprecisely) in 12-tone equal temperament, is pretty well explored territory. There is only one major chord, and we won't find anything that sounds any more "major-chordish" than it. But there's a huge unexplored territory when it comes to larger ratios that can't be played accurately enough to be intelligible on 12-tone equal tempered instruments. If you scroll down a bit on this page, I made a visualization of how 12-tone equal temperament lines up with a straightforward just-intonation scale based on the ratios implied by the 12-TET chromatic scale. It's really amazing both how well 12-tone equal temperament lines up, and at the same time how much better things could sound if you play the exact just intervals rather than this system that by some weird mathematical coincidence happens to be good enough for most simple musical purposes. http://jsnow.bootlegether.net/cbg/justintonation.html http://jsnow.bootlegether.net/cbg/justintonation.html