[elihu]

I like the demos. The transition from ratios to equal temperament was kind of jarring. It might help to not jump straight from the pentatonic scale to a chromatic scale and then go back to the major scale later, but to introduce the pentatonic scale, and then describe major and minor chords as 4:5:6 and 10:12:15 ratios, and then show how the major scale can be constructed simply by trying to get as many usable major and minor triads out of the least number of notes (while emphasizing that the major scale isn't the only solution, and that other "modes" exist).

Once you've established that the major scale is useful and in no way mysterious, then you can point out that if you divide the octave up in 12 logarithmically equal parts, you end up with equal tempered notes that almost line up with the ratio-based major scale. (I once threw together a diagram to illustate this that you can find here if you scroll down a bit: http://jsnow.bootlegether.net/cbg/justintonation.html) From then on, you can treat equal temperament as an approximation that implies the ratios you described at the beginning.

(Side note: One idea I try to impress on anyone who demonstrates the slightest inkling to write about music theory is that I really wish there existed something like Christopher Alexander's "A Pattern Language", but for music. Music is full of lots of little "tricks" that you can find scattered about in books, but I haven't ever seen anyone try to systematically collect as many of those as they can in one place, with a clear dependency graph.)

[dainichi]

> The transition from ratios to equal temperament was kind of jarring

I agree. I'd like the course to comment on the fact that the ratios used in the pentatone scale and the 0th, 2nd, 4th, 7th and 9th powers of the 12th root of 2 don't match exactly.