A bit of progress on the book
Added 2020-06-12 17:49:03 +0000 UTCHowdy patrons! Just a mini-update. I've made some progress on the section about degenerate well-formed scales; this was with a little help from Paul Sherrill (PhD), a music theorist and professor at University of Utah School of Music. The crux is: the set of well-formed scales - those that satisfy the symmetry and closure conditions - includes some scales that do not have Myhill's Property. Those are the EDO (equal division of the octave) scales, and they're called "degenerate" because much of the neat stuff that arises from well-formedness doesn't apply to them. The degenerates are only the true EDO; their truncations are not degenerate.
Anyhoo, it will all be explained much better (and with diagrams) in the book.
Paul pointed out the relation between well-formedness, and the seviconvergents of its generator. Yikes! That's getting into some heavy math, which will *not* be in the book.
I hope you are all well
Yours,
Ian
Comments
You're the man bro, keep doing this stuff dude. I'm barely scratching the surface, but this is what we need in the world of music. One love my friend, one love.
David Varosyan
2020-07-08 10:07:20 +0000 UTC
