RE: [tuning] Wilson's MOS

Jason Yust wrote,

>Accually, my original
>idea may be wrong because, as I have been looking closer at this point I
>find that slightly flat fifths work better as generators than more
>acoustically correct fifths.

All kinds of fifths can work well as generators for various purposes (see
Dave Keenan's work for more on this). What do you mean by "better"?
Certainly for 5-limit diatonicism, you're correct -- but would you not admit
other possibilities?

>Wilson's attractive method of showing how the
>various intervals generate scales pointed out to me that the fact that
>certain intervals generate good scales in Rothenberg's sense after fewer
>repetitions than others depends in a regular way upon the rough amount of
>the octave which that interval takes up, and that the best always seem to
>be those in the vicinity of the fifth.

Aha -- I think I see what you're getting at. I think you're mistaken. Try,
for example, a generator which is 2^phi or 741.64 cents. It produces more
evenly-spaced scales more often than any other generator (in a certain
mathematical sense). This will get into a discussion of noble numbers, etc.
-- see Wilson's excellent Scale Tree diagram.