RE: [tuning] Clarification on Wilson's MOS, Scale tree, etc. for Jason

Thanks Kraig! So for the phi-of-an-octave-generator itself, look at
http://www.anaphoria.com/hrgm28.html <http://www.anaphoria.com/hrgm28.html>
(this one also represents the way most flowers grow)
For the Kornerup generator, look at http://www.anaphoria.com/hrgm33.html
<http://www.anaphoria.com/hrgm33.html> .
For the other generator I mentioned, which is 868.33 cents, look at
http://www.anaphoria.com/hrgm17.html <http://www.anaphoria.com/hrgm17.html>
. This is also called the Lucas series, and describes the growth of those
few plants not described by phi itself.

Comparing the three on Jason's basis, it appears the latter wins:

phi 1 2 3 5 8 13 21 34 55 89 . . .
Kornerup 1 2 3 5 7 12 19 31 50 81 . . .
Lucas 1 2 3 4 7 11 18 29 47 76 . . .

since it produces as many proper scales as the others with fewer notes.

Although http://www.anaphoria.com/hrgm12.html
<http://www.anaphoria.com/hrgm12.html> looks even better at first glance,
since it begins 1, 2, 3, 4, 5, 9, 14, ..., it is not better by Jason's
criteria because the 3-tone scale is not proper.

Note that Wilson puts the continued fraction expansion of these noble
fractions (always ending with phi, representing an infinite sequence of 1s)
in the first column of http://www.anaphoria.com/hrgm01.html
<http://www.anaphoria.com/hrgm01.html> . Some of the expansions differ from
the ones I showed yesterday because of the arbitrary operation of
subtracting the generator from 1 (i.e, using the octave inversion) to keep
all generators below a half octave.