the area under the curve

Margo Schulter wrote,

> the area under that curve, so to speak -- or the area between
Pythagorean and 17-tet or 22-tet or whatever, the Golden Mediant
provides one very useful cardinal point of orientation,

Something just occurred to me that I probably should have noticed when
I was doing the "3/5 Phi Trail" posts: If you start from a Pythagorean
weighting, i.e., one where L and s initially equal the Pythagorean
major and minor seconds (this is very close to the square root of five
incidentally), and then expand out and contract back towards the
Golden Meantone L/s=Phi constant it might give a more Pythagorean like
scope to this logarithmic "area under the curve".

Using a 1/2 3/5 4/7 7/12 11/19 18/31 Fibonacci expansion, you'd have
the following "area under the curve":

0 204 408 498 702 906 996 1200
0 214 428 493 707 921 986 1200
0 219 439 490 710 929 981 1200
0 208 417 496 704 912 992 1200
0 206 412 497 703 909 994 1200

Once the expansion hits 29/50 the generator < 2:3, and you've started
to work things back thru to L/s = phi.

If you were to work the same 1/2 3/5 series out with the simplest
whole number relation where L>s and s>0, you'd get a 12-tET weighting,
and a "closed" 12, 17, 22, 29, 41-tET expansion segment.

--dan