Keenan 10-tone MOS

A while back Dave Keenan posted the results of his search for 7-limit
tetrads in MOS's of 10 or less tones. His results showed Erlich's
decatonics and a chain of 6/5's to be most promising. On this list, in the
last few months, these have been examined. But little mention has been
made of his next-most promising candidate, a 10-tone MOS of generator 125
cents, and interval of equivalence 2/1. Here is it's interval matrix...

2nds 3rds 4ths 5ths 6ths 7ths 8ths 9ths 10ths : 7o 7u 5o 5u
1 125 250 375 450 575 700 825 950 1075 : 479 369 47
2 125 250 325 450 575 700 825 950 1075 : 369 47
3 125 200 325 450 575 700 825 950 1075 : 47
4 75 200 325 450 575 700 825 950 1075 : 47
5 125 250 375 500 625 750 875 1000 1125 :
6 125 250 375 500 625 750 875 1000 1075 :
7 125 250 375 500 625 750 875 950 1075 : ~49 ~39
8 125 250 375 500 625 750 825 950 1075 : ~49 ~39
9 125 250 375 500 625 700 825 950 1075 : 479 ~39 47
10 125 250 375 500 575 700 825 950 1075 : 479 369 47

The scale is strictly proper. To the right, I've listed the 7- and 5-limit
chords that appear in each mode, by the scale degrees they occupy. We see
that, although this scale contains six 7-limit tetrads (the same number as
Erlich's Pentachordal decatonics), they are not distributed very well (as
are Erlich's). Particularly, the O- and Utonal versions are never
represented by the same pattern of scale degrees. I think the scale fails
as a 7-limit generalized diatonic for this reason. However, if you look at
the 5-limit, you'll notice that the traids are very well spread out, and
are tuned with greater accuracy than in 12-tET. Unfortunately, 10-tones
are a lot to cover with triads, especially when you've only got 6 of them.
But it's not all bad, and composing in this scale would certainly be
interesting.

-Carl