Paul Hahn's trichordal scales in 31-tET

Gene, do you know about these?

!
Four complete tetrads [3-3-4, 3-5-3, 4-3-3].
9
!
116.13 !....3
232.26 !....6
387.10 !...10
503.23 !...13
696.77 !...18
812.90 !...21
967.74 !...25
1083.87 !..28
2/1 !......31
!

!
Concise melodies [4-3-3, 5-3-3, 4-3-3].
9
!
154.84 !....4
270.97 !....7
387.10 !...10
580.64 !...15
696.77 !...18
812.90 !...21
967.74 !...25
1083.87 !..28
2/1 !......31
!

!
Well-distributed harmonies [4-4-2, 5-3-3, 4-3-3].
9
!
154.84 !....4
309.68 !....8
387.10 !...10
580.64 !...15
696.77 !...18
812.90 !...21
967.74 !...25
1083.87 !..28
2/1 !......31
!
! 4:6:7 triads on 1/1, 5/4, 8/5; otonal tetrads on 1/1 and 8/5.

?

-Carl

--- In tuning-math@yahoogroups.com, Carl Lumma <ekin@l...> wrote:
>
> Gene, do you know about these?

It doesn't ring a bell. I did a series of six four-tetrad JI scales
a while back. I'll give those again.

! ch9_1.scl
Four tetrads one <9 14 21 26| permutation epimorphic
9
!
21/20
6/5
5/4
21/16
3/2
12/7
7/4
9/5
2

! ch9_2.scl
Four tetrads two <9 14 21 26| permutation epimorphic
9
!
21/20
35/32
5/4
21/16
35/24
3/2
49/32
7/4
2

! ch9_3.scl
Four tetrads three
9
!
15/14
35/32
5/4
35/24
3/2
25/16
7/4
15/8
2

! ch9_4.scl
Four tetrads four
9
!
49/48
35/32
7/6
5/4
7/5
35/24
3/2
7/4
2

! ch9_5.scl
Four tetrads five
9
!
21/20
7/6
49/40
5/4
21/16
7/5
3/2
7/4
2

! ch9_6.scl
Four tetrads six
9
!
7/6
5/4
4/3
7/5
10/7
3/2
5/3
7/4
2