Designer chromas

It occurred to me that rather than checking known systems, I could try
to specifify what result I wanted and find systems which gave it. I
tried this using the idea that it would be nice to have something where
5/4 changed to 11/8 and 3/2 to 13/8. This means that (11/8)/(5/4) =
11/10 and (13/8)/(3/2) = 13/12 are both chromas, so that
(11/10)/(13/12) = 66/65 is a comma. I started by taking 11-limit
wedgies, adding 66/65 to get a 13-limit wedgie, and selecting the ones
which seemed most interesting. I got supermajor seconds on 20 notes,
and two members of the ever-proliferating meantone family on 14 and 17
notes. In practice these can both be taken as 31-et and identified,
which would mean reducing by [66/65,81/80,99/98,105/104,121/120], the
TM basis for h31. This would slightly change what I have here, in that
15/11 is equated to 11/8, 27/14 to 21/11 and 14/9 to 11/7, etc.

Meantone[14]
rms error 10.260

[66/65, 81/80, 99/98, 105/104]
[1, 4, 10, 18, 15, 4, 13, 25, 20, 12, 28, 20, 16, 5, -15]
[1, 21/20, 14/13, 9/8, 6/5, 5/4, 4/3, 7/5, 10/7, 3/2, 8/5, 5/3, 9/5, 13/7]
[10/7, 14/13, 8/5, 6/5, 9/5, 4/3, 1, 3/2, 9/8, 5/3, 5/4, 13/7, 7/5, 21/20]

Circles of tetrads
[1, 5/4, 3/2, 7/4] [1, 13/10, 3/2, 13/7]
[1, 5/4, 3/2, 7/4] [1, 13/10, 3/2, 13/7]
[1, 5/4, 3/2, 7/4] [1, 13/10, 3/2, 13/7]
[1, 5/4, 3/2, 7/4] [1, 6/5, 3/2, 13/7]
[1, 5/4, 3/2, 8/5] [1, 6/5, 3/2, 13/7]
[1, 5/4, 3/2, 8/5] [1, 6/5, 3/2, 13/7]
[1, 5/4, 3/2, 8/5] [1, 6/5, 3/2, 13/7]
[1, 5/4, 3/2, 8/5] [1, 6/5, 3/2, 13/7]
[1, 5/4, 3/2, 8/5] [1, 6/5, 3/2, 13/7]
[1, 5/4, 3/2, 8/5] [1, 6/5, 3/2, 12/7]
[1, 8/7, 3/2, 8/5] [1, 6/5, 3/2, 12/7]
[1, 8/7, 3/2, 8/5] [1, 6/5, 3/2, 12/7]
[1, 8/7, 3/2, 8/5] [1, 6/5, 3/2, 12/7]
[1, 8/7, 15/11, 8/5] [1, 6/5, 15/11, 12/7]

Circles of alternative tetrads
[1, 7/5, 3/2, 35/18] [1, 7/6, 3/2, 5/3] [1, 7/6, 3/2, 7/4]
[1, 7/5, 3/2, 35/18] [1, 7/6, 3/2, 5/3] [1, 7/6, 3/2, 7/4]
[1, 7/5, 3/2, 9/5] [1, 7/6, 3/2, 5/3] [1, 7/6, 3/2, 7/4]
[1, 7/5, 3/2, 9/5] [1, 7/6, 3/2, 5/3] [1, 7/6, 3/2, 7/4]
[1, 7/5, 3/2, 9/5] [1, 7/6, 3/2, 5/3] [1, 7/6, 3/2, 8/5]
[1, 7/5, 3/2, 9/5] [1, 14/13, 3/2, 5/3] [1, 14/13, 3/2, 8/5]
[1, 7/5, 3/2, 9/5] [1, 14/13, 3/2, 5/3] [1, 14/13, 3/2, 8/5]
[1, 7/5, 3/2, 9/5] [1, 14/13, 3/2, 5/3] [1, 14/13, 3/2, 8/5]
[1, 9/7, 3/2, 9/5] [1, 14/13, 3/2, 5/3] [1, 14/13, 3/2, 8/5]
[1, 9/7, 3/2, 9/5] [1, 14/13, 3/2, 5/3] [1, 14/13, 3/2, 8/5]
[1, 9/7, 3/2, 9/5] [1, 14/13, 3/2, 5/3] [1, 14/13, 3/2, 8/5]
[1, 9/7, 3/2, 9/5] [1, 14/13, 3/2, 20/13] [1, 14/13, 3/2, 8/5]
[1, 9/7, 3/2, 9/5] [1, 14/13, 3/2, 20/13] [1, 14/13, 3/2, 8/5]
[1, 9/7, 15/11, 9/5] [1, 14/13, 15/11, 20/13] [1, 14/13, 15/11, 8/5]

Meanplop[17]
rms error 10.082 cents

[66/65, 81/80, 126/125, 385/384]
[1, 4, 10, -13, -16, 4, 13, -24, -29, 12, -44, -52, -71, -82, -7]
[1, 21/20, 15/14, 9/8, 6/5, 5/4, 9/7, 4/3, 7/5, 10/7, 3/2, 14/9, 8/5,
5/3, 9/5, 15/8, 27/14]
[9/7, 27/14, 10/7, 15/14, 8/5, 6/5, 9/5, 4/3, 1, 3/2, 9/8, 5/3, 5/4,
15/8, 7/5, 21/20, 14/9]

Circles of tetrads
[1, 5/4, 3/2, 7/4] [1, 12/11, 3/2, 14/9]
[1, 5/4, 3/2, 7/4] [1, 12/11, 3/2, 14/9]
[1, 5/4, 3/2, 7/4] [1, 12/11, 3/2, 14/9]
[1, 5/4, 3/2, 7/4] [1, 6/5, 3/2, 14/9]
[1, 5/4, 3/2, 7/4] [1, 6/5, 3/2, 14/9]
[1, 5/4, 3/2, 7/4] [1, 6/5, 3/2, 14/9]
[1, 5/4, 3/2, 7/4] [1, 6/5, 3/2, 14/9]
[1, 5/4, 3/2, 27/14] [1, 6/5, 3/2, 14/9]
[1, 5/4, 3/2, 27/14] [1, 6/5, 3/2, 14/9]
[1, 5/4, 3/2, 27/14] [1, 6/5, 3/2, 12/7]
[1, 5/4, 3/2, 27/14] [1, 6/5, 3/2, 12/7]
[1, 5/4, 3/2, 27/14] [1, 6/5, 3/2, 12/7]
[1, 5/4, 3/2, 27/14] [1, 6/5, 3/2, 12/7]
[1, 11/8, 3/2, 27/14] [1, 6/5, 3/2, 12/7]
[1, 11/8, 3/2, 27/14] [1, 6/5, 3/2, 12/7]
[1, 11/8, 3/2, 27/14] [1, 6/5, 3/2, 12/7]
[1, 11/8, 13/8, 27/14] [1, 6/5, 13/8, 12/7]

Circles of alternative tetrads
[1, 7/6, 3/2, 18/11] [1, 7/6, 3/2, 5/3] [1, 7/6, 3/2, 7/4]
[1, 7/6, 3/2, 18/11] [1, 7/6, 3/2, 5/3] [1, 7/6, 3/2, 7/4]
[1, 7/6, 3/2, 9/5] [1, 7/6, 3/2, 5/3] [1, 7/6, 3/2, 7/4]
[1, 7/6, 3/2, 9/5] [1, 7/6, 3/2, 5/3] [1, 7/6, 3/2, 7/4]
[1, 7/6, 3/2, 9/5] [1, 7/6, 3/2, 5/3] [1, 7/6, 3/2, 7/4]
[1, 7/6, 3/2, 9/5] [1, 7/6, 3/2, 5/3] [1, 7/6, 3/2, 7/4]
[1, 7/6, 3/2, 9/5] [1, 7/6, 3/2, 5/3] [1, 7/6, 3/2, 7/4]
[1, 7/6, 3/2, 9/5] [1, 7/6, 3/2, 5/3] [1, 7/6, 3/2, 27/14]
[1, 9/7, 3/2, 9/5] [1, 9/7, 3/2, 5/3] [1, 9/7, 3/2, 27/14]
[1, 9/7, 3/2, 9/5] [1, 9/7, 3/2, 5/3] [1, 9/7, 3/2, 27/14]
[1, 9/7, 3/2, 9/5] [1, 9/7, 3/2, 5/3] [1, 9/7, 3/2, 27/14]
[1, 9/7, 3/2, 9/5] [1, 9/7, 3/2, 5/3] [1, 9/7, 3/2, 27/14]
[1, 9/7, 3/2, 9/5] [1, 9/7, 3/2, 5/3] [1, 9/7, 3/2, 27/14]
[1, 9/7, 3/2, 9/5] [1, 9/7, 3/2, 5/3] [1, 9/7, 3/2, 27/14]
[1, 9/7, 3/2, 9/5] [1, 9/7, 3/2, 11/6] [1, 9/7, 3/2, 27/14]
[1, 9/7, 3/2, 9/5] [1, 9/7, 3/2, 11/6] [1, 9/7, 3/2, 27/14]
[1, 9/7, 13/8, 9/5] [1, 9/7, 13/8, 11/6] [1, 9/7, 13/8, 27/14]

Supermajor seconds[20]
rms error 9.326 cents
commas [66/65, 81/80, 99/98, 385/384]

[3, 12, -1, -8, -17, 12, -10, -23, -38, -36, -60, -84, -19, -44, -29]

[1, 33/32, 9/8, 8/7, 7/6, 6/5, 9/7, 21/16, 4/3, 11/8, 16/11, 3/2,
32/21, 11/7, 5/3, 12/7, 7/4, 9/5, 21/11, 35/18]
[6/5, 11/8, 11/7, 9/5, 33/32, 7/6, 4/3, 32/21, 7/4, 1, 8/7, 21/16,
3/2, 12/7, 35/18, 9/8, 9/7, 16/11, 5/3, 21/11]

generator = 8/7

[1, 5/4, 3/2, 21/13] [1, 12/11, 3/2, 12/7]
[1, 5/4, 3/2, 7/4] [1, 12/11, 3/2, 12/7]
[1, 5/4, 3/2, 7/4] [1, 12/11, 3/2, 12/7]
[1, 5/4, 3/2, 7/4] [1, 12/11, 3/2, 12/7]
[1, 5/4, 3/2, 7/4] [1, 12/11, 3/2, 12/7]
[1, 5/4, 3/2, 7/4] [1, 12/11, 3/2, 12/7]
[1, 5/4, 3/2, 7/4] [1, 12/11, 3/2, 12/7]
[1, 5/4, 3/2, 7/4] [1, 12/11, 3/2, 12/7]
[1, 11/8, 3/2, 7/4] [1, 12/11, 3/2, 12/7]
[1, 11/8, 3/2, 7/4] [1, 6/5, 3/2, 12/7]
[1, 11/8, 3/2, 7/4] [1, 6/5, 3/2, 12/7]
[1, 11/8, 3/2, 7/4] [1, 6/5, 3/2, 12/7]
[1, 11/8, 3/2, 7/4] [1, 6/5, 3/2, 12/7]
[1, 11/8, 3/2, 7/4] [1, 6/5, 3/2, 12/7]
[1, 11/8, 3/2, 7/4] [1, 6/5, 3/2, 12/7]
[1, 11/8, 3/2, 7/4] [1, 6/5, 3/2, 12/7]
[1, 11/8, 3/2, 7/4] [1, 6/5, 3/2, 13/7]
[1, 11/8, 13/8, 7/4] [1, 6/5, 13/8, 13/7]
[1, 11/8, 13/8, 7/4] [1, 6/5, 13/8, 13/7]
[1, 11/8, 13/8, 7/4] [1, 6/5, 13/8, 13/7]

[1, 9/7, 3/2, 18/11] [1, 14/13, 3/2, 5/3] [1, 14/13, 3/2, 21/13]
[1, 9/7, 3/2, 18/11] [1, 14/13, 3/2, 5/3] [1, 14/13, 3/2, 7/4]
[1, 9/7, 3/2, 18/11] [1, 14/13, 3/2, 5/3] [1, 14/13, 3/2, 7/4]
[1, 9/7, 3/2, 18/11] [1, 14/13, 3/2, 5/3] [1, 14/13, 3/2, 7/4]
[1, 9/7, 3/2, 18/11] [1, 7/6, 3/2, 5/3] [1, 7/6, 3/2, 7/4]
[1, 9/7, 3/2, 18/11] [1, 7/6, 3/2, 5/3] [1, 7/6, 3/2, 7/4]
[1, 9/7, 3/2, 9/5] [1, 7/6, 3/2, 5/3] [1, 7/6, 3/2, 7/4]
[1, 9/7, 3/2, 9/5] [1, 7/6, 3/2, 5/3] [1, 7/6, 3/2, 7/4]
[1, 9/7, 3/2, 9/5] [1, 7/6, 3/2, 5/3] [1, 7/6, 3/2, 7/4]
[1, 9/7, 3/2, 9/5] [1, 7/6, 3/2, 5/3] [1, 7/6, 3/2, 7/4]
[1, 9/7, 3/2, 9/5] [1, 7/6, 3/2, 5/3] [1, 7/6, 3/2, 7/4]
[1, 9/7, 3/2, 9/5] [1, 7/6, 3/2, 11/6] [1, 7/6, 3/2, 7/4]
[1, 9/7, 3/2, 9/5] [1, 7/6, 3/2, 11/6] [1, 7/6, 3/2, 7/4]
[1, 7/5, 3/2, 9/5] [1, 7/6, 3/2, 11/6] [1, 7/6, 3/2, 7/4]
[1, 7/5, 3/2, 9/5] [1, 7/6, 3/2, 11/6] [1, 7/6, 3/2, 7/4]
[1, 7/5, 3/2, 9/5] [1, 7/6, 3/2, 11/6] [1, 7/6, 3/2, 7/4]
[1, 7/5, 3/2, 9/5] [1, 7/6, 3/2, 11/6] [1, 7/6, 3/2, 7/4]
[1, 7/5, 13/8, 9/5] [1, 7/6, 13/8, 11/6] [1, 7/6, 13/8, 7/4]
[1, 7/5, 13/8, 9/5] [1, 7/6, 13/8, 11/6] [1, 7/6, 13/8, 7/4]
[1, 7/5, 13/8, 9/5] [1, 7/6, 13/8, 11/6] [1, 7/6, 13/8, 7/4]