24 13-limit temperaments supported by 46

We've been on a 13-limit kick, and George thinks 46 may be his fav, so
I'm giving this. Note that valentine and semisixths have the same
Graham complexity and TOP error, so they are tied at the 7.5th place
by the criterion I used to sort this list. In terms of TOP tuning,
they share a tuning for 5, 7, and 13. Leapday came out #1; it's been
kicking around a while without a name so it's good Herman named it,
even if I still havn't figured out what 2/29 has to do with it. It's a
system with a sharp (about 2.4 cents) fifth as generator and 5 with
the highest complexity; it therefore seems perfect for Margo, who may
have mentioned it.

leapday
[1, 21, 15, 11, 8, 31, 21, 14, 9, -24, -47, -59, -21, -33, -13] [[1,
2, 11, 9, 8, 7], [0, -1, -21, -15, -11, -8]]
21 1.589486 254.071241

unidec
[12, 22, -4, -6, 4, 7, -40, -51, -38, -71, -90, -72, -3, 26, 36] [[2,
5, 8, 5, 6, 8], [0, -6, -11, 2, 3, -2]]
30 .899546 260.550493

hitchcock/amity
[5, 13, -17, 9, -6, 9, -41, -3, -28, -76, -24, -62, 84, 46, -54] [[1,
3, 6, -2, 6, 2], [0, -5, -13, 17, -9, 6]]
30 1.176228 340.690750

supersuper
[3, 17, -1, -13, -22, 20, -10, -31, -46, -50, -89, -114, -33, -58,
-28] [[1, 1, -1, 3, 6, 8], [0, 3, 17, -1, -13, -22]]
39 .958363 429.837463

twothirdtonic
[13, -3, 11, 5, 12, -35, -19, -37, -29, 34, 22, 39, -24, -7, 23] [[1,
3, 2, 4, 4, 5], [0, -13, 3, -11, -5, -12]]
29 1.697662 464.709140

srutar
[4, -8, 14, -2, -14, -22, 11, -17, -37, 55, 23, -3, -54, -91, -41]
[[2, 3, 5, 5, 7, 8], [0, 2, -4, 7, -1, -7]]
28 1.845166 476.393162

valentine
[9, 5, -3, 7, 26, -13, -30, -20, 8, -21, -1, 42, 30, 84, 64] [[1, 1,
2, 3, 3, 2], [0, 9, 5, -3, 7, 26]]
29 1.769869 484.474653

semisixths
[7, 9, 13, -15, 10, -2, 1, -48, -10, 5, -66, -10, -87, -20, 90] [[1,
-1, -1, -2, 9, 0], [0, 7, 9, 13, -15, 10]]
29 1.769869 484.474653

[6, -12, -2, 20, 2, -33, -20, 11, -19, 29, 88, 49, 63, 13, -67] [[2,
2, 7, 6, 3, 7], [0, 3, -6, -1, 10, 1]]
32 1.646850 531.174551

[16, 14, 10, -8, -10, -15, -29, -68, -75, -16, -67, -75, -57, -65, -5]
[[2, 7, 8, 8, 5, 5], [0, -8, -7, -5, 4, 5]]
42 1.278944 649.033350

valentino
[9, 5, -3, 7, -20, -13, -30, -20, -65, -21, -1, -65, 30, -45, -95]
[[1, 1, 2, 3, 3, 5], [0, 9, 5, -3, 7, -20]]
38 1.548127 664.935019

shrutar
[4, -8, 14, -2, 32, -22, 11, -17, 36, 55, 23, 104, -54, 38, 118] [[2,
3, 5, 5, 7, 6], [0, 2, -4, 7, -1, 16]]
40 1.425313 666.822498

[8, -16, -18, -4, 18, -44, -51, -34, -1, 3, 46, 101, 51, 117, 77] [[2,
3, 5, 6, 7, 7], [0, 4, -8, -9, -2, 9]]
36 1.704422 668.982422

superduper
[3, 17, -1, -13, 24, 20, -10, -31, 27, -50, -89, -7, -33, 71, 131]
[[1, 1, -1, 3, 6, -1], [0, 3, 17, -1, -13, 24]]
37 1.802476 740.523851

[2, -4, -16, 22, 16, -11, -31, 28, 18, -26, 65, 52, 117, 104, -26]
[[2, 3, 5, 7, 5, 6], [0, 1, -2, -8, 11, 8]]
38 1.769869 760.175249

[11, 1, -19, -17, -4, -24, -61, -65, -47, -47, -43, -13, 18, 59, 49]
[[1, -2, 2, 9, 9, 5], [0, 11, 1, -19, -17, -4]]
41 1.561845 761.396598

[18, 10, -6, 14, 6, -26, -60, -40, -57, -42, -2, -23, 60, 39, -31]
[[2, 2, 4, 6, 6, 7], [0, 9, 5, -3, 7, 3]]
42 1.535699 779.329982

[12, 22, -4, -6, -42, 7, -40, -51, -111, -71, -90, -179, -3, -103,
-123] [[2, 5, 8, 5, 6, 1], [0, -6, -11, 2, 3, 21]]
66 .748762 807.080623

[10, -20, 12, 18, -12, -55, -9, -6, -56, 84, 111, 46, 9, -78, -108]
[[2, 1, 9, 3, 3, 10], [0, 5, -10, 6, 9, -6]]
40 1.735774 812.069301

[23, 23, 23, 23, 0, -17, -28, -43, -85, -11, -26, -85, -15, -85, -85]
[[23, 36, 53, 64, 79, 85], [0, 1, 1, 1, 1, 0]]
46 1.533497 905.619955

[22, 2, 8, 12, 38, -48, -49, -57, -21, 13, 21, 81, 6, 77, 87] [[2, 7,
5, 7, 9, 14], [0, -11, -1, -4, -6, -19]]
44 1.667793 914.597575

[14, 18, -20, 16, -26, -4, -71, -23, -93, -97, -25, -127, 114, 1,
-149] [[2, 5, 7, 3, 9, 4], [0, -7, -9, 10, -8, 13]]
54 1.219228 940.606327

[16, 14, 10, -8, 36, -15, -29, -68, -2, -16, -67, 32, -57, 64, 154]
[[2, 7, 8, 8, 5, 16], [0, -8, -7, -5, 4, -18]]
44 1.769869 970.574458

[8, -16, -18, -4, -28, -44, -51, -34, -74, 3, 46, -6, 51, -12, -82]
[[2, 3, 5, 6, 7, 8], [0, 4, -8, -9, -2, -14]]
44 1.820926 998.573790

Gene Ward Smith wrote:
> We've been on a 13-limit kick, and George thinks 46 may be his fav, so
> I'm giving this. Note that valentine and semisixths have the same
> Graham complexity and TOP error, so they are tied at the 7.5th place
> by the criterion I used to sort this list. In terms of TOP tuning,
> they share a tuning for 5, 7, and 13. Leapday came out #1; it's been
> kicking around a while without a name so it's good Herman named it,
> even if I still havn't figured out what 2/29 has to do with it.

Its smallest MOS with full 13-limit hexads has 29 steps. I hadn't intended any meaning for the "2" from February.

"Hitchcock", although named in reference to the 39-step MOS, does have a smaller 32-step MOS with full 13-limit hexads, but my program was set to ignore scales with large steps more than 3 times the size of the small steps (which tend to be less useful musically), so I didn't notice it.