Proposed temperament names
11 June 2021
Haze (99&12d)
Subgroup: 2.3.5.7
Commas: 67108864/66430125, 4375/4374
Mapping: [⟨3 5 6 5], ⟨0 1 -4 23]]
POTE generator: ~3/2 = 703.050
Vals: 12d, 87d, 99, 111d, 186d, 198
Temperament finder: http://x31eq.com/cgi-bin/uv.cgi?uvs=4375%3A4374+%5B26%2C-12%2C-3%2C0%3E&page=2&limit=7
29 June 2021
Quasi-twelve
Subgroup: 2.3.5
Commas: [146 -76 -11⟩
Mapping: [⟨1 -3 34], ⟨0 11 -76]]
POTE generator: 500.180
Vals: 12, 547, 559, 1106, 1118, 1665, 1677
Temperament finder: http://x31eq.com/cgi-bin/uv.cgi?uvs=%5B146%2C-76%2C-11%3E&page=2&limit=5
Proposed temperament families/realms
7 August 2021
The Milky Way
Milkyway (Rank 4 parent temperament, named so after me :))
Subgroup: 2.5.7.17.19
Comma: 476/475 (The difference between 28/25 and 19/17)
Mapping:
[⟨1 0 0 0 2],
[⟨0 1 0 0 -2],
[⟨0 0 1 0 1],
[⟨0 0 0 1 1]]
POTE generators: 2/1, ~5/1 = 2787.1374, ~7/1 = 3368.7049, ~17/1 = 4904.4999
Vals: 12, 25, 31, 37, 43, 56, 68, 93
Temperament finder: http://x31eq.com/cgi-bin/uv.cgi?uvs=476%3A475&page=2&limit=2_5_7_17_19
Orion (Rank 3)
Subgroup: 2.5.7.17.19
Commas: 476/475, 1445/1444, 2128/2125, 3136/3125
Mapping:
[⟨1 0 -3 0 -1],
[⟨0 2 5 0 1],
[⟨0 0 0 1 1]]
POTE generators: 2/1, ~56/25 = 1393.7535, ~17/1 = 4905.0728
Vals: 12, 25, 31, 37, 43, 50, 56, 68, 93
Epsilon (Rank 2)
Subgroup: 2.5.7.17.19
Commas: 343/340, 476/475, 1225/1216, 2401/2375
Mapping: [⟨1 2 2 2 2], [⟨0 2 5 13 14]]
POTE generators: ~28/25 = 192.6270
Vals: 4, 6h, 21, 25, 27g, 29g, 31, 56
Luyten (Rank 2)
Subgroup: 2.5.7.17.19
Commas: 476/475, 32768/32585, 34391/34295
Mapping: [⟨1 2 2 2 2], [⟨0 2 5 -18 -17]]
POTE generators: ~28/25 = 194.0839
Vals: 16, 21, 31, 37, 47, 52, 68