Alphatricot family
The generator for tricot temperament is the real cube root of third harmonic, 31/3, tuned between 63/44 and 13/9. Tricot temperament can be described as 53&70 temperament, tempering out the tricot comma, [39 -29 3⟩ in the 5-limit. There are some mappings for 7-limit extension of this temperament: trimot (53&70) and trillium (53&441). Tempering out hemifamity comma (5120/5103) leads trimot (supported by 53edo and 70edo), and tempering out ragisma (4375/4374) leads trillium (supported by 53, 441, 494, 935, and 1376 edos).
See Hemifamity temperaments for more infomation.
5-limit Tricot
Comma: [39 -29 3⟩ = 68719476736000/68630377364883
POTE generator: ~59049/40960 = 634.012
Map: [<1 0 -13|, <0 3 29|]
Wedgie: <<3 29 39||
EDOs: 53, 229, 282, 335, 388, 441, 1376, 1817, 2258
Badness: 0.0461
Trimot (53&70)
Commas: 2430/2401, 5120/5103
POTE generator: ~81/56 = 634.0259
Map: [<1 0 -13 -3|, <0 3 29 11|]
Wedgie: <<3 29 11 39 9 -56||
EDOs: 17c, 36c, 53, 70, 229dd, 282dd
Badness: 0.1001
11-limit
Commas: 99/98, 121/120, 5120/5103
POTE generator: ~63/44 = 634.0273
Map: [<1 0 -13 -3 -5|, <0 3 29 11 16|]
Badness: 0.0561
13-limit
Commas: 99/98, 121/120, 169/168, 352/351
POTE generator: ~13/9 = 634.0115
Map: [<1 0 -13 -3 -5 0|, <0 3 29 11 16 7|]
Badness: 0.0321
Trident (53&229)
Commas: 6144/6125, 14348907/14336000
POTE generator: ~4096/2835 = 634.0480
Map: [<1 0 -13 25|, <0 3 29 -42|]
Wedgie: <<3 29 -42 39 -75 -179||
Badness: 0.1017
Trillium (53&441)
Commas: 4375/4374, 1099511627776/1098337086315
POTE generator: ~23625/16384 = 634.0118
Map: [<1 0 -13 53|, <0 3 29 -95|]
Wedgie: <<3 29 -95 39 -159 -302||
EDOs: 53, 441, 494, 935, 1376, 3193, 4569
Badness: 0.0309
11-limit 53&388
Commas: 4375/4374, 5632/5625, 4108797/4096000
POTE generator: ~1125/704 = 634.0190
Map: [<1 0 -13 53 -61|, <0 3 29 -95 122|]
Badness: 0.1119
11-limit 53&494
Commas: 4375/4374, 131072/130977, 759375/758912
POTE generator: ~3888/2695 = 634.0094
Map: [<1 0 -13 53 89|, <0 3 29 -95 175|]
Badness: 0.0468