Alphatricot family

The generator for tricot temperament is the real cube root of third harmonic, 3^1/3, 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), trident (53&229) and trillium (53&441). Tempering out hemifamity comma (5120/5103) leads trimot (supported by 53edo and 70edo), porwell comma (6144/6125) leads trident (supported by 53, 176, and 229 edos), and ragisma (4375/4374) leads trillium (supported by 53, 441, 494, 935, and 1429 edos).

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|]

EDOs: 17c, 36ce, 53, 70, 123de

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|]

EDOs: 17c, 36ce, 53, 70, 123de

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||

EDOs: 53, 176, 229, 282, 511

Badness: 0.1017

11-limit

Commas: 3388/3375, 6144/6125, 8019/8000

POTE generator: ~231/160 = 634.0669

Map: [<1 0 -13 25 -33|, <0 3 29 -42 69|]

EDOs: 53, 176, 229

Badness: 0.0743

13-limit

Commas: 351/350, 2080/2079, 2197/2187, 3146/3125

POTE generator: ~13/9 = 634.0652

Map: [<1 0 -13 25 -33 0|, <0 3 29 -42 69 7|]

EDOs: 53, 176, 229

Badness: 0.0466

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

Commas: 4375/4374, 131072/130977, 759375/758912

POTE generator: ~3888/2695 = 634.0094

Map: [<1 0 -13 53 -89|, <0 3 29 -95 175|]

EDOs: 53, 441, 494, 935, 1429

Badness: 0.0468

13-limit

Commas: 2080/2079, 4096/4095, 4375/4374, 78125/78078

POTE generator: ~75/52 = 634.0095

Map: [<1 0 -13 53 -89 -28|, <0 3 29 -95 175 60|]

EDOs: 53, 441, 494, 935, 1429

Badness: 0.0194

Pseudotrillium (53&388)

Commas: 4375/4374, 5632/5625, 4108797/4096000

POTE generator: ~231/160 = 634.0190

Map: [<1 0 -13 53 -61|, <0 3 29 -95 122|]

EDOs: 53, 335, 388

Badness: 0.1119

13-limit

Commas: 847/845, 1001/1000, 4096/4095, 4375/4374

POTE generator: ~75/52 = 634.0181

Map: [<1 0 -13 53 -61 -28|, <0 3 29 -95 122 60|]

EDOs: 53, 335, 388

Badness: 0.0548

Tritricot (159&282)

Commas: 250047/250000, 11785390260224/11767897353375

POTE generator: ~100352/91125 = 165.9837

Map: [<3 6 19 30|, <0 -3 -29 -52|]

Wedgie: <<9 87 156 117 222 118||

EDOs: 159, 282, 441, 2487, 2928, 3369

Badness: 0.0861

11-limit

Commas: 4000/3993, 166698/166375, 200704/200475

POTE generator: ~11/10 = 165.9835

Map: [<3 6 19 30 22|, <0 -3 -29 -52 -28|]

EDOs: 159, 282, 441

Badness: 0.0740

13-limit

Commas: 1575/1573, 2080/2079, 34398/34375, 43904/43875

POTE generator: ~11/10 = 165.9842

Map: [<3 6 19 30 22 36|, <0 -3 -29 -52 -28 -60|]

EDOs: 159, 282, 441

Badness: 0.0356

17-limit

Commas: 936/935, 1575/1573, 1701/1700, 2025/2023, 8624/8619

POTE generator: ~11/10 = 165.9805

Map: [<3 6 19 30 22 36 16|, <0 -3 -29 -52 -28 -60 -9|]

EDOs: 159, 282, 441

Badness: 0.0260