List of edo-distinct 15et rank two temperaments

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The temperaments listed are 15edo-distinct, meaning that they are all different even if tuned in 15edo. The ordering is by increasing complexity of 6/5. The temperament of lowest TE complexity was chosen as the representative for each class of edo-distinctness.

5-limit temperaments

Period,

generator

Wedgie Name Complexity Commas
15, 4 <<6 5 -6]] Hanson 2.685 15552/15625
15, 2 <<3 5 1]] Porcupine 1.663 250/243
5, 1 <<3 0 -7]] Augmented 1.549 128/125
15, 1 <<9 5 -13]] Valentine 4.056 1990656/1953125
3, 1 <<0 5 8]] Blackwood 1.767 256/243
5, 2 <<6 15 10]] Vinegar 4.599 16000000/14348907
15, 7 <<3 -5 -15]] Progress 2.877 32768/30375

7-limit temperaments

Period,

generator

Wedgie Name Complexity Commas
15, 4 <<6 5 3 -6 -12 -7]] Keemun 2.280 49/48 126/125
15, 2 <<3 5 9 1 6 7]] Opossum 1.895 28/27 126/125
5, 1 <<3 0 -6 -7 -18 -14]] Augene 2.336 64/63 126/125
15, 1 <<6 10 3 2 -12 -21]] Nautilus 2.943 49/48 250/243
3, 1 <<0 5 0 8 0 -14]] Blacksmith 1.526 28/27 49/48
5, 2 <<6 0 3 -14 -12 7]] Triforce 2.529 49/48 128/125
15, 7 <<3 10 9 9 6 -7]] Kangaroo 2.626 28/27 1029/1000

11-limit temperaments

Period,

generator

Wedgie Name Complexity Commas
15, 4 <<6 5 3 13 -6 -12 0 -7 13 26]] Darjeeling 2.347 49/48 55/54 77/75
15, 2 <<3 5 9 4 1 6 -4 7 -8 -20]] Opossum 1.692 28/27 55/54 77/75
5, 1 <<3 0 9 9 -7 6 4 21 21 -6]] Inflated 2.102 28/27 55/54 128/125
15, 1 <<6 10 3 8 2 -12 -8 -21 -16 12]] Nautilus 2.548 49/48 55/54 100/99
3, 1 <<0 5 0 -5 8 0 -8 -14 -29 -14]] Blacksmith 1.825 28/27 49/48 55/54
5, 2 <<6 0 3 3 -14 -12 -16 7 7 -2]] Triforce 2.201 49/48 56/55 77/75
15, 7 <<3 -5 -6 -1 -15 -18 -12 0 15 18]] Progress 2.399 56/55 64/63 77/75

13-limit temperaments

Period,

generator

Wedgie Name Complexity Commas
15, 4 <<6 5 3 13 14 -6 -12 0 0 -7 13 14 26 28 0]] Darjeeling 2.300 49/48 55/54 66/65 77/75
15, 2 <<3 5 9 4 2 1 6 -4 -8 7 -8 -14 -20 -28 -8]] Opossum 1.655 28/27 40/39 55/54 66/65
5, 1 <<3 0 -6 -6 -3 -7 -18 -20 -16 -14 -14 -7 4 14 12]] Augene 2.061 40/39 56/55 64/63 66/65
15, 1 <<6 10 3 8 4 2 -12 -8 -16 -21 -16 -28 12 0 -16]] Belauensis 2.391 40/39 49/48 55/54 66/65
3, 1 <<0 5 0 -5 5 8 0 -8 8 -14 -29 -7 -14 14 36]] Blacksmith 1.777 28/27 40/39 49/48 55/54
5, 2 <<6 0 3 3 9 -14 -12 -16 -8 7 7 21 -2 14 20]] Triforce 2.105 49/48 56/55 66/65 77/75
15, 7 <<3 10 9 14 7 9 6 12 0 -7 -2 -21 8 -14 -28]] Kangaroo 2.301 28/27 40/39 77/75 147/143