Porcupine rank three family

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These are the rank-3 temperaments tempering out the porcupine comma or maximal diesis, 250/243. If nothing else is tempered out we have a 7-limit planar temperament, with an 11-limit comma we get an 11-limit temperament, and so forth.

Rank-3 porcupine

Subgroup: 2.3.5.7

Comma list: 250/243

Mapping: [1 2 3 0], 0 -3 -5 0], 0 0 0 1]]

Mapping generators: ~2, ~10/9, ~7

POTE generators: ~10/9 = 163.9504, ~7/4 = 970.0552

Optimal GPV sequence7d, 8d, 14c, 15, 22, 37, 51, 73c

Badness: 0.535 × 10-3

Sonic

Subgroup: 2.3.5.7.11

Comma list: 55/54, 100/99

Mapping: [1 2 3 0 4], 0 -3 -5 0 -4], 0 0 0 1 0]]

POTE generators: ~11/10 = 164.0777, ~7/4 = 967.8413

Optimal GPV sequence7d, 8d, 14c, 15, 22, 37, 51, 88b

Badness: 0.523 × 10-3

Tikal

Subgroup: 2.3.5.7.11

Comma list: 56/55, 250/243

Mapping: [1 2 3 0 0], 0 -3 -5 0 5], 0 0 0 1 1]]

POTE generators: ~10/9 = 161.5193, ~7/4 = 971.0457

Optimal GPV sequence7d, 8d, 15, 30dee, 37ee, 52bee

Badness: 1.973 × 10-3