Porcupine rank three family
The porcupine rank-3 family of temperaments tempers 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
Mapping: [⟨1 2 3 0], ⟨0 -3 -5 0], ⟨0 0 0 1]]
- mapping generators: ~2, ~10/9, ~7
Optimal tuning (POTE): ~2 = 1\1, ~10/9 = 163.9504, ~7/4 = 970.0552
Optimal ET sequence: 7d, 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]]
Optimal tuning (POTE): ~2 = 1\1, ~11/10 = 164.0777, ~7/4 = 967.8413
Optimal ET sequence: 7d, 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]]
Optimal tuning (POTE): ~2 = 1\1, ~10/9 = 161.5193, ~7/4 = 971.0457
Optimal ET sequence: 7d, 8d, 15, 30dee, 37ee, 52bee
Badness: 1.973 × 10-3