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These are the rank three 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.

Sonic

Commas: 55/54, 100/99

Map: [<1 2 3 0 4|, <0 -3 -5 0 -4|, <0 0 0 1 0|]
Generators: ~10/9 = 164.078, ~7 = 3367.841
EDOs: 7, 14c, 15, 22, 37, 44d, 51, 66, 73ce, 139bce, 212bce
Badness: 0.000523

Tikal

Commas: 56/55, 250/243

Map: [<1 2 3 0 0], <0 -3 -5 0 5|, <0 0 0 1 1|]
POTE generators: ~10/9 = 161.519, ~7 = 3371.046
EDOs: 15, 37e, 52be
Badness: 0.001973