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The Laconic family tempers out the Laconic comma, 2187/2000, which is the difference between three 10/9's and a 3/2. Although a higher-error temperament, it does pop up enough in the low-numbered EDOs to be useful, most notably in 16-EDO and 21-EDO. The only 7-limit extension that makes any sense to use is gorgo, which also tempers out 1029/1024.

Laconic

Comma: 2187/2000

POTE generator: ~10/9 = 227.426

Map: [<1 1 1|, <0 3 7|>
EDOs: 5, 16, 21, 37b
Badness: 0.1618

Gorgo

Commas: 36/35, 1029/1024

POTE generator: ~8/7 = 228.334

Map: [<1 1 1 3|, <0 3 7 -1|>
EDOs: 5, 16, 21, 37b
Badness: 0.0607

11-limit

Commas: 36/35, 45/44, 1029/1024

POTE generator: ~8/7 = 227.373

Map: [<1 1 1 3 1|, <0 3 7 -1 13|>
EDOs: 16, 21, 37b
Badness: 0.0495

13-limit

Commas: 27/26, 36/35, 45/55, 507/500

POTE generator: ~8/7 = 227.230

Map: [<1 1 1 3 1 2|, <0 3 7 -1 13 9|>
EDOs 16, 21, 37b
Badness: 0.0327

Spartan

Commas: 36/35, 56/55, 1029/1024

POTE generator: ~8/7 = 229.535

Map: [<1 1 1 3 5|, <0 3 7 -1 -8|>
EDOs: 5, 21
Badness: 0.0627