Sengic family

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Sengic family is a collection of the planar temperaments tempering out the senga comma, 686/675.

Comma: 686/675

Map: [ 1 0 2 1], 0 1 0 1], 0 0 3 2] ]

POTE generators: 2, ~3/2 = 704.154, ~15/14 = 129.824

EDOs: 9, 10, 18, 19, 27, 46

Badness: 0.000320

Projection pairs: 5 3375/686 7 675/98 to 2.3.7/5

Demeter

Commas: 441/440, 686/675

Map: [ 1 0 2 1 -3], 0 1 0 1 4], 0 0 3 2 1] ]

POTE generators: 2, ~3/2 = 705.518, ~15/14 = 130.039

EDOs: 10, 17c, 19e, 27e, 29, 46

13-limit

Commas: 91/90, 169/168, 352/351

Map: [ 1 0 2 1 -3 2], 0 1 0 1 4 1], 0 0 3 2 1 1] ]

POTE generators: 2, ~3/2 = 705.113, ~13/12 = 129.673

EDOs: 10, 17c, 19e, 27e, 29, 46

17-limit

Commas: 91/90, 136/135, 154/153, 169/168

Map: [ 1 0 2 1 -3 2 -1], 0 1 0 1 4 1 3], 0 0 3 2 1 1 3] ]

POTE generators: 2, ~3/2 = 705.147, ~13/12 = 129.700

EDOs: 10, 17cg, 19eg, 27eg, 29g, 46

Krypton

Commas: 56/55, 540/539

Map: [ 1 0 2 1 2], 0 1 0 1 1], 0 0 3 2 -1] ]

POTE generators: 2, ~3/2 = 705.978, ~12/11 = 132.544

EDOs: 8d, 9, 10, 17c, 19, 27e, 36

Badness: 0.000856

Projection pairs: 5 6912/1331 7 854/121 to 2.3.11

13-limit

Commas: 56/55, 78/77, 91/90

Map: [ 1 0 2 1 2 2], 0 1 0 1 1 1], 0 0 3 2 -1 1] ]

POTE generators: 2, ~3/2 = 706.029, ~12/11 = 132.428

EDOs: 8d, 9, 10, 17c, 19, 27e, 36

Badness: 0.000727

Projection pairs: 5 6912/1331 7 854/121 13 144/11 to 2.3.11