Sengic family

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

Temperament discussed elsewhere include sensigh (→ Sensamagic family). Considered below are demeter and krypton.

Sengic

Subgroup: 2.3.5.7

Comma list: 686/675

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

Mapping generators: ~2, ~3, ~15/14

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

Optimal GPV sequence9, 10, 18, 19, 27, 46

Badness: 0.320 × 10-3

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

Demeter

Subgroup: 2.3.5.7.11

Comma list: 441/440, 686/675

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

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

Optimal GPV sequence10, 17c, 19e, 27e, 29, 46

Projection pairs: ~5 = 2725888/531441, ~7 = 15488/2187 to 2.3.11

13-limit

Subgroup: 2.3.5.7.11.13

Comma list: 91/90, 169/168, 352/351

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

POTE generators: ~3/2 = 705.113, ~14/13 = 129.673

Optimal GPV sequence: 10, 17c, 19e, 27e, 29, 46

Projection pairs: ~5 = 2725888/531441, ~7 = 15488/2187, ~13 = 352/27 to 2.3.11

17-limit

Subgroup: 2.3.5.7.11.13.17

Comma list: 91/90, 136/135, 154/153, 169/168

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

POTE generators: ~3/2 = 705.147, ~14/13 = 129.700

Optimal GPV sequence: 10, 17cg, 19eg, 27eg, 29g, 46

Projection pairs: ~5 = 2725888/531441, ~7 = 15488/2187, ~13 = 352/27, ~17 = 340736/19683 to 2.3.11

Krypton

Subgroup: 2.3.5.7.11

Comma list: 56/55, 540/539

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

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

Optimal GPV sequence8d, 9, 10, 17c, 19, 27e, 36

Badness: 0.856 × 10-3

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

13-limit

Subgroup: 2.3.5.7.11.13

Comma list: 56/55, 78/77, 91/90

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

POTE generators: ~3/2 = 706.029, ~14/13 = 132.428

Optimal GPV sequence: 8d, 9, 10, 17c, 19, 27e, 36

Badness: 0.727 × 10-3

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