Biyatismic clan

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The biyatismic clan of rank-3 temperaments tempers out the biyatisma, 121/120 = [-3 -1 -1 0 2.

Temperaments discussed elsewhere are:

Considered below are aphrodite, and the no-7 subgroup temperament, protomere, but we can begin by looking at the rank-4 temperament.

Biyatismic

Subgroup: 2.3.5.7.11

Comma list: 121/120

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

Mapping generators: ~2, ~3, ~11/10, ~7

POTE generators: ~3/2 = 701.4578, ~11/10 = 157.7466, ~7/4 = 966.9589

Optimal GPV sequence14c, 15, 22, 31, 46, 53, 60e, 68, 77, 91e, 99, 130e, 159ee, 190ee

Badness: 0.0345 × 10-6

Protomere

Subgroup: 2.3.5.11

Comma list: 121/120

Sval mapping: [1 0 1 2], 0 1 1 1], 0 0 -2 -1]]

Sval mapping generators: ~2, ~3, ~11/10

POTE generators: ~3/2 = 701.4578, ~11/10 = 157.7466

Optimal GPV sequence7, 15, 22, 31, 46, 53, 137e, 183ee, 190ee

Badness: 0.0297 × 10-3

Aphrodite

Aphrodite tempers out the squalentine comma, 64827/64000, in the 7-limit. Its generators can be taken to be 2, 3, and 21/20, and it equates (21/20)3 with 8/7.

7-limit (squalentine)

Subgroup: 2.3.5.7

Comma list: 64827/64000

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

Mapping generators: ~2, ~3, ~21/20

Optimal GPV sequence14c, 15, 29, 31, 46, 60, 77, 91, 122, 137d, 168d

Badness: 0.943 × 10-3

Projection pairs: 5 320000/64827 7 64000/9261 to 2.3.7/5

11-limit

Subgroup: 2.3.5.7.11

Comma list: 121/120, 441/440

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

Mapping generators: ~2, ~3, ~22/21

Optimal GPV sequence14c, 15, 29, 31, 46, 60e, 77, 91e, 137de, 168dee

Badness: 0.583 × 10-3

13-limit

Subgroup: 2.3.5.7.11.13

Comma list: 121/120, 351/350, 441/440

Mapping: [1 0 1 3 2 6], 0 1 1 0 1 -1], 0 0 4 3 2 11]]

Vals: 14cf, 31, 45ef, 46, 77, 122ee, 137def, 168deef

Badness: 1.456 × 10-3

Eros

Subgroup: 2.3.5.7.11.13

Comma list: 121/120, 196/195, 352/351

Mapping: [1 0 1 3 2 7], 0 1 1 0 1 -2], 0 0 4 3 2 2]]

Vals: 17c, 29, 31, 46, 60e, 77, 106de, 183dee

Badness: 1.150 × 10-3

Inanna

Subgroup: 2.3.5.7.11.13

Comma list: 105/104, 121/120, 275/273

Mapping: [1 0 1 3 2 1], 0 1 1 0 1 2], 0 0 4 3 2 7]]

Vals: 14cf, 15, 29, 31, 45ef, 60e

Badness: 1.077 × 10-3

Ishtar

Subgroup: 2.3.5.7.11.13

Comma list: 91/90, 121/120, 441/440

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

Vals: 14cf, 15, 17c, 29, 31f, 46, 106deff, 121def

Badness: 1.151 × 10-3