Biyatismic clan
This is a collection of rank-3 temperaments tempering out the biyatisma, 121/120 = [-3 -1 -1 0 2⟩.
Temperaments discussed elsewhere are:
- Sonic, {55/54, 100/99} → Porcupine rank-3 family
- Urania, {81/80, 121/120} → Didymus rank-3 family
- Big Brother, {99/98, 121/120} → Nuwell family
- Oxpecker, {121/120, 126/125} → Starling family
- Zeus, {121/120, 176/175} → Porwell family
- Artemis, {121/120, 225/224} → Marvel family
- Bisector, {121/120, 245/243} → Sensamagic family
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
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
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
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
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
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: Template:Val list
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: Template:Val list
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: Template:Val list
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: Template:Val list
Badness: 1.151 × 10-3