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 is protomere, the no-7 subgroup temperament, 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

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