Biyatismic clan: Difference between revisions
m Removing from Category:Regular temperament theory using Cat-a-lot |
Cmloegcmluin (talk | contribs) "optimal GPV sequence" → "optimal ET sequence", per Talk:Optimal_ET_sequence |
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[[POTE generator]]s: ~3/2 = 701.4578, ~11/10 = 157.7466, ~7/4 = 966.9589 | [[POTE generator]]s: ~3/2 = 701.4578, ~11/10 = 157.7466, ~7/4 = 966.9589 | ||
{{ | {{Optimal ET sequence|legend=1| 14c, 15, 22, 31, 46, 53, 60e, 68, 77, 91e, 99, 130e, 159ee, 190ee }} | ||
[[Badness]]: 0.0345 × 10<sup>-6</sup> | [[Badness]]: 0.0345 × 10<sup>-6</sup> | ||
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[[POTE generator]]s: ~3/2 = 701.4578, ~11/10 = 157.7466 | [[POTE generator]]s: ~3/2 = 701.4578, ~11/10 = 157.7466 | ||
{{ | {{Optimal ET sequence|legend=1| 7, 15, 22, 31, 46, 53, 137e, 183ee, 190ee }} | ||
[[Badness]]: 0.0297 × 10<sup>-3</sup> | [[Badness]]: 0.0297 × 10<sup>-3</sup> | ||
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Mapping generators: ~2, ~3, ~21/20 | Mapping generators: ~2, ~3, ~21/20 | ||
{{ | {{Optimal ET sequence|legend=1| 14c, 15, 29, 31, 46, 60, 77, 91, 122, 137d, 168d }} | ||
[[Badness]]: 0.943 × 10<sup>-3</sup> | [[Badness]]: 0.943 × 10<sup>-3</sup> | ||
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Mapping generators: ~2, ~3, ~22/21 | Mapping generators: ~2, ~3, ~22/21 | ||
{{ | {{Optimal ET sequence|legend=1| 14c, 15, 29, 31, 46, 60e, 77, 91e, 137de, 168dee }} | ||
[[Badness]]: 0.583 × 10<sup>-3</sup> | [[Badness]]: 0.583 × 10<sup>-3</sup> | ||
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Mapping: [{{val| 1 0 1 3 2 6 }}, {{val| 0 1 1 0 1 -1 }}, {{val| 0 0 4 3 2 11 }}] | Mapping: [{{val| 1 0 1 3 2 6 }}, {{val| 0 1 1 0 1 -1 }}, {{val| 0 0 4 3 2 11 }}] | ||
{{Optimal ET sequence|legend=1| 14cf, 31, 45ef, 46, 77, 122ee, 137def, 168deef }} | |||
Badness: 1.456 × 10<sup>-3</sup> | Badness: 1.456 × 10<sup>-3</sup> | ||
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Mapping: [{{val| 1 0 1 3 2 7 }}, {{val| 0 1 1 0 1 -2 }}, {{val| 0 0 4 3 2 2 }}] | Mapping: [{{val| 1 0 1 3 2 7 }}, {{val| 0 1 1 0 1 -2 }}, {{val| 0 0 4 3 2 2 }}] | ||
{{Optimal ET sequence|legend=1| 17c, 29, 31, 46, 60e, 77, 106de, 183dee }} | |||
Badness: 1.150 × 10<sup>-3</sup> | Badness: 1.150 × 10<sup>-3</sup> | ||
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Mapping: [{{val| 1 0 1 3 2 1 }}, {{val| 0 1 1 0 1 2 }}, {{val| 0 0 4 3 2 7 }}] | Mapping: [{{val| 1 0 1 3 2 1 }}, {{val| 0 1 1 0 1 2 }}, {{val| 0 0 4 3 2 7 }}] | ||
{{Optimal ET sequence|legend=1| 14cf, 15, 29, 31, 45ef, 60e }} | |||
Badness: 1.077 × 10<sup>-3</sup> | Badness: 1.077 × 10<sup>-3</sup> | ||
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Mapping: [{{val| 1 0 1 3 2 -1 }}, {{val| 0 1 1 0 1 3 }}, {{val| 0 0 4 3 2 1 }}] | Mapping: [{{val| 1 0 1 3 2 -1 }}, {{val| 0 1 1 0 1 3 }}, {{val| 0 0 4 3 2 1 }}] | ||
{{Optimal ET sequence|legend=1| 14cf, 15, 17c, 29, 31f, 46, 106deff, 121def }} | |||
Badness: 1.151 × 10<sup>-3</sup> | Badness: 1.151 × 10<sup>-3</sup> | ||
Revision as of 18:24, 7 May 2023
The biyatismic clan of rank-3 temperaments tempers 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
Optimal ET sequence: 14c, 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 ET sequence: 7, 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 ET sequence: 14c, 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 ET sequence: 14c, 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]]
Optimal ET sequence: 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]]
Optimal ET sequence: 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]]
Optimal ET sequence: 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]]
Optimal ET sequence: 14cf, 15, 17c, 29, 31f, 46, 106deff, 121def
Badness: 1.151 × 10-3