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Biyatismic clan: Difference between revisions

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Copypasted zeus here as a strong extension
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Temperaments discussed elsewhere are:  
Temperaments discussed elsewhere are:  
* ''[[Sonic]]'', {55/54, 100/99} → [[Porcupine rank three family #Sonic|Porcupine rank-3 family]]
* ''[[Sonic]]'' (+55/54 or 100/99) → [[Porcupine rank three family #Sonic|Porcupine rank-3 family]]
* ''[[Urania]]'', {81/80, 121/120} → [[Didymus rank three family #Urania|Didymus rank-3 family]]
* ''[[Urania]]'' (+81/80) → [[Didymus rank three family #Urania|Didymus rank-3 family]]
* ''[[Big brother]]'', {99/98, 121/120} → [[Nuwell family #big Brother|Nuwell family]]
* ''[[Big brother]]'' (+99/98) → [[Nuwell family #big Brother|Nuwell family]]
* ''[[Oxpecker]]'', {121/120, 126/125} → [[Starling family #Oxpecker|Starling family]]
* ''[[Oxpecker]]'' (+126/125) → [[Starling family #Oxpecker|Starling family]]
* [[Zeus]], {121/120, 176/175} → [[Porwell family #Zeus|Porwell family]]
* ''[[Artemis]]'' (+225/224) → [[Marvel family #Artemis|Marvel family]]
* ''[[Artemis]]'', {121/120, 225/224} → [[Marvel family #Artemis|Marvel family]]
* ''[[Bisector]]'' (+245/243) → [[Sensamagic family #Bisector|Sensamagic family]]
* ''[[Bisector]]'', {121/120, 245/243} → [[Sensamagic family #Bisector|Sensamagic family]]


Considered below are aphrodite, and the no-7 subgroup temperament, protomere. For the rank-4 biyatismic temperament, see [[Rank-4 temperament #Biyatismic (121/120)]].  
Considered below are zeus, aphrodite, and the no-7 subgroup temperament, protomere. For the rank-4 biyatismic temperament, see [[Rank-4 temperament #Biyatismic (121/120)]].  


== Protomere ==
== Protomere ==
Subgroup: 2.3.5.11
[[Subgroup]]: 2.3.5.11


[[Comma list]]: 121/120
[[Comma list]]: 121/120


[[Sval]] [[mapping]]: [{{val| 1 0 1 2 }}, {{val| 0 1 1 1 }}, {{val| 0 0 -2 -1 }}]
{{Mapping|legend=2| 1 0 1 2 | 0 1 1 1 | 0 0 -2 -1 }}


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


[[POTE generator]]s: ~3/2 = 701.4578, ~11/10 = 157.7466
[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~3/2 = 701.4578, ~11/10 = 157.7466


{{Optimal ET sequence|legend=1| 7, 15, 22, 31, 46, 53, 137e, 183ee, 190ee }}
{{Optimal ET sequence|legend=1| 7, 15, 22, 31, 46, 53, 137e, 183ee, 190ee }}
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=== 7-limit (squalentine) ===
=== 7-limit (squalentine) ===
Subgroup: 2.3.5.7
[[Subgroup]]: 2.3.5.7


[[Comma list]]: 64827/64000
[[Comma list]]: 64827/64000


[[Mapping]]: [{{val| 1 0 1 3 }}, {{val| 0 1 1 0 }}, {{val| 0 0 4 3 }}]
{{Mapping|legend=1| 1 0 1 3 | 0 1 1 0 | 0 0 4 3 }}


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 }}
{{Optimal ET sequence|legend=1| 14c, 15, 29, 31, 46, 60, 77, 91, 122, 137d, 168d }}
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=== 11-limit ===
=== 11-limit ===
Subgroup: 2.3.5.7.11
[[Subgroup]]: 2.3.5.7.11


[[Comma list]]: 121/120, 441/440
[[Comma list]]: 121/120, 441/440


[[Mapping]]: [{{val| 1 0 1 3 2 }}, {{val| 0 1 1 0 1 }}, {{val| 0 0 4 3 2 }}]
{{Mapping|legend=1| 1 0 1 3 2 | 0 1 1 0 1 | 0 0 4 3 2 }}


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 }}
{{Optimal ET sequence|legend=1| 14c, 15, 29, 31, 46, 60e, 77, 91e, 137de, 168dee }}
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Comma list: 121/120, 351/350, 441/440
Comma list: 121/120, 351/350, 441/440


Mapping: [{{val| 1 0 1 3 2 6 }}, {{val| 0 1 1 0 1 -1 }}, {{val| 0 0 4 3 2 11 }}]
Mapping: {{mapping| 1 0 1 3 2 6 | 0 1 1 0 1 -1 | 0 0 4 3 2 11 }}


{{Optimal ET sequence|legend=1| 14cf, 31, 45ef, 46, 77, 122ee, 137def, 168deef }}
{{Optimal ET sequence|legend=1| 14cf, 31, 45ef, 46, 77, 122ee, 137def, 168deef }}
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Comma list: 121/120, 196/195, 352/351
Comma list: 121/120, 196/195, 352/351


Mapping: [{{val| 1 0 1 3 2 7 }}, {{val| 0 1 1 0 1 -2 }}, {{val| 0 0 4 3 2 2 }}]
Mapping: {{mapping| 1 0 1 3 2 7 | 0 1 1 0 1 -2 | 0 0 4 3 2 2 }}


{{Optimal ET sequence|legend=1| 17c, 29, 31, 46, 60e, 77, 106de, 183dee }}
{{Optimal ET sequence|legend=1| 17c, 29, 31, 46, 60e, 77, 106de, 183dee }}
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Comma list: 105/104, 121/120, 275/273
Comma list: 105/104, 121/120, 275/273


Mapping: [{{val| 1 0 1 3 2 1 }}, {{val| 0 1 1 0 1 2 }}, {{val| 0 0 4 3 2 7 }}]
Mapping: {{mapping| 1 0 1 3 2 1 | 0 1 1 0 1 2 | 0 0 4 3 2 7 }}


{{Optimal ET sequence|legend=1| 14cf, 15, 29, 31, 45ef, 60e }}
{{Optimal ET sequence|legend=1| 14cf, 15, 29, 31, 45ef, 60e }}
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Comma list: 91/90, 121/120, 441/440
Comma list: 91/90, 121/120, 441/440


Mapping: [{{val| 1 0 1 3 2 -1 }}, {{val| 0 1 1 0 1 3 }}, {{val| 0 0 4 3 2 1 }}]
Mapping: {{mapping| 1 0 1 3 2 -1 | 0 1 1 0 1 3 | 0 0 4 3 2 1 }}


{{Optimal ET sequence|legend=1| 14cf, 15, 17c, 29, 31f, 46, 106deff, 121def }}
{{Optimal ET sequence|legend=1| 14cf, 15, 17c, 29, 31f, 46, 106deff, 121def }}
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[[Category:Temperament clans]]
[[Category:Temperament clans]]
[[Category:Biyatismic clan| ]] <!-- main article -->
[[Category:Biyatismic clan| ]] <!-- main article -->
[[Category:Biyatismic| ]] <!-- key article -->
[[Category:Rank 3]]
[[Category:Rank 3]]
Retrieved from "https://en.xen.wiki/w/Biyatismic_clan"