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| This is a collection of rank-3 temperaments tempering out [[441/440]], but we can begin by looking at the rank-4 temperament. | | This is a collection of rank-3 temperaments tempering out [[441/440]], but we can begin by looking at the rank-4 temperament. |
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| Temperaments discussed elsewhere are: | | Temperaments discussed elsewhere are: |
| * ''[[festival]]'', {45/44, 50/49} → [[Jubilismic family #Festival]] | | * ''[[Festival]]'', {45/44, 50/49} → [[Jubilismic family #Festival|Jubilismic family]] |
| * ''[[vulcan]]'', {56/55, 64/63} → [[Archytas family #Vulcan]] | | * ''[[Vulcan]]'', {56/55, 64/63} → [[Archytas family #Vulcan|Archytas family]] |
| * ''[[euterpe]]'', {81/80, 99/98} → [[Didymus rank three family #Euterpe]] | | * ''[[Euterpe]]'', {81/80, 99/98} → [[Didymus rank three family #Euterpe|Didymus rank-3 family]] |
| * ''[[nakika]]'', {100/99, 245/242} → [[Octagar family #Nakika]] | | * ''[[Nakika]]'', {100/99, 245/242} → [[Octagar family #Nakika|Octagar family]] |
| * ''[[thrush]]'', {126/125, 441/440} → [[Starling family #Thrush]] | | * ''[[Aphrodite]]'', {121/120, 441/440} → [[Biyatismic temperaments #Aphrodite|Biyatismic temperaments]] |
| * ''[[prodigy]]'', {225/224, 441/440} → [[Marvel family #Prodigy]] | | * ''[[Thrush]]'', {126/125, 441/440} → [[Starling family #Thrush|Starling family]] |
| * ''[[jove]]'', {243/242, 441/440} → [[Breed family #Jove]] | | * ''[[Prodigy]]'', {225/224, 441/440} → [[Marvel family #Prodigy|Marvel family]] |
| * ''[[sensawer]]'', {245/243, 441/440} → [[Sensamagic family #Sensawer]] | | * ''[[Jove]]'', {243/242, 441/440} → [[Breed family #Jove|Breed family]] |
| * ''[[portent]]'', {385/384, 441/440} → [[Gamelismic family #Portent]] | | * ''[[Sensawer]]'', {245/243, 441/440} → [[Sensamagic family #Sensawer|Sensamagic family]] |
| * ''[[demeter]]'', {441/440, 686/675} → [[Sengic family #Demeter]] | | * ''[[Portent]]'', {385/384, 441/440} → [[Gamelismic family #Portent|Gamelismic family]] |
| * ''[[pele]]'', {441/440, 896/891} → [[Hemifamity family #Pele]] | | * ''[[Demeter]]'', {441/440, 686/675} → [[Sengic family #Demeter|Sengic family]] |
| * ''[[tiberius]]'', {441/440, 2048/2025} → [[Diaschismic rank three family #Tiberius]] | | * ''[[Pele]]'', {441/440, 896/891} → [[Hemifamity family #Pele|Hemifamity family]] |
| * ''[[belobog]]'', {441/440, 3136/3125} → [[Hemimean family #Belobog]] | | * ''[[Tiberius]]'', {441/440, 2048/2025} → [[Diaschismic rank three family #Tiberius|Diaschismic rank-3 family]] |
| * ''[[turan]]'', {441/440, 10976/10935} → [[Hemimage family #Turan]] | | * ''[[Belobog]]'', {441/440, 3136/3125} → [[Hemimean family #Belobog|Hemimean family]] |
| * ''[[snape]]'', {441/440, 19683/19600} → [[Cataharry family #Snape]] | | * ''[[Turan]]'', {441/440, 10976/10935} → [[Hemimage family #Turan|Hemimage family]] |
| | * ''[[Snape]]'', {441/440, 19683/19600} → [[Cataharry family #Snape|Cataharry family]] |
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| == Werckismic == | | == Werckismic == |
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| Badness: 1.478 × 10<sup>-3</sup> | | Badness: 1.478 × 10<sup>-3</sup> |
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| == Aphrodite ==
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| 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)<sup>3</sup> with 8/7.
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| === 7-limit (squalentine) ===
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| Subgroup: 2.3.5.7
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| [[Comma list]]: 64827/64000
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| [[Mapping]]: [{{val| 1 0 1 3 }}, {{val| 0 1 1 0 }}, {{val| 0 0 4 3 }}]
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| Mapping generators: ~2, ~3, ~21/20
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| {{Val list|legend=1| 14c, 15, 29, 31, 46, 60, 77, 91, 122, 137d, 168d }}
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| [[Badness]]: 0.943 × 10<sup>-3</sup>
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| [[Projection pair]]s: 5 320000/64827 7 64000/9261 to 2.3.7/5
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| === 11-limit ===
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| Subgroup: 2.3.5.7.11
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| [[Comma list]]: 121/120, 441/440
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| [[Mapping]]: [{{val| 1 0 1 3 2 }}, {{val| 0 1 1 0 1 }}, {{val| 0 0 4 3 2 }}]
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| Mapping generators: ~2, ~3, ~22/21
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| {{Val list|legend=1| 14c, 15, 29, 31, 46, 60e, 77, 91e, 137de, 168dee }}
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| [[Badness]]: 0.583 × 10<sup>-3</sup>
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| ==== 13-limit ====
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| Subgroup: 2.3.5.7.11.13
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| Comma list: 121/120, 351/350, 441/440
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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 }}]
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| Vals: {{Val list| 14cf, 31, 45ef, 46, 77, 122ee, 137def, 168deef }}
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| Badness: 1.456 × 10<sup>-3</sup>
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| ==== Eros ====
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| Subgroup: 2.3.5.7.11.13
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| Comma list: 121/120, 196/195, 352/351
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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 }}]
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| Vals: {{Val list| 17c, 29, 31, 46, 60e, 77, 106de, 183dee }}
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| Badness: 1.150 × 10<sup>-3</sup>
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| ==== Inanna ====
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| Subgroup: 2.3.5.7.11.13
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| Comma list: 105/104, 121/120, 275/273
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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 }}]
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| Vals: {{Val list| 14cf, 15, 29, 31, 45ef, 60e }}
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| Badness: 1.077 × 10<sup>-3</sup>
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| ==== Ishtar ====
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| Subgroup: 2.3.5.7.11.13
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| Comma list: 91/90, 121/120, 441/440
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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 }}]
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| Vals: {{Val list| 14cf, 15, 17c, 29, 31f, 46, 106deff, 121def }}
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| Badness: 1.151 × 10<sup>-3</sup>
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| [[Category:Regular temperament theory]] | | [[Category:Regular temperament theory]] |