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| == 2.5.7 temperaments == | | == 2.5.7 temperaments == |
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| === Didacus === | | === Didacus === |
| {{See also| Hemimean clan #Didacus }} | | {{See also| Hemimean clan #Didacus }} |
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| Related temperaments: [[Chromatic pairs #Roulette|roulette]], [[Gamelismic clan #Hemithirds|hemithirds]]
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| [[Subgroup]]: 2.5.7
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| [[Comma list]]: 3136/3125
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| [[Sval]] [[mapping]]: [{{val| 1 2 2 }}, {{val| 0 2 5 }}]
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| [[Gencom]]: [2 28/25; 3136/3125]
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| [[Gencom]] [[mapping]]: [{{val| 1 0 2 2 }}, {{val| 0 0 2 5 }}]
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| Optimal tuning ([[POTE]]): ~28/25 = 93.772
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| {{Optimal ET sequence|legend=1| 6, 19, 25, 31, 37, 99, 130, 161, 353 }}
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| [[Tp tuning #T2 tuning|RMS error]]: 0.2138 cents
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| === Rainy === | | === Rainy === |
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| === Bastille === | | === Bastille === |
| {{Main|Bastille}} | | {{Main| Bastille }} |
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| Described as the 2.5.7 subgroup 1407 & 1789 temperament, and named after an eponymous historical event which took place on July 14, 1789 (14/07/1789). Extensions discussed elsewhere include [[The Jacobins#Pure Bastille|pure bastille]]. | | Described as the 2.5.7 subgroup 1407 & 1789 temperament, and named after an eponymous historical event which took place on July 14, 1789 (14/07/1789). Extensions discussed elsewhere include [[The Jacobins#Pure Bastille|pure bastille]]. |
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| {{Optimal ET sequence|legend=1| 6, 23de, 29, 35, 41 }} | | {{Optimal ET sequence|legend=1| 6, 23de, 29, 35, 41 }} |
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| === Llywelyn aka shoe === | | === Llywelyn a.k.a. shoe === |
| {{See also| Chromatic pairs #Shoe }} | | {{See also| Llywelynsmic clan #Llywelyn a.k.a. shoe }} |
| {{See also| Llywelyn clan #Llywelyn aka shoe }}
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| [[Subgroup]]: 2.5.7
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| [[Comma list]]: 4194304/4117715
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| [[Sval]] [[mapping]]: [{{Val| 1 1 3 }}, {{Val| 0 7 -1 }}]
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| Mapping generators: 2, ~8/7
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| [[Gencom]] [[mapping]]: [{{Val| 1 0 1 3 }}, {{Val| 0 0 7 -1 }}]
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| [[Gencom]]: [2 8/7; 4194304/4117715]
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| [[Optimal tuning]] ([[POTE]]): ~8/7 = 226.910
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| {{Optimal ET sequence|legend=1| 5, 11c, 16, 21, 37 }}
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| ==== 2.5.7.11 subgroup ====
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| Subgroup: 2.5.7.11
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| Comma list: 176/175, 1310720/1294139
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| Sval mapping: [{{val| 1 1 3 1 }}, {{val| 0 7 -1 13 }}]
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| Gencom: [2 8/7; 176/175 1310720/1294139]
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| Gencom mapping: [{{val| 1 0 1 3 1 }}, {{val| 0 0 7 -1 13 }}]
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| Optimal tuning (POTE): ~8/7 = 227.114
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| {{Optimal ET sequence|legend=1| 16, 21, 37 }}
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| ==== 2.5.7.11.13 subgroup ====
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| Subgroup: 2.5.7.11.13
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| Comma list: 176/175, 640/637, 847/845
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| Sval mapping: [{{val| 1 1 3 1 2 }}, {{val| 0 7 -1 13 9 }}]
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| Gencom: [2 8/7; 176/175 640/637, 1304576/1294139]
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| Gencom mapping: [{{val| 1 0 1 3 1 2 }}, {{val| 0 0 7 -1 13 9 }}]
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| Optimal tuning (POTE): ~8/7 = 227.108
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| {{Optimal ET sequence|legend=1| 16, 21, 37 }}
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| ==== 2.5.7.11.13.17 subgroup ====
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| Subgroup: 2.5.7.11.13.17
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| Comma list: 176/175, 221/200, 640/637, 833/832
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| Sval mapping: [{{val| 1 1 3 1 2 2 }}, {{val| 0 7 -1 13 9 11 }}]
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| Gencom: [2 8/7; 176/175 221/200, 640/637, 833/832]
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| Gencom mapping: [{{val| 1 0 1 3 1 2 2 }}, {{val| 0 0 7 -1 13 9 11 }}]
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| Optimal tuning (POTE): ~8/7 = 227.242
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| {{Optimal ET sequence|legend=1| 16, 21, 37 }}
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| === French decimal === | | === French decimal === |
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| === Vengeance === | | === Vengeance === |
| ''Main article: [[vengeance]]''<br><br>
| | {{Main| Vengeance }} |
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| Another lower-error replica of mavila, with the fifth being ~[[25/17]] instead of ~[[3/2]]. | | Another lower-error replica of mavila, with the fifth being ~[[25/17]] instead of ~[[3/2]]. |