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| Optimal GPV sequence: {{Val list| 5, 13, 31}} | | Optimal GPV sequence: {{Val list| 5, 13, 31}} |
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| == 2.5.11.13 subgroup temperaments ==
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| 2.5.11.13 subgroup primarily contains temperaments developed for 1789edo, since it tempers out the jacobin comma 6656/6655, for which 2.5.11.13 is the subgroup, and the year 1789 is hallmark for the French revolution.
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| <!-- name conflict
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| === Jacobin ===
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| Subgroup: 2.5.11.13
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| Comma list: 6656/6655, {{monzo| -119 -46 15 47 }}
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| Mapping: [{{val| 1 74 3 74 }}, {{val| 0 -156 1 -153 }}]
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| Optimal tuning (POTE): ~11/8 = 551.370
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| Optimal GPV sequence: 37, 1789
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| -->
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| === Estates general ===
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| Named so because it is defined as the 1789 & 3125 temperament due to 3125 providing optimal patent val for the jacobin comma, 3125 is 5 to the 5th power, and Estates General were called by Louis XVI on 5th May 1789 (05/05). Defined for the 2.5.11.13.19 subgroup.
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| [[Subgroup]]: 2.5.11.13
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| [[Comma list]]: 6656/6655, {{monzo| 314 -78 14 -49 }}
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| [[Mapping]]: [{{val| 1 118 -107 -212 }}, {{val| 0 -133 127 248 }}]
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| [[Optimal tuning]] ([[POTE]]): ~995765040283203125/544935554911830016 = 1043.712
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| ==== 2.5.11.13.19 subgroup ====
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| {{Todo|inline=1| Weak extension, must use a different name }}
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| Subgroup: 2.5.11.13.19
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| Comma list: 6656/6655, 40960000000/40943078891, {{monzo| -133 50 -7 18 -6 }}
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| Mapping: [{{val| 1 118 -107 -212 450 }}, {{val| 0 -266 254 496 -1025 }}]
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| Optimal tuning (POTE): ~2588443885831192576/1914932769775390625 = 521.856
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| == Fractional subgroup temperaments == | | == Fractional subgroup temperaments == |