Subgroup temperaments: Difference between revisions
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→2.5.11.13 subgroup temperaments: comment out name conflicting temperament and mark out weak extension |
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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. | 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. | ||
<!-- name conflict | |||
=== Jacobin === | === Jacobin === | ||
Subgroup: 2.5.11.13 | Subgroup: 2.5.11.13 | ||
Comma list: 6656/6655, {{ | Comma list: 6656/6655, {{monzo| -119 -46 15 47 }} | ||
Mapping: {{ | Mapping: [{{val| 1 74 3 74 }}, {{val| 0 -156 1 -153 }}] | ||
Optimal tuning ( | Optimal tuning (POTE): ~11/8 = 551.370 | ||
Optimal GPV sequence: 37, 1789 | |||
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=== Estates general === | === Estates general === | ||
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. | 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. | ||
[[Subgroup]]: 2.5.11.13 | |||
[[Comma list]]: 6656/6655, {{monzo| 314 -78 14 -49 }} | |||
[[Mapping]]: [{{val| 1 118 -107 -212 }}, {{val| 0 -133 127 248 }}] | |||
[[Optimal tuning]] ([[POTE]]): ~995765040283203125/544935554911830016 = 1043.712 | |||
==== 2.5.11.13.19 subgroup ==== | |||
{{Todo|inline=1| Weak extension, must use a different name }} | |||
Subgroup: 2.5.11.13.19 | Subgroup: 2.5.11.13.19 | ||
Comma list: 6656/6655, 40960000000/40943078891, {{ | Comma list: 6656/6655, 40960000000/40943078891, {{monzo| -133 50 -7 18 -6 }} | ||
Mapping: {{ | Mapping: [{{val| 1 118 -107 -212 450 }}, {{val| 0 -266 254 496 -1025 }}] | ||
Optimal tuning ( | Optimal tuning (POTE): ~2588443885831192576/1914932769775390625 = 521.856 | ||
== Fractional subgroup temperaments == | == Fractional subgroup temperaments == | ||