Subgroup temperaments: Difference between revisions

@@ Line 174: / Line 174: @@
 Optimal GPV sequence: {{Val list| 5, 13, 31}}
+== 2.5.11.13 subgroup temperaments ==
+.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.
+=== Jacobin ===
+Subgroup: 2.5.11.13
+Comma list: 6656/6655, {{Monzo|-119 -46 15 47}}
+Mapping: {{Val|1 74 3 74}}, {{Val|0 -156 1 -153}}
+Optimal tuning (subgroup POTE): ~11/8 = 551.370
+Vals: 37, 1789
+=== 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.
+==== 2.5.11.13 ====
+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 (Subgroup POTE): ~995765040283203125/544935554911830016 = 1043.712
+==== 2.5.11.13.19 ====
+Subgroup: 2.5.11.13.19
+Comma list: 6656/6655, 40960000000/40943078891, {{Monzo|-133 50 -7 18 -6}}
+Mapping: {{Val|1 118 -107 -212 450}}, {{Val|0 -266 254 496 -1025}}
+Optimal tuning (Subgroup POTE): ~2588443885831192576/1914932769775390625 = 521.856
 == Fractional subgroup temperaments ==