Subgroup temperaments: Difference between revisions

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-"tricesimoprimal miracloid" (moved to no-3 subgroup)
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Optimal GPV sequence: {{Val list| 5, 13, 31}}
Optimal GPV sequence: {{Val list| 5, 13, 31}}
== 2.5.7.11.19.29.31 subgroup ==
=== Tricesimoprimal miracloid ===
Defined as the 52 & 1789 temperament for the 2.5.7.11.19.29.31 subgroup, with harmonics specifically selected for 52edo and 1789edo. It's generator is an interval [[31/29]], which is also close to secor. Since it is 31-limit in its conception, it makes no sense to define it for lower prime limits. In terms of microtempering, a circle of 52 generators is essentially a barely noticeable [[well temperament]] for 52edo.
Subgroup: 2.5.7.11.19.29.31
Comma list: 10241/10240, 5858783/5856400, 4093705/4090624, 15109493/15089800, 102942875/102834688
Mapping: [{{val|1 419 48 177 157 624 625}}, {{val|0 -461 -50 -192 -169 -685 -686}}]
Optimal tuning (CTE): ~58/31 = 1084.628
Vals: {{EDOs|52, 1737, 1789}}, ...


== Fractional subgroup temperaments ==
== Fractional subgroup temperaments ==