Subgroup temperaments: Difference between revisions
tricesimoprimal miracloid |
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=== Tricesimoprimal miracloid === | === 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. 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. | 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 | Subgroup: 2.5.7.11.19.29.31 | ||
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Comma list: 10241/10240, 5858783/5856400, 4093705/4090624, 15109493/15089800, 102942875/102834688 | Comma list: 10241/10240, 5858783/5856400, 4093705/4090624, 15109493/15089800, 102942875/102834688 | ||
Mapping: 1 419 48 177 157 624 625, 0 -461 -50 -192 -169 -685 -686 | Mapping: [{{val|1 419 48 177 157 624 625}}, {{val|0 -461 -50 -192 -169 -685 -686}}] | ||
Optimal tuning (CTE): ~58/31 = 1084.628 | Optimal tuning (CTE): ~58/31 = 1084.628 | ||
Vals: 52, 1737, 1789, ... | Vals: {{EDOs|52, 1737, 1789}}, ... | ||
== Fractional subgroup temperaments == | == Fractional subgroup temperaments == | ||