No-threes subgroup temperaments: Difference between revisions
→Estates general: moving estates general to a new temperamnet collectin page |
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Optimal tuning (POTE): ~19/14 = 529.003¢ | Optimal tuning (POTE): ~19/14 = 529.003¢ | ||
=== Pure onzonic === | |||
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The 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. | The 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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Optimal GPV sequence: 37, 1789 | Optimal GPV sequence: 37, 1789 | ||
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== 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}}, ... | |||