No-threes subgroup temperaments: Difference between revisions

+"tricesimoprimal miracloid" and resolve name conflict
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Optimal tuning (POTE): ~19/14 = 529.003¢
Optimal tuning (POTE): ~19/14 = 529.003¢


=== Pure onzonic ===
== Pure onzonic ==
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


== 2.5.7.11.19.29.31 subgroup ==
== 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. 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.
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.