No-threes subgroup temperaments: Difference between revisions

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== 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.

Described as the 52 & 1789 temperament in the 2.5.7.11.19.29.31 subgroup, with harmonics specifically selected for 52edo and 1789edo. Its generator is [[31/29]], which is also close to the secor. Since it is conceived as the temperament in the above specific subgroup, it makes no sense to name it for smaller subgroups. 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

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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}}]

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}}, ...

Vals: {{EDOs| 52, 1737, 1789 }}, ...

@@ Line 270: / Line 270: @@
 == 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.
+Described as the 52 & 1789 temperament in the 2.5.7.11.19.29.31 subgroup, with harmonics specifically selected for 52edo and 1789edo. Its generator is [[31/29]], which is also close to the secor. Since it is conceived as the temperament in the above specific subgroup, it makes no sense to name it for smaller subgroups. 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
@@ Line 276: / Line 276: @@
 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}}]
+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}}, ...
+Vals: {{EDOs| 52, 1737, 1789 }}, ...