No-threes subgroup temperaments: Difference between revisions
Switch to Sintel's badness, WE & CWE tunings (2/) |
+ some missing entries. "Since it is conceived as the temperament in the above specific subgroup, it makes no sense to name it for smaller subgroups." this is simply not how we do rtt |
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=== Ostara === | === Ostara === | ||
Ostara is a temperament that is derived from 93 & 524 solar calendar leap rule scale | Ostara is a temperament that is derived from 93 & 524 solar calendar leap rule scale, interpreted in general no-3's 19-limit. It is a weak extension of the unnamed 2.5.7-subgroup 28 & 31 temperament, which tempers out 8589934592/8544921875. | ||
Subgroup: 2.5.7.11 | Subgroup: 2.5.7.11 | ||
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Comma list: 8589934592/8544921875, 30691800524/30517578125 | Comma list: 8589934592/8544921875, 30691800524/30517578125 | ||
{{ | Subgroup-val mapping: {{mapping| 1 1 20 -49 | 0 3 -39 119 }} | ||
: mapping generators: ~2, ~5120/3773 | : mapping generators: ~2, ~5120/3773 | ||
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=== Tricesimoprimal miracloid === | === Tricesimoprimal miracloid === | ||
{{See also| Tricesimoprimal miracloid/Eliora's approach }} | {{See also| Tricesimoprimal miracloid/Eliora's approach }} | ||
{{Todo|inline=1| complete section | comment = Add missing data from 2.5.7 to 2.5.7.11.19.29. }} | |||
Tricesimoprimal miracloid is 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 | Tricesimoprimal miracloid is 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. In terms of microtempering, a circle of 52 generators is essentially a barely noticeable [[well temperament]] for 52edo. | ||
==== 2.5.7.11.19.29.31 subgroup ==== | |||
Subgroup: 2.5.7.11.19.29.31 | Subgroup: 2.5.7.11.19.29.31 | ||
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Huntington may be described as the 10 & 37 temperament in the 2.5.7.13 subgroup. | Huntington may be described as the 10 & 37 temperament in the 2.5.7.13 subgroup. | ||
[[Subgroup]]: 2.5.7 | |||
[[Comma list]]: 40960000/40353607 | |||
{{Mapping|legend=2| 1 -4 0 | 0 9 4 }} | |||
{{Mapping|legend=3| 1 0 -4 0 | 0 0 9 4 }} | |||
: mapping generators: ~2, ~80/49 | |||
[[Optimal tuning]]s: | |||
* [[WE]]: ~2 = 1199.5781{{c}}, ~80/49 = 842.6730{{c}} | |||
: [[error map]]: {{val| -0.422 -0.569 +1.866 }} | |||
* [[CWE]]: ~2 = 1200.0000{{c}}, ~80/49 = 842.9136{{c}} | |||
: error map: {{val| 0.000 -0.091 +2.828 }} | |||
{{Optimal ET sequence|legend=0| 7c, 10, 27, 37, 84, 121 }} | |||
Badness (Sintel): 1.87 | |||
==== 2.5.7.13 subgroup ==== | |||
Subgroup: 2.5.7.13 | Subgroup: 2.5.7.13 | ||
Comma list: | Comma list: 640/637, 10985/10976 | ||
Subgroup-val mapping: {{mapping| 1 -4 0 3 | 0 9 4 1 }} | Subgroup-val mapping: {{mapping| 1 -4 0 3 | 0 9 4 1 }} | ||
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Subgroup: 2.5.7.13.17 | Subgroup: 2.5.7.13.17 | ||
Comma list: | Comma list: 170/169, 640/637, 5525/5488 | ||
Subgroup-val mapping: {{mapping| 1 -4 0 3 9 | 0 9 4 1 -7 }} | Subgroup-val mapping: {{mapping| 1 -4 0 3 9 | 0 9 4 1 -7 }} | ||