31st-octave temperaments: Difference between revisions
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{{ | {{Technical data page}} | ||
{{Infobox fractional-octave|31}} | |||
This page collects rank-2 temperaments with a period that is 1/31 of an octave. | This page collects rank-2 temperaments with a period that is 1/31 of an octave. | ||
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[[Support]]ing [[ET]]s: {{EDOs|31, 62, 93}} | [[Support]]ing [[ET]]s: {{EDOs|31, 62, 93}} | ||
== 31-5-commatic == | |||
Subgroup: 2.3.5 | |||
Comma list: {{monzo| 72 0 -31 }} | |||
{{Mapping|legend=1| 31 31 72 | 0 1 0 }} | |||
[[Optimal tuning]] ([[CWE]]): ~128/125 = 1\31, ~3/2 = 702.133 | |||
[[Support]]ing [[ET]]s: 31, 217, 186, 248, 155, 465, 403, 279, 124, 93c, 62c, 682, 310, 620 | |||
== 31-17/13-commatic == | |||
A circle of 31 [[17/13]]'s closes at the octave with an error of only 2.74 cents. | |||
Subgroup: 2.13.17 | |||
Comma list: {{Monzo|12 0 0 0 0 31 -31}} | |||
{{Mapping|31 0 12|0 1 1|legend=2}} | |||
: sval mapping generators: ~2.13.17 {{monzo|-5 -13 13}} = 1\31, ~13 | |||
[[Optimal tuning]] ([[CTE]]): ~13/8 = 840.488 | |||
== Birds == | == Birds == | ||
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[[Mapping]]: [{{val| 31 49 72 87 }}, {{val| 0 1 0 0 }}] | [[Mapping]]: [{{val| 31 49 72 87 }}, {{val| 0 1 0 0 }}] | ||
[[POTE generator]]: ~1029/1024 = 5.1551 | [[POTE generator]]: ~1029/1024 = 5.1551 | ||
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Badness: 0.019963 | Badness: 0.019963 | ||
{{Navbox fractional-octave}} | |||