31st-octave temperaments: Difference between revisions
→31-17/13-commatic: 31edo is notable for approximating this interval precisely |
→Euphrosynean: oops |
||
| (15 intermediate revisions by 6 users not shown) | |||
| Line 1: | Line 1: | ||
{{ | {{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. | ||
| Line 18: | Line 19: | ||
[[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 == | == 31-17/13-commatic == | ||
| Line 40: | Line 52: | ||
[[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 | ||
| Line 101: | Line 111: | ||
Badness: 0.021271 | Badness: 0.021271 | ||
== | == Euphrosynean == | ||
''Euphrosynean'' (217 & 1178) temperament combines two multiples of 31, which are large equal divisions consistent in the 21-odd-limit. Named after the minor planet [[wikipedia:31 Euphrosyne|31 Euphrosyne]]. 1395edo, also consistent in 21-odd-limit, is also a tuning. | |||
Subgroup: 2.3.5.7 | Subgroup: 2.3.5.7 | ||
| Line 255: | Line 265: | ||
Badness: 0.019963 | Badness: 0.019963 | ||
{{Navbox fractional-octave}} | |||