61st-octave temperaments: Difference between revisions
No edit summary |
|||
| (6 intermediate revisions by 3 users not shown) | |||
| Line 1: | Line 1: | ||
{{Infobox fractional-octave|61}} | |||
61edo is not a usual edo to make fractional-octave temperaments out of, but one step of it is in direct proximity to the diaschisma, [[2048/2025]]. | 61edo is not a usual edo to make fractional-octave temperaments out of, but one step of it is in direct proximity to the diaschisma, [[2048/2025]]. | ||
== Dipromethium == | == Dipromethium == | ||
Dipromethium tempers out the [[dipromethia]], comma which associates the diaschisma exactly with 1/61st of the octave. | |||
Subgroup: 2.3.5 | Subgroup: 2.3.5 | ||
Comma list: -335 122 61 | Comma list: {{monzo|-335 122 61}} | ||
Mapping: 61 0 335, 0 1 -2 | Mapping: [{{val|61 0 335}}, {{val|0 1 -2}}] | ||
Optimal tuning (CTE): ~3/2 = 701.936 | Optimal tuning (CTE): ~3/2 = 701.936 | ||
Supporting ETs: 183, 976, 1159, 1342, 1525, 1769, 1891, ... | Supporting ETs: {{EDOs|183, 976, 1159, 1342, 1525, 1769, 1891}}, ... | ||
==Promethium== | == Promethium == | ||
Promethium splits the perfect fifth in two and can be described as the 183 & 2684 temperament. By tempering out 4100625/4100096 promethium identifies the diaschisma with [[2025/2002]] in the 13-limit and also in the 17-limit. | Promethium splits the perfect fifth in two and can be described as the 183 & 2684 temperament. By tempering out 4100625/4100096 promethium identifies the diaschisma with [[2025/2002]] in the 13-limit and also in the 17-limit. | ||
| Line 24: | Line 27: | ||
Optimal tuning (CTE): ~6875/3969 = 950.970 | Optimal tuning (CTE): ~6875/3969 = 950.970 | ||
====17-limit==== | |||
==== 17-limit ==== | |||
Subgroup: 2.3.5.7.11.13.17 | Subgroup: 2.3.5.7.11.13.17 | ||
| Line 36: | Line 40: | ||
{{Optimal ET sequence|legend=1|183, 2684}}, ... | {{Optimal ET sequence|legend=1|183, 2684}}, ... | ||
{{Navbox fractional-octave}} | |||
[[Category:61edo]] | |||