61st-octave temperaments: Difference between revisions
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{{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]]. | |||
==Promethium== | == Dipromethium == | ||
Promethium | Subgroup: 2.3.5 | ||
Comma list: {{monzo|-335 122 61}} | |||
Mapping: [{{val|61 0 335}}, {{val|0 1 -2}}] | |||
Optimal tuning (CTE): ~3/2 = 701.936 | |||
Supporting ETs: {{EDOs|183, 976, 1159, 1342, 1525, 1769, 1891}}, ... | |||
== 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. | |||
Subgroup: 2.3.5.7.11.13 | Subgroup: 2.3.5.7.11.13 | ||
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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 | ||
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{{Optimal ET sequence|legend=1|183, 2684}}, ... | {{Optimal ET sequence|legend=1|183, 2684}}, ... | ||
{{Navbox fractional-octave}} | |||
[[Category:61edo]] | |||
Latest revision as of 03:44, 14 February 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
Subgroup: 2.3.5
Comma list: [-335 122 61⟩
Mapping: [⟨61 0 335], ⟨0 1 -2]]
Optimal tuning (CTE): ~3/2 = 701.936
Supporting ETs: 183, 976, 1159, 1342, 1525, 1769, 1891, ...
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.
Subgroup: 2.3.5.7.11.13
Comma list: 10648/10647, 196625/196608, 4100625/4100096, 204800000/204788493
Mapping: [⟨61 0 335 703 66 -161], ⟨0 2 -4 -11 3 8]]
Mapping generators: ~2025/2002 = 1\61, ~6875/3969 = 950.970
Optimal tuning (CTE): ~6875/3969 = 950.970
17-limit
Subgroup: 2.3.5.7.11.13.17
Comma list: 14400/14399, 37180/37179, 121875/121856, 140800/140777, 3536379/3536000
Mapping: [⟨61 0 335 703 66 -161 201], ⟨0 2 -4 -11 3 8 1]]
Mapping generators: ~2025/2002 = 1\61, ~11907/6875 = 950.970
Optimal tuning (CTE): ~11907/6875 = 950.970
Optimal ET sequence: 183, 2684, ...