61st-octave temperaments: Difference between revisions
61st |
No edit summary |
||
| Line 1: | Line 1: | ||
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 == | |||
==Promethium== | ==Promethium== | ||
Revision as of 14:36, 15 June 2023
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
Promethium
Promethium tempers out the dipromethia 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, ...