61st-octave temperaments

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, ...