Dimipent family
The dimipent family tempers out the major diesis aka diminished comma, 648/625, the amount by which four 6/5 minor thirds exceed an octave, and so identifies the minor third with the quarter-octave. Hence it has the same 300-cent 6/5-approximations as 12edo.
Dimipent
Subgroup: 2.3.5
Comma list: 648/625
Mapping: [⟨4 0 3], ⟨0 1 1]]
Optimal tuning (POTE): ~6/5 = 1\4, ~3/2 = 699.507
Optimal ET sequence: 4, 8, 12
Badness: 0.047231
Diminished
Subgroup: 2.3.5.7
Comma list: 36/35, 50/49
Mapping: [⟨4 0 3 5], ⟨0 1 1 1]]
Wedgie: ⟨⟨4 4 4 -3 -5 -2]]
Optimal tuning (POTE): ~6/5 = 1\4, ~3/2 = 699.523
Optimal ET sequence: 4, 8d, 12
Badness: 0.022401
11-limit
Subgroup: 2.3.5.7.11
Comma list: 36/35, 50/49, 56/55
Mapping: [⟨4 0 3 5 14], ⟨0 1 1 1 0]]
Optimal tuning (POTE): ~6/5 = 1\4, ~3/2 = 709.109
Optimal ET sequence: 4, 8d, 12, 32cddee, 44cddeee
Badness: 0.022132
Scales: diminished12
13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 36/35, 40/39, 50/49, 66/65
Mapping: [⟨4 0 3 5 14 15], ⟨0 1 1 1 0 0]]
Optimal tuning (POTE): ~6/5 = 1\4, ~3/2 = 713.773
Optimal ET sequence: 4, 8d, 12f, 20cdef
Badness: 0.019509
Scales: diminished12
Demolished
Subgroup: 2.3.5.7.11
Comma list: 36/35, 45/44, 50/49
Mapping: [⟨4 0 3 5 -5], ⟨0 1 1 1 3]]
Optimal tuning (POTE): ~6/5 = 1\4, ~3/2 = 689.881
Optimal ET sequence: 12, 28, 40de
Badness: 0.026574
Cohedim
This temperament has been documented in Graham Breed's temperament finder as hemidim, the same name as 11-limit 4e & 24 and 13-limit 4ef & 24. For 11-limit 8bce & 12 temperament, cohedim arguably makes more sense.
Subgroup: 2.3.5.7.11
Comma list: 36/35, 50/49, 125/121
Mapping: [⟨4 1 4 6 6], ⟨0 2 2 2 3]]
Mapping generators: ~6/5, ~11/7
Optimal tuning (POTE): ~6/5 = 1\4, ~12/11 = 101.679
Badness: 0.054965
13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 36/35, 50/49, 66/65, 125/121
Mapping: [⟨4 1 4 6 6 7], ⟨0 2 2 2 3 3]]
Optimal tuning (POTE): ~6/5 = 1\4, ~12/11 = 102.299
Optimal ET sequence: 8bcef, 12f
Badness: 0.041707
Hemidim
Subgroup: 2.3.5.7
Comma list: 49/48, 648/625
Mapping: [⟨4 0 3 8], ⟨0 2 2 1]]
Wedgie: ⟨⟨8 8 4 -6 -16 -13]]
Optimal tuning (POTE): ~6/5 = 1\4, ~7/6 = 252.555
Optimal ET sequence: 4, 20c, 24, 52d, 76cdd
Badness: 0.086378
11-limit
Subgroup: 2.3.5.7.11
Comma list: 49/48, 77/75, 243/242
Mapping: [⟨4 0 3 8 -2], ⟨0 2 2 1 5]]
Optimal tuning (POTE): ~6/5 = 1\4, ~7/6 = 251.658
Optimal ET sequence: 4e, 20ce, 24, 76cdde
Badness: 0.056576
13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 49/48, 66/65, 77/75, 243/242
Mapping: [⟨4 0 3 8 -2 -1], ⟨0 2 2 1 5 5]]
Optimal tuning (POTE): ~6/5 = 1\4, ~7/6 = 252.225
Optimal ET sequence: 4ef, 20cef, 24, 52de, 76cdde
Badness: 0.039030
Semidim
Subgroup: 2.3.5.7
Comma list: 245/243, 392/375
Mapping: [⟨8 0 6 -3], ⟨0 1 1 2]]
Wedgie: ⟨⟨8 8 16 -6 3 15]]
Optimal tuning (POTE): ~15/14 = 1\8, ~3/2 = 707.014
Optimal ET sequence: 8d, 24, 32c, 56c
Badness: 0.107523
11-limit
Subgroup: 2.3.5.7.11
Comma list: 56/55, 77/75, 245/243
Mapping: [⟨8 0 6 -3 15], ⟨0 1 1 2 1]]
Optimal tuning (POTE): ~12/11 = 1\8, ~3/2 = 706.645
Optimal ET sequence: 8d, 24, 32c, 56c
Badness: 0.047598
13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 56/55, 66/65, 77/75, 507/500
Mapping: [⟨8 0 6 -3 15 17], ⟨0 1 1 2 1 1]]
Optimal tuning (POTE): ~12/11 = 1\8, ~3/2 = 707.376
Optimal ET sequence: 8d, 24, 32cf, 56cf
Badness: 0.030597