Diminished 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

Comma: 648/625

POTE generator: ~3/2 = 699.507

Map: [<4 0 3|, <0 1 1|]

Optimal ET sequence: 4, 8, 12

Badness: 0.047231

Diminished

See also: Jubilismic clan

Comma list: 36/35, 50/49

POTE generator: ~3/2 = 699.523

Map: [<4 0 3 5|, <0 1 1 1|]

Optimal ET sequence: 4, 8d, 12

Badness: 0.022401

Hemidim

Commas: 49/48, 648/625

POTE generator: ~8/7 = 252.555

Map: [<4 0 3 8|, <0 2 2 1|]

Wedgie: <<8 8 4 -6 -16 -13||

EDOs: 24, 52d, 76cd

Badness: 0.0864

11-limit

Commas: 49/48, 77/75, 243/242

POTE generator: ~8/7 = 251.658

Map: [<4 0 3 8 -2|, <0 2 2 1 5|]

EDOs: 24, 76cde

Badness: 0.0566

13-limit

Commas: 49/48, 66/65, 77/75, 648/625

POTE generator: ~8/7 = 252.225

Map: [<4 0 3 8 -2 -1|, <0 2 2 1 5 5|]

EDOs: 24, 52de, 76cde

Badness: 0.039

Semidim

Commas: 245/243, 392/375

POTE generator4: ~3/2 = 707.014

Map: [<8 0 6 -3|, <0 1 1 2|]

Wedgie: <<8 8 16 -6 3 15||

EDOs: 24, 32c, 56c

Badness: 0.1075

11-limit

Commas: 56/55, 77/75, 245/243

POTE generator: ~3/2 = 706.645

Map: [<8 0 6 -3 15|, <0 1 1 2 1|]

EDOs: 24, 32c, 56c

Badness: 0.0476

13-limit

Commas: 56/55, 66/65, 77/75, 507/500

POTE generator: ~3/2 = 707.376

Map: [<8 0 6 -3 15 17|, <0 1 1 2 1 1|]

EDOs: 24, 32cf, 56cf

Badness: 0.0306