Dimipent family

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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: 648/625

Mapping: [4 0 3], 0 1 1]]

POTE generator: ~3/2 = 699.507

Vals4, 8, 12

Badness: 0.047231

Diminished

See also: Jubilismic clan #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]]

POTE generator: ~3/2 = 699.523

Vals4, 8d, 12

Badness: 0.022401

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]]

POTE generator: ~7/6 = 252.555

Vals4, 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]]

POTE generator: ~7/6 = 251.658

Vals: 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]]

POTE generator: ~7/6 = 252.225

Vals: 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]]

POTE generator: ~3/2 = 707.014

Vals8d, 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]]

POTE generator: ~3/2 = 706.645

Vals: 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]]

POTE generator: ~3/2 = 707.376

Vals: 8d, 24, 32cf, 56cf

Badness: 0.030597