Diminished family: Difference between revisions
m Moving from Category:Temperament family to Category:Temperament families using Cat-a-lot |
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POTE generator: ~7/6 = 251.658 | POTE generator: ~7/6 = 251.658 | ||
Optimal GPV sequence: {{Val list| 4e, 20ce, 24, 76cdde }} | |||
Badness: 0.056576 | Badness: 0.056576 | ||
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POTE generator: ~7/6 = 252.225 | POTE generator: ~7/6 = 252.225 | ||
Optimal GPV sequence: {{Val list| 4ef, 20cef, 24, 52de, 76cdde }} | |||
Badness: 0.039030 | Badness: 0.039030 | ||
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POTE generator: ~3/2 = 706.645 | POTE generator: ~3/2 = 706.645 | ||
Optimal GPV sequence: {{Val list| 8d, 24, 32c, 56c }} | |||
Badness: 0.047598 | Badness: 0.047598 | ||
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POTE generator: ~3/2 = 707.376 | POTE generator: ~3/2 = 707.376 | ||
Optimal GPV sequence: {{Val list| 8d, 24, 32cf, 56cf }} | |||
Badness: 0.030597 | Badness: 0.030597 | ||
Revision as of 12:46, 3 March 2022
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
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 ]]
POTE generator: ~3/2 = 699.523
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
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
Optimal GPV sequence: Template:Val list
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
Optimal GPV sequence: Template:Val list
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
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]]
POTE generator: ~3/2 = 706.645
Optimal GPV sequence: Template:Val list
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
Optimal GPV sequence: Template:Val list
Badness: 0.030597