Diminished family: Difference between revisions
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=Dimipent= | =Dimipent= | ||
Subgroup: 2.3.5 | |||
[[Comma]]: 648/625 | [[Comma]]: 648/625 | ||
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=Diminished= | =Diminished= | ||
{{see also|Jubilismic clan}} | {{see also|Jubilismic clan}} | ||
Subgroup: 2.3.5.7 | |||
[[Comma list]]: 36/35, 50/49 | [[Comma list]]: 36/35, 50/49 | ||
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[[Map]]: [<4 0 3 5|, <0 1 1 1|] | [[Map]]: [<4 0 3 5|, <0 1 1 1|] | ||
Wedgie: <<4 4 4 -3 -5 -2|| | |||
{{Vals|legend=1| 4, 8d, 12 }} | {{Vals|legend=1| 4, 8d, 12 }} | ||
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=Hemidim= | =Hemidim= | ||
Subgroup: 2.3.5.7 | |||
[[Comma list]]: 49/48, 648/625 | |||
POTE generator: ~8/7 = 252.555 | [[POTE tuning|POTE generator]]: ~8/7 = 252.555 | ||
Map: [<4 0 3 8|, <0 2 2 1|] | [[Map]]: [<4 0 3 8|, <0 2 2 1|] | ||
Wedgie: <<8 8 4 -6 -16 -13|| | Wedgie: <<8 8 4 -6 -16 -13|| | ||
{{Vals|legend=1| 24, 52d, 76cd }} | |||
Badness: 0.0864 | [[Badness]]: 0.0864 | ||
==11-limit== | ==11-limit== | ||
Subgroup: 2.3.5.7.11 | |||
Comma list: 49/48, 77/75, 243/242 | |||
POTE generator: ~8/7 = 251.658 | POTE generator: ~8/7 = 251.658 | ||
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Map: [<4 0 3 8 -2|, <0 2 2 1 5|] | Map: [<4 0 3 8 -2|, <0 2 2 1 5|] | ||
{{Vals|legend=1| 24, 76cde }} | |||
Badness: 0.0566 | Badness: 0.0566 | ||
==13-limit== | ==13-limit== | ||
Subgroup: 2.3.5.7.11.13 | |||
Comma list: 49/48, 66/65, 77/75, 648/625 | |||
POTE generator: ~8/7 = 252.225 | POTE generator: ~8/7 = 252.225 | ||
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Map: [<4 0 3 8 -2 -1|, <0 2 2 1 5 5|] | Map: [<4 0 3 8 -2 -1|, <0 2 2 1 5 5|] | ||
{{Vals|legend=1| 24, 52de, 76cde }} | |||
Badness: 0.039 | Badness: 0.039 | ||
=Semidim= | =Semidim= | ||
Subgroup: 2.3.5.7 | |||
[[Comma list]]: 245/243, 392/375 | |||
Map: [<8 0 6 -3|, <0 1 1 2|] | [[POTE tuning|POTE generator]]: ~3/2 = 707.014 | ||
[[Map]]: [<8 0 6 -3|, <0 1 1 2|] | |||
Wedgie: <<8 8 16 -6 3 15|| | Wedgie: <<8 8 16 -6 3 15|| | ||
{{Vals|legend=1| 24, 32c, 56c }} | |||
Badness: 0.1075 | [[Badness]]: 0.1075 | ||
==11-limit== | ==11-limit== | ||
Subgroup: 2.3.5.7.11 | |||
Comma list: 56/55, 77/75, 245/243 | |||
POTE generator: ~3/2 = 706.645 | POTE generator: ~3/2 = 706.645 | ||
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Map: [<8 0 6 -3 15|, <0 1 1 2 1|] | Map: [<8 0 6 -3 15|, <0 1 1 2 1|] | ||
{{Vals|legend=1| 24, 32c, 56c }} | |||
Badness: 0.0476 | Badness: 0.0476 | ||
==13-limit== | ==13-limit== | ||
Subgroup: 2.3.5.7.11.13 | |||
Comma list: 56/55, 66/65, 77/75, 507/500 | |||
POTE generator: ~3/2 = 707.376 | POTE generator: ~3/2 = 707.376 | ||
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Map: [<8 0 6 -3 15 17|, <0 1 1 2 1 1|] | Map: [<8 0 6 -3 15 17|, <0 1 1 2 1 1|] | ||
{{Vals|legend=1| 24, 32cf, 56cf }} | |||
Badness: 0.0306 | Badness: 0.0306 | ||
Revision as of 03:06, 3 April 2021
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
POTE generator: ~3/2 = 699.507
Map: [<4 0 3|, <0 1 1|]
Optimal ET sequence: 4, 8, 12
Badness: 0.047231
Diminished
Subgroup: 2.3.5.7
Comma list: 36/35, 50/49
POTE generator: ~3/2 = 699.523
Map: [<4 0 3 5|, <0 1 1 1|]
Wedgie: <<4 4 4 -3 -5 -2||
Optimal ET sequence: 4, 8d, 12
Badness: 0.022401
Hemidim
Subgroup: 2.3.5.7
Comma list: 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||
Optimal ET sequence: 24, 52d, 76cd
Badness: 0.0864
11-limit
Subgroup: 2.3.5.7.11
Comma list: 49/48, 77/75, 243/242
POTE generator: ~8/7 = 251.658
Map: [<4 0 3 8 -2|, <0 2 2 1 5|]
Optimal ET sequence: 24, 76cde
Badness: 0.0566
13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 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|]
Optimal ET sequence: 24, 52de, 76cde
Badness: 0.039
Semidim
Subgroup: 2.3.5.7
Comma list: 245/243, 392/375
POTE generator: ~3/2 = 707.014
Map: [<8 0 6 -3|, <0 1 1 2|]
Wedgie: <<8 8 16 -6 3 15||
Optimal ET sequence: 24, 32c, 56c
Badness: 0.1075
11-limit
Subgroup: 2.3.5.7.11
Comma list: 56/55, 77/75, 245/243
POTE generator: ~3/2 = 706.645
Map: [<8 0 6 -3 15|, <0 1 1 2 1|]
Optimal ET sequence: 24, 32c, 56c
Badness: 0.0476
13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 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|]
Optimal ET sequence: 24, 32cf, 56cf
Badness: 0.0306