Father family: Difference between revisions
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The '''father family''' of temperaments tempers out [[16/15]], the just diatonic semitone. This equates [[4/3]] with [[5/4]], so these are "fourth-thirds", or father, temperaments. | |||
=Father= | = Father = | ||
Comma: 16/15 | Comma: 16/15 | ||
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Badness: 0.0149 | Badness: 0.0149 | ||
= 7-limit = | |||
{{see also| Trienstonic clan #Father }} | |||
Commas: 16/15, 28/27 | Commas: 16/15, 28/27 | ||
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[<1 0 0 0|, <3/2 0 -1/4 1/4|, <5/2 0 1/4 -1/4|, <5/2 0 -3/4 3/4|] | [<1 0 0 0|, <3/2 0 -1/4 1/4|, <5/2 0 1/4 -1/4|, <5/2 0 -3/4 3/4|] | ||
[[ | [[Eigenmonzo subgroup]]: 2.7/5 | ||
9-limit eigenmonzo subgroup: 2.9/5 | 9-limit eigenmonzo subgroup: 2.9/5 | ||
[[ | [[POTE generator]]: 742.002 | ||
Map: [<1 0 4 -2|, <0 1 -1 3|] | Map: [<1 0 4 -2|, <0 1 -1 3|] | ||
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Badness: 0.0213 | Badness: 0.0213 | ||
=Pater= | = Pater = | ||
Commas: 16/15, 126/125 | Commas: 16/15, 126/125 | ||
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Badness: 0.0530 | Badness: 0.0530 | ||
=Walid= | = Walid = | ||
Commas: 16/15, 50/49 | Commas: 16/15, 50/49 | ||
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Badness: 0.0490 | Badness: 0.0490 | ||
=Baba= | = Baba = | ||
Commas: 16/15, 49/45 | Commas: 16/15, 49/45 | ||
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Badness: 0.0443 | Badness: 0.0443 | ||
=Quint= | = Quint = | ||
Commas: 16/15, 27/25 | Commas: 16/15, 27/25 | ||
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Badness: 0.0483 | Badness: 0.0483 | ||
[[Category:Theory]] | |||
[[Category:Temperament family]] | |||
[[Category:Father]] | |||
[[Category:Rank 2]] | |||
Revision as of 15:15, 9 January 2021
The father family of temperaments tempers out 16/15, the just diatonic semitone. This equates 4/3 with 5/4, so these are "fourth-thirds", or father, temperaments.
Father
Comma: 16/15
POTE generator: ~3/2 = 743.986
Map: [<1 0 4|, <0 1 -1|]
EDOs: 1, 2, 3, 5, 8, 10c, 11b, 13c, 21bc
Badness: 0.0149
7-limit
Commas: 16/15, 28/27
7-limit minimax
[<1 0 0 0|, <3/2 0 -1/4 1/4|, <5/2 0 1/4 -1/4|, <5/2 0 -3/4 3/4|]
Eigenmonzo subgroup: 2.7/5
9-limit eigenmonzo subgroup: 2.9/5
POTE generator: 742.002
Map: [<1 0 4 -2|, <0 1 -1 3|]
Wedgie: <<1 -1 3 -4 2 10||
EDOs: 5, 8d, 13cd, 21bcd
Badness: 0.0213
Pater
Commas: 16/15, 126/125
POTE generator: ~3/2 = 753.113
Map: [<1 0 4 11|, <0 1 -1 -5|]
Wedgie: <<1 -1 -5 -4 -11 -9||
EDOs: 3, 11b, 16bcd, 27bcd
Badness: 0.0530
Walid
Commas: 16/15, 50/49
POTE generator: ~3/2 = 749.415
Map: [<2 0 8 9|, <0 1 -1 -1|]
Wedgie: <<2 -2 -2 -8 -9 1||
EDOs: 2, 6, 10cd, 14bd, 16bcd
Badness: 0.0490
Baba
Commas: 16/15, 49/45
POTE generator: ~8/7 = 226.704
Map: [<1 0 4 2|, <0 2 -2 1|]
Wedgie: <<2 -2 1 -8 -4 8||
EDOs: 1, 5, 11b, 16bc
Badness: 0.0443
Quint
Commas: 16/15, 27/25
POTE generator: ~8/7 = 182.097
Map: [<5 8 12 0|, <0 0 0 -1|]
Wedgie: <<0 0 5 0 8 12||
EDOs: 5, 15cd
Badness: 0.0483