Father family: Difference between revisions
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Subgroup: 2.3.5 | |||
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Subgroup: 2.3.5.7 | |||
Comma list: 16/15, 28/27 | Comma list: 16/15, 28/27 | ||
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Comma list: 16/15, 21/20 | Comma list: 16/15, 21/20 | ||
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Comma list: 16/15, 126/125 | Comma list: 16/15, 126/125 | ||
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Subgroup: 2.3.5.7 | |||
Comma list: 16/15, 50/49 | Comma list: 16/15, 50/49 | ||
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Subgroup: 2.3.5.7 | |||
Comma list: 16/15, 49/45 | Comma list: 16/15, 49/45 | ||
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Subgroup: 2.3.5.7 | |||
Comma list: 16/15, 27/25 | Comma list: 16/15, 27/25 | ||
Revision as of 07:42, 13 February 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
Period: 1\1
Optimal (POTE) generator: ~3/2 = 743.986
EDO generators: 3\5, 5\8, 8\13
Scales (Scala files):
7-limit
Period: 1\1
Optimal (POTE) generator: ~3/2 = 742.002
EDO generators: 3\5, 5\8, 8\13
Scales (Scala files):
Subgroup: 2.3.5.7
Comma list: 16/15, 28/27
Mapping: [⟨1 0 4 -2], ⟨0 1 -1 3]]
Wedgie: ⟨⟨1 -1 3 -4 2 10]]
Minimax tuning:
- 7-odd-limit
- [[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-odd-limit
- Eigenmonzo subgroup: 2.9/5
Badness: 0.0213
Mother
Period: 1\1
Optimal (POTE) generator: ~3/2 = 721.569
EDO generators: 3\5
Scales (Scala files):
Subgroup: 2.3.5.7
Comma list: 16/15, 21/20
Mapping: [⟨1 0 4 6], ⟨0 1 -1 -2]]
Wedgie: ⟨⟨1 -1 -2 -4 -6 -2]]
Badness: 0.0242
Pater
Period: 1\1
Optimal (POTE) generator: ~3/2 = 753.113
EDO generators: 5\8
Scales (Scala files):
Subgroup: 2.3.5.7
Comma list: 16/15, 126/125
Mapping: [⟨1 0 4 11], ⟨0 1 -1 -5]]
Wedgie: ⟨⟨1 -1 -5 -4 -11 -9]]
Badness: 0.0530
Walid
Period: 1\1
Optimal (POTE) generator: ~3/2 = 749.415
Scales (Scala files):
Subgroup: 2.3.5.7
Comma list: 16/15, 50/49
Mapping: [⟨2 0 8 9], ⟨0 1 -1 -1]]
Wedgie: ⟨⟨2 -2 -2 -8 -9 1]]
Badness: 0.0490
Baba
Period: 1\1
Optimal (POTE) generator: ~8/7 = 226.704
EDO generators: 1\5, 2\11, 3\16
Scales (Scala files):
Subgroup: 2.3.5.7
Comma list: 16/15, 49/45
POTE generator: ~8/7 = 226.704
Mapping: [⟨1 0 4 2], ⟨0 2 -2 1]]
Wedgie: ⟨⟨2 -2 1 -8 -4 8]]
Badness: 0.0443
Quint
Period: 1\5
Optimal (POTE) generator: ~8/7 = 182.097
EDO generators: 3\15
Scales (Scala files):
Subgroup: 2.3.5.7
Comma list: 16/15, 27/25
Mapping: [⟨5 8 12 0], ⟨0 0 0 -1]]
Wedgie: ⟨⟨0 0 5 0 8 12]]
Badness: 0.0483