Father family: Difference between revisions
m Some cleanup |
m Cleanup +1 |
||
| Line 48: | Line 48: | ||
= Pater = | = Pater = | ||
Comma list: 16/15, 126/125 | |||
POTE generator: ~3/2 = 753.113 | POTE generator: ~3/2 = 753.113 | ||
Mapping: [{{val| 1 0 4 11 }}, {{val| 0 1 -1 -5 }}] | |||
Wedgie: | Wedgie: {{wedgie| 1 -1 -5 -4 -11 -9 }} | ||
{{Val list|legend=1| 3, 11b, 16bcd, 27bcd }} | |||
Badness: 0.0530 | Badness: 0.0530 | ||
= Walid = | = Walid = | ||
Comma list: 16/15, 50/49 | |||
POTE generator: ~3/2 = 749.415 | POTE generator: ~3/2 = 749.415 | ||
Mapping: [{{val| 2 0 8 9 }}, {{val| 0 1 -1 -1 }}] | |||
Wedgie: | Wedgie: {{wedgie| 2 -2 -2 -8 -9 1 }} | ||
{{Val list|legend=1| 2, 6, 10cd, 14bd, 16bcd }} | |||
Badness: 0.0490 | Badness: 0.0490 | ||
= Baba = | = Baba = | ||
Comma list: 16/15, 49/45 | |||
POTE generator: ~8/7 = 226.704 | POTE generator: ~8/7 = 226.704 | ||
Mapping: [{{val| 1 0 4 2 }}, {{val| 0 2 -2 1 }}] | |||
Wedgie: | Wedgie: {{wedgie| 2 -2 1 -8 -4 8 }} | ||
{{Val list|legend=1| 1, 5, 11b, 16bc }} | |||
Badness: 0.0443 | Badness: 0.0443 | ||
= Quint = | = Quint = | ||
Comma list: 16/15, 27/25 | |||
POTE generator: ~8/7 = 182.097 | POTE generator: ~8/7 = 182.097 | ||
Mapping: [{{val| 5 8 12 0 }}, {{val| 0 0 0 -1 }}] | |||
Wedgie: | Wedgie: {{wedgie| 0 0 5 0 8 12 }} | ||
{{Val list|legend=1| 5, 15cd }} | |||
Badness: 0.0483 | Badness: 0.0483 | ||
Revision as of 15:09, 10 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
Comma list: 16/15
POTE generator: ~3/2 = 743.986
Mapping: [⟨1 0 4], ⟨0 1 -1]]
Badness: 0.0149
7-limit
Comma list: 16/15, 28/27
POTE generator: ~3/2 = 742.002
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
Comma list: 16/15, 21/20
POTE generator: ~3/2 = 721.569
Mapping: [⟨1 0 4 6], ⟨0 1 -1 -2]]
Wedgie: ⟨⟨1 -1 -2 -4 -6 -2]]
Badness: 0.0242
Pater
Comma list: 16/15, 126/125
POTE generator: ~3/2 = 753.113
Mapping: [⟨1 0 4 11], ⟨0 1 -1 -5]]
Wedgie: ⟨⟨1 -1 -5 -4 -11 -9]]
Badness: 0.0530
Walid
Comma list: 16/15, 50/49
POTE generator: ~3/2 = 749.415
Mapping: [⟨2 0 8 9], ⟨0 1 -1 -1]]
Wedgie: ⟨⟨2 -2 -2 -8 -9 1]]
Badness: 0.0490
Baba
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
Comma list: 16/15, 27/25
POTE generator: ~8/7 = 182.097
Mapping: [⟨5 8 12 0], ⟨0 0 0 -1]]
Wedgie: ⟨⟨0 0 5 0 8 12]]
Badness: 0.0483