Father family: Difference between revisions
+mother copied from archytas clan |
m Some cleanup |
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| Line 2: | Line 2: | ||
= Father = | = Father = | ||
Comma: 16/15 | Comma list: 16/15 | ||
POTE generator: ~3/2 = 743.986 | POTE generator: ~3/2 = 743.986 | ||
Mapping: [{{val| 1 0 4 }}, {{val| 0 1 -1 }}] | |||
{{Val list|legend=1| 1, 2, 3, 5, 8, 10c, 11b, 13c, 21bc }} | |||
Badness: 0.0149 | Badness: 0.0149 | ||
| Line 15: | Line 15: | ||
{{see also| Trienstonic clan #Father }} | {{see also| Trienstonic clan #Father }} | ||
Comma list: 16/15, 28/27 | |||
[[POTE generator]]: ~3/2 = 742.002 | |||
[ | Mapping: [{{val| 1 0 4 -2 }}, {{val| 0 1 -1 3 }}] | ||
Wedgie: {{wedgie| 1 -1 3 -4 2 10 }} | |||
9-limit | Minimax tuning: | ||
* 7-odd-limit | |||
: [{{monzo| 1 0 0 0 }}, {{monzo| 3/2 0 -1/4 1/4 }}, {{monzo| 5/2 0 1/4 -1/4 }}, {{monzo| 5/2 0 -3/4 3/4 }}] | |||
: [[Eigenmonzo subgroup]]: 2.7/5 | |||
* 9-odd-limit | |||
: Eigenmonzo subgroup: 2.9/5 | |||
{{Val list|legend=1| 5, 8d, 13cd, 21bcd }} | |||
Badness: 0.0213 | Badness: 0.0213 | ||
= Mother = | = Mother = | ||
Comma list: 16/15, 21/20 | |||
[[POTE generator]]: 721.569 | [[POTE generator]]: ~3/2 = 721.569 | ||
Mapping: [{{val| 1 0 4 6 }}, {{val| 0 1 -1 -2 }}] | |||
Wedgie: | Wedgie: {{wedgie| 1 -1 -2 -4 -6 -2 }} | ||
{{ | {{Val list|legend=1| 5, 148, 153 }} | ||
Badness: 0.0242 | Badness: 0.0242 | ||
| Line 104: | Line 103: | ||
[[Category:Father]] | [[Category:Father]] | ||
[[Category:Rank 2]] | [[Category:Rank 2]] | ||
{{todo|review|improve readability}} | |||
Revision as of 15:01, 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
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