Father family: Difference between revisions
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= Father = | = Father = | ||
Subgroup: 2.3.5 | |||
[[Comma list]]: 16/15 | |||
[[Mapping]]: [{{val| 1 0 4 }}, {{val| 0 1 -1 }}] | |||
[[POTE generator]]: ~3/2 = 743.986 | |||
{{Val list|legend=1| 1, 2, 3, 5, 8, 13c, 21bcc }} | {{Val list|legend=1| 1, 2, 3, 5, 8, 13c, 21bcc }} | ||
Badness: 0.0149 | [[Badness]]: 0.0149 | ||
= 7-limit = | = 7-limit = | ||
{{see also| Trienstonic clan #Father }} | {{see also| Trienstonic clan #Father }} | ||
Subgroup: 2.3.5.7 | |||
[[Comma list]]: 16/15, 28/27 | |||
[[Mapping]]: [{{val| 1 0 4 -2 }}, {{val| 0 1 -1 3 }}] | |||
{{Multival|legend=1| 1 -1 3 -4 2 10 }} | |||
[[POTE generator]]: ~3/2 = 742.002 | |||
[[Minimax tuning]]: | |||
* [[7-odd-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 }}] | : [{{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 | : [[Eigenmonzo subgroup]]: 2.7/5 | ||
* 9-odd-limit | * [[9-odd-limit]] | ||
: Eigenmonzo subgroup: 2.9/5 | : Eigenmonzo subgroup: 2.9/5 | ||
{{Val list|legend=1| 2d, 3d, 5, 8d, 13cd, 21bccdd }} | {{Val list|legend=1| 2d, 3d, 5, 8d, 13cd, 21bccdd }} | ||
Badness: 0.0213 | [[Badness]]: 0.0213 | ||
= Mother = | = Mother = | ||
Subgroup: 2.3.5.7 | |||
[[Comma list]]: 16/15, 21/20 | |||
[[Mapping]]: [{{val| 1 0 4 6 }}, {{val| 0 1 -1 -2 }}] | |||
{{Multival|legend=1| 1 -1 -2 -4 -6 -2 }} | |||
[[POTE generator]]: ~3/2 = 721.569 | |||
{{Val list|legend=1| 2, 3, 5 }} | {{Val list|legend=1| 2, 3, 5 }} | ||
Badness: 0.0242 | [[Badness]]: 0.0242 | ||
= Pater = | = Pater = | ||
Subgroup: 2.3.5.7 | |||
[[Comma list]]: 16/15, 126/125 | |||
[[Mapping]]: [{{val| 1 0 4 11 }}, {{val| 0 1 -1 -5 }}] | |||
{{Multival|legend=1| 1 -1 -5 -4 -11 -9 }} | |||
[[POTE generator]]: ~3/2 = 753.113 | |||
{{Val list|legend=1| 3, 5d, 8d, 27bbccdd, 35bbbcccddd }} | {{Val list|legend=1| 3, 5d, 8d, 27bbccdd, 35bbbcccddd }} | ||
Badness: 0.0530 | [[Badness]]: 0.0530 | ||
= Walid = | = Walid = | ||
Subgroup: 2.3.5.7 | |||
[[Comma list]]: 16/15, 50/49 | |||
[[Mapping]]: [{{val| 2 0 8 9 }}, {{val| 0 1 -1 -1 }}] | |||
{{Multival|legend=1| 2 -2 -2 -8 -9 1 }} | |||
[[POTE generator]]: ~3/2 = 749.415 | |||
{{Val list|legend=1| 2, 6, 8d }} | {{Val list|legend=1| 2, 6, 8d }} | ||
Badness: 0.0490 | [[Badness]]: 0.0490 | ||
= Baba = | = Baba = | ||
Subgroup: 2.3.5.7 | Subgroup: 2.3.5.7 | ||
Comma list: 16/15, 49/45 | [[Comma list]]: 16/15, 49/45 | ||
[[Mapping]]: [{{val| 1 0 4 2 }}, {{val| 0 2 -2 1 }}] | |||
[[POTE generator]]: ~8/7 = 226.704 | |||
{{Multival|legend=1| 2 -2 1 -8 -4 8 }} | |||
{{Val list|legend=1| 5, 11b, 16bc }} | {{Val list|legend=1| 5, 11b, 16bc }} | ||
Badness: 0.0443 | [[Badness]]: 0.0443 | ||
= Quint = | = Quint = | ||
Subgroup: 2.3.5.7 | |||
[[Comma list]]: 16/15, 27/25 | |||
[[Mapping]]: [{{val| 5 8 12 0 }}, {{val| 0 0 0 -1 }}] | |||
{{Multival|legend=1| 0 0 5 0 8 12 }} | |||
[[POTE generator]]: ~8/7 = 182.097 | |||
{{Val list|legend=1| 5, 15ccd }} | {{Val list|legend=1| 5, 15ccd }} | ||
Badness: 0.0483 | [[Badness]]: 0.0483 | ||
[[Category:Theory]] | [[Category:Theory]] | ||
| Line 209: | Line 123: | ||
[[Category:Father]] | [[Category:Father]] | ||
[[Category:Rank 2]] | [[Category:Rank 2]] | ||
Revision as of 10:05, 27 March 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
Subgroup: 2.3.5
Comma list: 16/15
Mapping: [⟨1 0 4], ⟨0 1 -1]]
POTE generator: ~3/2 = 743.986
Badness: 0.0149
7-limit
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 ]]
POTE generator: ~3/2 = 742.002
- [[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
- Eigenmonzo subgroup: 2.9/5
Badness: 0.0213
Mother
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 ]]
POTE generator: ~3/2 = 721.569
Badness: 0.0242
Pater
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 ]]
POTE generator: ~3/2 = 753.113
Badness: 0.0530
Walid
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 ]]
POTE generator: ~3/2 = 749.415
Badness: 0.0490
Baba
Subgroup: 2.3.5.7
Comma list: 16/15, 49/45
Mapping: [⟨1 0 4 2], ⟨0 2 -2 1]]
POTE generator: ~8/7 = 226.704
Wedgie: ⟨⟨ 2 -2 1 -8 -4 8 ]]
Badness: 0.0443
Quint
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 ]]
POTE generator: ~8/7 = 182.097
Badness: 0.0483