Hemimage family: Difference between revisions
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m Cleanup (1/2) |
m Cleanup (2/2) |
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| Line 5: | Line 5: | ||
[[Comma list]]: 10976/10935 | [[Comma list]]: 10976/10935 | ||
[[Mapping]]: [{{val| 1 0 2 -1 }}, {{val| 0 1 2 3 }}, {{val| 0 0 -3 -1 }}] | |||
Mapping generators: ~2, ~3, ~27/14 | |||
[[Minimax tuning]]: | [[Minimax tuning]]: | ||
* [[7-odd-limit]] | * [[7-odd-limit]] | ||
: [|1 0 0 0 | : [{{monzo| 1 0 0 0 }}, {{monzo| 5/8 1/8 -1/8 3/8 }}, {{monzo| 5/8 -7/8 7/8 3/8 }}, {{monzo| 0 0 0 1 }}] | ||
: [[Eigenmonzo]]s: 2, 8/7, 6/5 | : [[Eigenmonzo]]s: 2, 8/7, 6/5 | ||
* [[9-odd-limit]] | * [[9-odd-limit]] | ||
: [|1 0 0 0 | : [{{monzo| 1 0 0 0 }}, {{monzo| 5/9 2/9 -1/9 1/3 }}, {{monzo| 10/9 -14/9 7/9 2/3 }}, {{monzo| 0 0 0 1 }}] | ||
: [[Eigenmonzo]]s: 2, 10/9, 8/7 | : [[Eigenmonzo]]s: 2, 10/9, 8/7 | ||
{{Val list|legend=1| 14, 19, 41, 58, 77, 80, 99, 118, 140, 217, 316, 338, 357, 415, 456, 654, 695 }} | {{Val list|legend=1| 14, 19, 41, 58, 77, 80, 99, 118, 140, 217, 316, 338, 357, 415, 456, 654, 695 }} | ||
| Line 29: | Line 29: | ||
[[Comma list]]: 540/539, 896/891 | [[Comma list]]: 540/539, 896/891 | ||
Mapping: [ | [[Mapping]]: [{{val| 1 0 2 -1 6 }}, {{val| 0 1 2 3 -1 }}, {{val| 0 0 -3 -1 -1 }}] | ||
[[Minimax tuning]]: | [[Minimax tuning]]: | ||
* [[11-odd-limit]] | * [[11-odd-limit]] | ||
: [|1 0 0 0 0 | : [{{monzo| 1 0 0 0 0 }}, {{monzo| 16/11 6/11 1/11 0 -3/11 }}, {{monzo| 0 0 1 0 0 }}, {{monzo| 19/11 14/11 6/11 0 -7/11 }}, {{monzo| 32/11 -10/11 2/11 0 5/11 }}] | ||
: [[Eigenmonzo]]s: 2, 11/9, 5/4 | : [[Eigenmonzo]]s: 2, 11/9, 5/4 | ||
{{Val list|legend=1| 19, 22, 41, 58, 80, 121 }} | {{Val list|legend=1| 19, 22, 41, 58, 80, 121 }} | ||
Badness: 0.702 × 10<sup>-3</sup> | [[Badness]]: 0.702 × 10<sup>-3</sup> | ||
== 13-limit == | == 13-limit == | ||
| Line 45: | Line 45: | ||
Comma list: 352/351, 364/363, 540/539 | Comma list: 352/351, 364/363, 540/539 | ||
Mapping: [ | Mapping: [{{val| 1 0 2 -1 6 11 }}, {{val| 0 1 2 3 -1 -4 }}, {{val| 0 0 -3 -1 -1 -1 }}] | ||
Vals: {{Val list| 22, 41, 58, 80, 121 }} | Vals: {{Val list| 22, 41, 58, 80, 121 }} | ||
| Line 56: | Line 56: | ||
Comma list: 144/143, 196/195, 729/728 | Comma list: 144/143, 196/195, 729/728 | ||
Mapping: [ | Mapping: [{{val| 1 0 2 -1 6 -2 }}, {{val| 0 1 2 3 -1 3 }}, {{val| 0 0 -3 -1 -1 1 }}] | ||
Vals: {{Val list| 19, 36, 41, 58 }} | Vals: {{Val list| 19, 36, 41, 58 }} | ||
| Line 67: | Line 67: | ||
[[Comma list]]: 441/440, 10976/10935 | [[Comma list]]: 441/440, 10976/10935 | ||
[[Mapping]]: [ | [[Mapping]]: [{{val| 1 0 2 -1 -7 }}, {{val| 0 1 2 3 6 }}, {{val| 0 0 -3 -1 1 }}] | ||
[[Minimax tuning]]: | [[Minimax tuning]]: | ||
: [|1 0 0 0 0 | * [[11-odd-limit]] | ||
: [{{monzo| 1 0 0 0 0 }}, {{monzo| 19/12 -2/3 1/12 0 1/4 }}, {{monzo| 19/6 -10/3 7/6 0 1/2 }}, {{monzo| 37/12 -8/3 7/12 0 3/4 }}, {{monzo| 19/6 -10/3 1/6 0 3/2 }}] | |||
: [[Eigenmonzo]]s: 2, 10/9, 11/9 | : [[Eigenmonzo]]s: 2, 10/9, 11/9 | ||
{{Val list|legend=1| 41, 58, 118 | {{Val list|legend=1| 41, 58, 118, 159, 217, 335 }} | ||
[[Badness]]: 0.936 × 10<sup>-3</sup> | [[Badness]]: 0.936 × 10<sup>-3</sup> | ||
Revision as of 08:23, 10 May 2021
The hemimage family of temperaments are rank-3 temperaments tempering out 10976/10935.
Hemimage
Subgroup: 2.3.5.7
Comma list: 10976/10935
Mapping: [⟨1 0 2 -1], ⟨0 1 2 3], ⟨0 0 -3 -1]]
Mapping generators: ~2, ~3, ~27/14
- [[1 0 0 0⟩, [5/8 1/8 -1/8 3/8⟩, [5/8 -7/8 7/8 3/8⟩, [0 0 0 1⟩]
- Eigenmonzos: 2, 8/7, 6/5
- [[1 0 0 0⟩, [5/9 2/9 -1/9 1/3⟩, [10/9 -14/9 7/9 2/3⟩, [0 0 0 1⟩]
- Eigenmonzos: 2, 10/9, 8/7
Badness: 0.199 × 10-3
Projection pair: 5 10976/2187 to 2.3.7
Uni
Subgroup: 2.3.5.7.11
Comma list: 540/539, 896/891
Mapping: [⟨1 0 2 -1 6], ⟨0 1 2 3 -1], ⟨0 0 -3 -1 -1]]
- [[1 0 0 0 0⟩, [16/11 6/11 1/11 0 -3/11⟩, [0 0 1 0 0⟩, [19/11 14/11 6/11 0 -7/11⟩, [32/11 -10/11 2/11 0 5/11⟩]
- Eigenmonzos: 2, 11/9, 5/4
Badness: 0.702 × 10-3
13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 352/351, 364/363, 540/539
Mapping: [⟨1 0 2 -1 6 11], ⟨0 1 2 3 -1 -4], ⟨0 0 -3 -1 -1 -1]]
Vals: Template:Val list
Badness: 1.06 × 10-3
Tin
Subgroup: 2.3.5.7.11.13
Comma list: 144/143, 196/195, 729/728
Mapping: [⟨1 0 2 -1 6 -2], ⟨0 1 2 3 -1 3], ⟨0 0 -3 -1 -1 1]]
Vals: Template:Val list
Badness: 1.07 × 10-3
Turan
Subgroup: 2.3.5.7.11
Comma list: 441/440, 10976/10935
Mapping: [⟨1 0 2 -1 -7], ⟨0 1 2 3 6], ⟨0 0 -3 -1 1]]
- [[1 0 0 0 0⟩, [19/12 -2/3 1/12 0 1/4⟩, [19/6 -10/3 7/6 0 1/2⟩, [37/12 -8/3 7/12 0 3/4⟩, [19/6 -10/3 1/6 0 3/2⟩]
- Eigenmonzos: 2, 10/9, 11/9
Badness: 0.936 × 10-3