Hemimage family: Difference between revisions
Cmloegcmluin (talk | contribs) unchanged interval → unchanged-interval |
Cmloegcmluin (talk | contribs) "optimal GPV sequence" → "optimal ET sequence", per Talk:Optimal_ET_sequence |
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| Line 18: | Line 18: | ||
: [[Eigenmonzo]]s (unchanged-intervals): 2, 10/9, 8/7 | : [[Eigenmonzo]]s (unchanged-intervals): 2, 10/9, 8/7 | ||
{{ | {{Optimal ET sequence|legend=1| 17c, 19, 39d, 41, 58, 77, 80, 99, 217, 239, 338, 357, 456, 695 }} | ||
[[Badness]]: 0.199 × 10<sup>-3</sup> | [[Badness]]: 0.199 × 10<sup>-3</sup> | ||
| Line 36: | Line 36: | ||
: [[Eigenmonzo]]s (unchanged-intervals): 2, 11/9, 5/4 | : [[Eigenmonzo]]s (unchanged-intervals): 2, 11/9, 5/4 | ||
{{ | {{Optimal ET sequence|legend=1| 17c, 19, 22, 39d, 41, 58, 80, 99e, 121, 179e, 220e, 300bdee, 399bcdeee }} | ||
[[Badness]]: 0.702 × 10<sup>-3</sup> | [[Badness]]: 0.702 × 10<sup>-3</sup> | ||
| Line 47: | Line 47: | ||
Mapping: [{{val| 1 0 2 -1 6 11 }}, {{val| 0 1 2 3 -1 -4 }}, {{val| 0 0 -3 -1 -1 -1 }}] | Mapping: [{{val| 1 0 2 -1 6 11 }}, {{val| 0 1 2 3 -1 -4 }}, {{val| 0 0 -3 -1 -1 -1 }}] | ||
{{Optimal ET sequence|legend=1| 17c, 22, 36f, 39d, 41, 58, 80, 99ef, 121, 179ef, 300bdeef }} | |||
Badness: 1.06 × 10<sup>-3</sup> | Badness: 1.06 × 10<sup>-3</sup> | ||
| Line 58: | Line 58: | ||
Mapping: [{{val| 1 0 2 -1 6 -2 }}, {{val| 0 1 2 3 -1 3 }}, {{val| 0 0 -3 -1 -1 1 }}] | Mapping: [{{val| 1 0 2 -1 6 -2 }}, {{val| 0 1 2 3 -1 3 }}, {{val| 0 0 -3 -1 -1 1 }}] | ||
{{Optimal ET sequence|legend=1| 17c, 19, 22f, 36, 39df, 41, 58, 99ef, 157eff }} | |||
Badness: 1.07 × 10<sup>-3</sup> | Badness: 1.07 × 10<sup>-3</sup> | ||
| Line 74: | Line 74: | ||
: [[Eigenmonzo]]s (unchanged-intervals): 2, 10/9, 11/9 | : [[Eigenmonzo]]s (unchanged-intervals): 2, 10/9, 11/9 | ||
{{ | {{Optimal ET sequence|legend=1| 17c, 19, 36, 39d, 41, 58, 99e, 118, 159, 217, 335 }} | ||
[[Badness]]: 0.936 × 10<sup>-3</sup> | [[Badness]]: 0.936 × 10<sup>-3</sup> | ||
Revision as of 18:20, 7 May 2023
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 (unchanged-intervals): 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 (unchanged-intervals): 2, 10/9, 8/7
Optimal ET sequence: 17c, 19, 39d, 41, 58, 77, 80, 99, 217, 239, 338, 357, 456, 695
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 (unchanged-intervals): 2, 11/9, 5/4
Optimal ET sequence: 17c, 19, 22, 39d, 41, 58, 80, 99e, 121, 179e, 220e, 300bdee, 399bcdeee
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]]
Optimal ET sequence: 17c, 22, 36f, 39d, 41, 58, 80, 99ef, 121, 179ef, 300bdeef
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]]
Optimal ET sequence: 17c, 19, 22f, 36, 39df, 41, 58, 99ef, 157eff
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 (unchanged-intervals): 2, 10/9, 11/9
Optimal ET sequence: 17c, 19, 36, 39d, 41, 58, 99e, 118, 159, 217, 335
Badness: 0.936 × 10-3