Horwell family: Difference between revisions
Jump to navigation
Jump to search
m Cleanup |
Sort by generator complexity |
||
| Line 30: | Line 30: | ||
[[Projection pair]]: 7 65536/9375 | [[Projection pair]]: 7 65536/9375 | ||
== | == Zelda == | ||
Subgroup: 2.3.5.7.11 | Subgroup: 2.3.5.7.11 | ||
[[Comma list]]: | [[Comma list]]: 385/384, 3388/3375 | ||
[[Mapping]]: [{{val| 1 0 0 16 | [[Mapping]]: [{{val| 1 0 0 16 -9 }}, {{val| 0 1 0 -1 2 }}, {{val| 0 0 1 -5 4 }}] | ||
{{Val list|legend=1| 31, 87, 118, | {{Val list|legend=1| 22, 31, 53, 84, 87, 118, 258e, 376de, 547de, 665dee }} | ||
[[Badness]]: 0. | [[Badness]]: 0.642 × 10<sup>-3</sup> | ||
== | == Horwellic == | ||
Subgroup: 2.3.5.7.11 | Subgroup: 2.3.5.7.11 | ||
[[Comma list]]: | [[Comma list]]: 3025/3024, 65625/65536 | ||
[[Mapping]]: [{{val| 1 0 0 16 | [[Mapping]]: [{{val| 1 0 0 16 10 }}, {{val| 0 1 0 -1 1 }}, {{val| 0 0 2 -10 -7 }}] | ||
{{Val list|legend=1| | {{Val list|legend=1| 31, 87, 118, 193, 224, 311, 342 }} | ||
[[Badness]]: 0. | [[Badness]]: 0.505 × 10<sup>-3</sup> | ||
[[Category:Regular temperament theory]] | [[Category:Regular temperament theory]] | ||
Revision as of 18:18, 16 October 2021
The horwell family of rank-3 temperaments tempers out the horwell comma, 65625/65536.
Horwell
Subgroup: 2.3.5.7
Comma list: 65625/65536
Mapping: [⟨1 0 0 16], ⟨0 1 0 -1], ⟨0 0 1 -5]]
Mapping generators: ~2, ~3, ~5
Map to lattice: [⟨0 -1 1 -4], ⟨0 -1 0 -1]]
Lattice basis:
- 5/4 length = 0.6213, 16/15 length = 1.3863
- Angle (5/4, 16/15) = 64.6379
- [[1 0 0 0⟩, [16/7 6/7 -5/7 -1/7⟩, [16/7 -1/7 2/7 -1/7⟩, [16/7 -1/7 -5/7 6/7⟩]
- Eigenmonzos: 2, 7/6, 6/5
- [[1 0 0 0⟩, [16/13 12/13 -5/13 -1/13⟩, [32/13 -2/13 3/13 -2/13⟩, [32/13 -2/13 -10/13 11/13⟩]
- Eigenmonzos: 2, 9/7, 7/5
Badness: 0.173 × 10-3
Projection pair: 7 65536/9375
Zelda
Subgroup: 2.3.5.7.11
Comma list: 385/384, 3388/3375
Mapping: [⟨1 0 0 16 -9], ⟨0 1 0 -1 2], ⟨0 0 1 -5 4]]
Badness: 0.642 × 10-3
Horwellic
Subgroup: 2.3.5.7.11
Comma list: 3025/3024, 65625/65536
Mapping: [⟨1 0 0 16 10], ⟨0 1 0 -1 1], ⟨0 0 2 -10 -7]]
Badness: 0.505 × 10-3