Horwell family: Difference between revisions
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The '''horwell family''' of rank-3 temperaments tempers out the [[horwell comma]], 65625/65536. | The '''horwell family''' of rank-3 temperaments tempers out the [[horwell comma]], 65625/65536 = {{monzo| -16 1 5 1 }}. | ||
== Horwell == | == Horwell == | ||
| Line 24: | Line 24: | ||
: [[Eigenmonzo]]s: 2, 9/7, 7/5 | : [[Eigenmonzo]]s: 2, 9/7, 7/5 | ||
{{Val list|legend=1| | {{Val list|legend=1| 22, 31, 53, 84, 87, 118, 140, 171, 1592c, 1763c, 1934c, 2074c, 2105c, 2245cd, 2416cd, 2587cd, 2758cd, 2929cd, 3100cd, 3271ccd, 3442ccd, 3613ccd, 5034bcccdd, 5205bcccdd }} | ||
[[Badness]]: 0.173 × 10<sup>-3</sup> | [[Badness]]: 0.173 × 10<sup>-3</sup> | ||
| Line 37: | Line 37: | ||
[[Mapping]]: [{{val| 1 0 0 16 -9 }}, {{val| 0 1 0 -1 2 }}, {{val| 0 0 1 -5 4 }}] | [[Mapping]]: [{{val| 1 0 0 16 -9 }}, {{val| 0 1 0 -1 2 }}, {{val| 0 0 1 -5 4 }}] | ||
{{Val list|legend=1| 22, 31, 53, 84, 87, 118, 258e, 376de, 547de | {{Val list|legend=1| 22, 31, 53, 84, 87, 118, 258e, 376de, 547de }} | ||
[[Badness]]: 0.642 × 10<sup>-3</sup> | [[Badness]]: 0.642 × 10<sup>-3</sup> | ||
| Line 48: | Line 48: | ||
[[Mapping]]: [{{val| 1 0 0 16 10 }}, {{val| 0 1 0 -1 1 }}, {{val| 0 0 2 -10 -7 }}] | [[Mapping]]: [{{val| 1 0 0 16 10 }}, {{val| 0 1 0 -1 1 }}, {{val| 0 0 2 -10 -7 }}] | ||
{{Val list|legend=1| 31, 87, 118, 193, 224, 311, 342 }} | {{Val list|legend=1| 31, 75e, 87, 118, 193, 224, 311, 342, 1592c, 1934ce, 2276cde, 2587cde, 2929cde, 3271ccde, 3613ccde, 5205bcccddee }} | ||
[[Badness]]: 0.505 × 10<sup>-3</sup> | [[Badness]]: 0.505 × 10<sup>-3</sup> | ||
Revision as of 18:39, 16 October 2021
The horwell family of rank-3 temperaments tempers out the horwell comma, 65625/65536 = [-16 1 5 1⟩.
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