Horwell family: Difference between revisions
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Cmloegcmluin (talk | contribs) "optimal GPV sequence" → "optimal ET sequence", per Talk:Optimal_ET_sequence |
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{{Technical data page}} | |||
The '''horwell family''' of rank-3 temperaments tempers out the [[horwell comma]], 65625/65536 = {{monzo| -16 1 5 1 }}. | The '''horwell family''' of rank-3 temperaments tempers out the [[horwell comma]], 65625/65536 = {{monzo| -16 1 5 1 }}. | ||
== Horwell == | == Horwell == | ||
Subgroup: 2.3.5.7 | [[Subgroup]]: 2.3.5.7 | ||
[[Comma list]]: 65625/65536 | [[Comma list]]: 65625/65536 | ||
{{Mapping|legend=1| 1 0 0 16 | 0 1 0 -1 | 0 0 1 -5 }} | |||
: mapping generators: ~2, ~3, ~5 | |||
[[Mapping to lattice]]: [{{val| 0 -1 1 -4 }}, {{val| 0 -1 0 -1 }}] | [[Mapping to lattice]]: [{{val| 0 -1 1 -4 }}, {{val| 0 -1 0 -1 }}] | ||
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[[Minimax tuning]]: | [[Minimax tuning]]: | ||
* [[7-odd-limit]] | * [[7-odd-limit]] | ||
: | : {{monzo list| 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 }} | ||
: [[Eigenmonzo | : [[Eigenmonzo basis|unchanged-interval (eigenmonzo) basis]]: 2.5/3.7/3 | ||
* [[9-odd-limit]] | * [[9-odd-limit]] | ||
: | : {{monzo list| 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 }} | ||
: [[Eigenmonzo | : [[Eigenmonzo basis|unchanged-interval (eigenmonzo) basis]]: 2.9/5.9/7 | ||
{{Optimal ET sequence|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 }} | {{Optimal ET sequence|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 }} | ||
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== Zelda == | == Zelda == | ||
Subgroup: 2.3.5.7.11 | [[Subgroup]]: 2.3.5.7.11 | ||
[[Comma list]]: 385/384, 3388/3375 | [[Comma list]]: 385/384, 3388/3375 | ||
{{Mapping|legend=1| 1 0 0 16 -9 | 0 1 0 -1 2 | 0 0 1 -5 4 }} | |||
{{Optimal ET sequence|legend=1| 22, 31, 53, 84, 87, 118, 258e, 376de, 547de }} | {{Optimal ET sequence|legend=1| 22, 31, 53, 84, 87, 118, 258e, 376de, 547de }} | ||
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== Horwellic == | == Horwellic == | ||
Subgroup: 2.3.5.7.11 | [[Subgroup]]: 2.3.5.7.11 | ||
[[Comma list]]: 3025/3024, 65625/65536 | [[Comma list]]: 3025/3024, 65625/65536 | ||
{{Mapping|legend=1| 1 0 0 16 10 | 0 1 0 -1 1 | 0 0 2 -10 -7 }} | |||
{{Optimal ET sequence|legend=1| 31, 75e, 87, 118, 193, 224, 311, 342, 1592c, 1934ce, 2276cde, 2587cde, 2929cde, 3271ccde, 3613ccde, 5205bcccddee }} | {{Optimal ET sequence|legend=1| 31, 75e, 87, 118, 193, 224, 311, 342, 1592c, 1934ce, 2276cde, 2587cde, 2929cde, 3271ccde, 3613ccde, 5205bcccddee }} | ||
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[[Category:Temperament families]] | [[Category:Temperament families]] | ||
[[Category:Pages with mostly numerical content]] | |||
[[Category:Horwell family| ]] <!-- main article --> | [[Category:Horwell family| ]] <!-- main article --> | ||
[[Category:Horwell| ]] <!-- key article --> | |||
[[Category:Rank 3]] | [[Category:Rank 3]] | ||
Latest revision as of 00:38, 24 June 2025
- This is a list showing technical temperament data. For an explanation of what information is shown here, you may look at the technical data guide for regular temperaments.
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
Mapping 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⟩]
- unchanged-interval (eigenmonzo) basis: 2.5/3.7/3
- [[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⟩]
- unchanged-interval (eigenmonzo) basis: 2.9/5.9/7
Optimal ET sequence: 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 × 10-3
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]]
Optimal ET sequence: 22, 31, 53, 84, 87, 118, 258e, 376de, 547de
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]]
Optimal ET sequence: 31, 75e, 87, 118, 193, 224, 311, 342, 1592c, 1934ce, 2276cde, 2587cde, 2929cde, 3271ccde, 3613ccde, 5205bcccddee
Badness: 0.505 × 10-3