Horwell family: Difference between revisions
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{{Technical data page}} | {{Technical data page}} | ||
The '''horwell family''' of rank-3 | The '''horwell family''' of [[rank-3 temperament]]s [[tempering out|tempers out]] the [[horwell comma]] ({{monzo|legend=1| -16 1 5 1 }}, [[ratio]]: 65625/65536). | ||
== Horwell == | == Horwell == | ||
| Line 8: | Line 8: | ||
{{Mapping|legend=1| 1 0 0 16 | 0 1 0 -1 | 0 0 1 -5 }} | {{Mapping|legend=1| 1 0 0 16 | 0 1 0 -1 | 0 0 1 -5 }} | ||
: mapping generators: ~2, ~3, ~5 | : mapping generators: ~2, ~3, ~5 | ||
| Line 16: | Line 15: | ||
: 5/4 length = 0.6213, 16/15 length = 1.3863 | : 5/4 length = 0.6213, 16/15 length = 1.3863 | ||
: Angle (5/4, 16/15) = 64.6379 | : Angle (5/4, 16/15) = 64.6379 | ||
[[Optimal tuning]]s: | |||
* [[WE]]: ~2 = 1200.0937{{c}}, ~3/2 = 701.8466{{c}}, ~5/4 = 385.9684{{c}} | |||
: [[error map]]: {{val| +0.094 -0.015 -0.158 -0.046 }} | |||
* [[CWE]]: ~2 = 1200.0000{{c}}, ~3/2 = 701.8243{{c}}, ~5/4 = 385.9221{{c}} | |||
: error map: {{val| 0.000 -0.131 -0.392 -0.261 }} | |||
[[Minimax tuning]]: | [[Minimax tuning]]: | ||
| Line 25: | Line 30: | ||
: [[Eigenmonzo basis|unchanged-interval (eigenmonzo) basis]]: 2.9/5.9/7 | : [[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, | {{Optimal ET sequence|legend=1| 22, 31, 53, 84, 87, 118, 140, 171, 1592c, 1763c, 1934c, 2074c, 2105c, 2245cd, 2416cd, …, 3442ccd, 3613ccd, 5034bcccdd, 5205bcccdd }} | ||
[[Badness]]: 0. | [[Badness]] (Sintel): 0.761 | ||
[[Projection pair]]: 7 65536/9375 | [[Projection pair]]: <code>7 65536/9375</code> | ||
== Zelda == | == Zelda == | ||
| Line 38: | Line 43: | ||
{{Mapping|legend=1| 1 0 0 16 -9 | 0 1 0 -1 2 | 0 0 1 -5 4 }} | {{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, | [[Optimal tuning]]s: | ||
* [[WE]]: ~2 = 1200.2765{{c}}, ~3/2 = 702.1662{{c}}, ~5/4 = 386.2362{{c}} | |||
: [[error map]]: {{val| +0.276 +0.488 +0.475 -0.791 -1.764 }} | |||
* [[CWE]]: ~2 = 1200.0000{{c}}, ~3/2 = 702.1206{{c}}, ~5/4 = 386.1124{{c}} | |||
: error map: {{val| 0.000 +0.166 -0.201 -1.508 -2.627 }} | |||
{{Optimal ET sequence|legend=1| 22, 31, 53, 84e, 87, 118, 258e, 376de, 547dee }} | |||
[[Badness]]: 0. | [[Badness]] (Sintel): 0.771 | ||
== Horwellic == | == Horwellic == | ||
| Line 48: | Line 59: | ||
{{Mapping|legend=1| 1 0 0 16 10 | 0 1 0 -1 1 | 0 0 2 -10 -7 }} | {{Mapping|legend=1| 1 0 0 16 10 | 0 1 0 -1 1 | 0 0 2 -10 -7 }} | ||
: mapping generators: ~2, ~3, ~352/315 | |||
[[Optimal tuning]]s: | |||
* [[WE]]: ~2 = 1200.0937{{c}}, ~3/2 = 701.8440{{c}}, ~352/315 = 192.9848{{c}} | |||
: [[error map]]: {{val| +0.094 -0.017 -0.157 -0.049 +0.007 }} | |||
* [[CWE]]: ~2 = 1200.0000{{c}}, ~3/2 = 701.8212{{c}}, ~352/315 = 192.9618{{c}} | |||
: error map: {{val| 0.000 -0.134 -0.390 -0.265 -0.229 }} | |||
{{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| 25e, 31, 75e, 87, 118, 193, 224, 311, 342, 1592c, 1934ce, 2276cde, 2587cde, 2929cde, 3271ccde, 3613ccde, 5205bcccddee }} | ||
[[Badness]]: 0. | [[Badness]] (Sintel): 0.607 | ||
[[Category:Temperament families]] | [[Category:Temperament families]] | ||
[[Category:Horwell family| ]] <!-- main article --> | [[Category:Horwell family| ]] <!-- main article --> | ||
[[Category:Rank 3]] | [[Category:Rank 3]] | ||
Latest revision as of 06:18, 29 June 2026
- 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 (monzo: [-16 1 5 1⟩, ratio: 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
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
- WE: ~2 = 1200.0937 ¢, ~3/2 = 701.8466 ¢, ~5/4 = 385.9684 ¢
- error map: ⟨+0.094 -0.015 -0.158 -0.046]
- CWE: ~2 = 1200.0000 ¢, ~3/2 = 701.8243 ¢, ~5/4 = 385.9221 ¢
- error map: ⟨0.000 -0.131 -0.392 -0.261]
- [[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, …, 3442ccd, 3613ccd, 5034bcccdd, 5205bcccdd
Badness (Sintel): 0.761
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]]
- WE: ~2 = 1200.2765 ¢, ~3/2 = 702.1662 ¢, ~5/4 = 386.2362 ¢
- error map: ⟨+0.276 +0.488 +0.475 -0.791 -1.764]
- CWE: ~2 = 1200.0000 ¢, ~3/2 = 702.1206 ¢, ~5/4 = 386.1124 ¢
- error map: ⟨0.000 +0.166 -0.201 -1.508 -2.627]
Optimal ET sequence: 22, 31, 53, 84e, 87, 118, 258e, 376de, 547dee
Badness (Sintel): 0.771
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]]
- mapping generators: ~2, ~3, ~352/315
- WE: ~2 = 1200.0937 ¢, ~3/2 = 701.8440 ¢, ~352/315 = 192.9848 ¢
- error map: ⟨+0.094 -0.017 -0.157 -0.049 +0.007]
- CWE: ~2 = 1200.0000 ¢, ~3/2 = 701.8212 ¢, ~352/315 = 192.9618 ¢
- error map: ⟨0.000 -0.134 -0.390 -0.265 -0.229]
Optimal ET sequence: 25e, 31, 75e, 87, 118, 193, 224, 311, 342, 1592c, 1934ce, 2276cde, 2587cde, 2929cde, 3271ccde, 3613ccde, 5205bcccddee
Badness (Sintel): 0.607