Horwell family: Difference between revisions

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-__FORCETOC__
+{{Technical data page}}
-The '''horwell family''' of rank three temperaments tempers out the [[horwell comma]], 65625/65536.
+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 ==
-Comma: 65625/65536
+[[Subgroup]]: 2.3.5.7
--limit minimax
+[[Comma list]]: 65625/65536
-[|1 0 0 0&gt;, |16/7 6/7 -5/7 -1/7&gt;,
+{{Mapping|legend=1| 1 0 0 16 | 0 1 0 -1 | 0 0 1 -5 }}
-|16/7 -1/7 2/7 -1/7&gt;, |16/7 -1/7 -5/7 6/7&gt;]
+: mapping generators: ~2, ~3, ~5
-Eigenmonzos: 2, 7/6, 6/5
+[[Mapping to lattice]]: [{{val| 0 -1 1 -4 }}, {{val| 0 -1 0 -1 }}]
--limit minimax
+Lattice basis:
+: 5/4 length = 0.6213, 16/15 length = 1.3863
+: Angle (5/4, 16/15) = 64.6379
-[|1 0 0 0&gt;, |16/13 12/13 -5/13 -1/13&gt;,
+[[Optimal tuning]]s:
-|32/13 -2/13 3/13 -2/13&gt;, |32/13 -2/13 -10/13 11/13&gt;]
+* [[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 }}
-Eigenmonzos: 2, 9/7, 7/5
+[[Minimax tuning]]:
+* [[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 basis|unchanged-interval (eigenmonzo) basis]]: 2.5/3.7/3
+* [[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 basis|unchanged-interval (eigenmonzo) basis]]: 2.9/5.9/7
-Lattice basis: 5/4 length=0.6213 16/15 length=1.3863
+{{Optimal ET sequence|legend=1| 22, 31, 53, 84, 87, 118, 140, 171, 1592c, 1763c, 1934c, 2074c, 2105c, 2245cd, 2416cd, …, 3442ccd, 3613ccd, 5034bcccdd, 5205bcccdd }}
-Angle(5/4, 16/15) = 64.6379
+[[Badness]] (Sintel): 0.761
-Map to lattice: [&lt;0 -1 1 -4|, &lt;0 -1 0 -1|]
+[[Projection pair]]: <code>7 65536/9375</code>
-Map: [&lt;1 0 0 16|, &lt;0 1 0 -1|, &lt;0 0 1 -5|]
+== Zelda ==
+[[Subgroup]]: 2.3.5.7.11
-Generators: 2, 3, 5
+[[Comma list]]: 385/384, 3388/3375
-Edos: 9, 22, 25, 28, 31, 34, 40, 53, 56, 65, 75, 84, 87, 118, 140, 171, 824, 995
+{{Mapping|legend=1| 1 0 0 16 -9 | 0 1 0 -1 2 | 0 0 1 -5 4 }}
-Badness: 0.000173
+[[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 }}
-[[Projection pair]]: 7 65536/9375
+{{Optimal ET sequence|legend=1| 22, 31, 53, 84e, 87, 118, 258e, 376de, 547dee }}
-== Horwellic  ==
+[[Badness]] (Sintel): 0.771
-Commas: 3025/3024, 65625/65536
-Map: [&lt;1 0 0 16 10|, &lt;0 1 0 -1 1|, &lt;0 0 2 -10 -7|]
+== Horwellic ==
+[[Subgroup]]: 2.3.5.7.11
-EDOs: 31, 87, 118, 193, 224, 311, 342
+[[Comma list]]: 3025/3024, 65625/65536
-Badness: 0.000505
+{{Mapping|legend=1| 1 0 0 16 10 | 0 1 0 -1 1 | 0 0 2 -10 -7 }}
+: mapping generators: ~2, ~3, ~352/315
-== Zelda  ==
+[[Optimal tuning]]s:
-Commas: 385/384, 3388/3375
+* [[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 }}
-Map: [&lt;1 0 0 16 -9|, &lt;0 1 0 -1 2|, &lt;0 0 1 -5 4|]
+{{Optimal ET sequence|legend=1| 25e, 31, 75e, 87, 118, 193, 224, 311, 342, 1592c, 1934ce, 2276cde, 2587cde, 2929cde, 3271ccde, 3613ccde, 5205bcccddee }}
-EDOs: 22, 31, 53, 84, 87, 118, 258e, 376de, 547de, 665dee
+[[Badness]] (Sintel): 0.607
-Badness: 0.000642
+[[Category:Temperament families]]
+[[Category:Horwell family| ]] <!-- main article -->
-[[Category:Theory]]
-[[Category:Temperament family]]
-[[Category:Horwell]]
 [[Category:Rank 3]]