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 three temperaments tempers out the [[horwell comma]], 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]]: [{{val| 1 0 0 16 }}, {{val| 0 1 0 -1 }}, {{val| 0 0 1 -5 }}]
-|16/7 -1/7 2/7 -1/7&gt;, |16/7 -1/7 -5/7 6/7&gt;]
-Eigenmonzos: 2, 7/6, 6/5
+Mapping generators: ~2, ~3, ~5
--limit minimax
+Map to lattice: [{{val| 0 -1 1 -4 }}, {{val| 0 -1 0 -1 }}]
-[|1 0 0 0&gt;, |16/13 12/13 -5/13 -1/13&gt;,
+Lattice basis:
-|32/13 -2/13 3/13 -2/13&gt;, |32/13 -2/13 -10/13 11/13&gt;]
+: 5/4 length = 0.6213, 16/15 length = 1.3863
+: Angle (5/4, 16/15) = 64.6379
-Eigenmonzos: 2, 9/7, 7/5
+[[Minimax tuning]]:
+* [[7-odd-limit]]
+: [{{monzo| 1 0 0 0 }}, {{monzo| 16/7 6/7 -5/7 -1/7 }}, {{monzo| 16/7 -1/7 2/7 -1/7 }}, {{monzo| 16/7 -1/7 -5/7 6/7 }}]
+: [[Eigenmonzo]]s: 2, 7/6, 6/5
+* [[9-odd-limit]]
+: [{{monzo| 1 0 0 0 }}, {{monzo| 16/13 12/13 -5/13 -1/13 }}, {{monzo| 32/13 -2/13 3/13 -2/13 }}, {{monzo| 32/13 -2/13 -10/13 11/13 }}]
+: [[Eigenmonzo]]s: 2, 9/7, 7/5
-Lattice basis: 5/4 length=0.6213 16/15 length=1.3863
+{{Val list|legend=1| 9, 22, 25, 28, 31, 34, 40, 53, 56, 65, 75, 84, 87, 118, 140, 171, 824, 995 }}
-Angle(5/4, 16/15) = 64.6379
+[[Badness]]: 0.173 × 10<sup>-3</sup>
-Map to lattice: [&lt;0 -1 1 -4|, &lt;0 -1 0 -1|]
+[[Projection pair]]: 7 65536/9375
-Map: [&lt;1 0 0 16|, &lt;0 1 0 -1|, &lt;0 0 1 -5|]
+== Horwellic  ==
+Subgroup: 2.3.5.7.11
-Generators: 2, 3, 5
-Edos: 9, 22, 25, 28, 31, 34, 40, 53, 56, 65, 75, 84, 87, 118, 140, 171, 824, 995
+[[Comma list]]: 3025/3024, 65625/65536
-Badness: 0.000173
+[[Mapping]]: [{{val| 1 0 0 16 10 }}, {{val| 0 1 0 -1 1 }}, {{val| 0 0 2 -10 -7 }}]
-[[Projection pair]]: 7 65536/9375
-== Horwellic  ==
-Commas: 3025/3024, 65625/65536
-Map: [&lt;1 0 0 16 10|, &lt;0 1 0 -1 1|, &lt;0 0 2 -10 -7|]
+{{Val list|legend=1| 31, 87, 118, 193, 224, 311, 342 }}
-EDOs: 31, 87, 118, 193, 224, 311, 342
+[[Badness]]: 0.505 × 10<sup>-3</sup>
-Badness: 0.000505
+== Zelda ==
+Subgroup: 2.3.5.7.11
-== Zelda  ==
+[[Comma list]]: 385/384, 3388/3375
-Commas: 385/384, 3388/3375
-Map: [&lt;1 0 0 16 -9|, &lt;0 1 0 -1 2|, &lt;0 0 1 -5 4|]
+[[Mapping]]: [{{val| 1 0 0 16 -9 }}, {{val| 0 1 0 -1 2 }}, {{val| 0 0 1 -5 4 }}]
-EDOs: 22, 31, 53, 84, 87, 118, 258e, 376de, 547de, 665dee
+{{Val list|legend=1| 22, 31, 53, 84, 87, 118, 258e, 376de, 547de, 665dee }}
-Badness: 0.000642
+[[Badness]]: 0.642 × 10<sup>-3</sup>
-[[Category:Theory]]
+[[Category:Regular temperament theory]]
 [[Category:Temperament family]]
-[[Category:Horwell]]
+[[Category:Horwell family| ]] <!-- main article -->
 [[Category:Rank 3]]