Keemic family: Difference between revisions

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-The '''keemic family''' of temperaments are [[planar temperament]]s tempering out the keema, [[875/864]].
+The '''keemic family''' of rank-3 temperaments are [[planar temperament]]s tempering out the keema, [[875/864]].
 = Supermagic =
-Comma: 875/864
+[[Comma list]]: 875/864
-and 9 limit minimax
+[[Mapping]]: [{{val| 1 0 0 5 }}, {{val| 0 1 0 3 }}, {{val| 0 0 1 -3 }}]
-[|1 0 0 0&gt;, |0 1 0 0&gt;, |5/4 3/4 1/4 -1/4&gt;,
+Mapping generators: ~2, ~3, ~5
-|5/4 3/4 -3/4 3/4&gt;]
-Eigenmonzos: 2, 4/3, 7/5
+Map to lattice: [{{val| 0 0 -1 3 }}, {{val| 0 1 1 0 }}]
-Lattice basis: 6/5 length=0.8879 3/2 length=1.3391
+Lattice basis:
+: 6/5 length = 0.8879, 3/2 length = 1.3391
+: Angle (6/5, 3/2) = 77.834
-Angle(6/5, 3/2) = 77.834
+[[Minimax tuning]]:
+* 7- and 9-odd-limit minimax
+: [{{monzo| 1 0 0 0 }}, {{monzo| 0 1 0 0 }}, {{monzo| 5/4 3/4 1/4 -1/4 }}, {{monzo| 5/4 3/4 -3/4 3/4 }}]
+: Eigenmonzos: 2, 4/3, 7/5
-Map to lattice: [&lt;0 0 -1 3|, &lt;0 1 1 0|]
+{{Val list|legend=1| 7, 15, 19, 41 }}
-Map: [&lt;1 0 0 5|, &lt;0 1 0 3|, &lt;0 0 1 -3|]
-Generators: 2, 3, 5
-{{EDOs|legend=1| 7, 15, 19, 41 }}
 [[Projection pair]]: 7 864/125
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 == 11-limit ==
-Commas: 100/99, 385/384
+Comma list: 100/99, 385/384
-Map: [&lt;1 0 0 5 2|, &lt;0 1 0 3 -2|, &lt;0 0 1 -3 2|]
+Mapping: [{{val| 1 0 0 5 2 }}, {{val| 0 1 0 3 -2 }}, {{val| 0 0 1 -3 2 }}]
-{{EDOs|legend=1| 7, 15, 19, 22, 37, 41, 104, 145c, 201ce, 264bce, 305bcce }}
+{{Val list|legend=1| 7, 15, 19, 22, 37, 41, 104, 145c, 201ce, 264bce, 305bcce }}
-Badness: 0.000641
+Badness: 0.641 × 10<sup>-3</sup>
 = Supernatural =
-Commas: 225/224, 245/243
+Comma list: 225/224, 245/243
-Map:[&lt;1 0 2 -1 0|, &lt;0 5 1 12 0|, &lt;0 0 0 0 1|]
+Mapping: [{{val| 1 0 2 -1 0 }}, {{val| 0 5 1 12 0 }}, {{val| 0 0 0 0 1 }}]
-{{EDOs|legend=1| 19, 22, 41, 82e, 101cd, (104), 224ccde, 265ccde }}
+{{Val list|legend=1| 19, 22, 41, 82e, 101cd, (104), 224ccde, 265ccde }}
-Badness: 0.000888
+Badness: 0.888 × 10<sup>-3</sup>
 [[Category:Theory]]