Archytas family: Difference between revisions

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@@ Line 3: / Line 3: @@
 = Archytas =
-[[Comma]]: 64/63
+[[Comma]] list: 64/63
--limit minimax
+Mapping: [{{val| 1 0 0 6 }}, {{val| 0 1 0 -2 }}, {{val| 0 0 1 0 }}]
-[|1 0 0 0&gt;, |2 1/3 0 -1/3&gt;,
+Mapping [[generator]]s: 2, 3, 5
-|2 -2/3 1 -1/3&gt;, |2 -2/3 0 2/3&gt;]
-[[Eigenmonzo]]s: 2, 6/5, 7/5
+Map to lattice: [{{val| 0 1 0 -2 }}, {{val| 0 0 1 0 }}]
--limit minimax
+Lattice basis:
+: 3/2 length = 1.0508, 5/4 length = 2.3219
+: Angle (3/2, 5/4) = 90 degrees
-[|1 0 0 0&gt;, |3/2 1/2 0 -1/4&gt;,
+Minimax tuning:
-|3/2 -1/2 1 -1/4&gt;, |3 -1 0 1/2&gt;]
+* [[7-odd-limit]]
+: [{{monzo| 1 0 0 0 }}, {{monzo| 2 1/3 0 -1/3 }}, {{monzo| 2 -2/3 1 -1/3 }}, {{monzo| 2 -2/3 0 2/3 }}]
+: [[Eigenmonzo]]s: 2, 6/5, 7/5
+* [[9-odd-limit]]
+: [{{monzo| 1 0 0 0 }}, {{monzo| 3/2 1/2 0 -1/4 }}, {{monzo| 3/2 -1/2 1 -1/4 }}, {{monzo| 3 -1 0 1/2 }}]
+: [[Eigenmonzo]]s: 2, 6/5, 9/7
-[[Eigenmonzo]]s: 2, 6/5, 9/7
+{{Val list|legend=1| 5, 7, 10, 12, 22, 27, 49 }}
-Lattice basis: 3/2 length 1.0508 5/4 length 2.3219
+Scales: [[archytas12]], [[archytas12synch]]
-Angle(3/2, 5/4) = 90 degrees
-Map to lattice: [&lt;0 1 0 -2|, &lt;0 0 1 0|]
-Map: [&lt;1 0 0 6|, &lt;0 1 0 -2|, &lt;0 0 1 0|]
-[[Generator]]s: 2, 3, 5
-{{EDOs|legend=1| 5, 7, 10, 12, 22, 27, 49 }}
-== Scales ==
-* [[archytas12]]
-* [[archytas12synch]]
 == Music ==
@@ Line 46: / Line 38: @@
 = Ares =
-[[Comma]]s: 64/63, 100/99
+[[Comma]] list: 64/63, 100/99
-[[Minimax tuning]]
-[|1 0 0 0 0&gt;, |3/2 1/2 0 -1/4 0&gt;,
-|2 0 0 -1/2 1/2&gt;, |3 -1 0 1/2 0&gt;,
-|3 -1 0 -1/2 1&gt;]
-[[Eigenmonzo]]s: 2, 11/9, 9/7
-Lattice basis: 3/2 0.9878 6/5 1.4312
+Mapping: [{{val| 1 0 0 6 2 }}, {{val| 0 1 0 -2 -2 }}, {{val| 0 0 1 0 2 }}]
-Angle(3/2, 6/5) = 75.0475 degrees
+Mapping [[generator]]s: 2, 3, 5
-Map to lattice: [&lt;0 1 1 -2 0|, &lt;0 0 -1 0 -2|]
+Map to lattice: [{{val| 0 1 1 -2 0 }}, {{val| 0 0 -1 0 -2 }}]
-Map: [&lt;1 0 0 6 2|, &lt;0 1 0 -2 -2|, &lt;0 0 1 0 2|]
+Lattice basis:
+: 3/2 0.9878, 6/5 1.4312
+: Angle (3/2, 6/5) = 75.0475 degrees
-[[Generator]]s: 2, 3, 5
+[[Minimax tuning]]:
+* [[11-odd-limit]]
+: [{{monzo| 1 0 0 0 0 }}, {{monzo| 3/2 1/2 0 -1/4 0 }}, {{monzo| 2 0 0 -1/2 1/2 }}, {{monzo| 3 -1 0 1/2 0 }}, {{monzo| 3 -1 0 -1/2 1 }}]
+: [[Eigenmonzo]]s: 2, 11/9, 9/7
-{{EDOs|legend=1| 12, 15, 22, 27e, 34d, 49 }}
+{{Val list|legend=1| 12, 15, 22, 27e, 34d, 49 }}
 Badness: 0.000469
@@ Line 73: / Line 62: @@
 = Vulcan =
-Commas: 56/55, 64/63
+Comma list: 56/55, 64/63
-Map: [&lt;1 0 0 6 9|, &lt;0 1 0 -2 -2|, &lt;0 0 1 0 -1|]
+Mapping: [{{val| 1 0 0 6 9 }}, {{val| 0 1 0 -2 -2 }}, {{val| 0 0 1 0 -1 }}]
-Generators: 2, 3, 5
+Mapping generators: 2, 3, 5
-{{EDOs|legend=1| 5, 10, 12, 15, 27e }}
+{{Val list|legend=1| 5, 10, 12, 15, 27e }}
 Badness: 0.000577