Marvel family: Difference between revisions

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@@ Line 29: / Line 29: @@
 [[Comma list]]: c = 225/224
+Subgroup: 2.3.5.7
 Mapping: [{{val| 1 0 0 -5 }}, {{val| 0 1 0 2 }}, {{val| 0 0 1 2 }}]
@@ Line 98: / Line 100: @@
 [[Comma list]]: 225/224, 385/384
+Subgroup: 2.3.5.7.11
 Mapping: [{{val| 1 0 0 -5 12 }}, {{val| 0 1 0 2 -1 }}, {{val| 0 0 1 2 -3 }}]
@@ Line 133: / Line 137: @@
 == 13-limit ==
 Comma list: 225/224, 385/384, 351/350
+Subgroup: 2.3.5.7.11.13
 Mapping: [{{val| 1 0 0 -5 12 -4 }}, {{val| 0 1 0 2 -1 -1 }}, {{val| 0 0 1 2 -3 4 }}]
@@ Line 148: / Line 154: @@
 == Hecate ==
 Comma list: 225/224, 385/384, 325/324
+Subgroup: 2.3.5.7.11.13
 Mapping: [{{val| 1 0 0 -5 12 2 }}, {{val| 0 1 0 2 -1 4 }}, {{val| 0 0 1 2 -3 -2 }}]
@@ Line 165: / Line 173: @@
 === 17-limit ===
 Comma list: 225/224, 385/384, 325/324, 595/594
+Subgroup: 2.3.5.7.11.13.17
 Mapping: [{{val| 1 0 0 -5 12 2 18 }}, {{val| 0 1 0 2 -1 4 0 }}, {{val| 0 0 1 2 -3 -2 -6 }}]
@@ Line 174: / Line 184: @@
 === Enodia ===
 Comma list: 225/224, 385/384, 325/324, 375/374
+Subgroup: 2.3.5.7.11.13.17
 Mapping: [{{val| 1 0 0 -5 12 2 18 }}, {{val| 0 1 0 2 -1 4 0 }}, {{val| 0 0 1 2 -3 -2 6 }}]
@@ Line 183: / Line 195: @@
 == Marvelcat ==
 Comma list: 169/168, 225/224, 385/384
+Subgroup: 2.3.5.7.11.13
 Mapping: [{{val| 1 0 0 -5 12 -1 }}, {{val| 0 2 0 4 -2 3 }}, {{val| 0 0 1 2 -3 1 }}]
@@ Line 192: / Line 206: @@
 == Marvell ==
 Comma list: 225/224, 385/384, 1573/1568
+Subgroup: 2.3.5.7.11.13
 Mapping: [{{val| 1 0 0 -5 12 -29 }}, {{val| 0 1 0 2 -1 6 }}, {{val| 0 0 1 2 -3 10 }}]
@@ Line 205: / Line 221: @@
 == Isis ==
 Comma list: 225/224, 385/384, 275/273
+Subgroup: 2.3.5.7.11.13
 Mapping: [{{val| 1 0 0 -5 12 17 }}, {{val| 0 1 0 2 -1 4 }}, {{val| 0 0 1 2 -3 -3 }}]
@@ Line 216: / Line 234: @@
 == Deecee ==
 Comma list: 225/224, 385/384, 364/363
+Subgroup: 2.3.5.7.11.13
 Mapping: [{{val| 1 0 0 -5 12 27 }}, {{val| 0 1 0 2 -1 -3 }}, {{val| 0 0 1 2 -3 -8 }}]
@@ Line 231: / Line 251: @@
 == Tripod ==
 Comma list: 105/104, 144/143, 196/195
+Subgroup: 2.3.5.7.11.13
 Minimax tuning:
@@ Line 245: / Line 267: @@
 = Mirage =
-Commas: 225/224, 243/242, 385/384
+Comma list: 225/224, 243/242, 385/384
-Map: [&lt;1 1 3 3 2 0|, &lt;0 6 -7 -2 15 0|, &lt;0 0 0 0 0 1|]
+Subgroup: 2.3.5.7.11.13
-{{EDOs|legend=1| 10, 31, 41, 62, 72, 103, 175f, 216c, 288cdf, 391bcdef }}
+Mapping: [{{val| 1 1 3 3 2 0 }}, {{val| 0 6 -7 -2 15 0 }}, {{val| 0 0 0 0 0 1 }}]
-Badness: 0.000738
+{{Val list|legend=1| 10, 31, 41, 62, 72, 103, 175f, 216c, 288cdf, 391bcdef }}
+Badness: 0.738 × 10<sup>-3</sup>
 = Minerva =
-[[Comma]]s: 99/98, 176/175
+[[Comma list]]: 99/98, 176/175
-Related linear temperament: [[Semicomma family#Orwell|orwell]]
+Subgroup: 2.3.5.7.11
-[[Eigenmonzo subgroup]]: 2.7/5.11/9
+[[Associated temperament]]: [[Semicomma family #Orwell|orwell]]
-Lattice basis: 16/15 length 0.8997 5/4 length 1.0457
+Mapping: [{{val| 1 0 0 -5 -9 }}, {{val| 0 1 0 2 2 }}, {{val| 0 0 1 2 4 }}]
-Angle(16/15, 5/4) = 98.6044 degrees
+Mapping generators: ~2, ~3, ~5
-Map to lattice: [&lt;0 -1 0 -2 -2|, &lt;0 -1 1 0 2|]
+Map to lattice: [{{val| 0 -1 0 -2 -2 }}, {{val| 0 -1 1 0 2 }}]
-Map: [&lt;1 0 0 -5 -9|, &lt;0 1 0 2 2|, &lt;0 0 1 2 4|]
+Lattice basis:
+: 16/15 length = 0.8997, 5/4 length = 1.0457
+: Angle (16/15, 5/4) = 98.6044 degrees
-[[Generator]]s: 2, 3, 5
+Minimax tuning: 11-odd-limit [[eigenmonzo subgroup]]: 2.7/5.11/9
-{{EDOs|legend=1| 9, 12, 21, 22, 31, 43, 53, 74, 75, 96, 127 }}
+{{Val list|legend=1| 9, 12, 21, 22, 31, 43, 53, 74, 75, 96, 127 }}
-Badness: 0.000381
+Badness: 0.381 × 10<sup>-3</sup>
 [[Projection pair]]s: 7 225/32 11 5625/512
@@ Line 279: / Line 305: @@
 == Athene ==
-Commas: 99/98, 176/175, 275/273
+Comma list: 99/98, 176/175, 275/273
--limit eigenmonzo subgroup: 2.11/9.13/7
+Subgroup: 2.3.5.7.11.13
--limit eigenmonzo subgroup: 2.11/9.13/7
+Mapping: [{{val| 1 0 0 -5 -9 -4 }}, {{val| 0 1 0 2 2 -1 }}, {{val| 0 0 1 2 4 4 }}]
-Map: [&lt;1 0 0 -5 -9 -4|, &lt;0 1 0 2 2 -1|, &lt;0 0 1 2 4 4|]
+Minimax tuning:
+* 13-odd-limit eigenmonzo subgroup: 2.11/9.13/7
+* 15-odd-limit eigenmonzo subgroup: 2.11/9.13/7
-{{EDOs|legend=1| 22, 31, 53, 84e, 118d, 149df, 171de, 202def }}
+{{Val list|legend=1| 22, 31, 53, 84e, 118d, 149df, 171de, 202def }}
-Badness: 0.000818
+Badness: 0.818 × 10<sup>-3</sup>
 [[Projection pair]]s: 7 225/32 11 5625/512 13 625/48
 = Spectacle =
-[[Comma]]s: 225/224, 243/242
+[[Comma list]]: 225/224, 243/242
-Related linear temperament: [[Marvel temperaments#Marvo|marvo]]
-[[Minimax tuning]]:
+Subgroup: 2.3.5.7.11
-[|1 0 0 0 0&gt;, |1/5 0 0 0 2/5&gt;, |2/5 -2 1 0 4/5&gt;, |-19/5 -4 2 0 12/5&gt;, |0 0 0 0 1&gt;]
+[[Associated temperament]]: [[Marvel temperaments #Marvo|marvo]]
-[[Eigenmonzo subgroup]]: 2.9/5.11
+Mapping: [{{val| 1 1 0 -3 2 }}, {{val| 0 2 0 4 5 }}, {{val| 0 0 1 2 0 }}]
-Map: [&lt;1 1 0 -3 2|, &lt;0 2 0 4 5|, &lt;0 0 1 2 0|]
+Mapping generators: ~2, ~11/9, ~5
-[[Generator]]s: 2, 11/9, 5
+[[Minimax tuning]]:
+* 11-odd-limit
+: [{{monzo| 1 0 0 0 0 }}, {{monzo| 1/5 0 0 0 2/5 }}, {{monzo| 2/5 -2 1 0 4/5 }}, {{monzo| -19/5 -4 2 0 12/5 }}, {{monzo| 0 0 0 0 1 }}]
+: [[Eigenmonzo subgroup]]: 2.9/5.11
-{{EDOs|legend=1| 10, 31, 41, 72, 240, 259b, 269ce, 310c, 331bc, 353c, 497bc, 569bc }}
+{{Val list|legend=1| 10, 31, 41, 72, 240, 259b, 269ce, 310c, 331bc, 353c, 497bc, 569bc }}
-Badness: 0.000499
+Badness: 0.499 × 10<sup>-3</sup>
 Projection pairs: 3 242/81 7 366025/52488 11 644204/59049 to 2.5.11/9
@@ Line 316: / Line 345: @@
 Scales: [[spectacle31]]
-==13-limit==
+== 13-limit ==
-Commas: 225/224, 243/242, 351/350
+Comma list: 225/224, 243/242, 351/350
+Subgroup: 2.3.5.7.11.13
-Map: [&lt;1 1 0 -3 2 -5|, &lt;0 2 0 4 5 -2|, &lt;0 0 1 2 0 4|]
+Mapping: [{{val| 1 1 0 -3 2 -5 }}, {{val| 0 2 0 4 5 -2 }}, {{val| 0 0 1 2 0 4 }}]
-{{EDOs|legend=1| 31, 72, 103, 175f, 209, 240 }}
+{{Val list|legend=1| 31, 72, 103, 175f, 209, 240 }}
-Badness: 0.001009
+Badness: 1.009 × 10<sup>-3</sup>
 =Apollo=