Valinorsmic clan: Difference between revisions

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+This is a collection of rank-3 temperaments tempering out the valinorsma, [[176/175]], which equates 48/35 with 15/11 (rather than 11/8, which is what the keenanisma 385/384 does).
-The valinorsmic rank three temperaments temper out the [[valinorsma]], 176/175, which equates 48/35 with 15/11 (rather than 11/8, which is what the keenanisma 385/384 does.)
+Discussed elsewhere are:
+* [[Julius]] or [[varda]], {176/175, 896/891} → [[Diaschismic rank three family #Julius aka varda]]
+Considered below are manwe, mandos and ulmo, but we can begin with the rank-4 temperament.
 == Valinorsmic ==
-Comma list: 176/175
+Subgroup: 2.3.5.7.11
-Mapping: [&lt;1 0 0 0 -4|, &lt;0 1 0 0 0|, &lt;0 0 1 0 2|, &lt;0 0 0 1 1|]
+[[Comma list]]: [[176/175]]
-EDOs: 22, 31, 46, 53, 58, 80, 111
+[[Mapping]]: [{{val| 1 0 0 0 -4 }}, {{val| 0 1 0 0 0 }}, {{val| 0 0 1 0 2 }}, {{val| 0 0 0 1 1 }}]
+{{Val list|legend=1| 22, 31, 46, 53, 58, 80, 111 }}
 == Manwe ==
-Comma list: 176/175, 1331/1323
+Subgroup: 2.3.5.7.11
-Mapping: [&lt;1 0 0 12 8|, &lt;0 1 0 3 3|, &lt;0 0 1 -6 -4|]
+[[Comma list]]: 176/175, 1331/1323
-EDOs: 15, 31, 46, 77, 80, 111
+[[Mapping]]: [{{val| 1 0 0 12 8 }}, {{val| 0 1 0 3 3 }}, {{val| 0 0 1 -6 -4 }}]
-Badness: 0.000679
+{{Val list|legend=1| 15, 31, 46, 77, 80, 111 }}
+[[Badness]]: 0.679 × 10<sup>-3</sup>
 === 13-limit ===
+Subgroup: 2.3.5.7.11.13
 Comma list: 176/175, 1331/1323, 351/350
-Mapping: [&lt;1 0 0 12 8|, &lt;0 1 0 3 3|, &lt;0 0 1 -6 -4|]
+Mapping: [{{val| 1 0 0 12 8 }}, {{val| 0 1 0 3 3 }}, {{val| 0 0 1 -6 -4 }}]
-EDOs: 31, 46, 77, 80, 111
+Vals: {{val list| 31, 46, 77, 80, 111 }}
-Badness: 0.001147
+Badness: 1.147 × 10<sup>-3</sup>
 == Mandos ==
-Comma list: 176/175, 243/242
+Subgroup: 2.3.5.7.11
-Mapping: [&lt;1 1 0 6 2|, &lt;0 2 0 5 5|, &lt;0 0 1 -2 0|]
+[[Comma list]]: 176/175, 243/242
-EDOs: 7, 24, 31, 58, 89
+[[Mapping]]: [{{val| 1 1 0 6 2 }}, {{val| 0 2 0 5 5 }}, {{val| 0 0 1 -2 0 }}]
-Badness: 0.000751
+{{Val list|legend=1| 7, 24, 31, 58, 89 }}
+[[Badness]]: 0.751 × 10<sup>-3</sup>
 === 13-limit ===
+Subgroup: 2.3.5.7.11.13
 Comma list: 144/143, 176/175, 243/242
-Mapping: [&lt;1 1 0 6 2 4|, &lt;0 2 0 5 5 -1|, &lt;0 0 1 -2 0 0|]
+Mapping: [{{val| 1 1 0 6 2 4 }}, {{val| 0 2 0 5 5 -1 }}, {{val| 0 0 1 -2 0 0 }}]
-EDOs: 7, 24, 31, 58
+Vals: {{val list| 7, 24, 31, 58 }}
-Badness: 0.000923
+Badness: 0.923 × 10<sup>-3</sup>
 == Ulmo ==
-Comma list: 176/175, 2200/2187
+Subgroup: 2.3.5.7.11
+[[Comma list]]: 176/175, 2200/2187
-Mapping: [&lt;1 0 0 1, -3|, &lt;0 1 0 7 7|, &lt;0 0 1 -4 -2|]
+[[Mapping]]: [{{val| 1 0 0 1, -3 }}, {{val| 0 1 0 7 7 }}, {{val| 0 0 1 -4 -2 }}]
-EDOs: 7, 39, 46, 53, 80, 126, 179, 259cd, 385bcd
+{{Val list|legend=1| 7, 39, 46, 53, 80, 126, 179, 259cd, 385bcd }}
-Badness: 0.00123
+[[Badness]]: 1.23 × 10<sup>-3</sup>
 === 13-limit ===
+Subgroup: 2.3.5.7.11.13
 Comma list: 169/168, 176/175, 325/324
-Mapping: [&lt;1 0 0 1, -3 2|, &lt;0 1 0 7 7 4|, &lt;0 0 1 -4 -2 -2|]
+Mapping: [{{val| 1 0 0 1, -3 2 }}, {{val| 0 1 0 7 7 4 }}, {{val| 0 0 1 -4 -2 -2 }}]
-EDOs: 7, 39, 46, 53, 80, 133d, 179, 312cdf
+Vals: {{val list| 7, 39, 46, 53, 80, 133d, 179, 312cdf }}
-Badness: 0.000932
+Badness: 0.932 × 10<sup>-3</sup>
 [[Category:Regular temperament theory]]