Ragismic microtemperaments: Difference between revisions

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@@ Line 1,214: / Line 1,214: @@
 Badness: 0.0213
+== Aluminium ==
+''Aluminium'' is named after the 13th element, and tempers out the {{monzo| 92 -39 -13 }} comma which sets [[135/128]] interval to be equal to 1/13th of the octave.
+[[Subgroup]]: 2.3.5
+[[Comma list]]: {{monzo| 92 -39 -13 }}
+[[Mapping]]: [{{val| 13 0 92 }}, {{val| 0 1 -3 }}]
+Mapping generators: ~135/128, ~3
+[[Optimal tuning]] ([[CTE]]): ~135/128 = 1\13, ~3/2 = 701.9897
+{{Val list|legend=1| 65, 299, 364, 429, 494, 559, 1053, 1612, 5889, 7501, 9113, 10725, 23062bc, 33787bcc, 44512bbcc }}
+[[Badness]]: 0.123
+=== 7-limit ===
+[[Subgroup]]: 2.3.5.7
+[[Comma list]]: 4375/4374, {{monzo| 92 -39 -13 }}
+[[Mapping]]: [{{val| 13 0 92 -355 }}, {{val| 0 1 -3 19 }}]
+[[Optimal tuning]] ([[CTE]]): ~135/128 = 1\13, ~3/2 = 702.0024
+{{Val list|legend=1| 494, 1053, 1547, 8788, 10335, 11882, 13429b, 14976b }}
+[[Badness]]: 0.126
+=== 11-limit ===
+Subgroup: 2.3.5.7.11
+Comma list: 4375/4374, 234375/234256, 2097152/2096325
+Mapping: [{{val| 13 0 92 -355 148 }}, {{val| 0 1 -3 19 -5 }}]
+Optimal tuning (CTE): ~135/128 = 1\13, ~3/2 = 702.0042
+Optimal GPV sequence: {{val list| 494, 1053, 1547, 3588e, 5135e }}
+Badness: 0.0421
+=== 13-limit ===
+Subgroup: 2.3.5.7.11.13
+Comma list: 4096/4095, 4375/4374, 6656/6655, 78125/78078
+Mapping: [{{val| 13 0 92 -355 148 419 }}, {{val| 0 1 -3 19 -5 -18 }}]
+Optimal tuning (CTE): ~135/128 = 1\13, ~3/2 = 702.0099
+Optimal GPV sequence: {{val list| 494, 1547, 2041, 4576def }}
+Badness: 0.0286
 == Quatracot ==
@@ Line 2,171: / Line 2,227: @@
 Badness: 0.052366
-== Aluminium ==
-Aluminium is named after the 13th element, and tempers out the {{monzo| 92 -39 -13 }} comma which sets [[135/128]] interval to be equal to 1/13th of the octave.
-=== 5-limit ===
-[[Subgroup]]: 2.3.5
-[[Comma list]]: {{monzo| 92 -39 -13 }}
-[[Mapping]]: [{{val| 13 0 92 }}, {{val| 0 1 -3 }}]
-Mapping generators: ~135/128, ~3
-[[Optimal tuning]] ([[CTE]]): ~135/128 = 1\13, ~3/2 = 701.9897
-{{Val list|legend=1| 65, 299, 364, 429, 494, 559, 1053, 1612, 5889, 7501, 9113, 10725, 23062bc, 33787bcc, 44512bbcc }}
-[[Badness]]: 0.123
-=== 7-limit ===
-[[Subgroup]]: 2.3.5.7
-[[Comma list]]: 4375/4374, {{monzo| 92 -39 -13 }}
-[[Mapping]]: [{{val| 13 0 92 -355 }}, {{val| 0 1 -3 19 }}]
-[[Optimal tuning]] ([[CTE]]): ~135/128 = 1\13, ~3/2 = 702.0024
-{{Val list|legend=1| 494, 1053, 1547, 8788, 10335, 11882, 13429b, 14976b }}
-[[Badness]]: 0.126
-=== 11-limit ===
-Subgroup: 2.3.5.7.11
-Comma list: 4375/4374, 234375/234256, 2097152/2096325
-Mapping: [{{val| 13 0 92 -355 148 }}, {{val| 0 1 -3 19 -5 }}]
-Optimal tuning (CTE): ~135/128 = 1\13, ~3/2 = 702.0042
-Optimal GPV sequence: {{val list| 494, 1053, 1547, 3588e, 5135e }}
-Badness: 0.0421
-=== 13-limit ===
-Subgroup: 2.3.5.7.11.13
-Comma list: 4096/4095, 4375/4374, 6656/6655, 78125/78078
-Mapping: [{{val| 13 0 92 -355 148 419 }}, {{val| 0 1 -3 19 -5 -18 }}]
-Optimal tuning (CTE): ~135/128 = 1\13, ~3/2 = 702.0099
-Optimal GPV sequence: {{val list| 494, 1547, 2041, 4576def }}
-Badness: 0.0286
 [[Category:Temperament collections]]