Metric microtemperaments: Difference between revisions

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@@ Line 2: / Line 2: @@
 Temperaments not dicussed here include [[Breedsmic temperaments #Tertiaseptal|tertiaseptal]], [[Ragismic microtemperaments #Enneadecal|enneadecal]], [[Schismatic family #Term|term]], [[Mirkwai clan #Grendel|grendel]], [[Hemifamity temperaments #Undim|undim]], [[Wizmic microtemperaments #Qak|qak]], [[Meantone family|meantone]], [[Kleismic family #Marfifths|marfifths]], and [[Semicomma family #Triwell|triwell]].
+= Luminal =
+Luminal tempers out the [[meter comma|meter]] and the [[lux comma|lux]] in the 7-limit, [[3025/3024]] in the 11-limit, [[2080/2079]], [[4096/4095]] in the 13-limit, and [[1156/1155]] and [[2601/2600]] in the 17-limit.
+Subgroup: 2.3.5.7
+[[Comma list]]: 703125/702464, 26843545600/26795786661
+[[Mapping]]: [{{val| 1 0 5 8 }}, {{val| 0 29 -49 -95 }}]
+{{Multival|legend=1| 29 -49 -95 -145 -232 -82 }}
+[[POTE generator]]: ~8505/8192 = 65.5883
+{{Val list|legend=1| 55d, 128, 183, 311, 494, 1299, 1793 }}
+[[Badness]]: 0.1348
+== 11-limit ==
+Subgroup: 2.3.5.7.11
+Comma list: 3025/3024, 131072/130977, 703125/702464
+Mapping: [{{val| 1 0 5 8 1 }}, {{val| 0 29 -49 -95 45 }}]
+POTE generator: ~80/77 = 65.5881
+Vals: {{val list| 55d, 128, 183, 311, 494, 1299, 1793, 2287d }}
+Badness: 0.03282
+== 13-limit ==
+Subgroup: 2.3.5.7.11.13
+Comma list: 2080/2079, 3025/3024, 4096/4095, 31250/31213
+Mapping: [{{val| 1 0 5 8 1 -1 }}, {{val| 0 29 -49 -95 45 86 }}]
+POTE generator: ~27/26 = 65.5883
+Vals: {{val list| 128, 183, 311, 494, 1299, 1793 }}
+Badness: 0.01685
+== 17-limit ==
+Subgroup: 2.3.5.7.11.13.17
+Comma list: 1156/1155, 1275/1274, 2080/2079, 2431/2430, 4096/4095
+Mapping: [{{val| 1 0 5 8 1 -1 6 }}, {{val| 0 29 -49 -95 45 86 -35 }}]
+POTE generator: ~27/26 = 65.5878
+Vals: {{val list| 128, 183, 311, 494 }}
+Badness: 0.01467
 = Decimetra =
@@ Line 12: / Line 68: @@
 [[Mapping]]: [{{val|10 15 23 27}}, {{val|0 4 1 5}}]
-{{Multival|legend=1|40 10 50 -77 -33 88}}
+{{Multival|legend=1| 40 10 50 -77 -33 88 }}
 [[POTE generator]]: ~5/4 = 385.495