Lehmerismic temperaments: Difference between revisions

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-These are rank three temperaments tempering out [[3025/3024]], but we can begin by looking at the rank four temperament.
+These are rank-3 temperaments tempering out [[3025/3024]], but we can begin by looking at the rank-4 temperament.
-Comma: 3025/3024
+= Lehmerismic =
+Subgroup: 2.3.5.7.11
-Map: [&lt;1 0 0 0 2|, &lt;0 1 0 1 2|, &lt;0 0 1 0 -1|, &lt;0 0 0 2 1|]
+[[Comma list]]: 3025/3024
-Generators: 2, 3, 5, 55/36
+[[Mapping]]: [{{val| 1 0 0 0 2 }}, {{val| 0 1 0 1 2 }}, {{val| 0 0 1 0 -1 }}, {{val| 0 0 0 2 1 }}]
-EDOs: 5, 10, 15, 26, 31, 41, 72, 118, 224, 270, 342, 612, 836, 1106, 1448, 2554
+Mapping generators: ~2, ~3, ~5, ~55/36
+{{Val list|legend=1| 5, 10, 15, 26, 31, 41, 72, 118, 224, 270, 342, 612, 836, 1106, 1448, 2554 }}
 = Tyr =
 {{see also| Landscape family }}
-Commas: 3025/3024, 102487/102400
+Subgroup: 2.3.5.7.11
-Map: [&lt;3 0 0 4 8|, &lt;0 2 0 -4 1|, &lt;0 0 1 2 0|]
+[[Comma list]]: 3025/3024, 102487/102400
-Generators: 63/50, 400/231, 5
+[[Mapping]]: [{{val| 3 0 0 4 8 }}, {{val| 0 2 0 -4 1 }}, {{val| 0 0 1 2 0 }}]
-EDOs: 15, 57, 72, 159, 183, 198, 255, 270, 342, 612, 954, 1566
+Mapping generators: ~63/50, ~400/231, ~5
-Badness: 0.000259
+{{Val list|legend=1| 15, 57, 72, 159, 183, 198, 255, 270, 342, 612, 954, 1566 }}
+[[Badness]]: 0.259 × 10<sup>-3</sup>
 = Skadi =
-Commas: 3025/3024, 703125/702464
-Map: [&lt;1 0 5 8 1|, &lt;0 1 1 3 2|, &lt;0 0 -6 -14 -1|]
+Subgroup: 2.3.5.7.11
-Generators: 2, 3, 18/11
+[[Comma list]]: 3025/3024, 703125/702464
-EDOs: 31, 97, 121, 152, 311, 342, 836, 1178, 2014
+[[Mapping]]: [{{val| 1 0 5 8 1 }}, {{val| 0 1 1 3 2 }}, {{val| 0 0 -6 -14 -1 }}]
-Badness: 0.000349
+Mapping generators: ~2, ~3, ~18/11
+{{Val list|legend=1| 31, 97, 121, 152, 311, 342, 836, 1178, 2014 }}
+[[Badness]]: 0.349 × 10<sup>-3</sup>
 = Ganesha =
-Commas: 3025/3024, 5632/5625
-Map: [&lt;1 0 0 -22 -9|, &lt;0 1 0 1 2|, &lt;0 0 1 10 4|]
+Subgroup: 2.3.5.7.11
+[[Comma list]]: 3025/3024, 5632/5625
+[[Mapping]]: [{{val| 1 0 0 -22 -9 }}, {{val| 0 1 0 1 2 }}, {{val| 0 0 1 10 4 }}]
-Generators: 2, 3, 5
+Mapping generators: ~2, ~3, ~5
-EDOs: 31, 87, 118, 152, 239, 270, 962, 1232, 1502
+{{Val list|legend=1| 31, 87, 118, 152, 239, 270, 962, 1232, 1502 }}
-Badness: 0.000390
+[[Badness]]: 0.390 × 10<sup>-3</sup>
 = Hanuman =
-Commas: 3025/3024, 4000/3993
-Map: [&lt;1 2 0 -8 1|, &lt;0 -3 0 11 1|, &lt;0 0 1 4 1|]
+Subgroup: 2.3.5.7.11
-Generators: 2, 11/10, 5
+[[Comma list]]: 3025/3024, 4000/3993
-EDOs: 15, 57, 72, 152, 224, 311, 463, 535, 998, 1533ce, 2307ce, 2531cde, 2842bce
+[[Mapping]]: [{{val| 1 2 0 -8 1 }}, {{val| 0 -3 0 11 1 }}, {{val| 0 0 1 4 1 }}]
-Badness: 0.000500
+Mapping generators: ~2, ~11/10, ~5
+{{Val list|legend=1| 15, 57, 72, 152, 224, 311, 463, 535, 998, 1533ce, 2307ce, 2531cde, 2842bce }}
+[[Badness]]: 0.500 × 10<sup>-3</sup>
 == 13-limit ==
-Commas: 625/624, 1575/1573, 2080/2079
-Map: [&lt;1 2 0 -8 1 -6|, &lt;0 -3 0 11 1 3|, &lt;0 0 1 4 1 4|]
+Subgroup: 2.3.5.7.11.13
+Comma list: 625/624, 1575/1573, 2080/2079
+Mapping: [{{val| 1 2 0 -8 1 -6 }}, {{val| 0 -3 0 11 1 3 }}, {{val| 0 0 1 4 1 4 }}]
-Generators: 2, 11/10, 5
+Mapping generators: ~2, ~11/10, ~5
-EDOs: 15, 72, 87, 137, 159, 224, 311, 535, 918c, 1142c, 1453c
+Vals: {{Val list| 15, 72, 87, 137, 159, 224, 311, 535, 918c, 1142c, 1453c }}
-Badness: 0.000653
+Badness: 0.653 × 10<sup>-3</sup>
-[[Category:Theory]]
+[[Category:Regular temperament theory]]
 [[Category:Temperament]]
 [[Category:Lehmerismic]]
 [[Category:Rank 3]]