Lehmerismic temperaments: Difference between revisions
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These are rank three temperaments tempering out 3025/3024, but we can | These are rank three temperaments tempering out [[3025/3024]], but we can begin by looking at the rank four temperament. | ||
Comma: 3025/3024 | Comma: 3025/3024 | ||
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EDOs: 5, 10, 15, 26, 31, 41, 72, 118, 224, 270, 342, 612, 836, 1106, 1448, 2554 | EDOs: 5, 10, 15, 26, 31, 41, 72, 118, 224, 270, 342, 612, 836, 1106, 1448, 2554 | ||
=Tyr= | = Tyr = | ||
{{see also| Landscape family }} | |||
Commas: 3025/3024, 102487/102400 | Commas: 3025/3024, 102487/102400 | ||
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Badness: 0.000259 | Badness: 0.000259 | ||
=Skadi= | = Skadi = | ||
Commas: 3025/3024, 703125/702464 | Commas: 3025/3024, 703125/702464 | ||
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Badness: 0.000349 | Badness: 0.000349 | ||
=Ganesha= | = Ganesha = | ||
Commas: 3025/3024, 5632/5625 | Commas: 3025/3024, 5632/5625 | ||
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Badness: 0.000390 | Badness: 0.000390 | ||
=Hanuman= | = Hanuman = | ||
Commas: 4000/3993 | Commas: 3025/3024, 4000/3993 | ||
Map: [<1 2 0 -8 1|, <0 -3 0 11 1|, <0 0 1 4 1|] | Map: [<1 2 0 -8 1|, <0 -3 0 11 1|, <0 0 1 4 1|] | ||
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Badness: 0.000500 | Badness: 0.000500 | ||
==13-limit== | == 13-limit == | ||
Commas: 625/624, 1575/1573, 2080/2079 | Commas: 625/624, 1575/1573, 2080/2079 | ||
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Badness: 0.000653 | Badness: 0.000653 | ||
[[Category:Theory]] | |||
[[Category:Temperament]] | |||
[[Category:Lehmerismic]] | |||
[[Category:Rank 3]] | |||
Revision as of 06:07, 12 January 2021
These are rank three temperaments tempering out 3025/3024, but we can begin by looking at the rank four temperament.
Comma: 3025/3024
Map: [<1 0 0 0 2|, <0 1 0 1 2|, <0 0 1 0 -1|, <0 0 0 2 1|]
Generators: 2, 3, 5, 55/36
EDOs: 5, 10, 15, 26, 31, 41, 72, 118, 224, 270, 342, 612, 836, 1106, 1448, 2554
Tyr
Commas: 3025/3024, 102487/102400
Map: [<3 0 0 4 8|, <0 2 0 -4 1|, <0 0 1 2 0|]
Generators: 63/50, 400/231, 5
EDOs: 15, 57, 72, 159, 183, 198, 255, 270, 342, 612, 954, 1566
Badness: 0.000259
Skadi
Commas: 3025/3024, 703125/702464
Map: [<1 0 5 8 1|, <0 1 1 3 2|, <0 0 -6 -14 -1|]
Generators: 2, 3, 18/11
EDOs: 31, 97, 121, 152, 311, 342, 836, 1178, 2014
Badness: 0.000349
Ganesha
Commas: 3025/3024, 5632/5625
Map: [<1 0 0 -22 -9|, <0 1 0 1 2|, <0 0 1 10 4|]
Generators: 2, 3, 5
EDOs: 31, 87, 118, 152, 239, 270, 962, 1232, 1502
Badness: 0.000390
Hanuman
Commas: 3025/3024, 4000/3993
Map: [<1 2 0 -8 1|, <0 -3 0 11 1|, <0 0 1 4 1|]
Generators: 2, 11/10, 5
EDOs: 15, 57, 72, 152, 224, 311, 463, 535, 998, 1533ce, 2307ce, 2531cde, 2842bce
Badness: 0.000500
13-limit
Commas: 625/624, 1575/1573, 2080/2079
Map: [<1 2 0 -8 1 -6|, <0 -3 0 11 1 3|, <0 0 1 4 1 4|]
Generators: 2, 11/10, 5
EDOs: 15, 72, 87, 137, 159, 224, 311, 535, 918c, 1142c, 1453c
Badness: 0.000653