Valinorsmic clan: Difference between revisions
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The valinorsmic rank three temperaments temper out the [[valinorsma]], | 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.) | ||
=Rank four valinorsmic temperament= | = Rank four valinorsmic temperament = | ||
Comma: 176/175 | Comma: 176/175 | ||
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EDOs: 22, 31, 46, 53, 58, 80, 111 | EDOs: 22, 31, 46, 53, 58, 80, 111 | ||
=Manwe= | = Manwe = | ||
Commas: 176/175, 1331/1323 | Commas: 176/175, 1331/1323 | ||
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Badness: 0.000679 | Badness: 0.000679 | ||
==13-limit== | == 13-limit == | ||
Commas: 176/175, 1331/1323, 351/350 | Commas: 176/175, 1331/1323, 351/350 | ||
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Badness: 0.001147 | Badness: 0.001147 | ||
=Varda= | = Varda = | ||
Commas: 176/175, 896/891 | Commas: 176/175, 896/891 | ||
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Badness: 0.000728 | Badness: 0.000728 | ||
==13-limit== | == 13-limit == | ||
Commas: 176/175, 352/351, 364/363 | Commas: 176/175, 352/351, 364/363 | ||
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Badness: 0.000970 | Badness: 0.000970 | ||
=Mandos= | = Mandos = | ||
Commas: 176/175, 243/242 | Commas: 176/175, 243/242 | ||
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Badness: 0.000751 | Badness: 0.000751 | ||
==13-limit== | == 13-limit == | ||
Commas: 144/143, 176/175, 243/242 | Commas: 144/143, 176/175, 243/242 | ||
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Badness: 0.000923 | Badness: 0.000923 | ||
=Ulmo= | = Ulmo = | ||
Commas: 176/175, 2200/2187 | Commas: 176/175, 2200/2187 | ||
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Badness: 0.00123 | Badness: 0.00123 | ||
==13-limit== | == 13-limit == | ||
Commas: 169/168, 176/175, 325/324 | Commas: 169/168, 176/175, 325/324 | ||
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Badness: 0.000932 | Badness: 0.000932 | ||
[[Category:Theory]] | |||
[[Category:Temperament]] | |||
[[Category:Valinorsmic]] | [[Category:Valinorsmic]] | ||
[[Category:Rank 3]] | |||
Revision as of 06:28, 12 January 2021
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.)
Rank four valinorsmic temperament
Comma: 176/175
Map: [<1 0 0 0 -4|, <0 1 0 0 0|, <0 0 1 0 2|, <0 0 0 1 1|]
EDOs: 22, 31, 46, 53, 58, 80, 111
Manwe
Commas: 176/175, 1331/1323
Map: [<1 0 0 12 8|, <0 1 0 3 3|, <0 0 1 -6 -4|]
EDOs: 15, 31, 46, 77, 80, 111
Badness: 0.000679
13-limit
Commas: 176/175, 1331/1323, 351/350
Map: [<1 0 0 12 8|, <0 1 0 3 3|, <0 0 1 -6 -4|]
EDOs: 31, 46, 77, 80, 111
Badness: 0.001147
Varda
Commas: 176/175, 896/891
Map: [<2 0 11 0 14|, <0 1 -2 0 -4|, <0 0 0 1 1|]
EDOs: 12, 22, 46, 58, 80, 126
Badness: 0.000728
13-limit
Commas: 176/175, 352/351, 364/363
Map: [<2 0 11 0 14 24|, <0 1 -2 0 -4 -7|, <0 0 0 1 1 1|]
EDOs: 22, 46, 58, 80, 138cde, 242cde, 322bcde
Badness: 0.000970
Mandos
Commas: 176/175, 243/242
Map: [<1 1 0 6 2|, <0 2 0 5 5|, <0 0 1 -2 0|]
EDOs: 7, 24, 31, 58, 89
Badness: 0.000751
13-limit
Commas: 144/143, 176/175, 243/242
Map: [<1 1 0 6 2 4|, <0 2 0 5 5 -1|, <0 0 1 -2 0 0|]
EDOs: 7, 24, 31, 58
Badness: 0.000923
Ulmo
Commas: 176/175, 2200/2187
Map: [<1 0 0 1, -3|, <0 1 0 7 7|, <0 0 1 -4 -2|]
EDOs: 7, 39, 46, 53, 80, 126, 179, 259cd, 385bcd
Badness: 0.00123
13-limit
Commas: 169/168, 176/175, 325/324
Map: [<1 0 0 1, -3 2|, <0 1 0 7 7 4|, <0 0 1 -4 -2 -2|]
EDOs: 7, 39, 46, 53, 80, 133d, 179, 312cdf
Badness: 0.000932