Turkish maqam music temperaments: Difference between revisions
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The first mapping may be called 79&159 in terms of [[patent val]]s, and the second 80&159. In any event both mappings can be used inconsistently. A Pythagorean tuning, i.e. one with pure fifths, is also possible. | The first mapping may be called 79&159 in terms of [[patent val]]s, and the second 80&159. In any event both mappings can be used inconsistently. A Pythagorean tuning, i.e. one with pure fifths, is also possible. | ||
== | == 80&159 temperament == | ||
Commas: 10976/10935, 244140625/243045684 | Commas: 10976/10935, 244140625/243045684 | ||
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Badness: 0.193315 | Badness: 0.193315 | ||
== | === 11-limit yarman === | ||
Commas: 3025/3024, 4000/3993, 10976/10935 | |||
POTE generator: ~121/120 = 15.0658 | |||
Map: [<1 2 3 4 4|, <0 -33 -54 -95 -43|] | |||
EDOs: {{EDOs|79d, 80, 159, 239}} | |||
Badness: 0.049170 | |||
=== 13-limit yarman === | |||
Commas: 325/324, 364/363, 1001/1000, 10976/10935 | |||
POTE generator: ~121/120 = 15.0752 | |||
Map: [<1 2 3 4 4 4|, <0 -33 -54 -95 -43 -24|] | |||
EDOs: {{EDOs|79d, 80, 159, 239}} | |||
Badness: 0.040929 | |||
== 79&159 temperament == | |||
Commas: 5359375/5308416, 390625000/387420489 | Commas: 5359375/5308416, 390625000/387420489 | ||
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Badness: 0.655487 | Badness: 0.655487 | ||
=== 11-limit 79&159 === | |||
Commas: 385/384, 4000/3993, 78121827/77948684 | |||
POTE generator: ~121/120 = 15.1071 | |||
Map: [<1 2 3 2 4|, <0 -33 -54 64 -43|] | |||
EDOs: {{EDOs|79, 80d, 159, 238c, 239d}} | |||
Badness: 0.143477 | |||
=== 13-limit 79&159 === | |||
Commas: 325/324, 385/384, 1575/1573, 85683/85184 | |||
POTE generator: ~121/120 = 15.1071 | |||
Map: [<1 2 3 2 4 4|, <0 -33 -54 64 -43 -24|] | |||
EDOs: {{EDOs|79, 80d, 159, 238cf, 239d}} | |||
Badness: 0.068150 | |||
=Karadeniz temperament= | =Karadeniz temperament= | ||
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Commas: 225/224, 243/242, 3125/3087 | Commas: 225/224, 243/242, 3125/3087 | ||
[[POTE_tuning|POTE generator]]: 350.994 | [[POTE_tuning|POTE generator]]: ~11/9 = 350.994 | ||
Map: [<1 1 7 11 2|, <0 2 -16 -28 5|] | Map: [<1 1 7 11 2|, <0 2 -16 -28 5|] | ||
EDOs: 41, 106, 147, | EDOs: {{EDOs|41, 106, 147}} | ||
Badness: 0.041562 | |||
== 13-limit == | |||
Commas: 225/224, 243/242, 325/324, 640/637 | |||
POTE generator: ~11/9 = 351.014 | |||
Map: [<1 1 7 11 2 -8|, <0 2 -16 -28 5 40|] | |||
EDOs: {{EDOs|41, 106, 147}} | |||
Badness: 0.042564 | |||
[[Category:temperament]] | [[Category:temperament]] | ||