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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 yarman ==
== Yarman I (80&159) ==
[[Comma list]]: 10976/10935, 244140625/243045684
[[Comma list]]: 10976/10935, 244140625/243045684


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Badness: 0.040929
Badness: 0.040929


== 79&159 yarman ==
=== 17-limit ===
Comma list: 325/324, 364/363, 595/594, 1001/1000, 10976/10935
 
Mapping: [<1 2 3 4 4 4 4|, <0 -33 -54 -95 -43 -24 7|]
 
POTE generator: ~120/119 = 15.0715
 
Vals: {{Val list| 79d, 80, 159, 239 }}
 
Badness: 0.031015
 
=== 19-limit ===
Comma list: 325/324, 361/360, 364/363, 595/594, 1001/1000, 1521/1520
 
Mapping: [<1 2 3 4 4 4 4 5|, <0 -33 -54 -95 -43 -24 7 -60|]
 
POTE generator: ~120/119 = 15.0713
 
Vals: {{Val list| 79dh, 80, 159, 239 }}
 
Badness: 0.023193
 
== Yarman II (79&159) ==
[[Comma list]]: 5359375/5308416, 390625000/387420489
[[Comma list]]: 5359375/5308416, 390625000/387420489


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[[POTE generator]]: ~6144/6125 = 15.1062
[[POTE generator]]: ~6144/6125 = 15.1062


{{Val list|legend=1| 79, 80d, 159, 238c, 239d }}
{{Val list|legend=1| 79, 80d, 159 }}


[[Badness]]: 0.655487
[[Badness]]: 0.655487
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POTE generator: ~121/120 = 15.1071
POTE generator: ~121/120 = 15.1071


Vals: {{Val list| 79, 80d, 159, 238c, 239d }}
Vals: {{Val list| 79, 80d, 159 }}


Badness: 0.143477
Badness: 0.143477
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Mapping: [<1 2 3 2 4 4|, <0 -33 -54 64 -43 -24|]
Mapping: [<1 2 3 2 4 4|, <0 -33 -54 64 -43 -24|]


POTE generator: ~121/120 = 15.1071
POTE generator: ~105/104 = 15.1071


Vals: {{Val list| 79, 80d, 159, 238cf, 239d }}
Vals: {{Val list| 79, 80d, 159 }}


Badness: 0.068150
Badness: 0.068150
=== 17-limit ===
Comma list: 273/272, 325/324, 385/384, 1575/1573, 4928/4913
Mapping: [<1 2 3 2 4 4 4|, <0 -33 -54 64 -43 -24 7|]
POTE generator: ~105/104 = 15.1037
Vals: {{Val list| 79, 80d, 159 }}
Badness: 0.051019


= Karadeniz temperament =
= Karadeniz temperament =
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