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Turkish maqam music temperaments: Difference between revisions

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==Yarman temperament==
=Yarman temperament=
[[Ozan Yarman]] has proposed defining the tuning of Turkish maqam <span style="">music</span> using a [[MOSScales|MOS]] of 79 or 80 notes out of 159. This means a generator of 2/159, which suggests the 19-limit mapping:
[[Ozan Yarman]] has proposed defining the tuning of Turkish maqam <span style="">music</span> using a [[MOSScales|MOS]] of 79 or 80 notes out of 159. This means a generator of 2/159, which suggests the 19-limit mapping:


[&lt;1 2 3 2 4 4 4 5|, &lt;0 -33 -54 64 -43 -24 7 -60|]
[&lt;1 2 3 2 4 4 4 5|, &lt;0 -33 -54 64 -43 -24 7 -60|] <br>vs. <br>[&lt;1 2 3 4 4 4 4 5|, &lt;0 -33 -54 -95 -43 -24 7 -60|]


or
The first mapping may be called 79&amp;159 in terms of [[patent val]]s, and the second 80&amp;159. In any event both mappings can be used inconsistently. A Pythagorean tuning, i.e. one with pure fifths, is also possible.
 
== 7-limit 80&amp;159 ==
Commas: 10976/10935, 244140625/243045684
 
[[POTE_tuning|POTE generator]]: ~126/125 = 15.0667
 
Map: [&lt;1 2 3 4|, &lt;0 -33 -54 -95|]
 
EDOs: {{EDOs|79d, 80, 159, 239}}
 
Badness: 0.193315


[&lt;1 2 3 4 4 4 4 5|, &lt;0 -33 -54 -95 -43 -24 7 -60|]
== 7-limit 79&amp;159 ==
Commas: 5359375/5308416, 390625000/387420489


The first mapping may be called 79&amp;159 in terms of [[patent val]]s, and the second 80&amp;159. In any event both mappings can be used inconsistently. A Pythagorean tuning, i.e. one with pure fifths, is also possible.
[[POTE_tuning|POTE generator]]: ~6144/6125 = 15.1062
 
Map: [&lt;1 2 3 2|, &lt;0 -33 -54 64|]
 
EDOs: {{EDOs|79, 80d, 159, 238c, 239d}}
 
Badness: 0.655487


==Karadeniz temperament==
=Karadeniz temperament=
K. E. Karadeniz proposed a 41 note MOS with generator 31/106, giving a "hemigaribaldi" type of tuning, with an 11/9 neutral third generator. It's more plausible as an 11-limit system than 13-limit; the 13-limit wedgie is:
K. E. Karadeniz proposed a 41 note MOS with generator 31/106, giving a "hemigaribaldi" type of tuning, with an 11/9 neutral third generator. It's more plausible as an 11-limit system than 13-limit; the 13-limit wedgie is:


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It tempers out 3125/3087, 4000/3969, 243/242, 5120/5103, 225/224, and 3025/3024, and can also be called 41&amp;106. Aside from 31/106, 43/147 or 74/253 can be recommended as generators.
It tempers out 3125/3087, 4000/3969, 243/242, 5120/5103, 225/224, and 3025/3024, and can also be called 41&amp;106. Aside from 31/106, 43/147 or 74/253 can be recommended as generators.


== 11-limit ==
Commas: 225/224, 243/242, 3125/3087
Commas: 225/224, 243/242, 3125/3087


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