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:


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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.
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.


== 80&amp;159 temperament ==
== 80&amp;159 yarman ==
Commas: 10976/10935, 244140625/243045684
[[Comma list]]: 10976/10935, 244140625/243045684


[[POTE_tuning|POTE generator]]: ~126/125 = 15.0667
[[Mapping]]: [&lt;1 2 3 4|, &lt;0 -33 -54 -95|]


Map: [&lt;1 2 3 4|, &lt;0 -33 -54 -95|]
{{Multival|legend=1| 33 54 95 9 58 69}}


EDOs: {{EDOs|79d, 80, 159, 239}}
[[POTE generator]]: ~126/125 = 15.0667


Badness: 0.193315
{{Val list|legend=1| 79d, 80, 159, 239 }}


=== 11-limit yarman ===
[[Badness]]: 0.193315
Commas: 3025/3024, 4000/3993, 10976/10935
 
=== 11-limit ===
Comma list: 3025/3024, 4000/3993, 10976/10935
 
Mapping: [&lt;1 2 3 4 4|, &lt;0 -33 -54 -95 -43|]


POTE generator: ~121/120 = 15.0658
POTE generator: ~121/120 = 15.0658


Map: [&lt;1 2 3 4 4|, &lt;0 -33 -54 -95 -43|]
Vals: {{Val list| 79d, 80, 159, 239 }}


EDOs: {{EDOs|79d, 80, 159, 239}}
Badness: 0.049170


Badness: 0.049170
=== 13-limit ===
Comma list: 325/324, 364/363, 1001/1000, 10976/10935


=== 13-limit yarman ===
Mapping: [&lt;1 2 3 4 4 4|, &lt;0 -33 -54 -95 -43 -24|]
Commas: 325/324, 364/363, 1001/1000, 10976/10935


POTE generator: ~121/120 = 15.0752
POTE generator: ~121/120 = 15.0752


Map: [&lt;1 2 3 4 4 4|, &lt;0 -33 -54 -95 -43 -24|]
Vals: {{Val list| 79d, 80, 159, 239 }}


EDOs: {{EDOs|79d, 80, 159, 239}}
Badness: 0.040929


Badness: 0.040929
== 79&amp;159 yarman ==
[[Comma list]]: 5359375/5308416, 390625000/387420489


== 79&amp;159 temperament ==
[[Mapping]]: [&lt;1 2 3 2|, &lt;0 -33 -54 64|]
Commas: 5359375/5308416, 390625000/387420489


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


Map: [&lt;1 2 3 2|, &lt;0 -33 -54 64|]
{{Val list|legend=1| 79, 80d, 159, 238c, 239d }}


EDOs: {{EDOs|79, 80d, 159, 238c, 239d}}
[[Badness]]: 0.655487


Badness: 0.655487
=== 11-limit ===
Comma list: 385/384, 4000/3993, 78121827/77948684


=== 11-limit 79&amp;159 ===
Mapping: [&lt;1 2 3 2 4|, &lt;0 -33 -54 64 -43|]
Commas: 385/384, 4000/3993, 78121827/77948684


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


Map: [&lt;1 2 3 2 4|, &lt;0 -33 -54 64 -43|]
Vals: {{Val list| 79, 80d, 159, 238c, 239d }}


EDOs: {{EDOs|79, 80d, 159, 238c, 239d}}
Badness: 0.143477


Badness: 0.143477
=== 13-limit ===
Comma list: 325/324, 385/384, 1575/1573, 85683/85184


=== 13-limit 79&amp;159 ===
Mapping: [&lt;1 2 3 2 4 4|, &lt;0 -33 -54 64 -43 -24|]
Commas: 325/324, 385/384, 1575/1573, 85683/85184


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


Map: [&lt;1 2 3 2 4 4|, &lt;0 -33 -54 64 -43 -24|]
Vals: {{Val list| 79, 80d, 159, 238cf, 239d }}
 
EDOs: {{EDOs|79, 80d, 159, 238cf, 239d}}


Badness: 0.068150
Badness: 0.068150


=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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== 11-limit ==
== 11-limit ==
Commas: 225/224, 243/242, 3125/3087
[[Comma list]]: 225/224, 243/242, 3125/3087


[[POTE_tuning|POTE generator]]: ~11/9 = 350.994
[[Mapping]]: [&lt;1 1 7 11 2|, &lt;0 2 -16 -28 5|]


Map: [&lt;1 1 7 11 2|, &lt;0 2 -16 -28 5|]
[[POTE generator]]: ~11/9 = 350.994


EDOs: {{EDOs|41, 106, 147}}
{{Val list| 41, 106, 147 }}


Badness: 0.041562
[[Badness]]: 0.041562


== 13-limit ==
== 13-limit ==
Commas: 225/224, 243/242, 325/324, 640/637
Comma list: 225/224, 243/242, 325/324, 640/637
 
Mapping: [&lt;1 1 7 11 2 -8|, &lt;0 2 -16 -28 5 40|]


POTE generator: ~11/9 = 351.014
POTE generator: ~11/9 = 351.014


Map: [&lt;1 1 7 11 2 -8|, &lt;0 2 -16 -28 5 40|]
Vals: {{Val list| 41, 106, 147 }}
 
EDOs: {{EDOs|41, 106, 147}}


Badness: 0.042564
Badness: 0.042564


[[Category:temperament]]
[[Category:Temperament]]
[[Category:Rank 2]]

Revision as of 21:33, 26 April 2021

Yarman temperament

Ozan Yarman has proposed defining the tuning of Turkish maqam music using a MOS of 79 or 80 notes out of 159. This means a generator of 2/159, which suggests the 19-limit mapping:

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

The first mapping may be called 79&159 in terms of patent vals, 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

Comma list: 10976/10935, 244140625/243045684

Mapping: [<1 2 3 4|, <0 -33 -54 -95|]

Wedgie: ⟨⟨ 33 54 95 9 58 69 ]]

POTE generator: ~126/125 = 15.0667

Template:Val list

Badness: 0.193315

11-limit

Comma list: 3025/3024, 4000/3993, 10976/10935

Mapping: [<1 2 3 4 4|, <0 -33 -54 -95 -43|]

POTE generator: ~121/120 = 15.0658

Vals: Template:Val list

Badness: 0.049170

13-limit

Comma list: 325/324, 364/363, 1001/1000, 10976/10935

Mapping: [<1 2 3 4 4 4|, <0 -33 -54 -95 -43 -24|]

POTE generator: ~121/120 = 15.0752

Vals: Template:Val list

Badness: 0.040929

79&159 yarman

Comma list: 5359375/5308416, 390625000/387420489

Mapping: [<1 2 3 2|, <0 -33 -54 64|]

POTE generator: ~6144/6125 = 15.1062

Template:Val list

Badness: 0.655487

11-limit

Comma list: 385/384, 4000/3993, 78121827/77948684

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

POTE generator: ~121/120 = 15.1071

Vals: Template:Val list

Badness: 0.143477

13-limit

Comma list: 325/324, 385/384, 1575/1573, 85683/85184

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

POTE generator: ~121/120 = 15.1071

Vals: Template:Val list

Badness: 0.068150

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:

<<2 -16 -28 5 40 -30 -50 1 56 -20 67 152 111 216 120||

which in the 11-limit becomes:

<<2 -16 -28 5 -30 -50 1 -20 67 111||

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

11-limit

Comma list: 225/224, 243/242, 3125/3087

Mapping: [<1 1 7 11 2|, <0 2 -16 -28 5|]

POTE generator: ~11/9 = 350.994

Template:Val list

Badness: 0.041562

13-limit

Comma list: 225/224, 243/242, 325/324, 640/637

Mapping: [<1 1 7 11 2 -8|, <0 2 -16 -28 5 40|]

POTE generator: ~11/9 = 351.014

Vals: Template:Val list

Badness: 0.042564

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