Turkish maqam music temperaments: Difference between revisions

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


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.
Line 9: Line 9:
[[Comma list]]: 10976/10935, 244140625/243045684
[[Comma list]]: 10976/10935, 244140625/243045684


[[Mapping]]: [&lt;1 2 3 4|, &lt;0 -33 -54 -95|]
[[Mapping]]: [{{val|1 2 3 4}}, {{val|0 -33 -54 -95}}]


{{Multival|legend=1| 33 54 95 9 58 69}}
{{Multival|legend=1| 33 54 95 9 58 69}}
Line 22: Line 22:
Comma list: 3025/3024, 4000/3993, 10976/10935
Comma list: 3025/3024, 4000/3993, 10976/10935


Mapping: [&lt;1 2 3 4 4|, &lt;0 -33 -54 -95 -43|]
Mapping: [{{val|1 2 3 4 4}}, {{val|0 -33 -54 -95 -43}}]


POTE generator: ~121/120 = 15.0658
POTE generator: ~121/120 = 15.0658
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Comma list: 325/324, 364/363, 1001/1000, 10976/10935
Comma list: 325/324, 364/363, 1001/1000, 10976/10935


Mapping: [&lt;1 2 3 4 4 4|, &lt;0 -33 -54 -95 -43 -24|]
Mapping: [{{val|1 2 3 4 4 4}}, {{val|0 -33 -54 -95 -43 -24}}]


POTE generator: ~121/120 = 15.0752
POTE generator: ~121/120 = 15.0752
Line 44: Line 44:
Comma list: 325/324, 364/363, 595/594, 1001/1000, 10976/10935
Comma list: 325/324, 364/363, 595/594, 1001/1000, 10976/10935


Mapping: [&lt;1 2 3 4 4 4 4|, &lt;0 -33 -54 -95 -43 -24 7|]
Mapping: [{{val|1 2 3 4 4 4 4}}, {{val|0 -33 -54 -95 -43 -24 7}}]


POTE generator: ~120/119 = 15.0715
POTE generator: ~120/119 = 15.0715
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Comma list: 325/324, 361/360, 364/363, 595/594, 1001/1000, 1521/1520
Comma list: 325/324, 361/360, 364/363, 595/594, 1001/1000, 1521/1520


Mapping: [&lt;1 2 3 4 4 4 4 5|, &lt;0 -33 -54 -95 -43 -24 7 -60|]
Mapping: [{{val|1 2 3 4 4 4 4 5}}, {{val|0 -33 -54 -95 -43 -24 7 -60}}]


POTE generator: ~120/119 = 15.0713
POTE generator: ~120/119 = 15.0713
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[[Comma list]]: 5359375/5308416, 390625000/387420489
[[Comma list]]: 5359375/5308416, 390625000/387420489


[[Mapping]]: [&lt;1 2 3 2|, &lt;0 -33 -54 64|]
[[Mapping]]: [{{val|1 2 3 2}}, {{val|0 -33 -54 64}}]


[[POTE generator]]: ~6144/6125 = 15.1062
[[POTE generator]]: ~6144/6125 = 15.1062
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Comma list: 385/384, 4000/3993, 78121827/77948684
Comma list: 385/384, 4000/3993, 78121827/77948684


Mapping: [&lt;1 2 3 2 4|, &lt;0 -33 -54 64 -43|]
Mapping: [{{val|1 2 3 2 4}}, {{val|0 -33 -54 64 -43}}]


POTE generator: ~121/120 = 15.1071
POTE generator: ~121/120 = 15.1071
Line 88: Line 88:
Comma list: 325/324, 385/384, 1575/1573, 85683/85184
Comma list: 325/324, 385/384, 1575/1573, 85683/85184


Mapping: [&lt;1 2 3 2 4 4|, &lt;0 -33 -54 64 -43 -24|]
Mapping: [{{val|1 2 3 2 4 4}}, {{val|0 -33 -54 64 -43 -24}}]


POTE generator: ~105/104 = 15.1071
POTE generator: ~105/104 = 15.1071
Line 99: Line 99:
Comma list: 273/272, 325/324, 385/384, 1575/1573, 4928/4913
Comma list: 273/272, 325/324, 385/384, 1575/1573, 4928/4913


Mapping: [&lt;1 2 3 2 4 4 4|, &lt;0 -33 -54 64 -43 -24 7|]
Mapping: [{{val|1 2 3 2 4 4 4}}, {{val|0 -33 -54 64 -43 -24 7}}]


POTE generator: ~105/104 = 15.1037
POTE generator: ~105/104 = 15.1037
Line 106: Line 106:


Badness: 0.051019
Badness: 0.051019
=== 19-limit ===
Comma list: 273/272, 325/324, 385/384, 665/663, 969/968, 1575/1573
Mapping: [{{val|1 2 3 2 4 4 4 5}}, {{val|0 -33 -54 64 -43 -24 7 -60}}]
POTE generator: ~105/104 = 15.1013
Vals: {{Val list| 79h, 159 }}
Badness: 0.038430


= 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:


&lt;&lt;2 -16 -28 5 40 -30 -50 1 56 -20 67 152 111 216 120||
{{multival|2 -16 -28 5 40 -30 -50 1 56 -20 67 152 111 216 120}}


which in the 11-limit becomes:
which in the 11-limit becomes:


&lt;&lt;2 -16 -28 5 -30 -50 1 -20 67 111||
{{multival|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&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.
Line 121: Line 132:
[[Comma list]]: 225/224, 243/242, 3125/3087
[[Comma list]]: 225/224, 243/242, 3125/3087


[[Mapping]]: [&lt;1 1 7 11 2|, &lt;0 2 -16 -28 5|]
[[Mapping]]: [{{val|1 1 7 11 2}}, {{val|0 2 -16 -28 5}}]


[[POTE generator]]: ~11/9 = 350.994
[[POTE generator]]: ~11/9 = 350.994


{{Val list| 41, 106, 147 }}
{{Val list|legend=1| 41, 106, 147 }}


[[Badness]]: 0.041562
[[Badness]]: 0.041562
Line 132: Line 143:
Comma list: 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|]
Mapping: [{{val|1 1 7 11 2 -8}}, {{val|0 2 -16 -28 5 40}}]


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

Revision as of 09:50, 15 May 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.

Yarman I (80&159)

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

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: Template:Val list

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: Template:Val list

Badness: 0.023193

Yarman II (79&159)

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: ~105/104 = 15.1071

Vals: Template:Val list

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: Template:Val list

Badness: 0.051019

19-limit

Comma list: 273/272, 325/324, 385/384, 665/663, 969/968, 1575/1573

Mapping: [⟨1 2 3 2 4 4 4 5], ⟨0 -33 -54 64 -43 -24 7 -60]]

POTE generator: ~105/104 = 15.1013

Vals: Template:Val list

Badness: 0.038430

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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