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


Line 41: Line 41:
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


Line 48: Line 70:
[[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
Line 59: Line 81:
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
Line 68: Line 90:
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 =

Revision as of 13:57, 28 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.

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

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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