Turkish maqam music temperaments: Difference between revisions

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This is a collection of some proposed temperaments for Turkish maqam music.  
This is a collection of some proposed [[temperament]]s for [[Arabic, Turkish, Persian music|Turkish maqam music]].  


== Yarman I ==
== Yarman I ==
[[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 mappings:
[[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 mappings:


[{{val| 1 2 3 2 4 4 4 5 }}, {{val| 0 -33 -54 64 -43 -24 7 -60 }}]
* {{Mapping| 1 2 3 2 4 4 4 5 | 0 -33 -54 64 -43 -24 7 -60 }}
* {{Mapping| 1 2 3 4 4 4 4 5 | 0 -33 -54 -95 -43 -24 7 -60 }}


[{{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 & 159 in terms of [[patent val]]s, and the second 80 & 159. In any event both mappings can be used inconsistently, and both temperaments are weak [[7-limit]] extensions of [[Orwellismic temperaments #Quartonic|quartonic]] temperament. 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, and both temperaments are weak [[7-limit]] extensions of [[Orwellismic temperaments #Quartonic|quartonic]] temperament. A Pythagorean tuning, i.e. one with pure fifths, is also possible.
[[Subgroup]]: 2.3.5.7
 
Subgroup: 2.3.5.7


[[Comma list]]: 10976/10935, 244140625/243045684
[[Comma list]]: 10976/10935, 244140625/243045684


[[Mapping]]: [{{val| 1 2 3 4 }}, {{val| 0 -33 -54 -95 }}]
{{Mapping|legend=1| 1 2 3 4 | 0 -33 -54 -95 }}


{{Multival|legend=1| 33 54 95 9 58 69}}
{{Multival|legend=1| 33 54 95 9 58 69}}


[[POTE generator]]: ~126/125 = 15.0667
[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~126/125 = 15.0667


{{Optimal ET sequence|legend=1| 79d, 80, 159, 239 }}
{{Optimal ET sequence|legend=1| 79d, 80, 159, 239 }}
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Comma list: 3025/3024, 4000/3993, 10976/10935
Comma list: 3025/3024, 4000/3993, 10976/10935


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


POTE generator: ~121/120 = 15.0658
Optimal tuning (POTE): ~2 = 1\1, ~121/120 = 15.0658


{{Optimal ET sequence|legend=1| 79d, 80, 159, 239 }}
{{Optimal ET sequence|legend=1| 79d, 80, 159, 239 }}
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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: [{{val| 1 2 3 4 4 4 }}, {{val| 0 -33 -54 -95 -43 -24 }}]
Mapping: {{mapping| 1 2 3 4 4 4 | 0 -33 -54 -95 -43 -24 }}


POTE generator: ~121/120 = 15.0752
Optimal tuning (POTE): ~2 = 1\1, ~121/120 = 15.0752


{{Optimal ET sequence|legend=1| 79d, 80, 159, 239 }}
{{Optimal ET sequence|legend=1| 79d, 80, 159, 239 }}
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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: [{{val| 1 2 3 4 4 4 4 }}, {{val| 0 -33 -54 -95 -43 -24 7 }}]
Mapping: {{mapping| 1 2 3 4 4 4 4 | 0 -33 -54 -95 -43 -24 7 }}


POTE generator: ~120/119 = 15.0715
Optimal tuning (POTE): ~2 = 1\1, ~120/119 = 15.0715


{{Optimal ET sequence|legend=1| 79d, 80, 159, 239 }}
{{Optimal ET sequence|legend=1| 79d, 80, 159, 239 }}
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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: [{{val| 1 2 3 4 4 4 4 5 }}, {{val| 0 -33 -54 -95 -43 -24 7 -60 }}]
Mapping: {{mapping| 1 2 3 4 4 4 4 5 | 0 -33 -54 -95 -43 -24 7 -60 }}


POTE generator: ~120/119 = 15.0713
Optimal tuning (POTE): ~2 = 1\1, ~120/119 = 15.0713


{{Optimal ET sequence|legend=1| 79dh, 80, 159, 239 }}
{{Optimal ET sequence|legend=1| 79dh, 80, 159, 239 }}
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== Yarman II ==
== Yarman II ==
Subgroup: 2.3.5.7
[[Subgroup]]: 2.3.5.7


[[Comma list]]: 5359375/5308416, 390625000/387420489
[[Comma list]]: 5359375/5308416, 390625000/387420489


[[Mapping]]: [{{val| 1 2 3 2 }}, {{val| 0 -33 -54 64 }}]
{{Mapping|legend=1| 1 2 3 2 | 0 -33 -54 64 }}


[[POTE generator]]: ~6144/6125 = 15.1062
[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~6144/6125 = 15.1062


{{Optimal ET sequence|legend=1| 79, 80d, 159 }}
{{Optimal ET sequence|legend=1| 79, 80d, 159 }}
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Comma list: 385/384, 4000/3993, 78121827/77948684
Comma list: 385/384, 4000/3993, 78121827/77948684


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


POTE generator: ~121/120 = 15.1071
Optimal tuning (POTE): ~2 = 1\1, ~121/120 = 15.1071


{{Optimal ET sequence|legend=1| 79, 80d, 159 }}
{{Optimal ET sequence|legend=1| 79, 80d, 159 }}
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Comma list: 325/324, 385/384, 1575/1573, 85683/85184
Comma list: 325/324, 385/384, 1575/1573, 85683/85184


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


POTE generator: ~105/104 = 15.1071
Optimal tuning (POTE): ~2 = 1\1, ~105/104 = 15.1071


{{Optimal ET sequence|legend=1| 79, 80d, 159 }}
{{Optimal ET sequence|legend=1| 79, 80d, 159 }}
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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: [{{val| 1 2 3 2 4 4 4 }}, {{val| 0 -33 -54 64 -43 -24 7 }}]
Mapping: {{mapping| 1 2 3 2 4 4 4 | 0 -33 -54 64 -43 -24 7 }}


POTE generator: ~105/104 = 15.1037
Optimal tuning (POTE): ~2 = 1\1, ~105/104 = 15.1037


{{Optimal ET sequence|legend=1| 79, 80d, 159 }}
{{Optimal ET sequence|legend=1| 79, 80d, 159 }}
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Comma list: 273/272, 325/324, 385/384, 665/663, 969/968, 1575/1573
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 }}]
Mapping: {{mapping| 1 2 3 2 4 4 4 5 | 0 -33 -54 64 -43 -24 7 -60 }}


POTE generator: ~105/104 = 15.1013
Optimal tuning (POTE): ~2 = 1\1, ~105/104 = 15.1013


{{Optimal ET sequence|legend=1| 79h, 159 }}
{{Optimal ET sequence|legend=1| 79h, 159 }}
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{{See also| Schismatic family #Garibaldi }}
{{See also| Schismatic family #Garibaldi }}


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 is more plausible as an 11-limit system than 13-limit; the 13-limit wedgie is:


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


=== 11-limit ===
=== 11-limit ===
Subgroup: 2.3.5.7.11
[[Subgroup]]: 2.3.5.7.11


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


[[Mapping]]: [{{val| 1 1 7 11 2 }}, {{val| 0 2 -16 -28 5 }}]
{{Mapping|legend=1| 1 1 7 11 2 | 0 2 -16 -28 5 }}


[[POTE generator]]: ~11/9 = 350.994
[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~11/9 = 350.994


{{Optimal ET sequence|legend=1| 41, 106, 147 }}
{{Optimal ET sequence|legend=1| 41, 106, 147 }}
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Comma list: 225/224, 243/242, 325/324, 640/637
Comma list: 225/224, 243/242, 325/324, 640/637


Mapping: [{{val| 1 1 7 11 2 -8 }}, {{val| 0 2 -16 -28 5 40 }}]
Mapping: {{mapping| 1 1 7 11 2 -8 | 0 2 -16 -28 5 40 }}


POTE generator: ~11/9 = 351.014
Optimal tuning (POTE): ~2 = 1\1, ~11/9 = 351.014


{{Optimal ET sequence|legend=1| 41, 106, 147 }}
{{Optimal ET sequence|legend=1| 41, 106, 147 }}
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[[Category:Temperament collections]]
[[Category:Temperament collections]]
[[Category:Rank 2]]
[[Category:Rank 2]]
[[Category:Turkish music]]

Revision as of 06:52, 22 September 2023

This is a collection of some proposed temperaments for Turkish maqam music.

Yarman I

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 mappings:

  • [⟨1 2 3 2 4 4 4 5], ⟨0 -33 -54 64 -43 -24 7 -60]]
  • [⟨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, and both temperaments are weak 7-limit extensions of quartonic temperament. A Pythagorean tuning, i.e. one with pure fifths, is also possible.

Subgroup: 2.3.5.7

Comma list: 10976/10935, 244140625/243045684

Mapping: [⟨1 2 3 4], ⟨0 -33 -54 -95]]

Wedgie: ⟨⟨ 33 54 95 9 58 69 ]]

Optimal tuning (POTE): ~2 = 1\1, ~126/125 = 15.0667

Optimal ET sequence: 79d, 80, 159, 239

Badness: 0.193315

11-limit

Subgroup: 2.3.5.7.11

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

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

Optimal tuning (POTE): ~2 = 1\1, ~121/120 = 15.0658

Optimal ET sequence: 79d, 80, 159, 239

Badness: 0.049170

13-limit

Subgroup: 2.3.5.7.11.13

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

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

Optimal tuning (POTE): ~2 = 1\1, ~121/120 = 15.0752

Optimal ET sequence: 79d, 80, 159, 239

Badness: 0.040929

17-limit

Subgroup: 2.3.5.7.11.13.17

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]]

Optimal tuning (POTE): ~2 = 1\1, ~120/119 = 15.0715

Optimal ET sequence: 79d, 80, 159, 239

Badness: 0.031015

19-limit

Subgroup: 2.3.5.7.11.13.17.19

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]]

Optimal tuning (POTE): ~2 = 1\1, ~120/119 = 15.0713

Optimal ET sequence: 79dh, 80, 159, 239

Badness: 0.023193

Yarman II

Subgroup: 2.3.5.7

Comma list: 5359375/5308416, 390625000/387420489

Mapping: [⟨1 2 3 2], ⟨0 -33 -54 64]]

Optimal tuning (POTE): ~2 = 1\1, ~6144/6125 = 15.1062

Optimal ET sequence: 79, 80d, 159

Badness: 0.655487

11-limit

Subgroup: 2.3.5.7.11

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

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

Optimal tuning (POTE): ~2 = 1\1, ~121/120 = 15.1071

Optimal ET sequence: 79, 80d, 159

Badness: 0.143477

13-limit

Subgroup: 2.3.5.7.11.13

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

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

Optimal tuning (POTE): ~2 = 1\1, ~105/104 = 15.1071

Optimal ET sequence: 79, 80d, 159

Badness: 0.068150

17-limit

Subgroup: 2.3.5.7.11.13.17

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]]

Optimal tuning (POTE): ~2 = 1\1, ~105/104 = 15.1037

Optimal ET sequence: 79, 80d, 159

Badness: 0.051019

19-limit

Subgroup: 2.3.5.7.11.13.17.19

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]]

Optimal tuning (POTE): ~2 = 1\1, ~105/104 = 15.1013

Optimal ET sequence: 79h, 159

Badness: 0.038430

Karadeniz

See also: Schismatic family § Garibaldi

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

11-limit

Subgroup: 2.3.5.7.11

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

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

Optimal tuning (POTE): ~2 = 1\1, ~11/9 = 350.994

Optimal ET sequence: 41, 106, 147

Badness: 0.041562

13-limit

Subgroup: 2.3.5.7.11.13

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

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

Optimal tuning (POTE): ~2 = 1\1, ~11/9 = 351.014

Optimal ET sequence: 41, 106, 147

Badness: 0.042564

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