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| This is a collection some proposed temperaments for Turkish maqam music. | | This is a collection of some proposed [[temperament]]s for [[Arabic, Turkish, Persian music|Turkish maqam music]]. |
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| == Yarman I == | | == 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 mappings:
| | {{See also| Quartonic family }} |
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| [{{val| 1 2 3 2 4 4 4 5 }}, {{val| 0 -33 -54 64 -43 -24 7 -60 }}] | | [[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: |
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| [{{val| 1 2 3 4 4 4 4 5 }}, {{val| 0 -33 -54 -95 -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 }} |
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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, 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 [[Quartonic family|quartonic temperament]]. A Pythagorean tuning, i.e. one with pure fifths, is also possible. |
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| Subgroup: 2.3.5.7
| | == Karadeniz temperament == |
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| [[Comma list]]: 10976/10935, 244140625/243045684
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| [[Mapping]]: [{{val| 1 2 3 4 }}, {{val| 0 -33 -54 -95 }}]
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| {{Multival|legend=1| 33 54 95 9 58 69}}
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| [[POTE generator]]: ~126/125 = 15.0667
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| {{Val list|legend=1| 79d, 80, 159, 239 }}
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| [[Badness]]: 0.193315
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| === 11-limit ===
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| Subgroup: 2.3.5.7.11
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| Comma list: 3025/3024, 4000/3993, 10976/10935
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| Mapping: [{{val| 1 2 3 4 4 }}, {{val| 0 -33 -54 -95 -43 }}]
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| POTE generator: ~121/120 = 15.0658
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| Vals: {{Val list| 79d, 80, 159, 239 }}
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| Badness: 0.049170
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| === 13-limit ===
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| Subgroup: 2.3.5.7.11.13
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| Comma list: 325/324, 364/363, 1001/1000, 10976/10935
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| Mapping: [{{val| 1 2 3 4 4 4 }}, {{val| 0 -33 -54 -95 -43 -24 }}]
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| POTE generator: ~121/120 = 15.0752
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| Vals: {{Val list| 79d, 80, 159, 239 }}
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| Badness: 0.040929
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| === 17-limit ===
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| Subgroup: 2.3.5.7.11.13.17
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| Comma list: 325/324, 364/363, 595/594, 1001/1000, 10976/10935
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| Mapping: [{{val| 1 2 3 4 4 4 4 }}, {{val| 0 -33 -54 -95 -43 -24 7 }}]
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| POTE generator: ~120/119 = 15.0715
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| Vals: {{Val list| 79d, 80, 159, 239 }}
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| Badness: 0.031015
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| === 19-limit ===
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| Subgroup: 2.3.5.7.11.13.17.19
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| Comma list: 325/324, 361/360, 364/363, 595/594, 1001/1000, 1521/1520
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| Mapping: [{{val| 1 2 3 4 4 4 4 5 }}, {{val| 0 -33 -54 -95 -43 -24 7 -60 }}]
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| POTE generator: ~120/119 = 15.0713
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| Vals: {{Val list| 79dh, 80, 159, 239 }}
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| Badness: 0.023193
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| == Yarman II ==
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| Subgroup: 2.3.5.7
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| [[Comma list]]: 5359375/5308416, 390625000/387420489
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| [[Mapping]]: [{{val| 1 2 3 2 }}, {{val| 0 -33 -54 64 }}]
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| [[POTE generator]]: ~6144/6125 = 15.1062
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| {{Val list|legend=1| 79, 80d, 159 }}
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| [[Badness]]: 0.655487
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| === 11-limit ===
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| Subgroup: 2.3.5.7.11
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| Comma list: 385/384, 4000/3993, 78121827/77948684
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| Mapping: [{{val| 1 2 3 2 4 }}, {{val| 0 -33 -54 64 -43 }}]
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| POTE generator: ~121/120 = 15.1071
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| Vals: {{Val list| 79, 80d, 159 }}
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| Badness: 0.143477
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| === 13-limit ===
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| Subgroup: 2.3.5.7.11.13
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| Comma list: 325/324, 385/384, 1575/1573, 85683/85184
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| Mapping: [{{val| 1 2 3 2 4 4 }}, {{val| 0 -33 -54 64 -43 -24 }}]
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| POTE generator: ~105/104 = 15.1071
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| Vals: {{Val list| 79, 80d, 159 }}
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| Badness: 0.068150
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| === 17-limit ===
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| Subgroup: 2.3.5.7.11.13.17
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| Comma list: 273/272, 325/324, 385/384, 1575/1573, 4928/4913
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| Mapping: [{{val| 1 2 3 2 4 4 4 }}, {{val| 0 -33 -54 64 -43 -24 7 }}]
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| POTE generator: ~105/104 = 15.1037
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| Vals: {{Val list| 79, 80d, 159 }}
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| Badness: 0.051019
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| === 19-limit ===
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| Subgroup: 2.3.5.7.11.13.17.19
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| Comma list: 273/272, 325/324, 385/384, 665/663, 969/968, 1575/1573
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| Mapping: [{{val| 1 2 3 2 4 4 4 5 }}, {{val| 0 -33 -54 64 -43 -24 7 -60 }}]
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| POTE generator: ~105/104 = 15.1013
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| Vals: {{Val list| 79h, 159 }}
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| Badness: 0.038430
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| == Karadeniz == | |
| {{See also| Schismatic family #Garibaldi }} | | {{See also| Schismatic family #Garibaldi }} |
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| 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. |
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| {{Multival| 2 -16 -28 5 40 -30 -50 1 56 -20 67 152 111 216 120 }}
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| which in the 11-limit becomes:
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| {{Multival| 2 -16 -28 5 -30 -50 1 -20 67 111 }}
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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&106. Aside from 31/106, 43/147 or 74/253 can be recommended as generators.
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| === 11-limit ===
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| Subgroup: 2.3.5.7.11
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| [[Comma list]]: 225/224, 243/242, 3125/3087
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| [[Mapping]]: [{{val| 1 1 7 11 2 }}, {{val| 0 2 -16 -28 5 }}]
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| [[POTE generator]]: ~11/9 = 350.994
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| {{Val list|legend=1| 41, 106, 147 }}
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| [[Badness]]: 0.041562
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| === 13-limit ===
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| Subgroup: 2.3.5.7.11.13
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| Comma list: 225/224, 243/242, 325/324, 640/637
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| Mapping: [{{val| 1 1 7 11 2 -8 }}, {{val| 0 2 -16 -28 5 40 }}]
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| POTE generator: ~11/9 = 351.014
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| Vals: {{Val list| 41, 106, 147 }}
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| Badness: 0.042564
| | 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. |
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| [[Category:Regular temperament theory]] | | [[Category:Temperament collections]] |
| [[Category:Temperament collection]] | | [[Category:Pages with mostly numerical content]] |
| [[Category:Rank 2]] | | [[Category:Rank 2]] |
| | [[Category:Turkish music]] |
This is a collection of some proposed temperaments for Turkish maqam music.
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 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.
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 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.