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| = Yarman temperament =
| | This is a collection of some proposed [[temperament]]s for [[Arabic, Turkish, Persian music|Turkish maqam music]]. |
| [[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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| [<1 2 3 2 4 4 4 5|, <0 -33 -54 64 -43 -24 7 -60|] <br>vs. <br>[<1 2 3 4 4 4 4 5|, <0 -33 -54 -95 -43 -24 7 -60|]
| | == Yarman temperament == |
| | {{See also| Quartonic family }} |
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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.
| | [[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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| == 80&159 yarman ==
| | * {{Mapping| 1 2 3 2 4 4 4 5 | 0 -33 -54 64 -43 -24 7 -60 }} |
| [[Comma list]]: 10976/10935, 244140625/243045684
| | * {{Mapping| 1 2 3 4 4 4 4 5 | 0 -33 -54 -95 -43 -24 7 -60 }} |
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| [[Mapping]]: [<1 2 3 4|, <0 -33 -54 -95|] | | 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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| {{Multival|legend=1| 33 54 95 9 58 69}} | | == Karadeniz temperament == |
| | {{See also| Schismatic family #Garibaldi }} |
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| [[POTE generator]]: ~126/125 = 15.0667
| | 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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| {{Val list|legend=1| 79d, 80, 159, 239 }}
| | 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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| [[Badness]]: 0.193315 | | [[Category:Temperament collections]] |
| | | [[Category:Pages with mostly numerical content]] |
| === 11-limit ===
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| Comma list: 3025/3024, 4000/3993, 10976/10935
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| Mapping: [<1 2 3 4 4|, <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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| Comma list: 325/324, 364/363, 1001/1000, 10976/10935
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| Mapping: [<1 2 3 4 4 4|, <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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| == 79&159 yarman ==
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| [[Comma list]]: 5359375/5308416, 390625000/387420489 | |
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| [[Mapping]]: [<1 2 3 2|, <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, 238c, 239d }}
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| [[Badness]]: 0.655487
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| === 11-limit ===
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| Comma list: 385/384, 4000/3993, 78121827/77948684
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| Mapping: [<1 2 3 2 4|, <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, 238c, 239d }}
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| Badness: 0.143477
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| === 13-limit ===
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| Comma list: 325/324, 385/384, 1575/1573, 85683/85184
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| Mapping: [<1 2 3 2 4 4|, <0 -33 -54 64 -43 -24|]
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| POTE generator: ~121/120 = 15.1071
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| Vals: {{Val list| 79, 80d, 159, 238cf, 239d }}
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| Badness: 0.068150
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| = Karadeniz temperament =
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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:
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| <<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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| <<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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| [[Comma list]]: 225/224, 243/242, 3125/3087
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| [[Mapping]]: [<1 1 7 11 2|, <0 2 -16 -28 5|]
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| [[POTE generator]]: ~11/9 = 350.994
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| {{Val list| 41, 106, 147 }}
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| [[Badness]]: 0.041562
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| == 13-limit ==
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| Comma list: 225/224, 243/242, 325/324, 640/637
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| Mapping: [<1 1 7 11 2 -8|, <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
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| [[Category:Temperament]]
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| [[Category:Rank 2]] | | [[Category:Rank 2]] |
| | [[Category:Turkish music]] |