Turkish maqam music temperaments
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
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
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
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