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|]

or

[<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, ie 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'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.

Commas: 225/224, 243/242, 3125/3087

POTE generator: 350.994

Map: [<1 1 7 11 2|, <0 2 -16 -28 5|]

EDOs: 41, 106, 147, 253