Turkish maqam music temperaments: Difference between revisions
m category maintenance, clean up formatting |
No edit summary |
||
| Line 1: | Line 1: | ||
=Yarman temperament= | |||
[[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: | [[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: | ||
[<1 2 3 2 4 4 4 5|, <0 -33 -54 64 -43 -24 7 -60|] | [<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|] | ||
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. | |||
== 7-limit 80&159 == | |||
Commas: 10976/10935, 244140625/243045684 | |||
[[POTE_tuning|POTE generator]]: ~126/125 = 15.0667 | |||
Map: [<1 2 3 4|, <0 -33 -54 -95|] | |||
EDOs: {{EDOs|79d, 80, 159, 239}} | |||
Badness: 0.193315 | |||
== 7-limit 79&159 == | |||
Commas: 5359375/5308416, 390625000/387420489 | |||
[[POTE_tuning|POTE generator]]: ~6144/6125 = 15.1062 | |||
Map: [<1 2 3 2|, <0 -33 -54 64|] | |||
EDOs: {{EDOs|79, 80d, 159, 238c, 239d}} | |||
Badness: 0.655487 | |||
=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: | 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: | ||
| Line 21: | Line 39: | ||
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 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 == | |||
Commas: 225/224, 243/242, 3125/3087 | Commas: 225/224, 243/242, 3125/3087 | ||
Revision as of 17:23, 14 March 2021
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.
7-limit 80&159
Commas: 10976/10935, 244140625/243045684
POTE generator: ~126/125 = 15.0667
Map: [<1 2 3 4|, <0 -33 -54 -95|]
Badness: 0.193315
7-limit 79&159
Commas: 5359375/5308416, 390625000/387420489
POTE generator: ~6144/6125 = 15.1062
Map: [<1 2 3 2|, <0 -33 -54 64|]
EDOs: 79, 80d, 159, 238c, 239d
Badness: 0.655487
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
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