Turkish maqam music temperaments
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==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 13-limit wedgie: <<33 54 95 43 24 9 58 -46 -84 69 -87 -144 -208 -284 -76|| which gives a temperament tempering out 325/324, 364/363, 6250/6237, 4000/3993, 1001/1000, 3025/3024 and 123201/123200, and which can also be called 80&159. Note that another mapping for 7 is possible, and that in any event both can be used inconsistently. The generators 3/239 or 5/398 provide a little more accuracy than 159, at the expense of a slightly sharp fifth. However a Pythagorean tuning, ie one with pure fifths, is also possible and perhaps accords better with Yarman's ideas. ==Karadeniz temperament== K. E. Karadeniz proposed a 41 note MOS with generator 31/106. giving a "hemigarabaldi" 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, 74/253 can be recommended as a generator.
Original HTML content:
<html><head><title>Turkish maqam music temperaments</title></head><body><!-- ws:start:WikiTextHeadingRule:0:<h2> --><h2 id="toc0"><a name="x-Yarman temperament"></a><!-- ws:end:WikiTextHeadingRule:0 -->Yarman temperament</h2> <a class="wiki_link" href="/Ozan%20Yarman">Ozan Yarman</a> 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 13-limit wedgie:<br /> <br /> <<33 54 95 43 24 9 58 -46 -84 69 -87 -144 -208 -284 -76||<br /> <br /> which gives a temperament tempering out 325/324, 364/363, 6250/6237, 4000/3993, 1001/1000, 3025/3024 and 123201/123200, and which can also be called 80&159. Note that another mapping for 7 is possible, and that in any event both can be used inconsistently. The generators 3/239 or 5/398 provide a little more accuracy than 159, at the expense of a slightly sharp fifth. However a Pythagorean tuning, ie one with pure fifths, is also possible and perhaps accords better with Yarman's ideas.<br /> <br /> <!-- ws:start:WikiTextHeadingRule:2:<h2> --><h2 id="toc1"><a name="x-Karadeniz temperament"></a><!-- ws:end:WikiTextHeadingRule:2 -->Karadeniz temperament</h2> K. E. Karadeniz proposed a 41 note MOS with generator 31/106. giving a "hemigarabaldi" 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:<br /> <br /> <<2 -16 -28 5 40 -30 -50 1 56 -20 67 152 111 216 120||<br /> <br /> 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, 74/253 can be recommended as a generator.</body></html>