Turkish maqam music temperaments
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==Yarman temperament== [[Ozan Yarman]] has proposed defining the tuning of Turkish maqam <span class="wiki_link_ext">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|] 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 val|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 tuning|POTE generator]]: 350.994 Map: [<1 1 7 11 2|, <0 2 -16 -28 5|] EDOs: 41, 106, 147, 253
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 <span class="wiki_link_ext">music</span> using a <a class="wiki_link" href="/MOSScales">MOS</a> of 79 or 80 notes out of 159. This means a generator of 2/159, which suggests the 19-limit mapping:<br /> <br /> [<1 2 3 2 4 4 4 5|, <0 -33 -54 64 -43 -24 7 -60|]<br /> <br /> or<br /> <br /> [<1 2 3 4 4 4 4 5|, <0 -33 -54 -95 -43 -24 7 -60|]<br /> <br /> The first mapping may be called 79&159 in terms of <a class="wiki_link" href="/Patent%20val">patent vals</a>, 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.<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 "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:<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, 43/147 or 74/253 can be recommended as generators.<br /> <br /> Commas: 225/224, 243/242, 3125/3087<br /> <br /> <a class="wiki_link" href="/POTE%20tuning">POTE generator</a>: 350.994<br /> <br /> Map: [<1 1 7 11 2|, <0 2 -16 -28 5|]<br /> EDOs: 41, 106, 147, 253</body></html>