Turkish maqam music temperaments: Difference between revisions
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Wikispaces>genewardsmith **Imported revision 147854703 - Original comment: ** |
Wikispaces>genewardsmith **Imported revision 190117482 - Original comment: ** |
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<h2>IMPORTED REVISION FROM WIKISPACES</h2> | <h2>IMPORTED REVISION FROM WIKISPACES</h2> | ||
This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br> | This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br> | ||
: This revision was by author [[User:genewardsmith|genewardsmith]] and made on <tt>2010- | : This revision was by author [[User:genewardsmith|genewardsmith]] and made on <tt>2010-12-28 11:02:11 UTC</tt>.<br> | ||
: The original revision id was <tt> | : The original revision id was <tt>190117482</tt>.<br> | ||
: The revision comment was: <tt></tt><br> | : The revision comment was: <tt></tt><br> | ||
The revision contents are below, presented both in the original Wikispaces Wikitext format, and in HTML exactly as Wikispaces rendered it.<br> | The revision contents are below, presented both in the original Wikispaces Wikitext format, and in HTML exactly as Wikispaces rendered it.<br> | ||
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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. | 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. | ||
Commas: 325/324, 364/363, 1001/1000, 10976/10935 | |||
[[POTE tuning|POTE generator]]: 15.075 | |||
Map: [<1 2 3 4 4 4|, <0 -33 -54 -95 -43 -24|] | |||
EDOs: 80, 159, 239, 398 | |||
==Karadeniz temperament== | ==Karadeniz temperament== | ||
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<<2 -16 -28 5 40 -30 -50 1 56 -20 67 152 111 216 120|| | <<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 | 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 | |||
</pre></div> | [[POTE tuning|POTE generator]]: 350.994 | ||
Map: [<1 1 7 11 2|, <0 2 -16 -25 5|] | |||
EDOs: 41, 106, 147, 253</pre></div> | |||
<h4>Original HTML content:</h4> | <h4>Original HTML content:</h4> | ||
<div style="width:100%; max-height:400pt; overflow:auto; background-color:#f8f9fa; border: 1px solid #eaecf0; padding:0em"><pre style="margin:0px;border:none;background:none;word-wrap:break-word;width:200%;white-space: pre-wrap ! important" class="old-revision-html"><html><head><title>Turkish maqam music temperaments</title></head><body><!-- ws:start:WikiTextHeadingRule:0:&lt;h2&gt; --><h2 id="toc0"><a name="x-Yarman temperament"></a><!-- ws:end:WikiTextHeadingRule:0 -->Yarman temperament</h2> | <div style="width:100%; max-height:400pt; overflow:auto; background-color:#f8f9fa; border: 1px solid #eaecf0; padding:0em"><pre style="margin:0px;border:none;background:none;word-wrap:break-word;width:200%;white-space: pre-wrap ! important" class="old-revision-html"><html><head><title>Turkish maqam music temperaments</title></head><body><!-- ws:start:WikiTextHeadingRule:0:&lt;h2&gt; --><h2 id="toc0"><a name="x-Yarman temperament"></a><!-- ws:end:WikiTextHeadingRule:0 -->Yarman temperament</h2> | ||
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<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&amp;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 /> | 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&amp;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 /> | |||
Commas: 325/324, 364/363, 1001/1000, 10976/10935<br /> | |||
<br /> | |||
<a class="wiki_link" href="/POTE%20tuning">POTE generator</a>: 15.075<br /> | |||
<br /> | |||
Map: [&lt;1 2 3 4 4 4|, &lt;0 -33 -54 -95 -43 -24|]<br /> | |||
EDOs: 80, 159, 239, 398<br /> | |||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule:2:&lt;h2&gt; --><h2 id="toc1"><a name="x-Karadeniz temperament"></a><!-- ws:end:WikiTextHeadingRule:2 -->Karadeniz temperament</h2> | <!-- ws:start:WikiTextHeadingRule:2:&lt;h2&gt; --><h2 id="toc1"><a name="x-Karadeniz temperament"></a><!-- ws:end:WikiTextHeadingRule:2 -->Karadeniz temperament</h2> | ||
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&lt;&lt;2 -16 -28 5 40 -30 -50 1 56 -20 67 152 111 216 120||<br /> | &lt;&lt;2 -16 -28 5 40 -30 -50 1 56 -20 67 152 111 216 120||<br /> | ||
<br /> | <br /> | ||
which in the 11-limit becomes &lt;&lt;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&amp;106. Aside from 31/106, 74/253 can be recommended as a generator.</body></html></pre></div> | which in the 11-limit becomes &lt;&lt;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&amp;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: [&lt;1 1 7 11 2|, &lt;0 2 -16 -25 5|]<br /> | |||
EDOs: 41, 106, 147, 253</body></html></pre></div> | |||
Revision as of 11:02, 28 December 2010
IMPORTED REVISION FROM WIKISPACES
This is an imported revision from Wikispaces. The revision metadata is included below for reference:
- This revision was by author genewardsmith and made on 2010-12-28 11:02:11 UTC.
- The original revision id was 190117482.
- The revision comment was:
The revision contents are below, presented both in the original Wikispaces Wikitext format, and in HTML exactly as Wikispaces rendered it.
Original Wikitext content:
==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. Commas: 325/324, 364/363, 1001/1000, 10976/10935 [[POTE tuning|POTE generator]]: 15.075 Map: [<1 2 3 4 4 4|, <0 -33 -54 -95 -43 -24|] EDOs: 80, 159, 239, 398 ==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, 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 -25 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 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 /> Commas: 325/324, 364/363, 1001/1000, 10976/10935<br /> <br /> <a class="wiki_link" href="/POTE%20tuning">POTE generator</a>: 15.075<br /> <br /> Map: [<1 2 3 4 4 4|, <0 -33 -54 -95 -43 -24|]<br /> EDOs: 80, 159, 239, 398<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, 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 -25 5|]<br /> EDOs: 41, 106, 147, 253</body></html>