159edo: Difference between revisions

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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>2011-04-02 22:19:50 UTC</tt>.<br>
: This revision was by author [[User:genewardsmith|genewardsmith]] and made on <tt>2011-04-02 22:38:38 UTC</tt>.<br>
: The original revision id was <tt>216530788</tt>.<br>
: The original revision id was <tt>216532726</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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<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;white-space: pre-wrap ! important" class="old-revision-html">The //159 equal division// divides the octave into 159 equal parts of 7.547 cents each. A salient fact about it is that 159 = 3*53, so that it shares the same 5-limit thirds and fifths with [[53edo]]. In the 7-limit it tempers out 1029/1024 and 10976/19935 in addition to the 5-limit commas 32805/32768 and 15625/15552. This makes it among other things an excellent tuning for [[Gamelismic clan|guiron]] and [[Gamelismic clan|tritikleismic]] temperaments. It has a very accurate 11, and in the 11-limit tempers out 385/384, 441/440 and 4000/3993. In the 13-limit it tempers out 325/324 and 364/363, in the 17-limit 273/272 and 375/374, and in the 19-limit 343/342 and 361/360. It also provides the [[optimal patent val]] for 11-limit guiron and 13-limit tritikleismic, as well as the 13-limit rank three temperament [[Gamelismic family|portending]].
<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;white-space: pre-wrap ! important" class="old-revision-html">The //159 equal division// divides the octave into 159 equal parts of 7.547 cents each. A salient fact about it is that 159 = 3*53, so that it shares the same 5-limit thirds and fifths with [[53edo]]. In the 7-limit it tempers out 1029/1024 and 10976/19935 in addition to the 5-limit commas 32805/32768 and 15625/15552. This makes it among other things an excellent tuning for [[Gamelismic clan|guiron]] and [[Gamelismic clan|tritikleismic]] temperaments. It has a very accurate 11, and in the 11-limit tempers out 385/384, 441/440 and 4000/3993. In the 13-limit it tempers out 325/324 and 364/363, in the 17-limit 273/272 and 375/374, and in the 19-limit 343/342 and 361/360. It also provides the [[optimal patent val]] for 11-limit guiron and 13-limit tritikleismic, as well as the 13-limit rank three temperament [[Gamelismic family|portending]].


A 79-tone [[MOSScales|MOS]] subset of 159EDO has been proposed by &lt;span class="wiki_link_ext"&gt;Ozan Yarman&lt;/span&gt; as tuning standard for [[Arabic, Turkish, Persian|arabic/turkish/persian]] music.  
Another and notable temperament supported by 159 is [[Turkish maqam music temperaments|yarman temperament]], with a generator of 2\159 which can be taken as an approximate 105/104. 159 supplies the optimal patent val for 7, 11, 13, 17 and 19-limit yarman, so they are very closely associated. Curiously, the temperament does not temper out 1029/1024, however.
 
Yarman temperament has [[MOSScales|MOS]] of 79 and 80 notes to the octave, and the 79-note MOS has been proposed by &lt;span class="wiki_link_ext"&gt;Ozan Yarman&lt;/span&gt; as a tuning standard for [[Arabic, Turkish, Persian|arabic/turkish/persian]] music.  


=Articles=
=Articles=
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<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">&lt;html&gt;&lt;head&gt;&lt;title&gt;159edo&lt;/title&gt;&lt;/head&gt;&lt;body&gt;The &lt;em&gt;159 equal division&lt;/em&gt; divides the octave into 159 equal parts of 7.547 cents each. A salient fact about it is that 159 = 3*53, so that it shares the same 5-limit thirds and fifths with &lt;a class="wiki_link" href="/53edo"&gt;53edo&lt;/a&gt;. In the 7-limit it tempers out 1029/1024 and 10976/19935 in addition to the 5-limit commas 32805/32768 and 15625/15552. This makes it among other things an excellent tuning for &lt;a class="wiki_link" href="/Gamelismic%20clan"&gt;guiron&lt;/a&gt; and &lt;a class="wiki_link" href="/Gamelismic%20clan"&gt;tritikleismic&lt;/a&gt; temperaments. It has a very accurate 11, and in the 11-limit tempers out 385/384, 441/440 and 4000/3993. In the 13-limit it tempers out 325/324 and 364/363, in the 17-limit 273/272 and 375/374, and in the 19-limit 343/342 and 361/360. It also provides the &lt;a class="wiki_link" href="/optimal%20patent%20val"&gt;optimal patent val&lt;/a&gt; for 11-limit guiron and 13-limit tritikleismic, as well as the 13-limit rank three temperament &lt;a class="wiki_link" href="/Gamelismic%20family"&gt;portending&lt;/a&gt;.&lt;br /&gt;
<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">&lt;html&gt;&lt;head&gt;&lt;title&gt;159edo&lt;/title&gt;&lt;/head&gt;&lt;body&gt;The &lt;em&gt;159 equal division&lt;/em&gt; divides the octave into 159 equal parts of 7.547 cents each. A salient fact about it is that 159 = 3*53, so that it shares the same 5-limit thirds and fifths with &lt;a class="wiki_link" href="/53edo"&gt;53edo&lt;/a&gt;. In the 7-limit it tempers out 1029/1024 and 10976/19935 in addition to the 5-limit commas 32805/32768 and 15625/15552. This makes it among other things an excellent tuning for &lt;a class="wiki_link" href="/Gamelismic%20clan"&gt;guiron&lt;/a&gt; and &lt;a class="wiki_link" href="/Gamelismic%20clan"&gt;tritikleismic&lt;/a&gt; temperaments. It has a very accurate 11, and in the 11-limit tempers out 385/384, 441/440 and 4000/3993. In the 13-limit it tempers out 325/324 and 364/363, in the 17-limit 273/272 and 375/374, and in the 19-limit 343/342 and 361/360. It also provides the &lt;a class="wiki_link" href="/optimal%20patent%20val"&gt;optimal patent val&lt;/a&gt; for 11-limit guiron and 13-limit tritikleismic, as well as the 13-limit rank three temperament &lt;a class="wiki_link" href="/Gamelismic%20family"&gt;portending&lt;/a&gt;.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
A 79-tone &lt;a class="wiki_link" href="/MOSScales"&gt;MOS&lt;/a&gt; subset of 159EDO has been proposed by &lt;span class="wiki_link_ext"&gt;Ozan Yarman&lt;/span&gt; as tuning standard for &lt;a class="wiki_link" href="/Arabic%2C%20Turkish%2C%20Persian"&gt;arabic/turkish/persian&lt;/a&gt; music. &lt;br /&gt;
Another and notable temperament supported by 159 is &lt;a class="wiki_link" href="/Turkish%20maqam%20music%20temperaments"&gt;yarman temperament&lt;/a&gt;, with a generator of 2\159 which can be taken as an approximate 105/104. 159 supplies the optimal patent val for 7, 11, 13, 17 and 19-limit yarman, so they are very closely associated. Curiously, the temperament does not temper out 1029/1024, however.&lt;br /&gt;
&lt;br /&gt;
Yarman temperament has &lt;a class="wiki_link" href="/MOSScales"&gt;MOS&lt;/a&gt; of 79 and 80 notes to the octave, and the 79-note MOS has been proposed by &lt;span class="wiki_link_ext"&gt;Ozan Yarman&lt;/span&gt; as a tuning standard for &lt;a class="wiki_link" href="/Arabic%2C%20Turkish%2C%20Persian"&gt;arabic/turkish/persian&lt;/a&gt; music. &lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:0:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc0"&gt;&lt;a name="Articles"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:0 --&gt;Articles&lt;/h1&gt;
&lt;!-- ws:start:WikiTextHeadingRule:0:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc0"&gt;&lt;a name="Articles"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:0 --&gt;Articles&lt;/h1&gt;
&lt;ul&gt;&lt;li&gt;&lt;a class="wiki_link_ext" href="http://www.ozanyarman.com/files/doctorate_thesis.pdf" rel="nofollow"&gt;Ozan Yarman's dissertation&lt;/a&gt;&lt;/li&gt;&lt;li&gt;&lt;a class="wiki_link_ext" href="http://www.ozanyarman.com/files/34ten79a.pdf" rel="nofollow"&gt;paper&lt;/a&gt;, also by Ozan Yarman, gives a summary.&lt;/li&gt;&lt;li&gt;&lt;a class="wiki_link_ext" href="http://www.bestii.com/~mschulter/17-MOS-tunings_Letter-to-Ozan.txt" rel="nofollow"&gt;Letter to Ozan Yarman&lt;/a&gt; by Margo Schulter &lt;a class="wiki_link_ext" href="http://www.webcitation.org/5xepptaan" rel="nofollow"&gt;Permalink&lt;/a&gt;&lt;/li&gt;&lt;/ul&gt;&lt;/body&gt;&lt;/html&gt;</pre></div>
&lt;ul&gt;&lt;li&gt;&lt;a class="wiki_link_ext" href="http://www.ozanyarman.com/files/doctorate_thesis.pdf" rel="nofollow"&gt;Ozan Yarman's dissertation&lt;/a&gt;&lt;/li&gt;&lt;li&gt;&lt;a class="wiki_link_ext" href="http://www.ozanyarman.com/files/34ten79a.pdf" rel="nofollow"&gt;paper&lt;/a&gt;, also by Ozan Yarman, gives a summary.&lt;/li&gt;&lt;li&gt;&lt;a class="wiki_link_ext" href="http://www.bestii.com/~mschulter/17-MOS-tunings_Letter-to-Ozan.txt" rel="nofollow"&gt;Letter to Ozan Yarman&lt;/a&gt; by Margo Schulter &lt;a class="wiki_link_ext" href="http://www.webcitation.org/5xepptaan" rel="nofollow"&gt;Permalink&lt;/a&gt;&lt;/li&gt;&lt;/ul&gt;&lt;/body&gt;&lt;/html&gt;</pre></div>

Revision as of 22:38, 2 April 2011

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 2011-04-02 22:38:38 UTC.
The original revision id was 216532726.
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:

The //159 equal division// divides the octave into 159 equal parts of 7.547 cents each. A salient fact about it is that 159 = 3*53, so that it shares the same 5-limit thirds and fifths with [[53edo]]. In the 7-limit it tempers out 1029/1024 and 10976/19935 in addition to the 5-limit commas 32805/32768 and 15625/15552. This makes it among other things an excellent tuning for [[Gamelismic clan|guiron]] and [[Gamelismic clan|tritikleismic]] temperaments. It has a very accurate 11, and in the 11-limit tempers out 385/384, 441/440 and 4000/3993. In the 13-limit it tempers out 325/324 and 364/363, in the 17-limit 273/272 and 375/374, and in the 19-limit 343/342 and 361/360. It also provides the [[optimal patent val]] for 11-limit guiron and 13-limit tritikleismic, as well as the 13-limit rank three temperament [[Gamelismic family|portending]].

Another and notable temperament supported by 159 is [[Turkish maqam music temperaments|yarman temperament]], with a generator of 2\159 which can be taken as an approximate 105/104. 159 supplies the optimal patent val for 7, 11, 13, 17 and 19-limit yarman, so they are very closely associated. Curiously, the temperament does not temper out 1029/1024, however.

Yarman temperament has [[MOSScales|MOS]] of 79 and 80 notes to the octave, and the 79-note MOS has been proposed by <span class="wiki_link_ext">Ozan Yarman</span> as a tuning standard for [[Arabic, Turkish, Persian|arabic/turkish/persian]] music. 

=Articles=
* [[http://www.ozanyarman.com/files/doctorate_thesis.pdf|Ozan Yarman's dissertation]] 
* [[http://www.ozanyarman.com/files/34ten79a.pdf|paper]], also by Ozan Yarman, gives a summary.
* [[http://www.bestii.com/~mschulter/17-MOS-tunings_Letter-to-Ozan.txt|Letter to Ozan Yarman]] by Margo Schulter [[http://www.webcitation.org/5xepptaan|Permalink]]

Original HTML content:

<html><head><title>159edo</title></head><body>The <em>159 equal division</em> divides the octave into 159 equal parts of 7.547 cents each. A salient fact about it is that 159 = 3*53, so that it shares the same 5-limit thirds and fifths with <a class="wiki_link" href="/53edo">53edo</a>. In the 7-limit it tempers out 1029/1024 and 10976/19935 in addition to the 5-limit commas 32805/32768 and 15625/15552. This makes it among other things an excellent tuning for <a class="wiki_link" href="/Gamelismic%20clan">guiron</a> and <a class="wiki_link" href="/Gamelismic%20clan">tritikleismic</a> temperaments. It has a very accurate 11, and in the 11-limit tempers out 385/384, 441/440 and 4000/3993. In the 13-limit it tempers out 325/324 and 364/363, in the 17-limit 273/272 and 375/374, and in the 19-limit 343/342 and 361/360. It also provides the <a class="wiki_link" href="/optimal%20patent%20val">optimal patent val</a> for 11-limit guiron and 13-limit tritikleismic, as well as the 13-limit rank three temperament <a class="wiki_link" href="/Gamelismic%20family">portending</a>.<br />
<br />
Another and notable temperament supported by 159 is <a class="wiki_link" href="/Turkish%20maqam%20music%20temperaments">yarman temperament</a>, with a generator of 2\159 which can be taken as an approximate 105/104. 159 supplies the optimal patent val for 7, 11, 13, 17 and 19-limit yarman, so they are very closely associated. Curiously, the temperament does not temper out 1029/1024, however.<br />
<br />
Yarman temperament has <a class="wiki_link" href="/MOSScales">MOS</a> of 79 and 80 notes to the octave, and the 79-note MOS has been proposed by <span class="wiki_link_ext">Ozan Yarman</span> as a tuning standard for <a class="wiki_link" href="/Arabic%2C%20Turkish%2C%20Persian">arabic/turkish/persian</a> music. <br />
<br />
<!-- ws:start:WikiTextHeadingRule:0:&lt;h1&gt; --><h1 id="toc0"><a name="Articles"></a><!-- ws:end:WikiTextHeadingRule:0 -->Articles</h1>
<ul><li><a class="wiki_link_ext" href="http://www.ozanyarman.com/files/doctorate_thesis.pdf" rel="nofollow">Ozan Yarman's dissertation</a></li><li><a class="wiki_link_ext" href="http://www.ozanyarman.com/files/34ten79a.pdf" rel="nofollow">paper</a>, also by Ozan Yarman, gives a summary.</li><li><a class="wiki_link_ext" href="http://www.bestii.com/~mschulter/17-MOS-tunings_Letter-to-Ozan.txt" rel="nofollow">Letter to Ozan Yarman</a> by Margo Schulter <a class="wiki_link_ext" href="http://www.webcitation.org/5xepptaan" rel="nofollow">Permalink</a></li></ul></body></html>