|
|
| Line 1: |
Line 1: |
| <h2>IMPORTED REVISION FROM WIKISPACES</h2>
| | 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|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|optimal patent val]] for 11-limit guiron and 13-limit tritikleismic, as well as the 13-limit rank three temperament [[Gamelismic_family|portending]]. |
| 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 22:38:38 UTC</tt>.<br>
| |
| : The original revision id was <tt>216532726</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>
| |
| <h4>Original Wikitext 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;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]].
| |
|
| |
|
| 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. | | 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. | | Yarman temperament has [[MOSScales|MOS]] of 79 and 80 notes to the octave, and the 79-note MOS has been proposed by <span style="">Ozan Yarman</span> as a tuning standard for [[Arabic,_Turkish,_Persian|arabic/turkish/persian]] music. |
|
| |
|
| =Articles= | | =Articles= |
| * [[http://www.ozanyarman.com/files/doctorate_thesis.pdf|Ozan Yarman's dissertation]]
| | <ul><li>[http://www.ozanyarman.com/files/doctorate_thesis.pdf Ozan Yarman's dissertation]</li><li>[http://www.ozanyarman.com/files/34ten79a.pdf paper], also by Ozan Yarman, gives a summary.</li><li>[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]</li></ul> [[Category:53]] |
| * [[http://www.ozanyarman.com/files/34ten79a.pdf|paper]], also by Ozan Yarman, gives a summary.
| | [[Category:edo]] |
| * [[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]]</pre></div>
| | [[Category:guiron]] |
| <h4>Original HTML content:</h4>
| | [[Category:maqam]] |
| <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>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 />
| | [[Category:tritikleismic]] |
| <br />
| | [[Category:yarman]] |
| 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></pre></div>
| |
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 guiron and 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 portending.
Another and notable temperament supported by 159 is 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 MOS of 79 and 80 notes to the octave, and the 79-note MOS has been proposed by Ozan Yarman as a tuning standard for arabic/turkish/persian music.
Articles