159edo
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:<h1> --><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>