159edo: Difference between revisions

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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]].

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 style="">~~Ozan Yarman~~</span>~~ as a tuning standard for [[Arabic,_Turkish,_Persian|arabic/turkish/persian]] music.

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|arabic/turkish/persian]] music.

=Articles=

~~<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/doctorate_thesis.pdf Ozan Yarman's dissertation]

*[http://www.ozanyarman.com/files/34ten79a.pdf This 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)]

[[Category:edo]]

[[Category:guiron]]

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-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]].
+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 style="">Ozan Yarman</span> as a tuning standard for [[Arabic,_Turkish,_Persian|arabic/turkish/persian]] music.
+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|arabic/turkish/persian]] music.
 =Articles=
-<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/doctorate_thesis.pdf Ozan Yarman's dissertation]
+*[http://www.ozanyarman.com/files/34ten79a.pdf This 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)]
 [[Category:edo]]
 [[Category:guiron]]