159edo: Difference between revisions
Added 10985/10976 to the list of 13-limit commas tempered out. I noticed this was the case while compiling a list of justonic intervals corresponding to the steps of 159edo. |
m minor (mostly formal) changes |
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'''159edo''' is the ''159 equal division of the octave'' into equal parts of 7.547 [[cent]]s each. A salient fact about it is that 159 = 3*53, so that it shares the same 5-limit thirds and fifths with [[53edo]]. However, compared to 53edo, the patent vals differ on the mapping for 7. 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, 364/363, and 10985/10976. It also has an accurate 17, and in the 17-limit 273/272 and 375/374. In the 19-limit it tempers out 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. | ||
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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. | 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= | == Articles == | ||
*[http://www.ozanyarman.com/files/doctorate_thesis.pdf Ozan Yarman's dissertation] | * [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.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)] | * [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: | [[Category:Edo]] | ||
[[Category: | [[Category:Guiron]] | ||
[[Category: | [[Category:Maqam]] | ||
[[Category: | [[Category:Tritikleismic]] | ||
[[Category: | [[Category:Yarman]] | ||
Revision as of 16:02, 4 September 2020
159edo is the 159 equal division of the octave into 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. However, compared to 53edo, the patent vals differ on the mapping for 7. 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, 364/363, and 10985/10976. It also has an accurate 17, and in the 17-limit 273/272 and 375/374. In the 19-limit it tempers out 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
- Ozan Yarman's dissertation
- This paper, also by Ozan Yarman, gives a summary.
- Letter to Ozan Yarman by Margo Schulter (permalink)