159edo: Difference between revisions

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* In the 19-limit, it is known to temper out 343/342 and 361/360, but since it is inconsistent in the 19-limit, there are other potential mappings available that temper out different commas.

Notably, 159edo 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|portending]]. In addition to this, it also supports both forms of [[Turkish maqam music temperaments #Yarman temperament|yarman temperament]], with a generator of 2\159 which can be taken as an approximate 105/104~~, and 159 supplies the optimal patent val for 7, 11, 13, 17 and 19-limit yarman II~~. Yarman I temperament has a [[MOS]] of 80 notes to the octave, while yarman II temperament has a MOS of 79 notes, ~~the latter~~ of ~~which~~ has been proposed by Ozan Yarman as a tuning standard for [[Arabic, Turkish, Persian|Arabic, Turkish and Persian]] music.

Notably, 159edo 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|portending]]. In addition to this, it also supports both forms of [[Turkish maqam music temperaments #Yarman temperament|yarman temperament]], with a generator of 2\159 which can be taken as an approximate 105/104. Yarman I temperament has a [[MOS]] of 80 notes to the octave, while yarman II temperament has a MOS of 79 notes, and has its optimal patent val supplied by 159edo in 7-limit, 11-limit, 13-limit, 17-limit and even 19-limit forms- either way, a form of yarman temperament has been proposed by [[Ozan Yarman]] as a tuning standard for [[Arabic, Turkish, Persian|Arabic, Turkish and Persian]] music.

=== MOSes and other scales ===

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 * In the 19-limit, it is known to temper out 343/342 and 361/360, but since it is inconsistent in the 19-limit, there are other potential mappings available that temper out different commas.
-Notably, 159edo 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|portending]].  In addition to this, it also supports both forms of [[Turkish maqam music temperaments #Yarman temperament|yarman temperament]], with a generator of 2\159 which can be taken as an approximate 105/104, and 159 supplies the optimal patent val for 7, 11, 13, 17 and 19-limit yarman II.  Yarman I temperament has a [[MOS]] of 80 notes to the octave, while yarman II temperament has a MOS of 79 notes, the latter of which has been proposed by Ozan Yarman as a tuning standard for [[Arabic, Turkish, Persian|Arabic, Turkish and Persian]] music.
+Notably, 159edo 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|portending]].  In addition to this, it also supports both forms of [[Turkish maqam music temperaments #Yarman temperament|yarman temperament]], with a generator of 2\159 which can be taken as an approximate 105/104.  Yarman I temperament has a [[MOS]] of 80 notes to the octave, while yarman II temperament has a MOS of 79 notes, and has its optimal patent val supplied by 159edo in 7-limit, 11-limit, 13-limit, 17-limit and even 19-limit forms- either way, a form of yarman temperament has been proposed by [[Ozan Yarman]] as a tuning standard for [[Arabic, Turkish, Persian|Arabic, Turkish and Persian]] music.
 === MOSes and other scales ===