159edo: Difference between revisions

Line 30:

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.

~~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|portending~~]].

In addition to the above, 159edo actually tempers out the 7-limit [[termite comma]] and the 13-limit [[chalmersia]], as well as the 17-limit [[sparkisma]], the latter of which is also tempered out by 53edo despite it having a different mapping for 17.

~~In addition to the above~~, 159edo ~~actually tempers out~~ the ~~7-limit~~ [[~~termite comma~~]] and ~~the~~ 13-limit ~~[[chalmersia]]~~, as well as the 17-limit [[~~sparkisma~~]]~~, the latter of which is also tempered out by 53edo despite it having a different mapping for 17~~.

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]].

Another 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 [[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.

@@ Line 30: / Line 30: @@
 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.
-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|portending]].
+In addition to the above, 159edo actually tempers out the 7-limit [[termite comma]] and the 13-limit [[chalmersia]], as well as the 17-limit [[sparkisma]], the latter of which is also tempered out by 53edo despite it having a different mapping for 17.
-In addition to the above, 159edo actually tempers out the 7-limit [[termite comma]] and the 13-limit [[chalmersia]], as well as the 17-limit [[sparkisma]], the latter of which is also tempered out by 53edo despite it having a different mapping for 17.
+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]].
 Another 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 [[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.