159edo: Difference between revisions
Two new tempered-out commas have been found. |
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Notably, while 159edo plays host to a number of fun temperaments like [[gamelismic]], a number of [[microtemperaments]] have also been found hiding within its structure, as is indicated to some extent by the following list of tempered commas. | |||
In the | - In the 5-limit, it tempers out the same commas as 53edo, including [[15625/15552]], [[32805/32768]], [[amity comma|1600000/1594323]], [[semicomma|2109375/2097152]], and [[vulture comma|10485760000/10460353203]]. | ||
In the | - In the 7-limit, it tempers out [[1029/1024]], [[10976/10935]], 117649/116640, [[Landscape comma|250047/250000]], 235298/234375 and [[Meter comma|703125/702464]]; this makes it among other things an excellent tuning for [[Schismatic family #Guiron|guiron]] and [[Gamelismic clan #Tritikleismic|tritikleismic]] temperaments, as well as a possible tuning for metric temperament. In addition, it also tempers out the [[termite comma]]. | ||
In the | - In the 11-limit, it tempers out not only [[385/384]], [[441/440]], [[3025/3024]], [[4000/3993]], [[4375/4356]], and [[6250/6237]], but both [[Nexus comma|1771561/1769472]] and [[Quartisma|117440512/117406179]], which in turn means that [[Symbiotic comma|19712/19683]] is tempered out as well. In addition, it also tempers out the [[frameshift comma]]- a comma known to be associated with higher-accuracy systems. | ||
In the | - In the 13-limit it tempers out [[325/324]], [[364/363]], [[625/624]], [[676/675]], [[1001/1000]], [[1575/1573]], [[2080/2079]], [[6656/6655]], [[cantonisma|10985/10976]], 13720/13689 and [[43904/43875]]. In addition, it also tempers out the [[chalmersia]]. | ||
In the | - In the 17-limit tempers out [[273/272]], 375/374, 595/594, [[715/714]], [[833/832]], [[936/935]], [[1089/1088]], [[1701/1700]], [[2025/2023]], 2028/2023, [[2431/2430]], 8624/8619, [[11271/11264]], 15379/15300, [[24576/24565]] and [[57375/57344]]. In addition, it also tempers out the [[sparkisma]], which is also tempered out by 53edo despite 53edo having a different mapping for 17. | ||
In | - 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 [[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. | 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 [[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. | ||