159edo: Difference between revisions

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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 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 the 11-limit, it tempers out not only [[385/384]], [[441/440]], [[3025/3024]], [[4000/3993]], [[4375/4356]], and [[6250/6237]], but both [[~~Nexuma~~|1771561/1769472]] and [[Quartisma|117440512/117406179]], which, in turn means that [[~~Symbiosma~~|19712/19683]] is tempered out as well.

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 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]] and 13720/13689.

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]] and 13720/13689. This means that 159edo supports 13-limit [[Mercator family#Cartography|cartography]].

In the 17-limit tempers out [[273/272]], 375/374, 595/594, 715/714, [[936/935]], [[1089/1088]], [[1701/1700]], 8624/8619, [[11271/11264]] and 15379/15300.

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 {{todo|improve readability}}
 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 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 the 11-limit, it tempers out not only [[385/384]], [[441/440]], [[3025/3024]], [[4000/3993]], [[4375/4356]], and [[6250/6237]], but both [[Nexuma|1771561/1769472]] and [[Quartisma|117440512/117406179]], which, in turn means that [[Symbiosma|19712/19683]] is tempered out as well.
+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 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]] and 13720/13689.
+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]] and 13720/13689.  This means that 159edo supports 13-limit [[Mercator family#Cartography|cartography]].
 In the 17-limit tempers out [[273/272]], 375/374, 595/594, 715/714, [[936/935]], [[1089/1088]], [[1701/1700]], 8624/8619, [[11271/11264]] and 15379/15300.