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{{Infobox ET}}
{{Infobox ET}}
'''139edo''' is the [[EDO|equal division of the octave]] into 139 parts of 8.6331 [[cent]]s each. 139edo is the 34th [[prime EDO]].
{{EDO intro}}


It is inconsistent to the 5-limit and higher limit, with three mappings possible for the 5-limit: <139 220 323| (patent val), <139 221 323| (139b), and <139 220 322| (139c).  
== Theory ==
139edo is in[[consistent]] to the [[5-odd-limit]] and higher limits, with three mappings possible for the 5-limit: {{val| 139 220 323 }} ([[patent val]]), {{val| 139 '''221''' 323 }} (139b), and {{val| 139 220 '''322''' }} (139c).  


== Commas ==
Using the patent val, it [[tempering out|tempers out]] 1990656/1953125 ([[valentine comma]]) and 43046721/41943040 ([[python comma]]) in the 5-limit; [[126/125]], [[1029/1024]], and 4782969/4705960 in the 7-limit, [[support]]ing the 7-limit [[valentine]] temperament; [[540/539]], 1944/1925, 2835/2816, and 12005/11979 in the 11-limit; [[364/363]], [[676/675]], [[1287/1280]], 1701/1690, and [[1716/1715]] in the 13-limit. Using the alternative 139f val, it tempers out [[144/143]], [[196/195]], [[351/350]], [[4096/4095]], and 4455/4394 in the 13-limit.
Using the patent val, it tempers out the valentine comma, 1990656/1953125 and the lalagu comma, 43046721/41943040 in the 5-limit; 126/125, 1029/1024, and 4782969/4705960 in the 7-limit, supporting the 7-limit [[Starling temperaments|valentine temperament]]; 540/539, 1944/1925, 2835/2816, and 12005/11979 in the 11-limit; 364/363, 676/675, 1287/1280, 1701/1690, and 1716/1715 in the 13-limit.  


Using the 139bdf val, it tempers out [[Würschmidt comma]], 393216/390625 and 409600000/387420489 in the 5-limit; 245/243, 3125/3087, and 131072/127575 in the 7-limit; 176/175, 1232/1215, and 2560/2541 in the 11-limit; 275/273, 512/507, 625/624, 847/845, and 1625/1617 in the 13-limit.  
Using the 139df val, it tempers out [[225/224]], 51200/50421, and 157464/153125 in the 7-limit; [[99/98]], [[176/175]], and 15309/15125 in the 11-limit, supporting the 11-limit [[Marvel temperaments #Interpental|interpental]] temperament; 144/143, 648/637, [[847/845]], [[1575/1573]], and 3159/3125 in the 13-limit.  


Using the 139ce val, it tempers out the [[Magic family|small diesis]], 3125/3072 and 22876792454961/21990232555520 in the 5-limit; 1029/1024, 3125/3087, and 19683/19600 in the 7-limit, supporting the 7-limit [[Magic family|trismegistus temperament]]; 540/539, 1331/1323, and 1815/1792 in the 11-limit; 275/273, 325/324, 847/845, 1287/1280, and 1575/1573 in the 13-limit.  
Using the 139ce val, it tempers out 3125/3072 ([[magic comma]]) and 22876792454961/21990232555520 in the 5-limit; 1029/1024, [[3125/3087]], and [[19683/19600]] in the 7-limit, supporting the 7-limit [[trismegistus]] temperament; 540/539, 1331/1323, and 1815/1792 in the 11-limit; [[275/273]], [[325/324]], 847/845, 1287/1280, and 1575/1573 in the 13-limit.  


Using the 139df val, it tempers out 225/224, 51200/50421, and 157464/153125 in the 7-limit; 99/98, 176/175, and 15309/15125 in the 11-limit, supporting the 11-limit [[Marvel temperaments|interpental temperament]]; 144/143, 648/637, 847/845, 1575/1573, and 3159/3125 in the 13-limit.  
Using the 139bdf val, it tempers out 393216/390625 ([[würschmidt comma]]), and 409600000/387420489 in the 5-limit; [[245/243]], 3125/3087, and 131072/127575 in the 7-limit; 176/175, 1232/1215, and 2560/2541 in the 11-limit; 275/273, [[512/507]], [[625/624]], 847/845, and 1625/1617 in the 13-limit.  


Using 139f val, it tempers out 144/143, 196/195, 351/350, 4096/4095, and 4455/4394 in the 13-limit.
=== Odd harmonics ===
 
== Harmonics ==
{{Harmonics in equal|139}}
{{Harmonics in equal|139}}
[[Category:Equal divisions of the octave|###]] <!-- 3-digit number -->
[[Category:Prime EDO]]
Retrieved from "https://en.xen.wiki/w/139edo"