139edo: Difference between revisions

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'''139edo''' is the [[EDO|equal division of the octave]] into 139 parts of 8.6331 [[cent]]s each. 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). 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 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 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 139f val, it tempers out 144/143, 196/195, 351/350, 4096/4095, and 4455/4394 in the 13-limit.

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

~~139edo~~ is the ~~34th [[prime EDO]]~~.

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).

== Commas ==

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 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 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 139f val, it tempers out 144/143, 196/195, 351/350, 4096/4095, and 4455/4394 in the 13-limit.

== Harmonics ==

[[Category:Equal divisions of the octave|###]]

[[Category:Prime EDO]]

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 {{Infobox ET}}
-'''139edo''' is the [[EDO|equal division of the octave]] into 139 parts of 8.6331 [[cent]]s each. It is inconsistent to the 5-limit and higher limit, with three mappings possible for the 5-limit: &lt;139 220 323| (patent val), &lt;139 221 323| (139b), and &lt;139 220 322| (139c). 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 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 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 139f val, it tempers out 144/143, 196/195, 351/350, 4096/4095, and 4455/4394 in the 13-limit.
+'''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 is the 34th [[prime EDO]].
+It is inconsistent to the 5-limit and higher limit, with three mappings possible for the 5-limit: &lt;139 220 323| (patent val), &lt;139 221 323| (139b), and &lt;139 220 322| (139c).
+== Commas ==
+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 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 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 139f val, it tempers out 144/143, 196/195, 351/350, 4096/4095, and 4455/4394 in the 13-limit.
+== Harmonics ==
+{{Harmonics in equal|139}}
 [[Category:Equal divisions of the octave|###]] <!-- 3-digit number -->
 [[Category:Prime EDO]]