292edo: Difference between revisions

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'''292edo''' is the [[EDO|equal division of the octave]] into 292 parts of 4.1095 cents each.  
The '''292 equal divisions of the octave''' ('''292edo''') is the [[EDO|equal division of the octave]] into 292 parts of 4.1095 [[cent]]s each.  


292edo is closely related to [[146edo]], but the patent vals differ on the mapping for 3. It tempers out 390625000/387420489 (quartonic comma) and 274877906944/274658203125 (luna/hemithirds comma) in the [[5-limit]]; 5120/5103 ([[5120/5103|hemifamity]]), 390625/388962 ([[dimcomp comma|dimcomp]]), 420175/419904 (wizma), and 4802000/4782969 ([[canousma]]) in the [[7-limit]]; 1375/1372, 5632/5625, 6250/6237, 9801/9800 and [[14641/14580]] in the [[11-limit]]; [[352/351]], 625/624, 847/845, 1716/1715, and 2080/2079 in the [[13-limit]].  
292edo is closely related to [[146edo]], but the patent vals differ on the mapping for 3. It tempers out {{monzo| 3 -18 11 }} (quartonic comma) and {{monzo| 38 -2 -15 }} (luna/hemithirds comma) in the [[5-limit]]; 5120/5103 ([[5120/5103|hemifamity]]), 390625/388962 ([[dimcomp comma|dimcomp]]), 420175/419904 (wizma), and 4802000/4782969 ([[canousma]]) in the [[7-limit]]; 1375/1372, 5632/5625, [[6250/6237]], [[9801/9800]] and [[14641/14580]] in the [[11-limit]]; [[352/351]], [[625/624]], [[847/845]], [[1716/1715]], and [[2080/2079]] in the [[13-limit]].  


It notably supports [[Hemifamity temperaments #Semiseptiquarter|semiseptiquarter]] and [[Luna family #Semiluna|semiluna]]. It also provides a nice tuning for the rank-3 [[Dimcomp family|dimcomp]] and [[Canou family #Semicanou|semicanou]].  
It provides the [[optimal patent val]] for the [[undim]] temperament in the 7-, 11-, and 13-limit, and notably supports [[Hemifamity temperaments #Semiseptiquarter|semiseptiquarter]] and [[Luna family #Semiluna|semiluna]].  


[[Category:Theory]]
[[Category:Theory]]
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[[Category:Septiquarter]]
[[Category:Septiquarter]]
[[Category:Semiluna]]
[[Category:Semiluna]]
[[Category:Canou]]
[[Category:Undim]]
[[Category:Semicanousmic]]

Revision as of 21:28, 11 December 2021

The 292 equal divisions of the octave (292edo) is the equal division of the octave into 292 parts of 4.1095 cents each.

292edo is closely related to 146edo, but the patent vals differ on the mapping for 3. It tempers out [3 -18 11 (quartonic comma) and [38 -2 -15 (luna/hemithirds comma) in the 5-limit; 5120/5103 (hemifamity), 390625/388962 (dimcomp), 420175/419904 (wizma), and 4802000/4782969 (canousma) in the 7-limit; 1375/1372, 5632/5625, 6250/6237, 9801/9800 and 14641/14580 in the 11-limit; 352/351, 625/624, 847/845, 1716/1715, and 2080/2079 in the 13-limit.

It provides the optimal patent val for the undim temperament in the 7-, 11-, and 13-limit, and notably supports semiseptiquarter and semiluna.