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]]

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[[Category:Septiquarter]]

[[Category:Semiluna]]

[[Category:~~Canou]]~~

[[Category:Undim]]

~~[[Category:Semicanousmic~~]]

@@ Line 1: / Line 1: @@
-'''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.
-edo 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]].
+edo 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]]
@@ Line 10: / Line 10: @@
 [[Category:Septiquarter]]
 [[Category:Semiluna]]
-[[Category:Canou]]
+[[Category:Undim]]
-[[Category:Semicanousmic]]