267edo: Difference between revisions

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~~'''267edo''' is the [[~~EDO~~|equal division of the octave]] into 267 parts of 4.494382 [[cent]]s each.~~

~~In the~~ 5-limit~~, it tempers out both [[Graviton|129140163/128000000~~]] ~~and 274877906944/274658203125~~, ~~enabling it to support both~~ [[~~Gravity_family|gravity~~]] ~~and~~ [[~~Luna_family|luna~~]] ~~temperaments~~. In the 7-limit, it tempers out ~~1029~~/~~1024, 3136/3125, 50421/50000, 65625/65536, 9882516/9765625~~ and ~~28824005~~/~~28697814~~, enabling it to ~~support~~ [[~~Gamelismic_clan|gamelismic~~]], [[~~Hemimean_family|hemimean~~]] and [[~~Trimyna_family|trimyna~~]] temperaments among others. In the 11-limit, it tempers out 243/242, 1375/1372, 4000/3993, 6144/6125, 8019/8000, 16896/16807, 30375/30184, 43923/43904 and [[Quartisma|117440512/117406179]]. In the 13-limit, it tempers out 351/350, 1375/1372, 1575/1573, 2080/2079, [[4096/4095]], 4225/4224 and 59535/59488.

267edo is a fairly good [[5-limit]] tuning, but in[[consistent]] in the [[7-odd-limit]]. In the 5-limit, the equal temperament [[tempering out|tempers out]] both 129140163/128000000 ([[graviton]]) and 274877906944/274658203125 (luna comma), enabling it to [[support]] [[gravity]] and [[luna]] temperaments.

The 267d [[val]] being the best, tempers out [[1029/1024]], [[3136/3125]], [[50421/50000]], [[65625/65536]], 9882516/9765625 and 28824005/28697814, supporting [[gamelismic]], [[hemimean]] and [[trimyna]] temperaments among others; in the 11-limit, [[243/242]], 1375/1372, [[4000/3993]], [[6144/6125]], [[8019/8000]]; in the 13-limit, [[351/350]], 1375/1372, [[1575/1573]], [[2080/2079]], [[4096/4095]], [[4225/4224]] and 59535/59488.

=== Prime harmonics ===

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

[[Category:Gravity]]

[[Category:Luna]]

~~[[Category:Quartismic]]~~

@@ Line 1: / Line 1: @@
 {{Infobox ET}}
-'''267edo''' is the [[EDO|equal division of the octave]] into 267 parts of 4.494382 [[cent]]s each.
+{{EDO intro}}
-In the 5-limit, it tempers out both [[Graviton|129140163/128000000]] and 274877906944/274658203125, enabling it to support both [[Gravity_family|gravity]] and [[Luna_family|luna]] temperaments.  In the 7-limit, it tempers out 1029/1024, 3136/3125, 50421/50000, 65625/65536, 9882516/9765625 and 28824005/28697814, enabling it to support [[Gamelismic_clan|gamelismic]], [[Hemimean_family|hemimean]] and [[Trimyna_family|trimyna]] temperaments among others.  In the 11-limit, it tempers out 243/242, 1375/1372, 4000/3993, 6144/6125, 8019/8000, 16896/16807, 30375/30184, 43923/43904 and [[Quartisma|117440512/117406179]].  In the 13-limit, it tempers out 351/350, 1375/1372, 1575/1573, 2080/2079, [[4096/4095]], 4225/4224 and 59535/59488.
+edo is a fairly good [[5-limit]] tuning, but in[[consistent]] in the [[7-odd-limit]]. In the 5-limit, the equal temperament [[tempering out|tempers out]] both 129140163/128000000 ([[graviton]]) and 274877906944/274658203125 (luna comma), enabling it to [[support]] [[gravity]] and [[luna]] temperaments.
+The 267d [[val]] being the best, tempers out [[1029/1024]], [[3136/3125]], [[50421/50000]], [[65625/65536]], 9882516/9765625 and 28824005/28697814, supporting [[gamelismic]], [[hemimean]] and [[trimyna]] temperaments among others; in the 11-limit, [[243/242]], 1375/1372, [[4000/3993]], [[6144/6125]], [[8019/8000]]; in the 13-limit, [[351/350]], 1375/1372, [[1575/1573]], [[2080/2079]], [[4096/4095]], [[4225/4224]] and 59535/59488.
+=== Prime harmonics ===
 {{Harmonics in equal|267}}
-[[Category:Equal divisions of the octave|###]] <!-- 3-digit number -->
 [[Category:Gravity]]
 [[Category:Luna]]
-[[Category:Quartismic]]