144edo: Difference between revisions

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~~'''~~144edo~~'''~~ is the [[EDO~~|equal division of the octave]] into 144 parts of 8.3333 cents each~~, ~~making it~~ the square of [[12edo]] ~~and the 12th number in the fibonacci sequence~~. It is closely related to [[72edo]], but the patent vals differ on the mapping for 13 and 17. It is [[contorted]] in the 11-limit, tempering out 225/224, 243/242, 385/384, 441/440, and 4000/3993. Using the patent val, it tempers out 847/845, 1188/1183, 1701/1690, 1875/1859, and 4225/4224 in the 13-limit; 273/272, 715/714, 833/832, 875/867, 891/884, and 1275/1274 in the 17-limit; 210/209, 325/323, 343/342, 363/361, 400/399, 513/512, and 665/663 in the 19-limit. It can produce extremely precise ~~approximations~~ of ~~both~~ the ~~linear and~~ logarithmic ~~versions of the~~ golden ratio, at 89~~\144 and~~ 100~~\144 respectively~~.

== Theory ==

144edo is the 12th Fibonacci EDO, and the square of world-dominant [[12edo]].

It is closely related to [[72edo]], but the patent vals differ on the mapping for 13 and 17. It is [[contorted]] in the 11-limit, tempering out 225/224, 243/242, 385/384, 441/440, and 4000/3993. Using the patent val, it tempers out 847/845, 1188/1183, 1701/1690, 1875/1859, and 4225/4224 in the 13-limit; 273/272, 715/714, 833/832, 875/867, 891/884, and 1275/1274 in the 17-limit; 210/209, 325/323, 343/342, 363/361, 400/399, 513/512, and 665/663 in the 19-limit.

As a consequence of being a Fibonacci EDO, it can produce extremely precise approximation of the logarithmic golden ratio at 89 steps. In addition, it ''also'' excellently represents the acoustic golden ratio by 100 steps.

The 144gh val is a tuning for semihemisecordite temperament, while 144eff val is a tuning for hemimiracle. 144ee is a tuning for oracle. 144cf val supports necromanteion.

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

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-'''144edo''' is the [[EDO|equal division of the octave]] into 144 parts of 8.3333 cents each, making it the square of [[12edo]] and the 12th number in the fibonacci sequence. It is closely related to [[72edo]], but the patent vals differ on the mapping for 13 and 17. It is [[contorted]] in the 11-limit, tempering out 225/224, 243/242, 385/384, 441/440, and 4000/3993. Using the patent val, it tempers out 847/845, 1188/1183, 1701/1690, 1875/1859, and 4225/4224 in the 13-limit; 273/272, 715/714, 833/832, 875/867, 891/884, and 1275/1274 in the 17-limit; 210/209, 325/323, 343/342, 363/361, 400/399, 513/512, and 665/663 in the 19-limit. It can produce extremely precise approximations of both the linear and logarithmic versions of the golden ratio, at 89\144 and 100\144 respectively.
+{{EDO intro|144}}
+== Theory ==
+edo is the 12th Fibonacci EDO, and the square of world-dominant [[12edo]].
+It is closely related to [[72edo]], but the patent vals differ on the mapping for 13 and 17. It is [[contorted]] in the 11-limit, tempering out 225/224, 243/242, 385/384, 441/440, and 4000/3993. Using the patent val, it tempers out 847/845, 1188/1183, 1701/1690, 1875/1859, and 4225/4224 in the 13-limit; 273/272, 715/714, 833/832, 875/867, 891/884, and 1275/1274 in the 17-limit; 210/209, 325/323, 343/342, 363/361, 400/399, 513/512, and 665/663 in the 19-limit.
+As a consequence of being a Fibonacci EDO, it can produce extremely precise approximation of the logarithmic golden ratio at 89 steps. In addition, it ''also'' excellently represents the acoustic golden ratio by 100 steps.
+The 144gh val is a tuning for semihemisecordite temperament, while 144eff val is a tuning for hemimiracle. 144ee is a tuning for oracle. 144cf val supports necromanteion.
 [[Category:Equal divisions of the octave|###]] <!-- 3-digit number -->