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 | '''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. | ||
[[Category:Equal divisions of the octave]] | [[Category:Equal divisions of the octave]] | ||
Revision as of 02:53, 29 August 2021
144edo is the 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.