144edo: Difference between revisions
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Notes on it's properties as part of the fibonacci sequence. |
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'''144edo''' is the [[EDO|equal division of the octave]] into 144 parts of 8.3333 cents each. 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. | '''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 steps respectively. | ||
[[Category:Edo]] | [[Category:Edo]] | ||