223edo: Difference between revisions

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=<span style="color: #2230ff; font-family: 'Times New Roman',Times,serif; font-size: 113%;">223 equal divisions per octave</span>=

'''223edo''' is the [[EDO|equal division of the octave]] into 223 parts of 5.38117 [[cent]]s each. It contains an excellent proportion of Hornbostel Temperament (via 7L2s), between Square root of Pi (184\223), Aureus interval (34/21 in 155\223) and the 6/5 interval (58\223). It is inconsistent to the 5-limit and higher limit, with three mappings possible for the 5-limit: <223 353 518| (patent val), <223 354 518| (223b), and <223 353 517| (223c). Using the patent val, it tempers out the [[Würschmidt family|würschmidt comma]], 393216/390625 and 22876792454961/21990232555520 in the 5-limit; 2401/2400, 3136/3125, and 14348907/14000000 in the 7-limit. Using the ~~223b~~ val, it tempers out the [[Kleismic family|kleisma]], 15625/15552 and |58 -38 1> in the 5-limit; 245/243, 3136/3125, and 67108864/66706983 in the 7-limit. Using the 223c val, it tempers out the [[Graviton|gravity comma]], 129140163/128000000 and 35595703125/34359738368 in the 5-limit; 4375/4374, 33075/32768, and 78125/76832 in the 7-limit.

'''223edo''' is the [[EDO|equal division of the octave]] into 223 parts of 5.38117 [[cent]]s each. It contains an excellent proportion of Hornbostel Temperament (via 7L2s), between Square root of Pi (184\223), Aureus interval (34/21 in 155\223) and the 6/5 interval (58\223). It is inconsistent to the 5-limit and higher limit, with three mappings possible for the 5-limit: <223 353 518| (patent val), <223 354 518| (223b), and <223 353 517| (223c). Using the patent val, it tempers out the [[Würschmidt family|würschmidt comma]], 393216/390625 and 22876792454961/21990232555520 in the 5-limit; 2401/2400, 3136/3125, and 14348907/14000000 in the 7-limit; 243/242, 441/440, 5632/5625, and 1449459/1433600 in the 11-limit; 847/845, 1188/1183, 1287/1280, and 1573/1568 in the 13-limit. Using the 223be val, it tempers out the [[Kleismic family|kleisma]], 15625/15552 and |58 -38 1> in the 5-limit; 245/243, 3136/3125, and 67108864/66706983 in the 7-limit; 3025/3024, 3388/3375, 4375/4356, and 65536/65219 in the 11-limit; 352/351, 1001/1000, 2197/2178, and 2704/2695 in the 13-limit. Using the 223bef val, it tempers out 196/195, 325/324, 364/363, 625/624, and 49152/49049 in the 13-limit. Using the 223c val, it tempers out the [[Graviton|gravity comma]], 129140163/128000000 and 35595703125/34359738368 in the 5-limit; 4375/4374, 33075/32768, and 78125/76832 in the 7-limit; 243/242, 385/384, and 4000/3993 in the 11-limit; 1188/1183, 1573/1568, 1625/1617, 1716/1715, and 3159/3136 in the 13-limit. Using the 223e val, it tempers out 1944/1925, 2835/2816, and 4000/3993 in the 11-limit; 364/363, 1001/1000, 1701/1690, and 1716/1715 in the 13-limit.

223edo is the 48th [[prime EDO]].

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 =<span style="color: #2230ff; font-family: 'Times New Roman',Times,serif; font-size: 113%;">223 equal divisions per octave</span>=
-'''223edo''' is the [[EDO|equal division of the octave]] into 223 parts of 5.38117 [[cent]]s each. It contains an excellent proportion of Hornbostel Temperament (via 7L2s), between Square root of Pi (184\223), Aureus interval (34/21 in 155\223) and the 6/5 interval (58\223). It is inconsistent to the 5-limit and higher limit, with three mappings possible for the 5-limit: &lt;223 353 518| (patent val), &lt;223 354 518| (223b), and &lt;223 353 517| (223c). Using the patent val, it tempers out the [[Würschmidt family|würschmidt comma]], 393216/390625 and 22876792454961/21990232555520 in the 5-limit; 2401/2400, 3136/3125, and 14348907/14000000 in the 7-limit. Using the 223b val, it tempers out the [[Kleismic family|kleisma]], 15625/15552 and |58 -38 1&gt; in the 5-limit; 245/243, 3136/3125, and 67108864/66706983 in the 7-limit. Using the 223c val, it tempers out the [[Graviton|gravity comma]], 129140163/128000000 and 35595703125/34359738368 in the 5-limit; 4375/4374, 33075/32768, and 78125/76832 in the 7-limit.
+'''223edo''' is the [[EDO|equal division of the octave]] into 223 parts of 5.38117 [[cent]]s each. It contains an excellent proportion of Hornbostel Temperament (via 7L2s), between Square root of Pi (184\223), Aureus interval (34/21 in 155\223) and the 6/5 interval (58\223). It is inconsistent to the 5-limit and higher limit, with three mappings possible for the 5-limit: &lt;223 353 518| (patent val), &lt;223 354 518| (223b), and &lt;223 353 517| (223c). Using the patent val, it tempers out the [[Würschmidt family|würschmidt comma]], 393216/390625 and 22876792454961/21990232555520 in the 5-limit; 2401/2400, 3136/3125, and 14348907/14000000 in the 7-limit; 243/242, 441/440, 5632/5625, and 1449459/1433600 in the 11-limit; 847/845, 1188/1183, 1287/1280, and 1573/1568 in the 13-limit. Using the 223be val, it tempers out the [[Kleismic family|kleisma]], 15625/15552 and |58 -38 1&gt; in the 5-limit; 245/243, 3136/3125, and 67108864/66706983 in the 7-limit; 3025/3024, 3388/3375, 4375/4356, and 65536/65219 in the 11-limit; 352/351, 1001/1000, 2197/2178, and 2704/2695 in the 13-limit. Using the 223bef val, it tempers out 196/195, 325/324, 364/363, 625/624, and 49152/49049 in the 13-limit. Using the 223c val, it tempers out the [[Graviton|gravity comma]], 129140163/128000000 and 35595703125/34359738368 in the 5-limit; 4375/4374, 33075/32768, and 78125/76832 in the 7-limit; 243/242, 385/384, and 4000/3993 in the 11-limit; 1188/1183, 1573/1568, 1625/1617, 1716/1715, and 3159/3136 in the 13-limit. Using the 223e val, it tempers out 1944/1925, 2835/2816, and 4000/3993 in the 11-limit; 364/363, 1001/1000, 1701/1690, and 1716/1715 in the 13-limit.
 edo is the 48th [[prime EDO]].