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 ~~2/1~~</span>=

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

~~Divides~~ the ~~2/1 ratio in~~ 5.38117 ~~Cents~~ each ~~step~~. ~~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).

'''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| (optimal patent val), <223 354 518| (223b), and <223 353 517| (223c). Using the optimal 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.

[[Category:~~edo~~]]

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

[[Category:Edo]]

[[Category:Prime EDO]]

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-=<span style="color: #2230ff; font-family: 'Times New Roman',Times,serif; font-size: 113%;">223 equal divisions per 2/1</span>=
+=<span style="color: #2230ff; font-family: 'Times New Roman',Times,serif; font-size: 113%;">223 equal divisions per octave</span>=
-Divides the 2/1 ratio in 5.38117 Cents each step. 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).
+'''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| (optimal patent val), &lt;223 354 518| (223b), and &lt;223 353 517| (223c). Using the optimal 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.
-[[Category:edo]]
+edo is the 48th [[prime EDO]].
+[[Category:Edo]]
+[[Category:Prime EDO]]