182edo: Difference between revisions
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'''182edo''' is the [[EDO|equal division of the octave]] into 182 parts of 6.5934 [[cent]]s each. It is inconsistent to the 5-limit and higher limit, with three mappings possible for the 5-limit: <182 288 423| (optimal patent val), <182 289 423| (182b), and <182 288 422| (182c). Using the | '''182edo''' is the [[EDO|equal division of the octave]] into 182 parts of 6.5934 [[cent]]s each. It is inconsistent to the 5-limit and higher limit, with three mappings possible for the 5-limit: <182 288 423| (optimal patent val), <182 289 423| (182b), and <182 288 422| (182c). Using the patent val, it tempers out the tenfold green comma, 10077696/9765625 and 3486784401/3355443200 in the 5-limit; 126/125, 1728/1715, and 1937102445/1879048192 in the 7-limit; 2187/2156, 2835/2816, 5632/5625, and 14700/14641 in the 11-limit. Using the 182b val, it tempers out the [[Diaschismic family|diaschisma]], 2048/2025 and |-4 -37 27> in the 5-limit; 245/243, 6144/6125, and 9882516/9765625 in the 7-limit; 3025/3024, 3773/3750, and 4000/3993 in the 11-limit. Using the 182c val, it tempers out the [[Kleismic family|kleisma]], 15625/15552 and the double large green comma, 43046721/41943040 in the 5-limit; 2430/2401, 33075/32768, and 78125/76832 in the 7-limit. | ||
[[Category:Edo]] | [[Category:Edo]] | ||
Revision as of 12:39, 13 December 2018
182edo is the equal division of the octave into 182 parts of 6.5934 cents each. It is inconsistent to the 5-limit and higher limit, with three mappings possible for the 5-limit: <182 288 423| (optimal patent val), <182 289 423| (182b), and <182 288 422| (182c). Using the patent val, it tempers out the tenfold green comma, 10077696/9765625 and 3486784401/3355443200 in the 5-limit; 126/125, 1728/1715, and 1937102445/1879048192 in the 7-limit; 2187/2156, 2835/2816, 5632/5625, and 14700/14641 in the 11-limit. Using the 182b val, it tempers out the diaschisma, 2048/2025 and |-4 -37 27> in the 5-limit; 245/243, 6144/6125, and 9882516/9765625 in the 7-limit; 3025/3024, 3773/3750, and 4000/3993 in the 11-limit. Using the 182c val, it tempers out the kleisma, 15625/15552 and the double large green comma, 43046721/41943040 in the 5-limit; 2430/2401, 33075/32768, and 78125/76832 in the 7-limit.