174edo: Difference between revisions
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'''174edo''' is the [[EDO|equal division of the octave]] into 174 parts of 6.8966 cents each. It is closely related to [[87edo]], but the patent vals differ on the mapping for 17 and some higher primes. It is contorted in the 13-limit, tempering out 196/195, 245/243, 352/351, 364/363, and 625/624. Using the patent val, it tempers out 289/288 in the 17-limit; 361/360, 476/475, and 665/663 in the 19-limit; 391/390, 392/391, 460/459, 529/528, and 760/759 in the 23-limit; 1309/1305, 1450/1449, and 4147/4140 in the 29-limit; 496/495 and 1365/1364 in the 31-limit. | '''174edo''' is the [[EDO|equal division of the octave]] into 174 parts of 6.8966 cents each. It is closely related to [[87edo]], but the patent vals differ on the mapping for 17 and some higher primes. It is [[contorted]] (or [[enfactored]]) in the 13-limit, tempering out 196/195, 245/243, 352/351, 364/363, and 625/624. Using the patent val, it tempers out 289/288 in the 17-limit; 361/360, 476/475, and 665/663 in the 19-limit; 391/390, 392/391, 460/459, 529/528, and 760/759 in the 23-limit; 1309/1305, 1450/1449, and 4147/4140 in the 29-limit; 496/495 and 1365/1364 in the 31-limit. | ||
[[Category:Equal divisions of the octave]] | [[Category:Equal divisions of the octave]] | ||
Revision as of 19:45, 29 September 2021
174edo is the equal division of the octave into 174 parts of 6.8966 cents each. It is closely related to 87edo, but the patent vals differ on the mapping for 17 and some higher primes. It is contorted (or enfactored) in the 13-limit, tempering out 196/195, 245/243, 352/351, 364/363, and 625/624. Using the patent val, it tempers out 289/288 in the 17-limit; 361/360, 476/475, and 665/663 in the 19-limit; 391/390, 392/391, 460/459, 529/528, and 760/759 in the 23-limit; 1309/1305, 1450/1449, and 4147/4140 in the 29-limit; 496/495 and 1365/1364 in the 31-limit.