139edo: Difference between revisions

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'''139edo''' is the [[EDO|equal division of the octave]] into 139 parts of 8.6331 [[cent]]s each. It is inconsistent to the 5-limit and higher limit, with three mappings possible for the 5-limit: <139 220 323| (optimal patent val), <139 221 323| (139b), and <139 220 322| (139c). Using the optimal patent val, it tempers out the valentine comma, 1990656/1953125 and the double large green comma, 43046721/41943040 in the 5-limit; 126/125, 1029/1024, and 4782969/4705960 in the 7-limit. Using the 139b val, it tempers out Würschmidt comma, 393216/390625 and 409600000/387420489 in the 5-limit; 686/675 and 2240/2187 in the 7-limit. Using the 139c val, it tempers out small diesis, 3125/3072 and 22876792454961/21990232555520 in the 5-limit; 1029/1024, 3125/3087, and 19683/19600 in the 7-limit.

'''139edo''' is the [[EDO|equal division of the octave]] into 139 parts of 8.6331 [[cent]]s each. It is inconsistent to the 5-limit and higher limit, with three mappings possible for the 5-limit: <139 220 323| (optimal patent val), <139 221 323| (139b), and <139 220 322| (139c). Using the optimal patent val, it tempers out the valentine comma, 1990656/1953125 and the double large green comma, 43046721/41943040 in the 5-limit; 126/125, 1029/1024, and 4782969/4705960 in the 7-limit. Using the 139b val, it tempers out [[Würschmidt comma]], 393216/390625 and 409600000/387420489 in the 5-limit; 686/675 and 2240/2187 in the 7-limit. Using the 139c val, it tempers out the [[Magic family|small diesis]], 3125/3072 and 22876792454961/21990232555520 in the 5-limit; 1029/1024, 3125/3087, and 19683/19600 in the 7-limit.

139edo is the 34th [[prime EDO]].

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	'''139edo''' is the [[EDO\|equal division of the octave]] into 139 parts of 8.6331 [[cent]]s each. It is inconsistent to the 5-limit and higher limit, with three mappings possible for the 5-limit: <139 220 323\| (optimal patent val), <139 221 323\| (139b), and <139 220 322\| (139c). Using the optimal patent val, it tempers out the valentine comma, 1990656/1953125 and the double large green comma, 43046721/41943040 in the 5-limit; 126/125, 1029/1024, and 4782969/4705960 in the 7-limit. Using the 139b val, it tempers out Würschmidt comma, 393216/390625 and 409600000/387420489 in the 5-limit; 686/675 and 2240/2187 in the 7-limit. Using the 139c val, it tempers out small diesis, 3125/3072 and 22876792454961/21990232555520 in the 5-limit; 1029/1024, 3125/3087, and 19683/19600 in the 7-limit.		'''139edo''' is the [[EDO\|equal division of the octave]] into 139 parts of 8.6331 [[cent]]s each. It is inconsistent to the 5-limit and higher limit, with three mappings possible for the 5-limit: <139 220 323\| (optimal patent val), <139 221 323\| (139b), and <139 220 322\| (139c). Using the optimal patent val, it tempers out the valentine comma, 1990656/1953125 and the double large green comma, 43046721/41943040 in the 5-limit; 126/125, 1029/1024, and 4782969/4705960 in the 7-limit. Using the 139b val, it tempers out [[Würschmidt comma]], 393216/390625 and 409600000/387420489 in the 5-limit; 686/675 and 2240/2187 in the 7-limit. Using the 139c val, it tempers out the [[Magic family\|small diesis]], 3125/3072 and 22876792454961/21990232555520 in the 5-limit; 1029/1024, 3125/3087, and 19683/19600 in the 7-limit.

	139edo is the 34th [[prime EDO]].		139edo is the 34th [[prime EDO]].