191edo: Difference between revisions

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'''191edo''' is the [[EDO|equal division of the octave]] into 191 parts of 6.2827 [[cent]]s each. It is inconsistent to the 5-limit and higher limit, with two mappings possible for the 5-limit: <191 303 443| (~~optimal~~ patent val) and <191 303 444| (191c). Using the patent val, it tempers out the [[Tetracot family|tetracot comma]], 20000/19683 and |-52 5 19> in the 5-limit; 245/243, 2401/2400, and 68359375/67108864 in the 7-limit. Using the 191c val, it tempers out the [[Amity family|amity comma]], 1600000/1594323 and 549755813888/533935546875 in the 5-limit; 4375/4374, 5120/5103, and 823543/810000 in the 7-limit. Using the alternative 191cd val, 1728/1715, 3136/3125, and 1605632/1594323 ~~are tempered out~~ in the 7-limit.

'''191edo''' is the [[EDO|equal division of the octave]] into 191 parts of 6.2827 [[cent]]s each. It is inconsistent to the 5-limit and higher limit, with two mappings possible for the 5-limit: <191 303 443| (patent val) and <191 303 444| (191c). Using the patent val, it tempers out the [[Tetracot family|tetracot comma]], 20000/19683 and |-52 5 19> in the 5-limit; 245/243, 2401/2400, and 68359375/67108864 in the 7-limit; 385/384, 896/891, 1375/1372, and 118125/117128 in the 11-limit; 352/351, 364/363, 1625/1617, 1875/1859, and 2197/2187 in the 13-limit. Using the 191c val, it tempers out the [[Amity family|amity comma]], 1600000/1594323 and 549755813888/533935546875 in the 5-limit; 4375/4374, 5120/5103, and 823543/810000 in the 7-limit; 441/440, 896/891, 6912/6875, and 14641/14580 in the 11-limit; 196/195, 352/351, 364/363, 2197/2187, and 3146/3125 in the 13-limit. Using the alternative 191cd val, it tempers out 1728/1715, 3136/3125, and 1605632/1594323 in the 7-limit; 176/175, 540/539, 1331/1323, and 655360/649539 in the 11-limit; 351/350, 352/351, 640/637, 1573/1568, and 2197/2187 in the 13-limit, supporting the [[Hemimean clan|semisept temperament]].

191edo is the 43rd [[prime EDO]].

Revision as of 12:31, 13 December 2018 view source Xenllium (talk \| contribs) autopatrolled, emailconfirmed 5,024 edits No edit summary Tags: Mobile edit Mobile web edit ← Older edit		Revision as of 12:25, 24 December 2018 view source Xenllium (talk \| contribs) autopatrolled, emailconfirmed 5,024 edits No edit summary Tags: Mobile edit Mobile web edit Newer edit →
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	'''191edo''' is the [[EDO\|equal division of the octave]] into 191 parts of 6.2827 [[cent]]s each. It is inconsistent to the 5-limit and higher limit, with two mappings possible for the 5-limit: <191 303 443\| (~~optimal~~ patent val) and <191 303 444\| (191c). Using the patent val, it tempers out the [[Tetracot family\|tetracot comma]], 20000/19683 and \|-52 5 19> in the 5-limit; 245/243, 2401/2400, and 68359375/67108864 in the 7-limit. Using the 191c val, it tempers out the [[Amity family\|amity comma]], 1600000/1594323 and 549755813888/533935546875 in the 5-limit; 4375/4374, 5120/5103, and 823543/810000 in the 7-limit. Using the alternative 191cd val, 1728/1715, 3136/3125, and 1605632/1594323 ~~are tempered out~~ in the 7-limit.		'''191edo''' is the [[EDO\|equal division of the octave]] into 191 parts of 6.2827 [[cent]]s each. It is inconsistent to the 5-limit and higher limit, with two mappings possible for the 5-limit: <191 303 443\| (patent val) and <191 303 444\| (191c). Using the patent val, it tempers out the [[Tetracot family\|tetracot comma]], 20000/19683 and \|-52 5 19> in the 5-limit; 245/243, 2401/2400, and 68359375/67108864 in the 7-limit; 385/384, 896/891, 1375/1372, and 118125/117128 in the 11-limit; 352/351, 364/363, 1625/1617, 1875/1859, and 2197/2187 in the 13-limit. Using the 191c val, it tempers out the [[Amity family\|amity comma]], 1600000/1594323 and 549755813888/533935546875 in the 5-limit; 4375/4374, 5120/5103, and 823543/810000 in the 7-limit; 441/440, 896/891, 6912/6875, and 14641/14580 in the 11-limit; 196/195, 352/351, 364/363, 2197/2187, and 3146/3125 in the 13-limit. Using the alternative 191cd val, it tempers out 1728/1715, 3136/3125, and 1605632/1594323 in the 7-limit; 176/175, 540/539, 1331/1323, and 655360/649539 in the 11-limit; 351/350, 352/351, 640/637, 1573/1568, and 2197/2187 in the 13-limit, supporting the [[Hemimean clan\|semisept temperament]].

	191edo is the 43rd [[prime EDO]].		191edo is the 43rd [[prime EDO]].