93edo: Difference between revisions

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Revision as of 19:39, 29 September 2021 view source Cmloegcmluin (talk \| contribs) autopatrolled 5,160 edits add link for defactoring ← Older edit		Revision as of 23:06, 12 November 2021 view source Cmloegcmluin (talk \| contribs) autopatrolled 5,160 edits remove temporary link to defactoring Newer edit →
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	The 93 equal division divides the octave into 93 equal parts of 12.903 cents each. 93 = 3 * 31, and 93 is a [[contorted]] ~~(or [[enfactored]])~~ 31 through the 7 limit. In the 11-limit the patent val tempers out 4000/3993 and in the 13-limit 144/143, 1188/1183 and 364/363. It provides the optimal patent val for the 11-limit prajapati and 13-limit kumhar temperaments, and the 11 and 13 limit 43&50 temperament.		The 93 equal division divides the octave into 93 equal parts of 12.903 cents each. 93 = 3 * 31, and 93 is a [[contorted]] 31 through the 7 limit. In the 11-limit the patent val tempers out 4000/3993 and in the 13-limit 144/143, 1188/1183 and 364/363. It provides the optimal patent val for the 11-limit prajapati and 13-limit kumhar temperaments, and the 11 and 13 limit 43&50 temperament.

	Since 93edo has good approximations of 13th, 17th and 19th harmonics unlike 31edo (as 838.710¢, 103.226¢, and 296.774¢ respectively), it also allows one to give a clearer harmonic identity to [[31edo]]'s excellent approximation of 13:17:19.		Since 93edo has good approximations of 13th, 17th and 19th harmonics unlike 31edo (as 838.710¢, 103.226¢, and 296.774¢ respectively), it also allows one to give a clearer harmonic identity to [[31edo]]'s excellent approximation of 13:17:19.