117edo: Difference between revisions

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117 ~~is a meantone edo with a step size~~ of 10.2564102564 cents. [[Category:~~Stub|#stub~~]]

'''117edo''' is the [[EDO|equal division of the octave]] into 117 parts of 10.2564102564 cents each. It is inconsistent to the 5-limit and higher limit, with four mappings possible for the 11-limit: <117 185 272 328 405| (optimal patent val), <117 186 272 329 405| (117bd), <117 185 271 328 404| (117ce), and <117 185 272 329 405| (117d). Using the patent val, it tempers out the [[syntonic comma]], 81/80 and |69 -1 -29> in the 5-limit; 6144/6125, 31104/30625, and 403368/390625 in the 7-limit, providing the [[optimal patent val]] for 7-limit [[Meantone family|mohajira temperament]]; 540/539, 1344/1331, 1617/1600, and 3168/3125 in the 11-limit, providing the optimal patent val for the [[Didymus rank three family|terpsichore rank-3 temperament]]. Using the 117bd val, it tempers out the [[Kleismic family|kleisma]], 15625/15552 and 17179869184/16142520375 in the 5-limit; 245/243, 3136/3125, and 51200/50421 in the 7-limit; 176/175, 1232/1215, 1375/1372, and 2560/2541 in the 11-limit. Using the 117ce val, it tempers out the [[Magic family|small diesis]], 3125/3072 and 282429536481/268435456000 in the 5-limit; 2401/2400, 3645/3584, and 4375/4374 in the 7-limit; 243/242, 441/440, and 1815/1792 in the 11-limit. Using the 117d val, it tempers out 126/125, 225/224, and 14495514624/13841287201 in the 7-limit; 99/98, 176/175, 441/440, and 12582912/12400927 in the 11-limit, supporting the 11-limit [[Meantone family|meantone temperament]].

[[Category:Edo]]

Revision as of 05:25, 24 September 2018 view source PiotrGrochowski (talk \| contribs) 981 edits Created page with "117 is a meantone edo with a step size of 10.2564102564 cents. #stub"		Revision as of 06:36, 14 December 2018 view source Xenllium (talk \| contribs) autopatrolled 4,516 edits No edit summary Tags: Mobile edit Mobile web edit Newer edit →
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	117 ~~is a meantone edo with a step size~~ of 10.2564102564 cents. [[Category:~~Stub\|#stub~~]]		'''117edo''' is the [[EDO\|equal division of the octave]] into 117 parts of 10.2564102564 cents each. It is inconsistent to the 5-limit and higher limit, with four mappings possible for the 11-limit: <117 185 272 328 405\| (optimal patent val), <117 186 272 329 405\| (117bd), <117 185 271 328 404\| (117ce), and <117 185 272 329 405\| (117d). Using the patent val, it tempers out the [[syntonic comma]], 81/80 and \|69 -1 -29> in the 5-limit; 6144/6125, 31104/30625, and 403368/390625 in the 7-limit, providing the [[optimal patent val]] for 7-limit [[Meantone family\|mohajira temperament]]; 540/539, 1344/1331, 1617/1600, and 3168/3125 in the 11-limit, providing the optimal patent val for the [[Didymus rank three family\|terpsichore rank-3 temperament]]. Using the 117bd val, it tempers out the [[Kleismic family\|kleisma]], 15625/15552 and 17179869184/16142520375 in the 5-limit; 245/243, 3136/3125, and 51200/50421 in the 7-limit; 176/175, 1232/1215, 1375/1372, and 2560/2541 in the 11-limit. Using the 117ce val, it tempers out the [[Magic family\|small diesis]], 3125/3072 and 282429536481/268435456000 in the 5-limit; 2401/2400, 3645/3584, and 4375/4374 in the 7-limit; 243/242, 441/440, and 1815/1792 in the 11-limit. Using the 117d val, it tempers out 126/125, 225/224, and 14495514624/13841287201 in the 7-limit; 99/98, 176/175, 441/440, and 12582912/12400927 in the 11-limit, supporting the 11-limit [[Meantone family\|meantone temperament]].

			[[Category:Edo]]