117edo: Difference between revisions
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m Added subheadings; added table of harmonics |
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It is inconsistent to the 5-limit and higher limit, with four mappings possible for the 11-limit: <117 185 272 328 405| (patent val), <117 186 272 329 405| (117bd), <117 185 271 328 404| (117ce), and <117 185 272 329 405| (117d). | It is inconsistent to the 5-limit and higher limit, with four mappings possible for the 11-limit: <117 185 272 328 405| (patent val), <117 186 272 329 405| (117bd), <117 185 271 328 404| (117ce), and <117 185 272 329 405| (117d). | ||
== Theory == | |||
=== Commas === | |||
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, supporting the 7-limit [[Mohajira]] temperament; 540/539, 1344/1331, 1617/1600, and 3168/3125 in the 11-limit, supporting the [[Didymus rank three family|terpsichore rank-3 temperament]]; 144/143, 196/195, 364/363, 729/715, and 3146/3125 in the 13-limit. | 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, supporting the 7-limit [[Mohajira]] temperament; 540/539, 1344/1331, 1617/1600, and 3168/3125 in the 11-limit, supporting the [[Didymus rank three family|terpsichore rank-3 temperament]]; 144/143, 196/195, 364/363, 729/715, and 3146/3125 in the 13-limit. | ||
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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; 144/143, 640/637, 648/637, 1001/1000, and 43940/43923 in the 13-limit, supporting the 13-limit [[Grosstone]] temperament. | 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; 144/143, 640/637, 648/637, 1001/1000, and 43940/43923 in the 13-limit, supporting the 13-limit [[Grosstone]] temperament. | ||
=== Harmonics === | |||
{{Harmonics in equal|117}} | |||
[[Category:Equal divisions of the octave|###]] <!-- 3-digit number --> | [[Category:Equal divisions of the octave|###]] <!-- 3-digit number --> | ||