117edo: Difference between revisions

117edo is in[[consistent]] to the [[5-odd-limit]] and higher odd limits, with four mappings possible for the [[11-limit]]: {{val| 117 185 272 328 405 }} ([[patent val]]), {{val| 117 186 '''272''' 329 '''405''' }} (117bd), {{val| 117 185 '''271''' 328 '''404''' }} (117ce), and {{val| 117 185 272 '''329''' 405 }} (117d).  

Using the patent val, it [[tempering out|tempers out]] 81/80 ([[syntonic comma]]) and {{monzo| 69 -1 -29 }} in the 5-limit; [[6144/6125]], 31104/30625, and 403368/390625 in the 7-limit, [[support]]ing the 7-limit [[mohajira]] temperament; [[540/539]], 1344/1331, 1617/1600, and 3168/3125 in the 11-limit, supporting the rank-3 [[Didymus rank three family #Terpsichore|terpsichore]] temperament; [[144/143]], [[196/195]], [[364/363]], 729/715, and 3146/3125 in the 13-limit.  

Using the 117d val, it tempers out [[126/125]], [[225/224]], and {{monzo| 29 3 0 -12 }} 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 117ce val, it tempers out 3125/3072 ([[magic comma]]) and {{monzo| -31 24 -3 }} 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; [[105/104]], [[275/273]], [[1287/1280]], and 2025/2002 in the 13-limit.  

Using the 117bd val, it tempers out 15625/15552 ([[15625/15552|kleisma]]) and {{monzo| 34 -17 -3 }} 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; [[169/168]], [[364/363]], 640/637, 832/825, and 3200/3159 in the 13-limit.  

=== Odd harmonics ===