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190edo divides the octave into 190 equal parts of size 6.316 cents each. It is interesting because of the utility of its approximations; it tempers out 1029/1024, 4375/4374, 385/384, 441/440, 3025/3024 and 9801/9800. It provides the optimal patent val for both the 7 and 11 limit versions of unidec, the 118&190 temperament, which tempers out 1029/1024, 4375/4374, and in the 11-limit, 385/384 and 441/440. It also provides the optimal patent val for the rank three 11-limit temperament portent, which tempers out 385/384 and 441/440, and gamelan, the rank three 7-limit temperament which tempers out 1029/1024, as well as slendric, the 2.3.7 subgroup temperament featured below. In the 13-limit, 190et tempers out 847/845, 625/624, 729/728, 1575/1573 and 1001/1000, and provides the optimal patent val for ekadash temperament and the rank three portentous temperament.


The 11th Slendric Fanfare
16 Slendric Virgins
by Chris Vaisvil