# 91edo

The *91 equal division* divides the octave into 91 parts of 13.187 cents each. The 3, 5 and 7 for 91 are on the flat side, making this a mostly flat system. It provides the optimal patent val for 7- and 11-limit septimin temperament, and the 13-limit rank three tripod temperament, as well as the 11-limit rank four temperament tempering out 245/242 and the 13-limit rank five temperament tempering out 105/104, or rank four tempering out 144/143, or else 196/195 and hence 225/224 also. It also gives the optimal patent val for the marvel extension tripod, which adds 105/104 to 225/224 and 385/384, and so also tempers out 144/143 and 196/195. It tempers out 15625/15552 in the 5-limit, 225/224 and 4375/4374 in the 7-limit, 245/242, 385/384 in the 11-limit, and 105/104, 144/143, 196/195 in the 13-limit.

91 is the smallest composite number whose composite character is not immediately evident; it is, in fact, the product of 7 and 13.