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The 771 equal division divides the octave into 771 equal parts of 1.556 cents each. It is uniquely consistent up to the 21-limit, with all of the primes to 19 having a flat tendency. In the 5-limit it tempers out the monzisma, |54 -37 2>, and |-44 -3 21>; in the 7-limit 65625/65536 and 250047/250000; in the 11-limit 3025/3024; in the 13-limit 4225/4224 and 10648/10647; in the 17-limit 833/832, 1225/1224, 2058/2057, 2431/2430 and 2601/2600; and in the 19-limit 1445/1444, 1540/1539, 1729/1728, 2926/2925, 3250/3249, 4200/4199 and 5985/5984. 771 provides the optimal patent val for the rank six temperament tempering out 833/832 and various other temperaments tempering it out.