289edo

The 289 equal temperament divides the octave into 289 equal parts of 4.1522491349481 cents each. It is the high end of commatonal edos, because 289edo supports very accurate the 1253/1250 Ratio (or Comma), having a step size only 0.002265408054801 cents sharp of 1253/1250. It is the optimal patent val for 13-limit history temperament, which tempers out 364/363, 441/440 and 1001/1000, and provides a good tuning for the 11-limit version also, and is also the optimal patent val for sextilififths in both the 11- and 13-limit. It is uniquely consistent in the 9-limit, and tempers out the schisma, 32805/32768 in the 5-limit; 4375/4374 and 65625/65536 in the 7-limit; 441/440 and 4000/3993 in the 11-limit; and 364/363, 676/675, 1001/1000, 1575/1573 and 2080/2079 in the 13-limit.