323edo

The 323 equal divisions of the octave (323edo) is the equal division of the octave into 323 parts of 3.7152 cents each.

Theory

323et tempers out the vulture comma, [24 -21 4⟩ and the luna comma, [38 -2 -15⟩, in the 5-limit; 4375/4374, 589824/588245 and 703125/702464 in the 7-limit, supporting 7-limit vulture, lunatic, enneadecal, and gamera. In the 11-limit, the 323e val and the patent val are comparable in errors. 1375/1372, 5632/5625, 14641/14580, and 19712/19683 are tempered out in the patent val; 540/539, 6250/6237, 12005/11979, and 16384/16335 are tempered out in the 323e val. It provides the optimal patent val for the rank-5 temperament tempering out 1573/1568, the lambeth comma, as well as the 2.3.5.11 subgroup temperament tempering out 14641/14580, the semicanousma.

323 = 17 × 19, and shares the excellent approximations of 25/24 in 17edo and of the 28/27 and the 6/5 in 19edo.