# 213edo

213edo is the equal division of the octave into 213 parts of 5.6338 cents each. It is (uniquely) consistent through the 7-odd-limit and tempers out the following commas up to the 13-limit: |3 -10 11> in the 5-limit; |6 -5 -4 4>, |10 -11 2 1> and 6144 / 6125 in the 7-limit; 896/891 in the 11-limit; |12 -7 0 1 0 -1>, 325 / 324, 352 / 351 and 364 / 363 in the 13-limit. The patent val for 213-EDO is <213 338 495 598|. The general approximations to pure 3- and 5-limit intervals are quite bad, but 7-limit intervals are slightly better tuned. However, intervals involving a factor of 5/3 or 3/5 are quite well approximated. Thus it makes sense to view this as a 2.5/3.7 subgroup temperament.