Sqrt(25/24)
Sqrt(25/24) is an interval that allows to pass from a major third (5/4) to a minor third (6/5) by equal counterpoint, and vice versa.
Let be two voices forming a 5/4 interval. If the lower voice goes up by a sqrt(25/24) and the upper voice goes down by the same interval, the next interval formed by the two voices will be a 6/5 interval.
34-edo has such an excellent sqrt(25/24) that the next EDO to have a better one is 441.