Sqrt(25/24)

Sqrt(25/24) is an interval that allows to pass from a just major third (5/4) to a just minor third (6/5) by equal contrary motion, 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.

xen-calc

Listen

Just major third and just minor third alternating by equal contrary motion

Just major seventh chord and just minor seventh chord alternating by equal contrary motion

Approximations

34-edo has such an excellent sqrt(25/24) that the next EDO to have a better one is 441.

EDOs that have both a good 5-odd-limit and a sqrt(25/24) distinct from 25/24 include (among others) 24, 27, 31 and 34.