Sqrt(25/24)

The square root of 25/24 (sqrt(25/24)) is an interval measuring approximately 35.336 ¢ 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

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.

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