2ed25/24

← 1ed25/24

2ed25/24

3ed25/24 →

Prime factorization	2 (prime)
Step size	35.3362¢
Octave	34\2ed25/24 (1201.43¢) (→17\1ed25/24)
Twelfth	54\2ed25/24 (1908.16¢) (→27\1ed25/24)
Consistency limit	6
Distinct consistency limit	1
Special properties	highly composite

2ed25/24 is a tuning system created by dividing the interval of 25/24 logarithmically into steps of about 35.336 cents each. Each step represents a frequency ratio of the square root of 25/24.

It is almost equal to 34edo.

Theory

One step of this tuning 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.

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.