Sqrt(25/24)

Interval information

Expression	[math]\displaystyle{ \sqrt{25/24} }[/math]
Size in cents	35.336¢
Names	classical semichroma, ptolemaic semichroma
Special properties	reduced
Harmonic entropy (Shannon, [math]\displaystyle{ \sqrt{nd} }[/math])	~4.51942 bits

Sqrt(25/24), the classical semichroma or ptolemaic semichroma, is a the difference between a 5-limit major or minor third and a pure neutral third Sqrt(3/2).

This 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.

The interval, when stacked, yields a tuning system close to 34edo, which consistently represents it as one step.

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.