648/625

Interval information

Ratio	648/625
Factorization	23 × 34 × 5-4
Monzo	[3 4 -4⟩
Size in cents	62.56515¢
Names	diminished comma, major diesis
Color name	g42, quadgu 2nd, Quadgu comma
FJS name	[math]\text{d2}_{5,5,5,5}[/math]
Special properties	reduced
Tenney height (log2 nd)	18.6276
Weil height (log2 max(n, d))	18.6797
Wilson height (sopfr(nd))	38
Harmonic entropy (Shannon, [math]\sqrt{nd}[/math])	~4.38126 bits
Comma size	medium
[sound info]
open this interval in xen-calc

The interval 648/625 is known as the diminished comma or major diesis. It is the amount by which four 6/5 minor thirds exceed an octave, in other words (6/5)⁴ / 2.

Approximations

This interval is approximately one step of 19edo, which is the amount by which four 19edo minor thirds exceed an octave.

Temperaments

Tempering out this comma leads to the 5-limit diminished temperament.