768/625

Interval information
Ratio	768/625
Factorization	2⁸ × 3 × 5^-4
Monzo	[8 1 -4⟩
Size in cents	356.70015¢
Names	(greater) pental neutral third, tetraptolemaic double-diminished fourth
Color name	quadgu 4th, g^44
FJS name	[math]\text{dd4}_{5,5,5,5}[/math]
Special properties	reduced
Tenney height (log₂ nd)	18.8727
Weil height (log₂ max(n, d))	19.1699
Wilson height (sopfr(nd))	39
Harmonic entropy (Shannon, [math]\sqrt{nd}[/math])	~4.26055 bits
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768/625, the (greater) pental neutral third or tetraptolemaic double-diminished fourth is a 5-limit interval of about 356.7 cents. It is sharp of the Pythagorean double-diminished fourth by four syntonic commas. Equivalently, it is equal to a fifth minus an octave-reduced stack of four classical major thirds, or equal to a classical minor third plus a diesis. In the 11-limit it is 6912/6875 sharp of 11/9, and 5632/5625 sharp of 27/22. In the 13-limit it is 625/624 flat of 16/13.

See also