88/63

Interval information

Ratio	88/63
Factorization	23 × 3-2 × 7-1 × 11
Monzo	[3 -2 0 -1 1⟩
Size in cents	578.582¢
Name	pentacircle diminished fifth
Color name	1or4, loru 4th
FJS name	[math]\displaystyle{ \text{P4}^{11}_{7} }[/math]
Special properties	reduced
Tenney height (log2 nd)	12.4367
Weil height (log2 max(n, d))	12.9189
Wilson height (sopfr(nd))	30
Harmonic entropy (Shannon, [math]\displaystyle{ \sqrt{nd} }[/math])	~4.14034 bits
Open this interval in xen-calc

88/63, the pentacircle diminished fifth, is 896/891 below 1024/729, the Pythagorean diminished fifth. It is also 441/440 (3.9 cents) below 7/5. It is 0.01 cent sharp of the 56edo augmented fourth of 27\56. It arises in 11-limit scales as the interval from 9/8 to 11/7, or 14/11 to 16/9.

Terminology

It could also be called werckismic augmented fourth if viewed as fudging from 7/5 instead.

See also

• Gallery of just intervals