88/63

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Interval information
Ratio 88/63
Factorization 23 × 3-2 × 7-1 × 11
Monzo [3 -2 0 -1 1
Size in cents 578.58203¢
Name pentacircle diminished fifth
Color name 1or4, loru 4th
FJS name [math]\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]\sqrt{n\cdot d}[/math])
~4.53153 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