108/77

From Xenharmonic Wiki
Jump to navigation Jump to search
Interval information
Ratio 108/77
Factorization 22 × 33 × 7-1 × 11-1
Monzo [2 3 0 -1 -1
Size in cents 585.72115¢
Name symbiotic diminished fifth
Color name 1ur4, luru 4th
FJS name [math]\text{A4}_{7,11}[/math]
Special properties reduced
Tenney height (log2 nd) 13.0217
Weil height (log2 max(n, d)) 13.5098
Wilson height (sopfr (nd)) 31
Harmonic entropy
(Shannon, [math]\sqrt{nd}[/math])
~4.13535 bits

[sound info]
open this interval in xen-calc

108/77 is the 11-limit interval between 11/9 and 12/7. It is 19712/19683 (symbiotic comma, 2.5 ¢) sharp of the Pythagorean diminished fifth 1024/729. Meanwhile, it is 540/539 (swetisma, 3.2 ¢) sharp of 7/5.

Terminology

This interval could also be called the swetismic augmented fourth if viewed as fudging from 7/5 instead.

See also