20/17

From Xenharmonic Wiki
Jump to navigation Jump to search
Interval information
Ratio 20/17
Factorization 22 × 5 × 17-1
Monzo [2 0 1 0 0 0 -1
Size in cents 281.3583¢
Name diatismic minor third
Color name 17uy2, suyo 2nd
FJS name [math]\text{A2}^{5}_{17}[/math]
Special properties reduced
Tenney height (log2 nd) 8.40939
Weil height (log2 max(n, d)) 8.64386
Wilson height (sopfr (nd)) 26
Harmonic entropy
(Shannon, [math]\sqrt{nd}[/math])
~4.20109 bits

[sound info]
open this interval in xen-calc

In 17-limit just intonation, 20/17 is the diatismic minor third, measuring about 281.4 ¢. It falls short of the Pythagorean minor third (32/27) by a diatisma (136/135), hence the name. It is the mediant of 7/6 and 13/11, as it is (7 + 13)/(6 + 11). It is found in the harmonic series between the 17th and 20th harmonics.

See also