31/16

Interval information
Ratio	31/16
Subgroup monzo	2.31 [-4 1⟩
Size in cents	1145.0356¢
Names	tricesimoprimal ultramajor seventh, tricesimoprimal semidiminished octave, octave-reduced 31st harmonic
Color name	31o7, thiwo 7th
FJS name	[math]\text{M7}^{31}[/math]
Special properties	reduced, reduced harmonic
Tenney height (log₂ nd)	8.9542
Weil height (log₂ max(n, d))	9.90839
Wilson height (sopfr (nd))	39
Harmonic entropy (Shannon, [math]\sqrt{nd}[/math])	~4.33259 bits
[sound info]
open this interval in xen-calc

In 31-limit just intonation, 31/16 is either the tricesimoprimal ultramajor seventh or tricesimoprimal semidiminished octave, which is also the octave-reduced 31st harmonic. It is sharp of the Pythagorean major seventh (243/128) by 248/243, and flat of the octave by 32/31.

Approximation

31/16 is very well approximated by 22edo, with 21\22 being 0.4 ¢ sharp of 31/16.