31/16
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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
| Interval information |
tricesimoprimal semidiminished octave,
octave-reduced 31st harmonic
reduced harmonic
(Shannon, [math]\sqrt{nd}[/math])
[sound info]
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.
See also
- 32/31 – its octave complement
- 48/31 – its twelfth complement