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 (log_{2} nd) | 8.9542 |
Weil height (log_{2} 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.
See also
- 32/31 – its octave complement
- 48/31 – its twelfth complement