31/16

Interval information

Ratio	31/16
Subgroup monzo	2.31 [-4 1⟩
Size in cents	1145.036¢
Names	tricesimoprimal ultramajor seventh, tricesimoprimal semidiminished octave, octave-reduced 31st harmonic
Color name	31o7, thiwo 7th
FJS name	[math]\displaystyle{ \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
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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