31/16

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Interval information

Ratio

31/16

2.31 [-4 1⟩

Size in cents

1145.036¢

Names

tricesimoprimal ultramajor seventh,
tricesimoprimal semidiminished octave,
octave-reduced 31st harmonic

31o7, thiwo 7th

[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

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

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