31/24

Interval information

Ratio	31/24
Subgroup monzo	2.3.31 [-3 -1 1⟩
Size in cents	443.0806¢
Names	tricesimoprimal ultramajor third, tricesimoprimal semidiminished fourth
Color name	31o3, thiwo 3rd
FJS name	[math]\text{M3}^{31}[/math]
Special properties	reduced
Tenney height (log2 nd)	9.53916
Weil height (log2 max(n, d))	9.90839
Wilson height (sopfr(nd))	40
Harmonic entropy (Shannon, [math]\sqrt{nd}[/math])	~4.21062 bits
[sound info]
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In 31-limit just intonation, 31/24 is either the tricesimoprimal ultramajor third or tricesimoprimal semidiminished fourth. It is sharp of the Pythagorean major third (81/64) by 248/243, and flat of the perfect fourth (4/3) by 32/31. It can be used as a generator tuning for the sensi temperament, especially for the 5-limit sensipent temperament, where it is equated to its complement relative to 5/3, that is, 40/31.

Approximation

31/24 is very closely approximated by 24\65 and 7\19.

See also

• 48/31 – its octave complement
• 36/31 – its fifth complement