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 subfourth
Color name	31o3, thiwo 3rd
FJS name	[math]\displaystyle{ \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]\displaystyle{ \sqrt{nd} }[/math])	~4.21062 bits
[sound info]
Open this interval in xen-calc

In 31-limit just intonation, 31/24 is either the tricesimoprimal ultramajor third or tricesimoprimal subfourth. 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, and more accurate interpretations of the extended harmony of the 5-limit sensipent temperament. In this context, it is equated to its complement relative to 5/3, that is, 40/31.

In general, it can serve as an alternative sharp supermajor third to 9/7, which is flat of it by 217/216, for greater flexibility in otonal chords containing intervals that do not have a 7 in their denominator.

Approximation

31/24 is approximated by 7\19, and is extremely close to 24\65 (being just 0.0036 ¢ sharp of it).

See also

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