40/31

Interval information

Ratio	40/31
Subgroup monzo	2.5.31 [3 1 -1⟩
Size in cents	441.2781¢
Names	tricesimoprimal semidiminished fourth, tricesimoprimal supermajor third
Color name	31o3, thiwo 3rd
FJS name	[math]\displaystyle{ \text{P4}^{5}_{31} }[/math]
Special properties	reduced
Tenney norm (log2 nd)	10.2761
Weil norm (log2 max(n, d))	10.6439
Wilson norm (sopfr(nd))	42
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In 31-limit just intonation, 40/31 is either the tricesimoprimal semidiminished fourth or tricesimoprimal supermajor third. It is sharp of the Pythagorean major third (81/64) by 2560/2511, and flat of the perfect fourth (4/3) by 31/30. 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, 31/24.

In general, it can serve as an alternative sharp supermajor third to 9/7, which is flat of it by 280/279, for greater flexibility in otonal chords containing intervals that do not have a 7 in their denominator.

Approximation

40/31 is approximated by 7\19, and is extremely close to 57\155 (being just 0.012 ¢ sharp of it).

See also

• 31/20 – its octave complement