40/31

Interval information

Ratio

40/31

2.5.31 [3 1 -1⟩

Size in cents

441.2781¢

Names

tricesimoprimal semidiminished fourth,
tricesimoprimal supermajor third

31uy4, thiwuyo 4th

[math]\displaystyle{ \text{P4}^{5}_{31} }[/math]

Special properties

10.2761

Weil height (log₂ max(n, d))

10.6439

42

Harmonic entropy
(Shannon, [math]\displaystyle{ \sqrt{nd} }[/math])

~4.20582 bits

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, sharp of the septimal major third (9/7) by 280/279, and flat of the perfect fourth (4/3) by 31/30.

Approximation

40/31 is approximated by 7\19 or 11\30, and is extremely close to 57\155 (being just 0.012 ¢ sharp of it).