51/40

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Interval information

Ratio

51/40

Factorization

2^-3 × 3 × 5^-1 × 17

[-3 1 -1 0 0 0 1⟩

Size in cents

420.5967¢

Name

diatismic major third

17og4, sogu 4th

[math]\displaystyle{ \text{d4}^{17}_{5} }[/math]

Special properties

Tenney height (log₂ nd)

10.9944

Weil height (log₂ max(n, d))

11.3449

Wilson height (sopfr(nd))

31

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

~4.24178 bits

Open this interval in xen-calc

In 17-limit just intonation, 51/40 is the diatismic major third. It exceeds the Pythagorean major third (81/64) by a diatisma (136/135), hence the name.

It is approximated by:

7\20 (420 cents)
1\3 (4\12) (400 cents)
6\17 (12\34) (423.529 cents)
13\37 (421.622 cents)

See also

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