1024/729

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Interval information

Ratio

1024/729

Factorization

2¹⁰ × 3^-6

[10 -6⟩

Size in cents

588.27¢

Names

Pythagorean narrow tritone,
Pythagorean diminished fifth

sw5, sawa 5th

[math]\text{d5}[/math]

Special properties

reduced,
reduced subharmonic

Tenney height (log₂ nd)

19.5098

Weil height (log₂ max(n, d))

20

Wilson height (sopfr(nd))

38

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

~4.14997 bits

Open this interval in xen-calc

1024/729, the Pythagorean diminished fifth, is the octave complement of the Pythagorean tritone (729/512). It may be reached by stacking six perfect fourths (4/3), and reducing by two octaves, it is separated from the 5-limit interval of 45/32 by the schisma (less than 2 cents).

See also

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