1024/729

Interval information

Ratio	1024/729
Factorization	210 × 3-6
Monzo	[10 -6⟩
Size in cents	588.27¢
Names	Pythagorean narrow tritone, Pythagorean diminished fifth
Color name	sw5, sawa 5th
FJS name	[math]\displaystyle{ \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]\displaystyle{ \sqrt{nd} }[/math])	~4.14997 bits
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1024/729, the Pythagorean diminished fifth, is the octave complement of the Pythagorean augmented fourth (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

• 2187/2048 – its fifth complement
• Pythagorean tuning
• Gallery of just intervals