729/512

Interval information

Ratio	729/512
Factorization	2-9 × 36
Monzo	[-9 6⟩
Size in cents	611.73¢
Names	Pythagorean tritone, Pythagorean augmented fourth, The Tyrant
Color name	Lw4, large wa 4th
FJS name	[math]\displaystyle{ \text{A4} }[/math]
Special properties	reduced, reduced harmonic
Tenney height (log2 nd)	18.5098
Weil height (log2 max(n, d))	19.0196
Wilson height (sopfr(nd))	36
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The Pythagorean augmented fourth, 729/512, may be reached by stacking six perfect fifths (3/2), and reducing by three octaves. It is separated from the 5-limit interval of 64/45 by the schisma (32805/32768), less than 2 cents.

In addition, it can be interpreted as a literal tritone, since it can be made by stacking three whole tones, 9/8.

See also

• 1024/729 – its octave complement
• 256/243 – its fifth complement
• Pythagorean tuning
• Gallery of just intervals