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
Color name	Lw4, lawa 4th
FJS name	[math]\displaystyle{ \text{A4} }[/math]
Special properties	reduced, reduced harmonic
Tenney norm (log2 nd)	18.5098
Weil norm (log2 max(n, d))	19.0196
Wilson norm (sopfr(nd))	36
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729/512, the Pythagorean augmented fourth, may be reached by stacking six perfect fifths (3/2), and reducing by three octaves. While nowadays "tritone" more commonly refers to a broader range of intervals, in Medieval music theory, "tritone" referred more specifically to 729/512, as this is the interval reached by stacking three (Pythagorean whole) tones (9/8). It is separated from the 5-limit interval of 64/45 by the schisma (32805/32768), less than 2 ¢.

See also

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