729/512

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Interval information
Ratio 729/512
Factorization 2-9 × 36
Monzo [-9 6
Size in cents 611.73001¢
Names Pythagorean tritone,
Pythagorean augmented fourth,
The Tyrant
Color name Lw4, lawa 4th
FJS name [math]\text{A4}[/math]
Special properties reduced
Tenney height (log2 nd) 18.5098
Weil height (log2 max(n, d)) 19.0196
Wilson height (sopfr (nd)) 36
Harmonic entropy
(Shannon, [math]\sqrt{nd}[/math])
~4.22099 bits

[sound info]
open this interval in xen-calc

729/512, the Pythagorean augmented fourth, 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 ¢.

From a literal point of view, this interval is the only one that rightly bears the name tritone, because it is created by combining three tones: (9/8)3.

See also