729/512
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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, lawa 4th
FJS name
[math]\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
Harmonic entropy
(Shannon, [math]\sqrt{nd}[/math])
~4.22099 bits
[sound info]
open this interval in xen-calc
| Interval information |
Pythagorean augmented fourth,
The Tyrant
reduced harmonic
(Shannon, [math]\sqrt{nd}[/math])
[sound info]
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 ¢.