729/512
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Ratio | 729/512 |
Factorization | 2^{-9} × 3^{6} |
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, reduced harmonic |
Tenney height (log_{2} nd) | 18.5098 |
Weil height (log_{2} max(n, d)) | 19.0196 |
Wilson height (sopfr (nd)) | 36 |
Harmonic entropy (Shannon, [math]\sqrt{n\cdot d}[/math]) |
~4.56588 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}
.