729/512
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| 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, 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{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.