531441/262144
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| Ratio | 531441/262144 |
| Factorization | 2-18 × 312 |
| Monzo | [-18 12⟩ |
| Size in cents | 1223.46¢ |
| Names | Pythagorean augmented seventh, hexatone |
| Color name | LLw7, lalawa 7th |
| FJS name | [math]\text{A7}[/math] |
| Tenney height (log2 nd) | 37.0196 |
| Weil height (log2 max(n, d)) | 38.0391 |
| Wilson height (sopfr (nd)) | 72 |
| Harmonic entropy (Shannon, [math]\sqrt{nd}[/math]) |
~4.21909 bits |
| open this interval in xen-calc | |
The Pythagorean augmented seventh, otherwise known as the hexatone, 531441/262144, is the interval found by stacking six (Pythagorean whole) tones (9/8). The Medieval music theorist Jacobus of Liège described it along with the ditone, tritone, tetratone, and pentatone, and noted that the hexatone was a rough discord, not equivalent to a pure octave;[1] it is wider than the octave by one Pythagorean comma.