59049/32768
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| Ratio | 59049/32768 |
| Factorization | 2-15 × 310 |
| Monzo | [-15 10⟩ |
| Size in cents | 1019.55¢ |
| Names | Pythagorean augmented sixth, pentatone |
| Color name | Lw6, lawa 6th |
| FJS name | [math]\text{A6}[/math] |
| Special properties | reduced, reduced harmonic |
| Tenney height (log2 nd) | 30.8496 |
| Weil height (log2 max(n, d)) | 31.6993 |
| Wilson height (sopfr (nd)) | 60 |
| Harmonic entropy (Shannon, [math]\sqrt{nd}[/math]) |
~4.16742 bits |
| open this interval in xen-calc | |
The Pythagorean augmented sixth, otherwise known as the pentatone, 59049/32768, is the interval found by stacking five (Pythagorean whole) tones (9/8). It exceeds the classical minor seventh (9/5) by a schisma. The Medieval music theorist Jacobus of Liège described it along with the ditone, tritone, tetratone, and hexatone, and considered the pentatone to be highly discordant.[1]
See also
- 32768/19683 – its twelfth complement
Notes
- ↑ Pythagorean Tuning and Medieval Polyphony, Margo Schulter, 10 June 1998