6561/4096
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Ratio | 6561/4096 |
Factorization | 2^{-12} × 3^{8} |
Monzo | [-12 8⟩ |
Size in cents | 815.64001¢ |
Names | Pythagorean augmented fifth, tetratone |
Color name | Lw5, lawa 5th |
FJS name | [math]\text{A5}[/math] |
Special properties | reduced, reduced harmonic |
Tenney height (log_{2} nd) | 24.6797 |
Weil height (log_{2} max(n, d)) | 25.3594 |
Wilson height (sopfr (nd)) | 48 |
Harmonic entropy (Shannon, [math]\sqrt{nd}[/math]) |
~4.1577 bits |
open this interval in xen-calc |
The Pythagorean augmented fifth, 6561/4096, may be reached by stacking two 81/64 major thirds. The Medieval music theorist Jacques de Liège referred to it as the tetratone (akin to the ditone and tritone), as it may be reached by stacking four (Pythagorean whole) tones (9/8), and he considered it highly discordant.^{[1]} It differs from 8/5 by the schisma, and from 3/2 by the apotome.
See also
Notes
- ↑ Pythagorean Tuning and Medieval Polyphony, Margo Schulter, 10 June 1998