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Interval information
Ratio 6561/4096
Factorization 2-12 × 38
Monzo [-12 8
Size in cents 815.64001¢
Names Pythagorean augmented fifth,
Color name Lw5, lawa 5th
FJS name [math]\text{A5}[/math]
Special properties reduced
Tenney height (log2 nd) 24.6797
Weil height (log2 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


  1. Pythagorean Tuning and Medieval Polyphony, Margo Schulter, 10 June 1998