6561/4096

Interval information

Ratio	6561/4096
Factorization	2-12 × 38
Monzo	[-12 8⟩
Size in cents	815.64¢
Names	Pythagorean augmented fifth, tetratone
Color name	Lw5, lawa 5th
FJS name	[math]\text{A5}[/math]
Special properties	reduced, reduced harmonic
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
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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. It differs from 8/5 by the schisma, and from 3/2 by the apotome.

See also

• 8192/6561 – its octave complement
• Gallery of just intervals
• Pythagorean tuning