59049/32768

Interval information

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
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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.

See also

• 32768/19683 – its twelfth complement