59049/32768

Interval information
Ratio	59049/32768
Factorization	2-15 × 310
Monzo	[-15 10⟩
Size in cents	1019.55¢
Names	Pythagorean augmented sixth,; pentatone
FJS name	[math]\displaystyle{ \text{A6} }[/math]
Special properties	reduced,; reduced harmonic
Tenney norm (log2 nd)	30.8496
Weil norm (log2 max(n, d))	31.6993
Wilson norm (sopfr(nd))	60
	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). 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]

Notes

↑ Pythagorean Tuning and Medieval Polyphony, Margo Schulter, 10 June 1998

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

[1]