59049/32768: Difference between revisions

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]\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

Revision as of 04:49, 14 January 2026

"Pentatone" redirects here. For systems with 5 note classes per octave, see Pentatonic.

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.^[1]

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 The '''Pythagorean augmented sixth''', otherwise known as the '''pentatone''', 59049/32768, is the interval found by stacking five [[9/8|(Pythagorean whole) tones (9/8)]]. It exceeds the [[9/5|classical minor seventh (9/5)]] by a [[schisma]]. The Medieval music theorist {{w|Jacobus of Liège}} described it along with the [[ditone]], [[tritone]], [[tetratone]], and [[hexatone]], and considered the pentatone to be highly discordant.<ref>''Pythagorean Tuning and Medieval Polyphony'', Margo Schulter, 10 June 1998</ref>