531441/262144

Interval information

Ratio	531441/262144
Factorization	2-18 × 312
Monzo	[-18 12⟩
Size in cents	1223.46¢
Names	Pythagorean augmented seventh, hexatone
Color name	LLw7, lalawa 7th
FJS name	[math]\displaystyle{ \text{A7} }[/math]
Tenney height (log2 nd)	37.0196
Weil height (log2 max(n, d))	38.0391
Wilson height (sopfr(nd))	72
Harmonic entropy (Shannon, [math]\displaystyle{ \sqrt{nd} }[/math])	~4.21909 bits
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The Pythagorean augmented seventh, otherwise known as the hexatone, 531441/262144, is the interval found by stacking six (Pythagorean whole) tones (9/8). The Medieval music theorist Jacobus of Liège described it along with the ditone, tritone, tetratone, and pentatone, and noted that the hexatone was a rough discord, not equivalent to a pure octave; it is wider than the octave by one Pythagorean comma.