81/64

Interval information

Ratio	81/64
Factorization	2-6 × 34
Monzo	[-6 4⟩
Size in cents	407.82¢
Name	Pythagorean major third
Color name	Lw3, lawa 3rd
FJS name	[math]\displaystyle{ \text{M3} }[/math]
Special properties	reduced, reduced harmonic
Tenney norm (log2 nd)	12.3399
Weil norm (log2 max(n, d))	12.6797
Wilson norm (sopfr(nd))	24
[sound info]
Open this interval in xen-calc

The Pythagorean major third, 81/64, may be reached by stacking four perfect fifths (3/2), and reducing by two octaves. In contrast to the more typical 5/4- with which it is conflated in meantone- this interval is a bit more dissonant when not bridged by a stack of 3/2 intervals within in a chord, with a harmonic entropy level somewhere between that of 9/8 and that of 8/7. Thus, some would argue that it is functionally an imperfect dissonance.

See also

• 128/81 – its octave complement
• 32/27 – its fifth complement
• Gallery of just intervals
• Pythagorean tuning