81/64

Interval information

Ratio	81/64
Factorization	2-6 × 34
Monzo	[-6 4⟩
Size in cents	407.82¢
Names	Pythagorean major third, ditone
Color name	Lw3, lawa 3rd
FJS name	[math]\text{M3}[/math]
Special properties	reduced, reduced harmonic
Tenney height (log2 nd)	12.3399
Weil height (log2 max(n, d))	12.6797
Wilson height (sopfr(nd))	24
Harmonic entropy (Shannon, [math]\sqrt{nd}[/math])	~4.24385 bits
[sound info]
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English Wikipedia has an article on:

Ditone

The Pythagorean major third, 81/64 may be reached by stacking four perfect fifths (3/2), and reducing by two octaves. It is also known as the ditone, as it may be reached by stacking two (Pythagorean whole) tones (9/8). 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
• 64:81:96:108 – A chord where it is the first step
• Gallery of just intervals
• Pythagorean tuning