81/64
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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]
open this interval in xen-calc
| Interval information |
ditone
reduced harmonic
(Shannon, [math]\sqrt{nd}[/math])
[sound info]
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