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 | |
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.