8192/6561
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Ratio
8192/6561
Factorization
213 × 3-8
Monzo
[13 -8⟩
Size in cents
384.36¢
Name
Pythagorean diminished fourth
Color name
sw4, sawa 4th
FJS name
[math]\text{d4}[/math]
Special properties
reduced,
reduced subharmonic
Tenney height (log2 nd)
25.6797
Weil height (log2 max(n, d))
26
Wilson height (sopfr(nd))
50
Harmonic entropy
(Shannon, [math]\sqrt{nd}[/math])
~4.01073 bits
open this interval in xen-calc
| Interval information |
reduced subharmonic
(Shannon, [math]\sqrt{nd}[/math])
The Pythagorean diminished fourth, 8192/6561, may be reached by subtracting two 81/64 intervals from the perfect octave. It differs from the classic major third, 5/4, by the schisma (around 2 cents), and, as a result, the Pythagorean diminished fourth is in fact rather consonant and some may consider it a major third (see Interval region).