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Interval information
Ratio 8192/6561
Factorization 213 × 3-8
Monzo [13 -8
Size in cents 384.35999¢
Name Pythagorean diminished fourth
Color name sw4, sawa 4th
FJS name [math]\text{d4}[/math]
Special properties reduced
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

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).

See also