From Xenharmonic Wiki
Jump to navigation Jump to search
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,
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{n\cdot d}[/math])
~4.455 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. According to Aura, while 8192/6561 may take the place of the classic major third in chords, its status as a diminished fourth means that it has a different function in terms of voice-leading.

Due to 8192/6561's extreme proximity to 5/4, some may consider it a major third (see Extended-diatonic interval names).

See also