8192/6561
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Ratio | 8192/6561 |
Factorization | 2^{13} × 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 (log_{2} nd) | 25.6797 |
Weil height (log_{2} 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).