8192/6561: Difference between revisions

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Cleaned it up and updated link from "Extended-diatonic interval names" to more comprehensive "Interval region" page.
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The '''Pythagorean diminished fourth''', '''8192/6561''', may be reached by subtracting two [[81/64]] intervals from the [[Octave|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 [[User:Aura|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. 
The '''Pythagorean diminished fourth''', '''8192/6561''', may be reached by subtracting two [[81/64]] intervals from the [[Octave|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]]).
 
Due to 8192/6561's extreme proximity to 5/4, some may consider it a major third (see [[Extended-diatonic interval names]]).  


== See also ==
== See also ==

Revision as of 09:46, 13 July 2024

Interval information
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]\displaystyle{ \text{d4} }[/math]
Special properties reduced,
reduced subharmonic
Tenney norm (log2 nd) 25.6797
Weil norm (log2 max(n, d)) 26
Wilson norm (sopfr(nd)) 50
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