8192/6561: Difference between revisions

From Xenharmonic Wiki
Jump to navigation Jump to search
Nick Vuci (talk | contribs)
Cleaned it up and updated link from "Extended-diatonic interval names" to more comprehensive "Interval region" page.
Squib (talk | contribs)
specified that it is smaller than 5/4
Tags: Mobile edit Mobile web edit Advanced mobile edit
 
Line 4: Line 4:
}}
}}


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]]).
The '''Pythagorean diminished fourth''', '''8192/6561''', may be reached by subtracting two [[81/64]] intervals from the [[Octave|perfect octave]].  It is flat of 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 ==
== See also ==

Latest revision as of 16:05, 13 July 2025

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 height (log2 nd) 25.6797
Weil height (log2 max(n, d)) 26
Wilson height (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 is flat of 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