4/3: Difference between revisions

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'''4/3''' is the [[frequency ratio]] of the just perfect fourth. Its inversion is the perfect fifth, [[3/2]]. In the [[Wikipedia: Medieval music #Early polyphony: organum|florid organum]] of Medieval music, 4/3 was reliably considered a consonance, and indeed was frequently emphasized.  Once major thirds with a tuning approximating [[5/4]] began to be treated as consonances, however, the perception of 4/3 was altered to where it was at times considered a dissonance. 
'''4/3''' is the [[frequency ratio]] of the just perfect fourth. Its inversion is the perfect fifth, [[3/2]]. In the [[Wikipedia: Medieval music #Early polyphony: organum|florid organum]] of Medieval music, 4/3 was reliably considered a consonance, and indeed was frequently emphasized.  Once major thirds with a tuning approximating [[5/4]] began to be treated as consonances, however, the perception of 4/3 was altered to where it was at times considered a dissonance.
 
In [[User:Aura|Aura]]'s music theory, which is in some respects derived from both florid organum and the practices of later counterpoint, it should be noted that the traditional 1/1-4/3-3/2 suspension is considered a dissonance purely because of the presence of the [[9/8]] interval between the 4/3 and the 3/2, and likewise, a 1/1-4/3-16/9 quartal chord is also considered a dissonance because of the [[16/9]] interval between the notes on the outside of the chord.  Furthermore, Aura also considers 4/3 to be the ideal interval to form the outer frame of a [[tetrachord]] in [[just intonation]], and thus, good approximations of 4/3 found in [[EDO]]s serve the same function.


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

Revision as of 20:38, 16 November 2021

Interval information
Ratio 4/3
Factorization 22 × 3-1
Monzo [2 -1⟩
Size in cents 498.045¢
Name just perfect fourth
Color name w4, wa 4th
FJS name [math]\displaystyle{ \text{P4} }[/math]
Special properties square superparticular,
reduced,
reduced subharmonic
Tenney norm (log2 nd) 3.58496
Weil norm (log2 max(n, d)) 4
Wilson norm (sopfr(nd)) 7

[sound info]
Open this interval in xen-calc

4/3 is the frequency ratio of the just perfect fourth. Its inversion is the perfect fifth, 3/2. In the florid organum of Medieval music, 4/3 was reliably considered a consonance, and indeed was frequently emphasized. Once major thirds with a tuning approximating 5/4 began to be treated as consonances, however, the perception of 4/3 was altered to where it was at times considered a dissonance.

See also

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