4/3: Difference between revisions

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Hopefully this is much better, I seriously wish I had had good ideas for explaining these usages earlier when I tried expanding this article.
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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.


The 4/3 interval is easily heavily discussed outside of xenharmony, as the [[Wikipedia: Perfect fourth|corresponding]] article makes abundantly clear.  In fact, some of the usages discussed there have gone on to inspire other music theories in xenharmonic contexts.
The 4/3 interval is easily heavily discussed outside of xenharmony, as the [[Wikipedia: Perfect fourth|corresponding Wikipedia article]] makes abundantly clear.  In fact, some of the usages discussed there have gone on to inspire other music theories in xenharmonic contexts.


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

Revision as of 20:48, 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.

The 4/3 interval is easily heavily discussed outside of xenharmony, as the corresponding Wikipedia article makes abundantly clear. In fact, some of the usages discussed there have gone on to inspire other music theories in xenharmonic contexts.

See also