4/3: Difference between revisions

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'''4/3''' is the [[frequency ratio]] of the '''just perfect fourth''', which is easily one of the more heavily discussed intervals outside of xenharmony- in fact, some of these usages have gone on to inspire other music theories within xenharmonic contexts, such as certain ideas about [[tetrachord]]s. As its inversion is the perfect fifth, [[3/2]], 4/3 is the [[octave reduced]] form of the third [[subharmonic]]. 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. However, as of late, the perfect fourth is once again being reevaluated as a consonance.

Much like 3/2, 4/3 is valuable as a framework for constructing chords. However, while 3/2 provides the framework for [[5-limit]] triads involving intervals like 5/4 and [[6/5]], 4/3 provides a possible framework for [[7-limit]] triads involving intervals like [[7/6]] and [[8/7]], though such triads are ambisonances at best. Because up to two instances of 4/3 can fit within the span of an octave, it is very easy to create xenharmonic chords using 4/3 as a framework, though because [[16/9]] clashes with the [[octave]] through crowding, these types of chords are dissonances. Regardless, the usage of 4/3 as a framework for chords is intimately connected with the use of [[tritave]]s in the same capacity- at least in [[octave-equivalent]] systems.

Much like 3/2, 4/3 is valuable as a framework for constructing chords. However, while 3/2 provides the framework for [[5-limit]] triads involving intervals like 5/4 and [[6/5]], 4/3 provides a possible framework for [[7-limit]] triads involving intervals like [[7/6]] and [[8/7]], though such triads are ambisonances at best. Because up to two instances of 4/3 can fit within the span of an octave, it is very easy to create xenharmonic chords using 4/3 as a framework, though because [[16/9]] clashes with the [[octave]] through crowding, these types of chords are dissonances. Regardless, the usage of 4/3 as a framework for chords is intimately connected with the use of [[tritave]]s in the same capacity- at least in [[Octave #Octave equivalence|octave-equivalent]] systems.

== Approximations by EDOs ==

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 '''4/3''' is the [[frequency ratio]] of the '''just perfect fourth''', which is easily one of the more heavily discussed intervals outside of xenharmony- in fact, some of these usages have gone on to inspire other music theories within xenharmonic contexts, such as certain ideas about [[tetrachord]]s. As its inversion is the perfect fifth, [[3/2]], 4/3 is the [[octave reduced]] form of the third [[subharmonic]]. 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.  However, as of late, the perfect fourth is once again being reevaluated as a consonance.
-Much like 3/2, 4/3 is valuable as a framework for constructing chords.  However, while 3/2 provides the framework for [[5-limit]] triads involving intervals like 5/4 and [[6/5]], 4/3 provides a possible framework for [[7-limit]] triads involving intervals like [[7/6]] and [[8/7]], though such triads are ambisonances at best.  Because up to two instances of 4/3 can fit within the span of an octave, it is very easy to create xenharmonic chords using 4/3 as a framework, though because [[16/9]] clashes with the [[octave]] through crowding, these types of chords are dissonances.  Regardless, the usage of 4/3 as a framework for chords is intimately connected with the use of [[tritave]]s in the same capacity- at least in [[octave-equivalent]] systems.
+Much like 3/2, 4/3 is valuable as a framework for constructing chords.  However, while 3/2 provides the framework for [[5-limit]] triads involving intervals like 5/4 and [[6/5]], 4/3 provides a possible framework for [[7-limit]] triads involving intervals like [[7/6]] and [[8/7]], though such triads are ambisonances at best.  Because up to two instances of 4/3 can fit within the span of an octave, it is very easy to create xenharmonic chords using 4/3 as a framework, though because [[16/9]] clashes with the [[octave]] through crowding, these types of chords are dissonances.  Regardless, the usage of 4/3 as a framework for chords is intimately connected with the use of [[tritave]]s in the same capacity- at least in [[Octave #Octave equivalence|octave-equivalent]] systems.
 == Approximations by EDOs ==