4/3: Difference between revisions

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Much like 3/2, 4/3 is valuable as a framework for constructing [[chord]]s. 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 [[Condissonance|ambisonances]] (that is, they're both consonant and dissonant at the same time) 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{{citation needed}}, these types of chords are dissonances~~.

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. 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- due to the same pitch classes being involved in both 6:7:8 and 4:7:12 where 7 is kept as the same note, thus rendering the two chords as different voicings of the same underlying harmonic unit.

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.~~{{clarify|please explain why this is in a bit more detail}}~~

== Approximations by EDOs ==

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== Temperaments ==

4/3 can be used as an alternative generator for temperaments generated by an octave and a fifth of 3/2, such as [[meantone]], [[superpyth]], and [[schismic]]. See [[3/2 #In regular temperament theory]] for details.

== See also ==

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 Much like 3/2, 4/3 is valuable as a framework for constructing [[chord]]s. 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 [[Condissonance|ambisonances]] (that is, they're both consonant and dissonant at the same time) 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{{citation needed}}, these types of chords are dissonances.
+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. 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- due to the same pitch classes being involved in both 6:7:8 and 4:7:12 where 7 is kept as the same note, thus rendering the two chords as different voicings of the same underlying harmonic unit.
-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.{{clarify|please explain why this is in a bit more detail}}
 == Approximations by EDOs ==
@@ Line 80: / Line 78: @@
 |}
 <references/>
+== Temperaments ==
+/3 can be used as an alternative generator for temperaments generated by an octave and a fifth of 3/2, such as [[meantone]], [[superpyth]], and [[schismic]]. See [[3/2 #In regular temperament theory]] for details.
 == See also ==