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Encyclopedia of Microtonal Music Theory

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[John Chalmers, Divisions of the Tetrachord]

Pertaining to the Perfect Fourth, 4/3.

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[Joe Monzo]

The term "quartal" is commonly used to designate chords which are built by stacking "4ths" (which may be augmented or perhaps even diminished, as well as perfect), following Schoenberg 1911, rather than the traditional method of stacking 3rds ("tertian").

As pointed out by Schoenberg, the entire 12-edo scale may be used to form a 12-note quartal chord, as in the following example:

C : F : Bb/A# : Eb/D# : Ab/G# : Db/C# : Gb/F# : B : E : A : D : G (: C)

It has been noted that the correct etymology, on analogy with "tertian", should be "quartian", but "quartal" has become established thru usage.

Schönberg, Arnold. 1911.
Vienna: Universal Edition.

English translation by Roy E. Carter, 1978. (based on 3rd edition of 1922)
Berkeley & Los Angeles: University of California Press.
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