All-interval tetrachord

All-interval tetrachords (Playⓘ).

An all-interval tetrachord is a tetrachord, a collection of four pitch classes, containing all six interval classes.[1] There are only two possible all-interval tetrachords (to within inversion), when expressed in prime form. In set theory notation, these are [0,1,4,6] (4-Z15)[2] and [0,1,3,7] (4-Z29).[3] Their inversions are [0,2,5,6] (4-Z15b) and [0,4,6,7] (4-Z29b).[4] The interval vector for all all-interval tetrachords is [1,1,1,1,1,1].

Table of interval classes as relating to all-interval tetrachords

All-interval tetrachord dyads[5] (Playⓘ).
4-Z15

In the examples below, the tetrachords [0,1,4,6] and [0,1,3,7] are built on E.

Interval class table for [0,1,4,6]
ic notes of [0,1,4,6] built on E diatonic counterparts
1 E to F minor 2nd and major 7th
2 A♭ to B♭ major 2nd and minor 7th
3 F to A♭ minor 3rd and major 6th
4 E to G♯ major 3rd and minor 6th
5 F to B♭ perfect 4th and perfect 5th
6 E to B♭ augmented 4th and diminished 5th
Interval class table for [0,1,3,7]
ic notes of [0,1,3,7] built on E diatonic counterparts
1 E to F minor 2nd and major 7th
2 F to G major 2nd and minor 7th
3 E to G minor 3rd and major 6th
4 G to B major 3rd and minor 6th
5 E to B perfect 4th and perfect 5th
6 F to B augmented 4th and diminished 5th

Use in modern music

The unique qualities of the all-interval tetrachord have made it very popular in 20th-century music. Composers including Frank Bridge, Elliott Carter (First String Quartet) and George Perle used it extensively.[citation needed]

See also

References

  1. ^ Whittall, Arnold. 2008. The Cambridge Introduction to Serialism, p.271. Cambridge Introductions to Music. New York: Cambridge University Press. ISBN 978-0-521-86341-4 (hardback) ISBN 978-0-521-68200-8 (pbk).
  2. ^ Schuijer, Michiel (2008). Analyzing Atonal Music: Pitch-Class Set Theory and Its Contexts, p.109. ISBN 978-1-58046-270-9.
  3. ^ Forte, Allen (1998), The Atonal Music of Anton Webern, p.17. ISBN 0-300-07352-6.
  4. ^ "Interval String Table". Archived from the original on 2006-02-04.
  5. ^ Schiff, David (1998). The Music of Elliott Carter, p.34. ISBN 0-8014-3612-5.


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