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 three possible all-interval tetrachords. In set theory notation, these are [0,1,4,6] (4-Z15),[2] [0,1,3,7] (4-Z29),[3] [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 Elliott Carter (First String Quartet) and George Perle used it extensively.

See also

Sources

  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. http://solomonsmusic.net/intstring.htm
  5. Schiff, David (1998). The Music of Elliott Carter, p.34. ISBN 0-8014-3612-5.

External links


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