Английская Википедия:All-interval tetrachord

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Файл:All-interval tetrachords.png
All-interval tetrachords (Шаблон:Audio).

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

Файл:All-interval tetrachord dyads.png
All-interval tetrachord dyads[5] (Шаблон:Audio).
Файл:All-interval tetrachord 4-Z15 diagram.svg
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 AШаблон:Music to BШаблон:Music major 2nd and minor 7th
3 F to AШаблон:Music minor 3rd and major 6th
4 E to GШаблон:Music major 3rd and minor 6th
5 F to BШаблон:Music perfect 4th and perfect 5th
6 E to BШаблон:Music 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.Шаблон:Citation needed

See also

References

Шаблон:Reflist

External links

Шаблон:Pitch segments Шаблон:Set theory (music)


Шаблон:Music-theory-stub

  1. Whittall, Arnold. 2008. The Cambridge Introduction to Serialism, p.271. Cambridge Introductions to Music. New York: Cambridge University Press. Шаблон:ISBN (hardback) Шаблон:ISBN (pbk).
  2. Schuijer, Michiel (2008). Analyzing Atonal Music: Pitch-Class Set Theory and Its Contexts, p.109. Шаблон:ISBN.
  3. Forte, Allen (1998), The Atonal Music of Anton Webern, p.17. Шаблон:ISBN.
  4. Шаблон:Cite web
  5. Schiff, David (1998). The Music of Elliott Carter, p.34. Шаблон:ISBN.