All-interval tetrachord

All-interval tetrachord

An all-interval tetrachord is a tetrachord from which any interval class can be extracted by means of various inversions. There are only two possible all-interval tetrachords. In set theory notation, these are [0,1,4,6] and [0,1,3,7] . The interval vector for both all-interval tetrachords is [1,1,1,1,1,1] .

Table of interval classes as relating to all-interval tetrachords

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

Use in modern music

The unique qualities of the all-interval tetrachord have made it very popular in 20th-century music. Composers such as Elliot Carter and George Perle used it extensively, as did Webern and Schoenberg. (Although the term all-interval tetrachord and indeed set theory itself was not in use during most of their life times.)

ee also

*Monad
*Dyad
*Trichord
*Tetrachord
*Hexachord
*musical set theory
*Interval class
*Serialism

External links

* [http://209.85.173.104/search?q=cache:Lg5b5ssRNO0J:uwacadweb.uwyo.edu/smaw/AIT.ppt+All-interval+tetrachord&hl=en&ct=clnk&cd=7&gl=us&client=opera The All-Interval Tetrachord, A Musical Application of Almost Difference Sets] all-interval tetrachord tutorial
* [http://www.wpunj.edu/coac/music/link/sonus/sonuspaper.html The Composition of Elliott Carter's Night Fantasies] the use of all-interval tetrachords in Elliot Carter
* [http://solomonsmusic.net/intstring.htm Interval String Table]
* [http://www.jaytomlin.com/music/settheory/help.html Musical Set Theory]
* [http://mto.societymusictheory.org/issues/mto.06.12.4/mto.06.12.4.childs.html Structural and Transformational Properties of All-Interval Tetrachords] a comprehensive analysis of all-interval tetrachords


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