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

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

^Whittall, Arnold. 2008. The Cambridge Introduction to Serialism, p.271. Cambridge Introductions to Music. New York: Cambridge University Press. ISBN978-0-521-86341-4 (hardback) ISBN978-0-521-68200-8 (pbk).

^Schuijer, Michiel (2008). Analyzing Atonal Music: Pitch-Class Set Theory and Its Contexts, p.109. ISBN978-1-58046-270-9.

^Forte, Allen (1998), The Atonal Music of Anton Webern, p.17. ISBN0-300-07352-6.