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].

  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.