All-trichord hexachord
All-trichord hexachord trichords.[1]

In music, the all-trichord hexachord is a unique hexachord that contains all twelve trichords, or from which all twelve possible trichords may be derived.[2] The prime form of this set class is {012478}[1] and its Forte number is 6-Z17. Its complement is 6-Z43 and they share the interval vector of <3,2,2,3,3,2>.

It appears in pieces by Robert Morris and Elliott Carter.[3] Carter uses all-interval twelve-tone sets consisting of all-trichord hexachords in his Symphonia: sum fluxae pretium spei.[4]

See also


  1. ^ a b Schiff, David (1998). The Music of Elliott Carter, p. 34. ISBN 0-8014-3612-5.
  2. ^ Whittall, Arnold (2008). The Cambridge Introduction to Serialism, p. 271. ISBN 978-0-521-68200-8.
  3. ^ Alegant, Brian (2010). The Twelve-Tone Music of Luigi Dallapiccola, p. 307n4. ISBN 1-58046-325-8.
  4. ^ Schiff (1998), p. 41.

Further reading