All-trichord hexachord

All-trichord hexachord ( Play ).
All-trichord hexachord trichords.[1] ( Play )

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. 1 2 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

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