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

• All-combinatorial hexachord
• All-interval tetrachord
• All-interval twelve-tone row

Sources

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

• Boland, Marguerite (1999). "The All-trichord Hexachord: Compositional Strategies in Elliott Carter's Con leggerezza pensosa and Gra and a Folio of Original Compositions". MA Thesis, La Trobe University (Alegant 2010, p.307n4). OCLC 224102530.
• Boland, Marguerite (2006). "'Linking' and 'Morphing': Harmonic Flow in Elliott Carter's Con Leggerezza Pensosa". Tempo 60, no. 237 (July): 33–43. doi:10.1017/S0040298206000209.
• Boros, James (1990). "Some Properties of the All-Trichord Hexachord", In Theory Only 11/6: 19-41.
• Capuzzo, Guy (2004). "The Complement Union Property in the Music of Elliott Carter". Journal of Music Theory 48, no. 1 (Spring): 1–24. doi:10.1215/00222909-48-1-1.
• Capuzzo, Guy (2007). "Registral Constraints on All-Interval Rows in Elliott Carter's Changes". Intégral 21:79-108. JSTOR 40214036.
• Morris, Robert D. (1990). "Pitch-Class Complementation and Its Generalizations". Journal of Music Theory 34, no. 2 (Autumn): 175–245. JSTOR 843837.
• Morris, Robert (1995). "Compositional Spaces and Other Territories". Perspectives of New Music 33, nos. 1 & 2 (Winter–Summer):328–58. JSTOR 833710.
• Ravenscroft, Brenda (2003). "Setting the Pace: The Role of Speeds in Elliott Carter's A Mirror on Which to Dwell". Music Analysis 22, no. 3 (October): 253–82. doi:10.1111/j.0262-5245.2003.00186.x. JSTOR 3700435.
• Roeder, John (2009). "A Transformational Space for Elliott Carter's Recent Complement-union Music". In Mathematics and Computation in Music, edited by Timour Klouche and Thomas Noll, 303–310. Communications in Computer and Information Science 37. New York: Springer. pp 303–10. ISBN 978-3-642-04579-0; ISBN 978-3-642-04578-3. doi:10.1007/978-3-642-04579-0_29.
• Sallmen, Mark (2007). "Listening to the Music Itself: Breaking Through the Shell of Elliott Carter's 'In Genesis'", Music Theory Online 13/3 (Alegant 2010, p.307n4). (Accessed 31 March 2014)

Twelve-tone technique and Serialism
Fundamentals	Combinatoriality Complementation Derivation Hexachord Invariance Partition Cross partition Tone row Aggregate List
Permutations	Prime row Retrograde Inversion Retrograde inversion Multiplication
Notable composers	Milton Babbitt Pierre Boulez Josef Matthias Hauer Second Viennese School Alban Berg Arnold Schoenberg Anton Webern Charles Wuorinen ...more...
Related articles	All-interval twelve-tone row All-trichord hexachord Atonality Chromatic scale Duration series Equivalence Formula composition Modernism (music) Punctualism Semitone Set theory Time point Trope
List of dodecaphonic and serial compositions