View source for All-trichord hexachord

[[File:All-trichord hexachord.png|thumb|upright=1.2|All-trichord hexachord[[File:All-trichord hexachord.mid]]]]
[[File:All-interval hexachord triads.png|thumb|upright=1.4|All-trichord hexachord trichords.<ref name=schiff>[[David Schiff|Schiff, David]] (1998). ''The Music of Elliott Carter'', p. 34. {{ISBN|0-8014-3612-5}}.</ref>[[File:All-interval hexachord triads.mid]]]]

In [[music]], the '''all-trichord hexachord''' is a unique [[hexachord]] that contains all twelve [[trichord]]s, or from which all twelve possible trichords may be derived.<ref>[[Arnold Whittall|Whittall, Arnold]] (2008). ''The Cambridge Introduction to Serialism'', p. 271. {{ISBN|978-0-521-68200-8}}.</ref> The [[prime form (music)|prime form]] of this set class is {012478}<ref name=schiff /> and its [[Forte number]] is '''6-Z17'''. Its [[Complement (music)#Aggregate complementation|complement]] is '''6-Z43''' and they share the [[interval vector]] of <3,2,2,3,3,2>.

It appears in pieces by [[Robert Morris (composer)|Robert Morris]] and [[Elliott Carter]].<ref>Alegant, Brian (2010). ''The Twelve-Tone Music of [[Luigi Dallapiccola]]'', p. 307n4. {{ISBN|1-58046-325-8}}.</ref> Carter uses [[all-interval twelve-tone set]]s consisting of all-trichord hexachords in his ''[[Symphonia: sum fluxae pretium spei]]''.<ref>Schiff (1998), p. 41.</ref>

==See also==
*[[All-combinatorial hexachord]]
*[[All-interval tetrachord]]
*[[All-interval twelve-tone row]]

==References==
<references />

==Further reading==
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*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 (journal)|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: The Journal of Applied Musical Thought|Intégral]]'' 21:79–108. {{JSTOR|40214036}}.
*[[Robert Morris (composer)|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):328–358. {{JSTOR|833710}}.
*Ravenscroft, Brenda (2003). "Setting the Pace: The Role of Speeds in Elliott Carter's ''A Mirror on Which to Dwell''". ''[[Music Analysis (journal)|Music Analysis]]'' 22, no. 3 (October): 253–282. {{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. 303–310. {{ISBN|978-3-642-04579-0|978-3-642-04578-3}}.{{doi|10.1007/978-3-642-04579-0_29}}.
*Sallmen, Mark (2007). "[http://www.mtosmt.org/issues/mto.07.13.3/mto.07.13.3.sallmen.html 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)
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{{Pitch segments}}
{{Set theory (music)}}
{{Twelve-tone technique}}

[[Category:Chords]]
[[Category:Hexachords]]
[[Category:Twelve-tone technique]]
[[Category:Hemitonic scales]]
[[Category:Musical set theory]]

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