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Schoenberg hexachord
6-Z44 (012569), known as the Schoenberg hexachord, is Arnold Schoenberg's signature hexachord, as one transposition contains the pitches (), Es, C, H, B, E, G (A. Schoenberg), E, B, and B being Es, H, and B in German.〔Friedmann, Michael L. (1990). ''Ear Training for Twentieth-Century Music'', p.109. ISBN 0-300-04537-9.〕
Its Z-related hexachord and complement is 6-Z19〔 (3478te or, in prime form, 013478). They have the interval vector of <3,1,3,4,3,1> in common.〔 6-Z44 lacks prime and inversional combinatoriality. 6-Z44 contains set 3-3 twice and set 3-4 twice.〔Williamson, John (2005). "Pyramids, Symbols, and Butterflies: 'Nacht' from ''Pierrot Lunaire''", ''Words and Music'', p.132-3. John Williamson, ed. Liverpool University. ISBN 9780853236191.〕 Set 7-22 contains 6-Z44 twice and 6-Z19 twice.〔January, 1978. ''The Musical quarterly'', Volume 64, p.145.〕
Schoenberg used the hexachord in the song "Seraphita" (op. 22 no. 1) and the monodrama ''Die glückliche Hand''.〔Simms, Bryan R. (2000). ''The Atonal Music of Arnold Schoenberg, 1908-1923'', p.145. ISBN 0-19-512826-5.〕 6-Z44 is associated with the character Hauptmann in Alban Berg's ''Wozzeck''.〔Forte, Allen (1973). ''The Structure of Atonal Music'', p.119. Yale University. ISBN 9780300021202.〕 Each movement of Berg's 1913 Four Pieces for Clarinet and Piano (op. 5) begins with a statement of 6-Z44 or 6-Z19.〔 (1978). ''The Musical quarterly'', Volume 64, p.135.〕 John Weinzweig uses two minor triads a semitone apart, 6-Z19, and their complement, 6-Z44, in an aggregate chord at the end of "City of Brass" from ''Wine of Peace'' as well as in the tone row for his Piano Concerto.〔Cherney, Brian (2011). ''Weinzweig: Essays on His Life and Music'', p.144-5. Wilfrid Laurier University. ISBN 9781554582563.〕 6-Z44 is one of the "fundamental harmonies in the last movement," of Igor Stravinsky's ''The Rite of Spring'', "Sacrificial Dance".〔Forte, Allen (2005). ''The Harmonic Organization of the Rite of Spring'', p.37. Yale. ISBN 9780300105377.〕
==Sources==
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