Schoenberg hexachord

6-Z44 (012569), known as the Schoenberg hexachord, is Arnold Schoenberg's signature hexachord, as one transposition contains the pitches [A], Es, C, H, B, E, G (A. Schoenberg), E, B, and B being Es, H, and B in German.[1]

Its Z-related hexachord and complement is 6-Z19[1] (3478te or, in prime form, 013478). They have the interval vector of <3,1,3,4,3,1> in common.[1] 6-Z44 lacks prime and inversional combinatoriality. 6-Z44 contains set 3-3 twice and set 3-4 twice.[2] Set 7-22 contains 6-Z44 twice and 6-Z19 twice.[3]

Schoenberg used the hexachord in the song "Seraphita" (op. 22 no. 1) and the monodrama Die glückliche Hand.[4] 6-Z44 is associated with the character Hauptmann in Alban Berg's Wozzeck.[5] Each movement of Berg's 1913 Four Pieces for Clarinet and Piano (op. 5) begins with a statement of 6-Z44 or 6-Z19.[6] 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.[7] 6-Z44 is one of the "fundamental harmonies in the last movement," of Igor Stravinsky's The Rite of Spring, "Sacrificial Dance".[8]

See also


  1. Friedmann, Michael L. (1990). Ear Training for Twentieth-Century Music, p.109. ISBN 0-300-04537-9.
  2. Williamson, John (2005). "Pyramids, Symbols, and Butterflies: 'Nacht' from Pierrot Lunaire", Words and Music, p.132-3. John Williamson, ed. Liverpool University. ISBN 9780853236191.
  3. January, 1978. The Musical quarterly, Volume 64, p.145.
  4. Simms, Bryan R. (2000). The Atonal Music of Arnold Schoenberg, 1908-1923, p.145. ISBN 0-19-512826-5.
  5. Forte, Allen (1973). The Structure of Atonal Music, p.119. Yale University. ISBN 9780300021202.
  6. (1978). The Musical quarterly, Volume 64, p.135.
  7. Cherney, Brian (2011). Weinzweig: Essays on His Life and Music, p.144-5. Wilfrid Laurier University. ISBN 9781554582563.
  8. Forte, Allen (2005). The Harmonic Organization of the Rite of Spring, p.37. Yale. ISBN 9780300105377.
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