Hexachord

In music, a hexachord is a collection of six pitch classes[2] including six-note segments of a scale or tone row. The term was adopted in the Middle Ages and adapted in the 20th century in Milton Babbitt's serial theory.

Contents

Middle Ages

Main article: Guidonian_hand#Hexachord_in_Middle_Ages

The hexachord as a mnemonic device was first described by Guido of Arezzo, in his Epistola de ignoto cantu and the treatise titled Micrologus.[3] In each hexachord, all adjacent pitches are a whole tone apart, except for the middle two, which are separated by a semitone. These six pitches are named ut, re, mi, fa, sol, and la, with the semitone between mi and fa. These six names are derived from the first syllable of each half-line of the 8th-century hymn Ut queant laxis.

20th century

Allen Forte in his The Structure of Atonal Music redefines the term hexachord to mean what other theorists (notably Howard Hanson in his Harmonic Materials of Modern Music: Resources of the Tempered Scale[5]) mean by the term hexad, a six-note pitch collection which is not necessarily a contiguous segment of a scale or a tone row. Carlton Gamer uses both terms interchangeably.[6]

The Sacher hexachord (musical cryptogram on the name of patron Paul Sacher) is notable for its use in multiple compositions including Messagesquisse by Pierre Boulez.

See also

Sources

  1. ^ Arnold Whittall, The Cambridge Introduction to Serialism, Cambridge Introductions to Music (New York: Cambridge University Press, 2008): 23 ISBN 978-0-521-86341-4 (hardback) ISBN 978-0-521-68200-8 (pbk).
  2. ^ Whittall 2008, 273.
  3. ^ Jehoash Hirshberg, "Hexachord", The New Grove Dictionary of Music and Musicians, second edition, edited by Stanley Sadie and John Tyrrell (London: Macmillan Publishers, 2001).
  4. ^ George Perle, Serial Composition and Atonality: An Introduction to the Music of Schoenberg, Berg, and Webern, sixth edition, revised (Berkeley: University of California Press, 1991): 145. ISBN 9780520074309.
  5. ^ Howard Hanson, Harmonic Materials of Modern Music: Resources of the Tempered Scale (New York: Appleton-Century-Crofts, 1960): .
  6. ^ Carlton Gamer, "Some Combinational Resources of Equal-Tempered Systems", Journal of Music Theory 11, no. 1 (Spring 1967): 32–59. The term "hexad" appears just once, in a table on p. 37; the word "hexachord" also occurs once, on p. 41.
  7. ^ Whittall 2008, p. 206

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