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Six-element set of rhythmic values used in Variazioni canoniche (1950) by Luigi Nono[1]

A duration row or duration series is an ordering of a set of durations, in analogy with the tone row or twelve-tone set.

Olivier Messiaen's "Mode de valeurs et d'intensitĂ©s" is often cited as the first serial piece, but, as well as being predated by Babbitt, both lacks order and views each note as a unit, rather than composing each parameter separately.[2] Messiaen had, however, previously used this chromatic duration series as an ordered set in the opening episode of "TurangalĂźla 2", a movement from the TurangalĂźla-Symphonie (1946–48).[3]

In 1946 Milton Babbitt wrote "The Function of Set Structures in the Twelve-Tone System", outlining a theory of complete (total) serialism.[4] Babbitt's Three Compositions for Piano (1947–48) uses the rhythmic set 5-1-4-2 (sum: 12), whose permutation and function varies with each piece.[2] In the first piece this governs the number of attacks within phrases, in the second rhythms are generated as multiples of a unit.[2] (for example: 5×sixteenth note, 1×sixteenth note, etc.)

Babbitt's Composition for Four Instruments (1948) uses a four-element duration row: 1 4 3 2 (the second note is four times the duration of the first, etc.). The duration of the initial note changes every phrase, varying the durations throughout the piece.[5] Babbitt's Composition for Twelve Instruments (1948) uses a twelve-element duration set to serialize the rhythms as well as the pitches.[6] He would later employ an approach based on time-points.

Babbitt's use of rhythm in the latter piece was criticized by Peter Westergaard in Perspectives of New Music: "can we be expected to hear a family resemblance between a dotted half note followed by a sixteenth note (the opening 'interval' of duration set P0) and an eighth note followed by a dotted eighth note (the opening 'interval' of duration set P2)?"[7]

Pierre Boulez used the values in Messiaen's piece to order the rhythms in his Structures I (1952).[4] These range from a demisemiquaver (thirty-second note, 1) to a dotted crotchet (dotted quarter note., 12).[8] In Structures Ic, for example, successive durations may be used for successive pitches of a row, or each pitch row may use only one duration, while in Ib new methods are constantly invented.[9]

In 1957 Karlheinz Stockhausen described this additive series as "a subharmonic proportional series" which, "compared to a scale constructed of chromatic intervals, 
 is a mode",[10][11] and criticized it because the intervals between successive degrees are perceived as having different sizes (unlike the chromatic scale of pitches).[10] For example, the first four notes equal about 13% of the total duration while the last four equal over 53% (each being 33% of the values).[12] A duration set based on the harmonic series would introduce irrational values.[11]

Sources

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  1. ↑ Whittall, Arnold (2008). The Cambridge Introduction to Serialism, p.165. New York: Cambridge University Press. ISBN 978-0-521-68200-8 (pbk).
  2. 1 2 3 Grant, M. J. (2005). Serial Music, Serial Aesthetics: Compositional Theory in Post-War Europe, p.62. ISBN 9780521619929.
  3. ↑ Robert Sherlaw Johnson, Messiaen, revised and updated edition (London: J. M. Dent; Berkeley: University of California Press, 1989): 94.
  4. 1 2 Sitsky, Larry (2002). Music of the Twentieth-Century Avant-Garde: A Biocritical Sourcebook, p.78. ISBN 9780313017230.
  5. ↑ Sitsky, Larry (2002). Music of the Twentieth-Century Avant-Garde: A Biocritical Sourcebook, p.18. ISBN 9780313296895.
  6. ↑ Taruskin, Richard (2009). The Oxford History of Western Music: Music in the Late Twentieth Century, p.168. ISBN 9780195384857.
  7. ↑ Westergaard, Peter (1965). "Some Problems Raised by the Rhythmic Procedures in Milton Babbitt's Composition for Twelve Instruments", Perspectives of New Music 4, no. 1: 109-18, citation on p.113. Quoted by Taruskin, Richard (with "half note" changed to "quarter note") (2009). The Oxford History of Western Music: Music in the Late Twentieth Century, p.168. ISBN 9780195384857.
  8. ↑ Pam Hurry, Mark Phillips, Mark Richards (2001). Heinemann Advanced Music, p.127. ISBN 9780435812584.
  9. ↑ Crispin, Darla, ed. (2009). Unfolding Time: Studies in Temporality in Twentieth Century Music, p.76. ISBN 9789058677358.
  10. 1 2 Stockhausen, Karlheinz (1957). "... wie die Zeit vergeht ...", Die Reihe 3:13–42. Translation by Cardew, Cornelius, as "... How Time Passes ..." in the English edition of Die Reihe 3 (1959): 10–40. Revised version, annotated by Heike, Dr. Georg, in Stockhausen's Texte zur Musik 1, edited by Schnebel, Dieter, 99–139 (Cologne: Verlag M. DuMont Schauberg, 1963). Citation on p.16 of Die Reihe (p.13 of the English edition), pp.103–104 of Texte 1.
  11. 1 2 Leeuw, Ton de (2006). Music of the Twentieth Century, p.171. ISBN 9789053567654.
  12. ↑ Roads, Curtis (2001). Microsound, p.74. Cambridge: MIT Press. ISBN 0-262-18215-7.

Further reading

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