A duration row or duration series is an ordering of a

set Set, The Set, SET or SETS may refer to: Science, technology, and mathematics Mathematics *Set (mathematics), a collection of elements *Category of sets, the category whose objects and morphisms are sets and total functions, respectively Electro ...

of durations, in analogy with the

tone row In music, a tone row or note row ( or '), also series or set, is a non-repetitive ordering of a set of pitch-classes, typically of the twelve notes in musical set theory of the chromatic scale, though both larger and smaller sets are sometime ...

twelve-tone The twelve-tone technique—also known as dodecaphony, twelve-tone serialism, and (in British usage) twelve-note composition—is a method of musical composition. The technique is a means of ensuring that all 12 notes of the chromatic scale ...

set.

Olivier Messiaen Olivier Eugène Prosper Charles Messiaen (, ; ; 10 December 1908 – 27 April 1992) was a French composer, organist, and ornithology, ornithologist. One of the major composers of the 20th-century classical music, 20th century, he was also an ou ...

's " Mode de valeurs et d'intensités" 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 A parameter (), generally, is any characteristic that can help in defining or classifying a particular system (meaning an event, project, object, situation, etc.). That is, a parameter is an element of a system that is useful, or critical, when ...

separately.Grant, M. J. (2005). ''Serial Music, Serial Aesthetics: Compositional Theory in Post-War Europe'', p.62. . Messiaen had, however, previously used this chromatic duration series as an ordered set in the opening episode of "Turangalîla 2", a movement from the ''

Turangalîla-Symphonie The ''Turangalîla-Symphonie'' is the only symphony by Olivier Messiaen (1908–1992). It was written for an orchestra of large forces from 1946 to 1948 on a commission by Serge Koussevitzky for the Boston Symphony Orchestra. Along with the ...

'' (1946–48). In 1946

Milton Babbitt Milton Byron Babbitt (May 10, 1916 – January 29, 2011) was an American composer, music theorist, mathematician, and teacher. He was a Pulitzer Prize and MacArthur Fellowship recipient, recognized for his serial and electronic music. Biography ...

wrote "The Function of Set Structures in the Twelve-Tone System", outlining a theory of complete (total) serialism.Sitsky, Larry (2002). ''Music of the Twentieth-Century Avant-Garde: A Biocritical Sourcebook'', p.78. . 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. In the first piece this governs the number of attacks within phrases, in the second rhythms are generated as multiples of a unit. (for example: 5×, 1×, 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. Babbitt's '' Composition for Twelve Instruments'' (1948) uses a twelve-element duration set to serialize the rhythms as well as the pitches. He would later employ an approach based on

time-point In music a time point or ''timepoint'' (point (geometry), point in time) is "an instant, analogous to a geometrical point in space". Because it has no duration (music), duration, it literally cannot be heard, but it may be used to represent "the p ...

s. Babbitt's use of rhythm in the latter piece was criticized by

Peter Westergaard Peter Talbot Westergaard (28 May 1931 – 26 June 2019) was an American composer and music theorist. He was Professor Emeritus of music at Princeton University. Biography Westergaard was born on 28 May 1931 in Champaign, Illinois. He pursued ...

in ''

Perspectives of New Music ''Perspectives of New Music'' (PNM) is a peer-reviewed academic journal specializing in music theory Music theory is the study of theoretical frameworks for understanding the practices and possibilities of music. ''The Oxford Companion to Musi ...

'': "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)?"

Pierre Boulez Pierre Louis Joseph Boulez (; 26 March 19255 January 2016) was a French composer, conductor and writer, and the founder of several musical institutions. He was one of the dominant figures of post-war contemporary classical music. Born in Montb ...

used the values in Messiaen's piece to order the rhythms in his '' Structures I'' (1952). These range from a demisemiquaver (, 1) to a dotted crotchet (, 12). 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. In 1957

Karlheinz Stockhausen Karlheinz Stockhausen (; 22 August 1928 – 5 December 2007) was a German composer, widely acknowledged by critics as one of the most important but also controversial composers of the 20th and early 21st centuries. He is known for his groun ...

described this additive series as "a subharmonic proportional series" which, "compared to a scale constructed of chromatic intervals, … is a

mode Mode ( meaning "manner, tune, measure, due measure, rhythm, melody") may refer to: Arts and entertainment * MO''D''E (magazine), a defunct U.S. women's fashion magazine * ''Mode'' magazine, a fictional fashion magazine which is the setting fo ...

",Stockhausen, Karlheinz (1957). "... wie die Zeit vergeht ...", ''

Die Reihe ''Die Reihe'' () was a German-language music academic journal, edited by Herbert Eimert and Karlheinz Stockhausen and published by Universal Edition (Vienna) between 1955 and 1962 (). An English edition was published, under the original German ...

'' 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. Leeuw, Ton de (2006). ''Music of the Twentieth Century'', p.171. . and criticized it because the intervals between successive degrees are perceived as having different sizes (unlike the

chromatic scale The chromatic scale (or twelve-tone scale) is a set of twelve pitches (more completely, pitch classes) used in tonal music, with notes separated by the interval of a semitone. Chromatic instruments, such as the piano, are made to produce the ...

of pitches). 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). Roads, Curtis (2001). ''Microsound'', p.74. Cambridge: MIT Press. . A duration set based on the harmonic series would introduce irrational values.

Sources

Further reading