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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'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 separately.〔Grant, M. J. (2005). ''Serial Music, Serial Aesthetics: Compositional Theory in Post-War Europe'', p.62. ISBN 9780521619929.〕 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'' (1946–48).〔Robert Sherlaw Johnson, ''Messiaen'', revised and updated edition (London: J. M. Dent; Berkeley: University of California Press, 1989): 94.〕 In 1946 Milton Babbitt 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. ISBN 9780313017230.〕 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.〔Sitsky, Larry (2002). ''Music of the Twentieth-Century Avant-Garde: A Biocritical Sourcebook'', p.18. ISBN 9780313296895.〕 Babbitt's ''Composition for Twelve Instruments'' (1948) uses a twelve-element duration set to serialize the rhythms as well as the pitches.〔Taruskin, Richard (2009). ''The Oxford History of Western Music: Music in the Late Twentieth Century'', p.168. ISBN 9780195384857.〕 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)?"〔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.〕 Pierre Boulez 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).〔Pam Hurry, Mark Phillips, Mark Richards (2001). ''Heinemann Advanced Music'', p.127. ISBN 9780435812584.〕 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.〔Crispin, Darla, ed. (2009). ''Unfolding Time: Studies in Temporality in Twentieth Century Music'', p.76. ISBN 9789058677358.〕 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",〔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.〕〔de Leeuw, Ton (2006). ''Music of the Twentieth Century'', p.171. ISBN 9789053567654.〕 and criticized it because the intervals between successive degrees are perceived as having different sizes (unlike the chromatic scale 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. ISBN 0-262-18215-7.〕 A duration set based on the harmonic series would introduce irrational values.〔 ==Sources== 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Duration series」の詳細全文を読む スポンサード リンク
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