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. [2] 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). [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× , 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. [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 ( , 1) to a dotted crotchet ( ., 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]