First array of four aggregates (numbered 1–4 at bottom), each vertical line (four trichords labeled a–d) is an aggregate while each horizontal line (four trichords labeled a-d) is also an aggregate.
Composition for Four Instruments (1948) is an early serial music composition written by American composer Milton Babbitt. It is Babbitt's first published ensemble work, following shortly after his Three Compositions for Piano (1947). In both these pieces, Babbitt expands upon the methods of twelve-tone composition developed by Arnold Schoenberg. He is notably innovative for his application of serial techniques to rhythm. Composition for Four Instruments is considered one of the early examples of “totally serialized” music. It is remarkable for a strong sense of integration and concentration on its particular premises—qualities that caused Elliott Carter, upon first hearing it in 1951, to persuade New Music Edition to publish it.[2]
Composition for Four Instruments is scored for flute, clarinet, violin, and cello. An immediate division is apparent between the two wind instruments and the two strings. In addition to this, Babbitt makes use of every possible subset of the ensemble group within the different sections of the piece. He uses every combination of instruments only once, saving the full ensemble for the conclusion. The piece can be broken up into fifteen sections according to the subset of instruments playing: four solos, four trios, six duos, one tutti.[3] The instrumental subsets are arranged in complementary pairs, so that each instrument plays only once in every pair of sections. The four solos occur with increasing frequency (at intervals of five, four, and three sections), "converging", so to speak, on the final quartet, which is just two sections after the violin [sic, recte: flute] solo.[4]
Composition for Four Instruments (instrumental list)
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
Fl.
Fl.
Fl.
Fl.
Fl.
Fl.
Fl.
Fl.
Cl.
Cl.
Cl.
Cl.
Cl.
Cl.
Cl.
Cl.
Vn.
Vn.
Vn.
Vn.
Vn.
Vn.
Vn.
Vn.
Vc.
Vc.
Vc.
Vc.
Vc.
Vc.
Vc.
Vc.
Tone row according to Perle, "explicitly stated only at the conclusion of the work", and Taruskin
The twelve-tone row upon which the entire composition is based is given by the composer as 0 4 1 11 3 2: 8 6 5 10 7 9, and generates the four main trichords of the piece.[7] It never once appears complete as a melodic succession, however,[8] though several authors[9]Cone 1967[10] have given different conflicting versions of a row claimed to be "made explicit only in the final section". While the set given by Babbitt concatenates the first trichords of all four instruments in the order of their entrances at the very beginning of the work, Perle's "basic set" from the end of the composition can be transformed into the composer's version "by wholesale inversion plus individual retrogression of the trichords".[11] The pitch array used in the first 35 bars of the piece is as follows:[12]
Composition for Four Instruments (Initial pitch array)
G♭
A
F
G♯
E
G,
C♯
B♭
D
B
D♯
C;
G
E
G♯
F
A
F♯,
C
D♯
B
D
B♭
C♯.
D♭
B♭
D
B
E♭
C,
F♯
A
F
G♯
E
G;
C
E♭
B
D
B♭
C♯,
G
E
G♯
F
A
F♯.
B
E♭
C
C♯
B♭
D,
G♯
E
G
F♯
A
F;
D
B♭
C♯
C
E♭
B,
F
A
F♯
G
E
A♭.
A♭
E
G
F♯
A
F,
B
D♯
C
C♯
B♭
D;
F
A
F♯
G
E
A♭,
D
B♭
D♭
C
E♭
B.
The first section of the piece begins with a solo in the clarinet, using the (014) trichord or its retrograde. The notes of this solo are separated by register into four distinct voices, though the notes of any one trichord are usually interrupted by notes from other trichords in other registers, making it hard to hear these structures individually.[13] Babbitt presents several instances of tone rows in the opening bars of the piece. A note-by-note analysis of the first nine measures reveals two such tone rows, the first beginning at measure one and the second at measure seven. A closer look at the separation of the opening into the four registers reveals two additional tone rows. The set of notes contained in the two high registers form a tone row, as do the notes in the lower two registers.[citation needed]
The piece begins with a three-note motive, or trichord (a collection of three distinct pitch classes), in the next-to-lowest register: B–E♭–C, with a succession of +4 then −3 semitone intervals. The following measures present three transformations of this opening trichord, in retrograde-inversion, retrograde, and inverse forms (D♭–B♭–D, G♭–A–F, and A♭–E–G, respectively) separated into the mid-high, high, and lowest registers, respectively (therefore with interval patterns of −3 +4, −4 + 3, and −4 +3). However, these three trichords overlap in time, so that the temporal order of the nine notes is D♭–G♭–A♭–E–B♭–A–G–D–F. In this way, the twelve-tone aggregate is compositionally ordered into a chromatic, thematic surface, with the properties of another ordered set underneath it.[14] The clarinet solo continues by adding more forms of the basic trichord until a complete twelve-tone aggregate is unfolded in each register.[15]
As a result, seeking for "the row" caused "even the friendliest people" to become baffled and resentful, because of a fundamental misunderstanding about Babbitt's approach to his material:
That's not the way I conceive of a set. This is not a matter of finding the lost set. This is not a matter of cryptoanalysis (where's the hidden set?). What I'm interested in is the effect it might have, the way it might assert itself not necessarily explicitly.[16]
The entire opening clarinet solo can be analyzed as an array of these trichords—an "array"" being two or more simultaneous sets presented in such a way that the sums of their horizontal segments form columnar twelve-tone aggregates[17]—and their various inversions and retrogrades. The trichordal relationships between the notes in the four registers of the clarinet foreshadow the interaction between the four instrument voices in the conclusion of the piece. Also, the way in which the instruments unfold throughout the piece directly corresponds to the progression of the trichords in the clarinet solo. The organization of the pitch classes throughout the piece is consistently and undeniably self-referential.[16]
In addition to his use of multi-dimensional tone rows,[clarification needed][clarification needed][clarification needed] Babbitt also serialized rhythmic patterns. He uses the duration row as his primary rhythmic structure in Composition for Four Instruments, each of which consist of four different durations. The durations can be represented by the sequence of numbers 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.[18] For example, the first four notes of the opening clarinet solo follow the 1 4 3 2 duration pattern. This rhythmic pattern is then manipulated under the same transformations as the pitches in a tone row. These transformations include the retrograde (2 3 4 1), the inversion (4 1 2 3) and the retrograde inversion (3 2 1 4). Babbitt expands this idea in later pieces, for example working instead with a set of twelve unique durational units in Composition for Twelve Instruments.
As he does in the pitch domain, Babbitt achieves additional variety in the rhythmic patterns of Composition for Four Instruments by manipulating the duration row and its three variations in different ways. At times, he expands the row by multiplying each duration in the pattern by the four other members. Applying this transformation to the original row 1 4 3 2 results in the duration rows 1 4 3 2, 4 16 12 8, 3 12 9 6, and 2 8 6 4. Following the same procedure with the multipliers for the retrograde, 2 3 4 1, yields 4 6 8 2, 6 9 12 3, 8 12 16 4, 2 3 4 1. The inversion of the multipliers is 4 1 2 3, and the retrograde inversion is 3 2 1 4, producing 16 4 8 12, 4 1 2 3, 8 2 4 6, 12 3 6 9, and 9 6 3 12, 6 4 2 8, 3 2 1 4, 12 8 4 16, respectively.[19] In the final three bars of the piece, the clarinet plays the retrograde of the opening duration row with each element multiplied by 4, giving the pattern 8 12 16 4.[citation needed]
Composition for Four Instruments holds a significant position as one of the early serial compositions, which draws from and reinvents techniques introduced in the work of Arnold Schoenberg and Anton Webern. Babbitt continued to explore serialism throughout his career.
Discography
Milton Babbitt: Composition for Four Instruments (1948), Composition for Viola and Piano (1950); John Bavicchi: Trio No. 4, op. 33, Short Sonata for Violin and Harpsichord, op. 39. John Wummer (flute), Stanley Drucker (clarinet), Peter Marsh (violin), Donald McCall (cello); Walter Trampler (viola), Alvin Bauman (piano); David Glazer (clarinet), Matthew Raimondi (violin), Assunta Dell'Aquila (harp); Robert Brink (violin), Daniel Pinkham (harpsichord). LP recording, 1 sound disc, 33⅓ rpm., 12 in. CRI 138. New York: Composers Recordings, 1960.
Contemporary American Chamber Music. Volume 9: Elliott Carter, Sonata for flute, oboe, cello, and harpsichord (1952); Milton Babbitt, Composition for Four Instruments, for flute, clarinet, violin, and cello; Igor Stravinsky, Fanfare for a New Theatre, for two trumpets; Henry Brant, Angels and Devils, concerto for flute and flute orchestra. New England Conservatory of Music Chamber Players (David Reskin, flute; Tom Hill, clarinet; Michael Levin, violin; Ronald Thomas, cello; John Heiss, cond.). New England Conservatory Series. LP recording, 1 sound disc, analog, 33⅓ rpm, stereo, 12 in. Golden Crest NEC 109. Huntington Station, New York: Golden Crest Records, 1975.
Slowly Expanding Milton Babbitt Album: Composition for Four Instruments (1948). Rachel Beetz (flute); Joshua Rubin (clarinet); Erik Carlson (violin); Michael Nicolas (cello), produced by Erik Carlson, 2018.[20]
In music, a tone row or note row, 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 sometimes found.
The twelve-tone technique—also known as dodecaphony, twelve-tone serialism, and twelve-note composition—is a method of musical composition first devised by Austrian composer Josef Matthias Hauer, who published his "law of the twelve tones" in 1919. In 1923, Arnold Schoenberg (1874–1951) developed his own, better-known version of 12-tone technique, which became associated with the "Second Viennese School" composers, who were the primary users of the technique in the first decades of its existence. The technique is a means of ensuring that all 12 notes of the chromatic scale are sounded as often as one another in a piece of music while preventing the emphasis of any one note through the use of tone rows, orderings of the 12 pitch classes. All 12 notes are thus given more or less equal importance, and the music avoids being in a key. Over time, the technique increased greatly in popularity and eventually became widely influential on 20th-century composers. Many important composers who had originally not subscribed to or actively opposed the technique, such as Aaron Copland and Igor Stravinsky, eventually adopted it in their music.
Milton Byron Babbitt 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.
In music theory, a trichord is a group of three different pitch classes found within a larger group. A trichord is a contiguous three-note set from a musical scale or a twelve-tone row.
In music using the twelve-tone technique, derivation is the construction of a row through segments. A derived row is a tone row whose entirety of twelve tones is constructed from a segment or portion of the whole, the generator. Anton Webern often used derived rows in his pieces. A partition is a segment created from a set through partitioning.
In music using the twelve tone technique, combinatoriality is a quality shared by twelve-tone tone rows whereby each section of a row and a proportionate number of its transformations combine to form aggregates. Much as the pitches of an aggregate created by a tone row do not need to occur simultaneously, the pitches of a combinatorially created aggregate need not occur simultaneously. Arnold Schoenberg, creator of the twelve-tone technique, often combined P-0/I-5 to create "two aggregates, between the first hexachords of each, and the second hexachords of each, respectively."
In music, a permutation (order) of a set is any ordering of the elements of that set. A specific arrangement of a set of discrete entities, or parameters, such as pitch, dynamics, or timbre. Different permutations may be related by transformation, through the application of zero or more operations, such as transposition, inversion, retrogradation, circular permutation, or multiplicative operations. These may produce reorderings of the members of the set, or may simply map the set onto itself.
Nummer 2 for thirteen instruments is a composition written in 1951 by the Belgian composer Karel Goeyvaerts.
A set in music theory, as in mathematics and general parlance, is a collection of objects. In musical contexts the term is traditionally applied most often to collections of pitches or pitch-classes, but theorists have extended its use to other types of musical entities, so that one may speak of sets of durations or timbres, for example.
Donald James Martino was a Pulitzer Prize winning American composer.
Richard G. Swift was an American composer and music theorist.
The Kammerkonzert für Klavier und Geige mit 13 Bläsern is a piece of chamber music composed by Austrian composer Alban Berg. It was composed between 1923 and 1925. The short score was completed on 9 February 1925; the full score was finished on 23 July 1925. The work was premiered on 19 March 1927.
Carlton Edwin Wesley Gamer was an American composer and music theorist. Gamer composed more than seventy works in a variety of genres, including songs, music for dance, solo piano pieces, chamber music, choral works, orchestral works, and computer music. His compositional approach has been fundamentally shaped by his theoretical interests, the latter influenced by an interest in mathematics.
Anton Webern's Concerto for Nine Instruments, Op. 24, written in 1934, is a twelve-tone concerto for nine instruments: flute, oboe, clarinet, horn, trumpet, trombone, violin, viola, and piano. It consists of three movements:
The Sonatina for Violin and Harpsichord is a three-movement, neoclassical chamber work composed by Walter Piston in 1945, that marks the beginning of his postwar style.
In music, the "Ode-to-Napoleon" hexachord is the hexachord named after its use in the twelve-tone piece Ode to Napoleon Buonaparte Op. 41 (1942) by Arnold Schoenberg. Containing the pitch-classes 014589 it is given Forte number 6–20 in Allen Forte's taxonomic system. The primary form of the tone row used in the Ode allows the triads of G minor, E♭ minor, and B minor to easily appear.
Composition for Twelve Instruments is a serial music composition written by American composer Milton Babbitt for flute, oboe, clarinet, bassoon, horn, trumpet, harp, celesta, violin, viola, cello, and double bass. In it Babbitt for the first time employs a twelve-element duration set to serialize the rhythms as well as the pitches, predating Olivier Messiaen's (non-serial) "Mode de valeurs et d'intensités", but not the Turangalîla-Symphonie (1946–1948), in which Messiaen used a duration series for the first time in the opening episode of the seventh movement, titled "Turangalîla II".
A duration row or duration series is an ordering of a set of durations, in analogy with the tone row or twelve-tone set.
String Quartet No. 2 (1954) is the second of six string quartets by the American composer Milton Babbitt.
Movements is a 1959 five-movement work for piano and orchestra by Igor Stravinsky lasting about ten minutes. It was written during his serial period and shows his dedication to that idiom as well as the influence of Anton Webern.
Arnold, Stephen, and Graham Hair. 1976. "An Introduction and a Study: String Quartet No. 3". Perspectives of New Music 14, no.2 and 15, no.1 (Spring-Summer/Fall-Winter): 155–186.
Babbitt, Milton. 1976. "Responses: A First Approximation". Perspectives of New Music 14, no. 2/15, no.1 (Spring-Summer/Fall-Winter): 8–10.
Babbitt, Milton. 1987. Words about Music, edited by Stephen Dembski and Joseph N. Straus. Madison: University of Wisconsin Press.
Carter, Elliott. 1976. "To Think of Milton Babbitt". Perspectives of New Music 14, no.2, and 15, no.1 ("Sounds and Words. A Critical Celebration of Milton Babbitt at 60") (Spring-Summer/Fall-Winter): 29–31.
Cone, Edward T. 1967. "Beyond Analysis". Perspectives of New Music 6, no. 1 (Fall-Winter): 33–51.
Dubiel, Joseph. 1990. "Three Essays on Milton Babbitt" [Part 1]. Perspectives of New Music 28, no.2 (Summer): 216–226.
Dubiel, Joseph. 1992. "Three Essays on Milton Babbitt (Part 3)". Perspectives of New Music 30, no.1 (Winter): 82–131.
Howland, Patricia L. 2010. "Formal Processes in Post-Tonal Music: A Study of Selected Works by Babbitt, Stockhausen, and Carter". PhD diss. New York: City University of New York.
Mead, Andrew. 1983. "Detail and the Array in Milton Babbitt's My Complements to Roger". Music Theory Spectrum 5 (Spring): 89–109.
Pearsall, Edward. 1997. "Interpreting Music Durationally: A Set-Theory Approach to Rhythm". Perspectives of New Music 35, no. 1 (Winter): 205–230.
Perle, George. 1981. Serial Composition and Atonality: An Introduction to the Music of Schoenberg, Berg, and Webern, fifth edition. Berkeley and Los Angeles: University of California Press.
Sitsky, Larry (2002). Music of the Twentieth-Century Avant-Garde: A Biocritical Sourcebook. Greenwood Publishing. ISBN9780313296895.
Swift, Richard. 1976. “Some Aspects of Aggregate Composition.” Perspectives of New Music 14, no.2 and 15, no.1 ("Sounds and Words. A Critical Celebration of Milton Babbitt at 60") (Spring-Summer/Fall-Winter): 236–248.
Whittall, Arnold. 2008. The Cambridge Introduction to Serialism. Cambridge Introductions to Music. Cambridge and New York: Cambridge University Press. ISBN978-0-521-68200-8 (pbk).
This page is based on this Wikipedia article Text is available under the CC BY-SA 4.0 license; additional terms may apply. Images, videos and audio are available under their respective licenses.
