Bernard, Jonathan W. "The Evolution of Elliott Carter's Rhythmic Practice." Perspectives of New Music 26/2 (Summer 1988): 164-203.
Jonathan Bernard traces the development of the most distinctive feature of Elliott Carter's musical language: his rhythmic practice. He notes the initial influence of three experimental American composers, Ives, Cowell, and Nancarrow. Carter himself has outlined the significant contributions of these three composers in the area of rhythm. With Ives, Carter noted his superimposition of different speeds notated in a common unit, noted rubati played against strict time, and unrelated levels heard simultaneously. Carter cites Cowell's New Musical Resources (1930) as having "furnished me with many ideas." Carter was also familiar with Nancarrow's studies for player piano as evidenced by his work for the New Music Quarterly during the 1940s.
Bernard is careful to note, however, that Carter did not adopt the experiments and theories of these three wholesale. He states that Carter was impressed with their ideas, but wanted to find a solution to the innovation of rhythm himself.
Bernard cites the Cello Sonata (1948) as "Carter's first great stride in the direction of controlling large-scale rhythmic structure." He achieved this though his first use of "metric-modulation" in which the tempo of a piece increases by way of proportional relationships among the surface rhythms. Bernard notes, however, that this initial use of metric-modulation was tentative, occurring largely at the beginning and the end of the work.
With his First String Quartet (1951), Carter began to employ his fluctuating tempos more extensively with an "extensive employment of the idea of simultaneity." With this work, Carter explores the possibilities of multiple tempos simultaneously, giving each line greater independence.
In the Variations for Orchestra (1954-55), Carter adds the use of ritardandos and decelerandos to give the lines even greater independence. With the addition of this parameter, Carter "thus achieves a gradual, almost completely smooth acceleration, in contrast to the shifts of speed in metric modulation, which occurs in a series of distinct steps."
The Second String Quartet (1959) expands these developments, increasing the independence of line by including the parameter of pitch material as a defining feature of a part. Thus each of the string instruments in the group is delineated by tempo, degree of rhythmic fluctuation, as well as its exclusive use of particular intervals, or in Carter's words "their repertoire of intervals, their repertoire of rhythms, and their repertoire of musical gestures."
With the Double Concerto (1961), Carter's musical techniques serve as the basis for the overall formal layout. The piano gradually increases in tempo while the harpsichord gradually decreases tempo. The two begin with the same tempo and gradually separate into a 2:1 tempo relationship. Though not entirely consistent, the pitch material matches these ratios, moving from a minor second to an octave.
The pitch and rhythmic relationship becomes integral in Carter's works after the Double Concerto, so much so that neither takes precedent over the other.
(Peter Schimpf)
Harvey, David I. H. The Later Music of Elliott Carter: A Study in Music Theory and Analysis. New York & London: Garland Publishing, Inc., 1989.
Harvey challenges the view of Elliott Carter as a "cerebral" or "intellectual" composer claiming that though his music may be based on certain structured principles, the final sound and communicative power of the music was always primary. "Carter's pre-compositional organization provides a set of materials which are limited within a work according to the context of a particular instrument or ensemble, section in a form, or expressive character. These materials are then used with varying degrees of strictness, sometimes according to a referential sonority or intervallic relation, sometimes spun out of flights of elaborate and virtuosic compositional freedom."
Harvey follows with an analysis of three of Carter's "mature" compositions: Second String Quartet, Double Concerto, and Concerto for Orchestra. He sets forth four basic premises in analyzing these works: (1)The musical surface is hierarchical in nature, (2) pitch relationships are the principal defining and articulating factors in the perception of structure, (3) certain pitches-through various means-may be weighted on a local level, and (4) there may be a hierarchic or processive between pitches and configurations of pitches.
Based on these criteria for analysis then, Harvey provides a detailed account of only the pitch material and is able to draw his own conclusions concerning the structural uses of pitch in Carter's music.
(Peter Schimpf)
Mead, Andrew. "The Role of Octave Equivalence in Elliott Carter's Recent Music: A Birthday Celebration." Sonus 14/2 (Spring 1994): 13-37.
Contrary to common approaches to the analysis of Carter's pitch material and use of specific intervals, Andrew Mead makes a case for also analyzing the pitch material of Carter's music with consideration of octave equivalence and pitch-class. Because Carter's music makes explicit use of very specific intervals-such as a minor tenth-octave equivalence and pitch-class analysis would incorrectly reduce intervals specifically used for their exact size. In pitch-class analysis, for example, a minor tenth would be placed in the same pitch class as a minor third and a major sixth. If that minor tenth is a significant motivic element, octave equivalence and pitch-class analysis cannot account for it.
Mead, however, makes the case that in certain instances octave equivalence may illuminate certain aspects of Carter's music that might otherwise be unexplainable. In the Fourth String Quartet for instance, Mead notes, "the combination of first violin and cello contains the complements of the intervals found in the remaining pair of instruments." Thus while the individual string parts are given independence through their exclusive use of particular intervals, there is an overall coherence to the piece through related and complementary intervals and pitch-class sets.
Mead also notes that the all-interval sonorities and series that Carter frequently employs are often created out of a hexachord and its inversion. Thus while all intervals are being used, a pitch-class analysis reveals the inner coherence of the sonority.
Mead recognizes the importance and relevance of both theoretical approaches for explaining Carter's pitch material stating, "If we can accept an awareness of interval-class membership in this music, still of course acknowledging the very real sonic differences between complementary intervals, we will have available the notion of recognizing pitch-classes in addition to pitch as a possible resource for comprehending musical structure in Carter's works."
(Peter Schimpf)
Mead, Andrew. "Twelve-tone Composition and the Music of Elliott Carter." In Concert Music, Rock, and Jazz Since 1945: Essays and Analytical Studies, ed. Elizabeth West Marvin and Richard Herrmann (Rochester: University of Rochester Press, 1995): 67-102.
Mead's article examines the ways in which Carter organizes his pitch material, and then compares it to the twelve-tone method of organization. Though Carter did not align himself with the twelve-tone method of Schoenberg, which continued to be vigorously applied in the works of Carter's contemporaries such as Milton Babbit, his musical language freely embraced the chromatic collection. Through the partial analysis of Carter's Piano Concerto, Second String Quartet, and Night Fantasies, Mead demonstrates the similarities and differences in the organization of pitch material between Carter and the twelve-tone composers.
Mead employs the tools and terminology of twelve-tone theory "in order to suggest commonalities with other composers practice, while highlighting the individual and creative ways Carter has enriched and extended certain familiar theoretical ideas." Mead specifically notes Carter's use of twelve-note chords, hierarchical orderings of trichords, and all interval collections, as well as hints of hexachordal combinatoriality. However, he observes that the "most crucial compositional differences between Carter's general practice and that usually associated with twelve-tone composition entails the dimension in which specified order is articulated." In an effort to bring independence to the individual layers of his compositions, Carter created pitch hierarchies in space rather than time. Thus various collections are differentiated largely by register.
(Peter Schimpf)
Moe, Orin. "The Music of Elliott Carter." College Music Symposium 22 (1982): 7-31.
Orin Moe takes a general overall look at the music of Elliott Carter, specifically examining the major works from what he terms Carter's "mature style." Moe identifies three phases in Carter's compositional career: "Neo-classic, Expressionist, and Mature." He briefly mentions the basic style characteristics of Carter's first two phases, before looking more thoroughly at the mature style.
In the first or "neo-classical" phase (1933-46), Moe notes the emphasis on vocal and extra-musical works with a strong linear quality and a "classical" sense of form and clarity. In the second or "Expressionist" phase, beginning in earnest with the The Minotaur (1947) and the Cello Sonata (1948) and continuing sporadically throughout his career, Moe notes a greater richness of thematic ideas and the first uses of Carter's trademark "metric-modulation" or fluctuating tempos. Moe also notes the use of contrasting instrumental groups and pitch material along with the rhythmic layers beginning during the expressionist phase.
The bulk of Moe's paper, however, is concerned with the last or "mature" phase of Carter's career, beginning with the Variations for Orchestra (1954-55). Moe states that during this phase, all of the elements of Carter's previous style periods work together creating the essential qualities of Carter's mature style. Through discussions of Variations, the first and second string quartets, Double Concerto for Harpsichord and Piano (1959-61), Piano Concerto (1964-65), Concerto for Orchestra (1969), and A Symphony of Three Orchestras (1976) Moe notes the basic techniques of Carter's style, such as the tendency towards contrasting layers of instruments, tempos, and pitch material. In discussing the Variations, he coins the term "character-complexes" referring to musical fragments that co-exist in varying timbral and metric forms. In the double concerto he notes Carter's use of a "mediator": a group of instruments that mediate between the two opposing forces of the work. In the string quartets this concept carries over to pitch intervals as well.
In discussing the Concerto for Orchestra, Moe notes the summation of these ideas with the technique of "simultaneous movements," in which a typical arrangement of successive symphonic movements of varying character are collapsed into a single movement, each distinguished by timbre, range, and pitch material. Carter manages these enormous layers by emphasizing certain "movements" while others fall into the background in the same way four contrapuntal lines would be.
Moe notes that the later works continue the same principles with different ensembles (such as the Brass Quintet), which nevertheless produces surprisingly different results.
(Peter Schimpf)
Schiff, David. The Music of Elliott Carter. New York: Da Capo, 1983.
This book is a comprehensive look at Elliott Carter's music from his "earliest surviving efforts to his latest work." As a former student of Carter's, Schiff is able to draw on specific statements and analysis of the music from Carter himself.
After an initial biographical section in which he outlines Carter's education and basic artistic aesthetics, Schiff describes the basic features of Carter's work including discussions of rhythm, form, texture, and harmony. He describes and categorizes the most salient features of Carter's music, citing specific examples from his scores.
In discussing rhythm, Schiff outlines Carter's development from the rhythmic activity of his early scores to the layered, superimposed rhythms and tempos of his later works. In discussing form, Schiff notes several original designs, such as circular forms in which the movements may be elided into one another, collage, in which various contrasting elements are superimposed against one another, and epiphanic, in which the dramatic importance of an isolated figure only gains significance when it interacts with subsequent contrasting material that gives it definition.
Schiff provides a thorough treatment of Carter's harmony as well. He provides a chart suggesting the character of each of the eleven basic intervals based on their use in Carter's music, noting that the eleven intervals serve as "primary colors" in Carter's musical language. He also notes Carter's use of the twelve possible tri-chords and twelve note sonorities in compositions such as the Piano Concerto.
Following this discussion of Carter's musical style, Schiff briefly discusses each one of Carter's compositions chronologically, beginning with his student compositions and continuing until the works prior to 1983. These discussions and analysis draw upon the theories of Carter's musical practice as outlined in the first half of the book. Schiff is thus able to show the development of many of Carter's compositional devices. The first and second string quartets, along with the Double Concerto and Variations for Orchestra receive the most extensive treatment.
(Peter Schimpf)