In music theory, the chromatic hexachord is the hexachord consisting of a consecutive six-note segment of the chromatic scale. It is the first hexachord as ordered by Forte number, and its complement is the chromatic hexachord at the tritone. For example, zero through five and six through eleven. On C:
C, C♯, D, D♯, E, F
and
F♯, G, G♯, A, A♯, B.
This is the first of the six hexachords identified by Milton Babbitt as all-combinatorial source sets, a "source set" being "a set considered only in terms of the content of its hexachords, and whose combinatorial characteristics are independent of the ordering imposed on this content" (Babbitt 1955, 57). In the larger context of thirty-five source hexachords catalogued by Donald Martino, it is designated "Type A" (Martino 1961, 229–30). Applying the circle of fifths transformation to the chromatic hexachord produces the diatonic hexachord(Babbitt 1987, 93). As with the diatonic scale, the chromatic hexachord is, "hierarchical in interval makeup," and may also be produced by, or contains, 3-1, 3-2, 3-3, 3-6, and 3-7 (Friedmann 1990, 111).
Row of Webern's Piano Variations, a fixed-order series derived from the (unordered) chromatic source hexachord, displaying its combinatorial propertiesThe "wedge" row, derived from the same source set, used by (amongst others) Nono in Il canto sospeso and Stockhausen in Kontakte
Stefan Wolpe's Suite in Hexachord (1936) begins with a chromatic hexachord on G, introducing the complementary hexachord in the final movement, while Elliott Carter calls his own piece, "Inner Song" for solo oboe—the second movement of Trilogy for oboe and harp (1992)—"some thoughts about Wolpe's hexachord" (Schiff 1998, 146).
Babbitt, Milton. 1955. "Some Aspects of Twelve-Tone Composition". The Score and I.M.A. Magazine 12:53–61.
Babbitt, Milton. 1987. Words About Music: The Madison Lectures, edited by Stephen Dembski and Joseph Straus. Madison: University of Wisconsin Press. ISBN9780299107949.
Duarte, John. 2008. Melody and Harmony for Guitarists. Pacific, Missouri: Mel Bay. ISBN9780786676880.
Friedmann, Michael L. 1990. Ear Training for Twentieth-century Music. New Haven and London: Yale University Press. ISBN9780300045376.
Martino, Donald. 1961. "The Source Set and Its Aggregate Formations." Journal of Music Theory 5, no. 2:224–73. Addendum in Journal of Music Theory 6, no. 2, 1962:322–23.
Nielinger, Carola. 2006. "'The Song Unsung': Luigi Nono's Il canto sospeso", Journal of the Royal Musical Association 131, no. 1:83–150.
Schiff, David. 1998. The Music of Elliott Carter, second edition. Ithaca, NY: Cornell University Press. ISBN9780801436123.
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.
In music, serialism is a method of composition using series of pitches, rhythms, dynamics, timbres or other musical elements. Serialism began primarily with Arnold Schoenberg's twelve-tone technique, though some of his contemporaries were also working to establish serialism as a form of post-tonal thinking. Twelve-tone technique orders the twelve notes of the chromatic scale, forming a row or series and providing a unifying basis for a composition's melody, harmony, structural progressions, and variations. Other types of serialism also work with sets, collections of objects, but not necessarily with fixed-order series, and extend the technique to other musical dimensions, such as duration, dynamics, and timbre.
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.
Contemporary classical music is classical music composed close to the present day. At the beginning of the 21st century, it commonly referred to the post-1945 modern forms of post-tonal music after the death of Anton Webern, and included serial music, electronic music, experimental music, and minimalist music. Newer forms of music include spectral music, and post-minimalism.
Luigi Nono was an Italian avant-garde composer of classical 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, a hexachord is a six-note series, as exhibited in a scale or tone row. The term was adopted in this sense during the Middle Ages and adapted in the 20th century in Milton Babbitt's serial theory. The word is taken from the Greek: ἑξάχορδος, compounded from ἕξ and χορδή, and was also the term used in music theory up to the 18th century for the interval of a sixth.
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 theory, complement refers to either traditional interval complementation, or the aggregate complementation of twelve-tone and serialism.
The Group for Contemporary Music is an American chamber ensemble dedicated to the performance of contemporary classical music. It was founded in New York City in 1962 by Joel Krosnick, Harvey Sollberger and Charles Wuorinen and gave its first concert on October 22, 1962 in Columbia University's MacMillin Theatre. Krosnik left the ensemble in 1963. It was the first contemporary music ensemble based at a university and run by composers.
Diatonic and chromatic are terms in music theory that are most often used to characterize scales, and are also applied to musical instruments, intervals, chords, notes, musical styles, and kinds of harmony. They are very often used as a pair, especially when applied to contrasting features of the common practice music of the period 1600–1900.
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:
In music, the "Ode-to-Napoleon" hexachord is the hexachord named after its use in the twelve-tone piece Ode to Napoleon Buonaparte (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.
In music, the all-trichord hexachord is a unique hexachord that contains all twelve trichords, or from which all twelve possible trichords may be derived. The prime form of this set class is {012478} and its Forte number is 6-Z17. Its complement is 6-Z43 and they share the interval vector of <3,2,2,3,3,2>.
A duration row or duration series is an ordering of a set of durations, in analogy with the tone row or twelve-tone set.
Il canto sospeso is a cantata for vocal soloists, choir, and orchestra by the Italian composer Luigi Nono, written in 1955–56. It is one of the most admired examples of serial composition from the 1950s, but has also excited controversy over the relationship between its political content and its compositional means.
All Set, for jazz ensemble, is a 1957 composition for small jazz band by the American composer Milton Babbitt.
The diatonic, Guidonian, or major hexachord (6-32) is a hexachord consisting of six consecutive pitches from the diatonic scale that are also a consecutive segment of the circle of fifths: F C G D A E = C D E F G A = "do-re-mi-fa-sol-la".
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