In music, serialism is a technique for composition that uses sets to describe musical elements, and allows the manipulation of those sets. Music is an Art form in which the medium is Sound organized in Time. Musical composition is an original piece of Music the structure of a musical piece the process of creating a new In musical set theory, a set is a collection of discrete entities for example pitch sets duration sets and Timbre sets (DeLone et al An aspect of music is any Characteristic, Dimension, or element taken as a part or component of Music. In Music, a permutation of a set is a transformation of its Prime form by applying zero or more of certain operations, specifically Serialism is often, though not universally, held to begin with twelve-tone technique, which uses a set of the 12 notes of the chromatic scale to form a row (a fixed sequence of the 12 tones of the chromatic scale) as the unifying basis for a composition's melody, harmony, structural progressions, and variations. Twelve-tone technique (also dodecaphony, especially in British usage twelve-note composition) is a method of musical composition devised by Arnold The chromatic scale is a Musical scale with twelve pitches each a Semitone or Half step apart In Music, a tone row or note row ( German: Reihe or Tonreihe) also series and set, refers to a non-repetitive In Music, a melody (from Greek μελῳδία - melōidía, "singing chanting" also tune, voice, or In Western music, harmony is the use of different pitches simultaneously and chords actual or implied in Music. Variation form Variation form include Ground bass, Passacaglia, Chaconne, and theme and variations When not used synonymously, serialism differs from twelve-tone technique in that any number of elements from any musical dimension (called "parameters"), such as duration, register, dynamics, or timbre, and/or pitches, may be ordered in sets of fewer or more than twelve elements. The term "series" should not be confused with the mathematical definition, which nevertheless comes into conjunction when the scales involved are projected from numerical sequences such as the arithmetic series, harmonic series (including its acoustical manifestation as the overtone series and its inversion, the so-called subharmonic series), geometric series, Fibonacci series, or infinity series. In Music, a scale is a group of musical notes collected in ascending and descending order that provides material for or is used to conveniently represent part or all In Mathematics, a sequence is an ordered list of objects (or events In Mathematics, an arithmetic progression or arithmetic sequence is a Sequence of Numbers such that the difference of any two successive members See Harmonic series (music for the (related musical concept In Mathematics, the harmonic series is the Infinite series Acoustics is the interdisciplinary science that deals with the study of Sound, Ultrasound and Infrasound (all mechanical waves in gases liquids and solids See Harmonic series (mathematics for the (related mathematical concept In Mathematics, a geometric progression, also known as a geometric sequence, is a Sequence of Numbers where each term after the first is found In Mathematics, the Fibonacci numbers are a Sequence of numbers named after Leonardo of Pisa, known as Fibonacci Per Nørgård (b July 13, 1932 in Gentofte, Denmark) is one of the most important Danish composers of the twentieth century

Important serial composers such as Arnold Schoenberg, Anton Webern, Alban Berg, Karlheinz Stockhausen, Pierre Boulez, Luigi Nono, and Jean Barraqué, went through extended periods of time in which they disciplined themselves always to use some variety of serialism in writing their music. Arnold Schoenberg ( pronounced ˈʃøːnbɛrk (13 September 1874 &ndash 13 July 1951 was an Austrian and later American Composer, associated with WikipediaWikiProject Composers#Lead section --> Anton Webern (December 3 1883 &ndash September 15 1945 was an Austrian Composer Alban Maria Johannes Berg (February 9 1885 &ndash December 24 1935 was an Austrian Composer. WikipediaWikiProject Classical music#Biographical_infoboxes --> Pierre Boulez (pjɛʁ buˈlɛz (b Luigi Nono ( January 29, 1924 – May 8, 1990) was an Italian Avant-garde Composer of Classical music Jean-Henri-Alphonse Barraqué ( January 17, 1928 &ndash August 17, 1973) was a French Composer and writer on music who Other composers such as Béla Bartók, Luciano Berio, Benjamin Britten, Aaron Copland, Arvo Pärt, Walter Piston, Alfred Schnittke, Dmitri Shostakovich, Igor Stravinsky, Henri Dutilleux and even some jazz composers such as Yusef Lateef and Bill Evans, used serialism only for some of their compositions or only for some sections of pieces. Béla Viktor János Bartók (March 25 1881&ndashSeptember 26 1945 was a Hungarian Composer and Pianist, considered to be one of the greatest Luciano Berio, Cavaliere di Gran Croce OMRI ( October 24, 1925 &ndash May 27, 2003) was an Italian Composer. Edward Benjamin Britten Baron Britten, OM CH (22 November 1913 – 4 December 1976 was an English Composer, conductor, Aaron Copland (November 14 1900 &ndash December 2 1990 was an American Composer of concert and film music as well as an accomplished Pianist. WikipediaWikiProject Composers#Lead section --> Arvo Pärt (born 11 September 1935 in Paide, Estonia) (ˈɑr̺vɔ Walter Hamor Piston Jr ( January 20, 1894 &ndash November 12, 1976) was an American composer and music theorist Alfred Garyevich Schnittke (Альфре́д Га́рриевич Шни́тке November 24, 1934 Engels - August 3, 1998 Hamburg Dmitri Dmitriyevich Shostakovich ( Russian: ru Дмитрий Дмитриевич Шостакович ( &ndash 9 August 1975 was a Russian Composer Igor Fyodorovich Stravinsky (Игорь Фёдорович Стравинский) ( &ndash 6 April 1971 was a Russian born Composer, considered by many to Henri Dutilleux (born January 22, 1916 in Angers France) is one of the most important French composers of the second half of the 20th century producing Jazz is an American Musical art form which originated in the beginning of the 20th century in African American communities in the Southern United States Dr Yusef Lateef (born William Emanuel Huddleston, October 9, 1920) is an American Jazz Multi-instrumentalist, Composer William John Evans (better known as Bill Evans) ( August 16, 1929 &ndash September 15, 1980) was one of the most famous and influential

Contents 1 Basic definition 2 History of serial music 2.1 Twelve-tone music 2.2 Serialism invented and described 2.3 Serialism and high modernism 2.4 Present 2.5 Reactions to and against serialism 3 Theory of serial music 4 Notable composers 5 References 6 External links

Basic definition

The use of the word "serial" in connection with music was first introduced in French by René Leibowitz (1947), and immediately afterward by Humphrey Searle in English, as an alternative translation of the German Zwölftontechnik Twelve-tone technique or Reihenmusik (row music); it was independently introduced by Herbert Eimert and Karlheinz Stockhausen into German in 1954 as serielle Musik, with a different meaning, translated into English also as "serial music". René Leibowitz (17 February 1913 &ndash 29 August 1972 was a French composer conductor music theorist and teacher born in Warsaw, Poland. Humphrey Searle ( August 26, 1915 - May 12, 1982) was a British Composer. Twelve-tone technique (also dodecaphony, especially in British usage twelve-note composition) is a method of musical composition devised by Arnold Herbert Eimert (born 8 April, 1897 in Bad Kreuznach, died 15 December, 1972 in Düsseldorf) was a German

Serialism is most specifically defined as the structural principle according to which a recurring series of ordered elements (normally a set—or 'row'—of pitches or 'pitch classes') which are used in order, or manipulated in particular ways, to give a piece unity. In Music, a pitch class is a set of all pitches that are a whole number of Octaves apart e Serialism is often broadly applied to all music written in what Arnold Schoenberg called "The Method of Composing with Twelve Notes related only to one another"^[1], or dodecaphony, and methods which evolved from his methods. Arnold Schoenberg ( pronounced ˈʃøːnbɛrk (13 September 1874 &ndash 13 July 1951 was an Austrian and later American Composer, associated with Twelve-tone technique (also dodecaphony, especially in British usage twelve-note composition) is a method of musical composition devised by Arnold It is sometimes used more specifically to apply only to music where at least one other element other than pitch is subjected to being treated as a row or series. The term Schoenbergian serialism is sometimes used to make the same distinction between use of pitch series only, particularly if there is an adherence to post-Romantic textures, harmonic procedures, voice-leading and other audible elements of 19th-century music. In such usages post-Webernian serialism will be used to denote works which extend serial techniques to other elements of music. Other terms used to make the distinction are 12-note serialism for the former, and integral serialism for the latter.

A row may be assembled 'pre-compositionally' (perhaps to embody particular intervallic or symmetrical properties), or it may be derived from a spontaneously invented thematic or motivic idea.

Each row or series is said to have three (or five) other canonical forms (the expression is borrowed from mathematics): retrograde (the basic set backwards), inversion (the basic set "upside down"), and retrograde-inversion (the basic set upside down and backwards), to which is sometimes added the M5 (perfect fourth) and M7 (perfect fifth) transformations. Generally in Mathematics, a canonical form (often called normal form or standard form) of an object is a standard way of presenting that object The basic set is usually required to have certain properties, and may have additional restrictions, such as the requirement that it use each interval only once. In Music theory, the term interval describes the relationship between the pitches of two Notes Intervals may be described as vertical The series in itself may be regarded as pre-compositional material: in the process of composition it is manipulated by various means to produce the musical substance.

Serial composition then involves the creation of classes of musical elements; dividing them into equipotential members, such as steps on the chromatic scale; and then using techniques of serial composition, presenting the original set or sets in a myriad of forms to create a work of music. Very generally the act of composition per se takes the form of fixing, or otherwise constraining, in the case of indeterminate music, a sequence of units with particular parameters.

Composers have often built their pieces from discrete, atomic units—in most cases one just calls them "notes"—that enjoy a fixed identity and status within an extended musical practice and beyond the confines of any one particular composition. To these units attach various quantifiable or at least decidable parameters: pitch, loudness, duration, onset time, articulation, timbre, spatial location, etc.

The first wave of post-war serialism focused on placing more and more of the musical elements in a piece under serial control. The serial composer aims to create musical meaning directly out the variation of parameters. This has led many serial composers to adopt a style that allows space for each individual unit to assert its identity, to "speak," often using a "punctual" or "pointillist" style modelled in part on the music of Webern as an example. Punctualism (commonly also called "pointillism" or "point music" is a style of musical composition prevalent in Europe between 1949 and 1955 "whose

History of serial music

The serialization of rhythm, dynamics, and other elements of music developed after the Second World War by arguing that the twelve-tone music of Arnold Schoenberg and his followers of the Second Viennese School had serialized pitch, and was partly fostered by the work of Olivier Messiaen and his analysis students, including Karel Goeyvaerts and Boulez, in post-war Paris. Rhythm (from Greek ῥυθμός - rhythmos, "any measured flow or movement symmetry" is the variation of the length and accentuation of In Music, dynamics normally refers to the volume of a Sound or note, but can also refer to every aspect of the execution of a given piece either stylistic Twelve-tone technique (also dodecaphony, especially in British usage twelve-note composition) is a method of musical composition devised by Arnold Arnold Schoenberg ( pronounced ˈʃøːnbɛrk (13 September 1874 &ndash 13 July 1951 was an Austrian and later American Composer, associated with The Second Viennese School is the term generally used in English -speaking countries to denote the group of Composers that comprised Arnold Schoenberg Olivier Messiaen ( December 10 1908 &ndash April 27 1992 was a French Composer, organist and ornithologist. Karel Goeyvaerts ( Antwerp 8 June 1923 – February 3 1993, Antwerp was a Belgian Composer. Paris (ˈpærɨs in English; in French) is the Capital of France and the country's largest city

Twelve-tone music

In the early 20th century composers began to struggle against the ordered system of chords and intervals known as "functional tonality", in an effort to find new forms of expression and underlying structural organizing principles (Delahoyd [n.d.]). Tonality is a system of Music in which specific hierarchical pitch relationships are based on a key "center" or tonic. Many composers used modal organization, and others began to use alternate scales, sometimes within a tonal context provided by jazz. In Music, a scale is an ordered series of Musical intervals which along with the key or tonic, define the pitches However mode Jazz is an American Musical art form which originated in the beginning of the 20th century in African American communities in the Southern United States There was an increasing movement to avoid any particular chord or pitch as being central, which was described as atonal or pantonal. Atonality in its broadest sense describes Music that lacks a tonal center, or key. Some composers seeking to extend this direction in music began to search for ways to compose systematically.

Serialism invented and described

The period after World War II represents the codification of serialism as a body of theory. Most of the major concepts were named, refined, and a series of notational conventions were developed in order to deal with the particular problems of serial composition.

After the Second World War, students of Olivier Messiaen saw Webern's structure, and Messiaen's techniques of parameterization as the next way forward in composition. They began creating individual sets or series for each element of music. The elements thus serially determined included the duration of notes, their dynamics, their orchestration, and many others. In Music, dynamics normally refers to the volume of a Sound or note, but can also refer to every aspect of the execution of a given piece either stylistic To differentiate these compositions from twelve-tone works, the terms "multiple serialism" or total serialism were used. René Leibowitz, as composer, conductor, teacher, and author was also influential in claiming the Second Viennese School as being the foundation for modern music. René Leibowitz (17 February 1913 &ndash 29 August 1972 was a French composer conductor music theorist and teacher born in Warsaw, Poland.

Schoenberg's arrival in the US in 1933 helped accelerate the acceptance of both twelve-tone music, and serialism more generally in American academia, at that time dominated by neo-classicism. Even before his death in 1951 two major theorists and composers, Milton Babbitt and George Perle, emerged as prominent figures actively involved with the analysis of serial music as well the creation of new works using sometimes radical extensions and revisions of the method. Milton Byron Babbitt (born May 10 1916 is an American Composer. George Perle (born May 6, 1915 in Bayonne New Jersey) is a Composer and music theorist.

In the late 1950s Allen Forte began working on ways to describe atonal harmony, making extensive use of set notation, pitch classes and families and other terms which would later become standard in the description of serial composition. Allen Forte (born December 23, 1926) is a music theorist and Musicologist. For example, in 1964 he published an article entilted "A Theory of Set-Complexes for Music". In 1973 he published the very influential work The Structure of Atonal Music.

Serialism and high modernism

Serialism, along with John Cage's indeterminate music (music composed with the use of chance operations), and Werner Meyer-Eppler's aleatoricism, was enormously influential in post-war music. WikipediaWikiProject Composers#Lead section --> John Milton Cage Jr Indeterminacy in music which began early in the twentieth century in the music of Charles Ives, and was continued in the 1930s by Henry Cowell and carried on by his Werner Meyer-Eppler (born 30 April 1913 in Antwerp, died 8 July 1960 in Bonn) was a German Physicist Aleatoric music (also aleatory music or chance music; from the Latin word alea, meaning " Dice " is Music Theorists such as George Perle codified serial systems, and his 1962 text Serial Composition and Atonality became a standard work on the origins of serial composition in the work of Schoenberg, Berg and Webern. George Perle (born May 6, 1915 in Bayonne New Jersey) is a Composer and music theorist. Alban Maria Johannes Berg (February 9 1885 &ndash December 24 1935 was an Austrian Composer.

Major centers for serialism were the Darmstadt School and the "School of Paris" centered around Pierre Boulez. Darmstadt School refers to a loose group of compositional styles created by composers who attended the Darmstadt International Summer Courses for New Music from the

Several of the composers associated with Darmstadt, notably Karlheinz Stockhausen, Karel Goeyvaerts, and Henri Pousseur developed a form of serialism which initially rejected the recurring rows characteristic of twelve-tone technique, in order to eradicate any lingering traces of thematicism (Felder 1977, 92). Karel Goeyvaerts ( Antwerp 8 June 1923 – February 3 1993, Antwerp was a Belgian Composer. Henri Pousseur (born 23 June 1929, Malmedy) is a Belgian Composer. In Music, a theme is the initial or primary Melody. The Encyclopédie Fasquelle (Michel 1958–61 defines a theme as follows "Any Instead of a recurring, referential row, "each musical component is subjected to control by a series of numerical proportions" (Morgan 1975, 3). In Europe, the style of some serial as well as non-serial music of the early 1950s emphasized the determination of all parameters for each note independently, often resulting in widely spaced, isolated "points" of sound, an effect called first in German "punktuelle Musik" ("pointist" or "punctual music"), then in French "musique ponctuelle", but quickly confused with "pointillistic" (German "pointillistische", French "pointilliste") the familiar term associated with the densely packed dots in paintings of Seurat, despite the fact that the conception was at the opposite extreme (Stockhausen and Frisius 1998, 451). Punctualism (commonly also called "pointillism" or "point music" is a style of musical composition prevalent in Europe between 1949 and 1955 "whose See also Neo-Impressionism Pointillism is a style of Painting in which small distinct points of Primary colors create the impression of a wide selection Georges-Pierre Seurat ( December 2, 1859  &ndash March 29, 1891) was a French painter and Draftsman.

Integral serialism had demanded that all parameters in a work be treated as scaled sets (not necessarily in fixed successions) with an equal right to participate in the compositional process, but beginning in the mid-1950s, Stockhausen and others began to focus on "serial principles" as well as methods. Pieces were structured by closed sets of proportions, a method closely related to certain works from the de Stijl and Bauhaus movements in design and architecture called "serial art" by some writers (Bochner 1967, Sykora 1983, Guderian 1985), specifically the paintings of Piet Mondrian, Theo van Doesberg, Bart van Leck, Georg van Tongerloo, Richard Paul Lohse, and Burgoyne Diller, who had been seeking to “avoid repetition and symmetry on all structural levels and working with a limited number of elements” (Bandur 2001, 54). For the album by The White Stripes see De Stijl (album. De Stijl (in English, generally də ˈstaɪl after style; from the ("House of Building" or "Building School" is the common term for the, a school in Germany that combined crafts and the fine arts and was famous Pieter Cornelis (Piet Mondriaan, after 1912 Mondrian, (pronounced Dutch pit 'mɔndrian later pit 'mɔndɹiɔn ( March 7, 1872 &ndash February Theo van Doesburg ( Utrecht, August 30, 1883 &ndash Davos, March 7, 1931) was a Dutch artist practicing in Burgoyne A Diller (1906 &ndash 1965 was an American abstract painter

Stockhausen described the final synthesis in this manner:

So serial thinking is something that's come into our consciousness and will be there forever: it's relativity and nothing else. It just says: Use all the components of any given number of elements, don't leave out individual elements, use them all with equal importance and try to find an equidistant scale so that certain steps are no larger than others. It's a spiritual and democratic attitude toward the world. The stars are organized in a serial way. Whenever you look at a certain star sign you find a limited number of elements with different intervals. If we more thoroughly studied the distances and proportions of the stars we'd probably find certain relationships of multiples based on some logarithmic scale or whatever the scale may be. (Cott 1973, 101)

Igor Stravinsky's adoption of serial techniques offers an example of the level of influence that serialism had after the Second World War. Previously Stravinsky had used series of notes without rhythmic or harmonic implications (Shatzkin 1977). Because many of the basic techniques of serial composition have analogs in traditional counterpoint, uses of inversion, retrograde and retrograde inversion from before the war are not necessarily indicative of Stravinsky adopting Schoenbergian techniques. However with his meeting Robert Craft and acquaintance with younger composers, Stravinsky began to consciously study Schoenberg's music, as well as the music of Webern and later composers, and began to use the techniques in his own work, using, for example, serial techniques applied to fewer than 12 notes. Robert Lawson Craft (born October 20, 1923) is an American conductor and writer Over the course of the 1950s he used procedures related to Messiaen, Webern and Berg. While it is difficult to label each and every work as "serial" in the strict definition, every major work of the period has clear uses and references to its ideas.

During this period, the concept of serialism influenced not only new compositions but also the scholarly analysis of the classical masters. Adding to their professional tools of sonata form and tonality, scholars began to analyze previous works in the light of serial techniques; for example they found the use of row technique in previous composers going back to Mozart (Keller 1955). Sonata form is a Musical form that has been used widely since the early Classical period. Tonality is a system of Music in which specific hierarchical pitch relationships are based on a key "center" or tonic. In particular, using the analytical tools of serialism, scholars noted that the orchestral outburst that introduces the development section half-way through the last movement of Mozart's next-to-last symphony is a tone row that Mozart punctuates in a very modern and violent episode that Michael Steinberg called "rude octaves and frozen silences" (Steinberg 1998:400). Sonata form is a Musical form that has been used widely since the early Classical period.

Furthermore, the organizing principles of serialism inspired mathematical analogues, such as uses of set theory, group theory, operators, and parametrization, for example in the post-war works of Elliott Carter, Iannis Xenakis, and Witold Lutosławski. Musical set theory provides concepts for categorizing musical objects and describing their relationships Group theory is a mathematical discipline the part of Abstract algebra that studies the Algebraic structures known as groups. In Mathematics, an operator is a function which operates on (or modifies another function In Mathematics, Statistics, and the mathematical Sciences a parameter ( G auxiliary measure) is a quantity that defines certain characteristics Elliott Cook Carter Jr (born in New York City on December 11, 1908) is an American Composer from New York City. Iannis Xenakis (Ιάννης Ξενάκης (May 29 1922 - February 4 2001 was a Greek modernist composer musical theoretician and architect Witold Lutosławski ( January 25 1913 &ndash February 7 1994 was one of the major European Composers Likewise, the mathematical analogues in integral serialism were influential in the development of electronic music and synthesized music. Electronic music is music that employs Electronic musical instruments and Electronic Music technology in its production The first European piece using total serialism may have been Nummer 2 (1951) for 13 instruments by Karel Goeyvaerts, although in America Milton Babbitt's Three Compositions for Piano (1947) is also credited with being the earliest total serial piece. Nummer 2 for thirteen instruments (1951 by Karel Goeyvaerts, (also called Opus 2 for thirteen instruments) has been claimed to be the first "total Karel Goeyvaerts ( Antwerp 8 June 1923 – February 3 1993, Antwerp was a Belgian Composer. Milton Byron Babbitt (born May 10 1916 is an American Composer.

Present

Reactions to and against serialism

Some music theorists have criticized serialism on the basis that the compositional strategies employed are often incompatible with the way information is extracted by the human mind from a piece of music. Nicolas Ruwet (1959) was one of the first to criticise serialism through a comparison with linguistic structures. Henri Pousseur (1959) questioned the equivalence made by Ruwet between phoneme and the single note, and suggested that analyses of serial compositions that Ruwet names as exceptions to his criticisms might "register the realities of perception more accurately. Henri Pousseur (born 23 June 1929, Malmedy) is a Belgian Composer. " Later writers have continued Ruwet's line of reasoning. Fred Lerdahl, for example, outlines this subject further in his essay "Cognitive Constraints on Compositional Systems" (Lerdahl 1988). Fred Lerdahl 's "Cognitive Constraints on Compositional Systems" cites Pierre Boulez 's Le Marteau sans Maître (1955 as an example Lehrdahl has in turn been criticized for excluding "the possibility of other, non-hierarchical methods of achieving musical coherence," and for concentrating on the audibility of tone rows (Grant 2001, 219), and the portion of his essay focussing on Boulez's "multiplication" technique (exemplified in three movements of Le Marteau sans maître) has been challenged on perceptual grounds by Stephen Heinemann (1998) and Ulrich Mosch (2004).

Within the community of modern music, exactly what constituted serialism was also a matter of debate. The conventional English usage is that the word "serial" applies to all 12-tone music, which is a "subset" of serial music, and it is this usage that is generally intended in reference works. Nevertheless, a large body of music exists that is called "serial" but does not employ note-rows at all, let alone twelve-tone technique (e. g. , Stockhausen's Stimmung, Pousseur's Scambi). Stimmung, for six vocalists and six microphones is a piece by Karlheinz Stockhausen, written in 1968 and commissioned by the City of Cologne for the Collegium

Theory of serial music

The vocabulary of serialism is rooted in set theory, and uses a quasi-mathematical language to describe how the basic sets are manipulated to produce the final result. Musical set theory is often used to analyze and compose serial music, but may also be used to study tonal music and nonserial atonal music. Musical set theory provides concepts for categorizing musical objects and describing their relationships Tonality is a system of Music in which specific hierarchical pitch relationships are based on a key "center" or tonic. Atonality in its broadest sense describes Music that lacks a tonal center, or key.

The basis for serial composition is Schoenberg's twelve-tone technique, where the 12 notes of the basic chromatic scale are organized into a row. Twelve-tone technique (also dodecaphony, especially in British usage twelve-note composition) is a method of musical composition devised by Arnold This "basic" row is then used to create permutations, that is, rows derived from the basic set by reordering its elements. The row may be used to produce a set of intervals, or a composer may have wanted to use a particular succession of intervals, from which the original row was created. A row which uses all of the intervals in their ascending form once is an all-interval row. In addition to permutations, the basic row may have some set of notes derived from it which is used to create a new row, these are derived sets.

Because there are tonal chord progressions which use all 12 notes, it is possible to create pitch rows with very strong tonal implications, and even to write tonal music using 12-tone technique. Most tone rows contain subsets that can imply a pitch center; a composer can create music centered on one or more of the row's constituent pitches by emphasizing or avoiding these subsets, respectively, as well as through other, more complex compositional devices (Newlin 1974; Perle 1977). The tonic is the first note of a musical scale in the tonal method of Musical composition.

To serialize other elements of music, a system quantifying an identifiable element must be created or defined (this is called "parametrization", after the term in mathematics). Parameterization (or parametrization parameterisation in British English) is the process of defining or deciding the Parameters - usually of some model - that are For example, if duration is to be serialized, then a set of durations must be specified. If tone colour, then the a set of separate tone colours must be identified, and so on.

The selected set or sets, their permutations and derived sets form the basic material with which the composer works.

Composition using 12-tone serial methods focuses on each appearance of the collection of twelve chromatic notes, called an aggregate. (Sets of more or fewer pitches, or of elements other than pitch may be treated analogously. ) The principle is that in a row, no element of the aggregate should be reused until all of the other members have been used, and each member must appear only in its place in the series. This rule is violated in numerous works still termed "serial".

An aggregate may be divided into subsets, and all the members of the aggregate not part of any one subset are said to be its complement. A subset is self-complementing if it contains half of the set and its complement is also a permutation of the original subset. This is most commonly seen with hexachords or 6 notes of a basic tone row. A hexachord which is self-complementing for a particular permutatition is referred to as prime combinatorial. A hexachord which is self complementing for all of the canonic operations – Inversion, Retrograde and Retrograde Inversion – is referred to as all-combinatorial.

The composer then presents the aggregate. If there are multiple serial sets, or if several parameters are associated with the same set, then a presentation will have these values calculated. Large-scale design may be achieved through the use of combinatorial devices, for example, subjecting a subset of the basic set to a series of combinatorial devices.

Notable composers

Further information: List of pieces which use serialism

Gilbert Amy Louis Andriessen Hans Erich Apostel Kees van Baaren Milton Babbitt Don Banks Jean Barraqué Alban Berg Arthur Berger Erik Bergman Luciano Berio André Boucourechliev Pierre Boulez Martin Boykan Jacques Calonne Niccolò Castiglioni Aldo Clementi Aaron Copland Luigi Dallapiccola Franco Donatoni Hanns Eisler Karlheinz Essl Franco Evangelisti Brian Ferneyhough Irving Fine Roberto Gerhard Frans Geysen Alberto Ginastera - middle and late periods Lucien Goethals

Karel Goeyvaerts Glenn Gould Lou Harrison Jonathan Harvey Hermann Heiss Hans Werner Henze York Höller Heinz Holliger Bill Hopkins Klaus Huber Hanns Jelinek Ben Johnston Rudolf Kelterborn Gottfried Michael Koenig Józef Koffler Ernst Krenek René Leibowitz Ingvar Lidholm Bruno Maderna Ursula Mamlok Philippe Manoury Donald Martino Paul Méfano Jacques-Louis Monod Robert Morris Luigi Nono Per Nørgård Krzysztof Penderecki - early period Barbara Pentland

Goffredo Petrassi Michel Philippot Walter Piston Henri Pousseur Roger Reynolds Terry Riley George Rochberg - middle period Peter Schat Dieter Schnebel Arnold Schoenberg - middle/late period Humphrey Searle Mátyás Seiber Roger Sessions Nikos Skalkottas Roger Smalley Ann Southam Leopold Spinner Karlheinz Stockhausen Igor Stravinsky - late period Richard Swift Camillo Togni Gilles Tremblay Wladimir Vogel Anton Webern Hugo Weisgall Peter Westergaard Stefan Wolpe Charles Wuorinen La Monte Young

References

• Bandur, Markus. List of pieces which use serialism, by composer Pierre Boulez Structures book I for two pianos Gilbert Amy (born August 29, 1936, Paris) is a French Composer and conductor. Louis Andriessen ( June 6, 1939) is a Dutch Composer and pianist based in Amsterdam. Hans Erich Apostel (1901 in Karlsruhe – 1972 in Vienna) was a German -born Austrian Composer of classical music. Kees van Baaren (born 22 October 1906 in Enschede &ndash died 2 September 1970 in Oegstgeest) was a Dutch composer and Milton Byron Babbitt (born May 10 1916 is an American Composer. Donald Oscar Banks (25 October 1923 - 5 September 1980 was an Australian composer of concert jazz and commercial music Jean-Henri-Alphonse Barraqué ( January 17, 1928 &ndash August 17, 1973) was a French Composer and writer on music who Alban Maria Johannes Berg (February 9 1885 &ndash December 24 1935 was an Austrian Composer. Arthur Berger ( May 15 1912 in New York City –- October 7 2003 in Boston Massachusetts was a Composer who has been described as Luciano Berio, Cavaliere di Gran Croce OMRI ( October 24, 1925 &ndash May 27, 2003) was an Italian Composer. André Boucourechliev ( July 28, 1925 &ndash November 13, 1997) was a French composer of Bulgarian origin WikipediaWikiProject Classical music#Biographical_infoboxes --> Pierre Boulez (pjɛʁ buˈlɛz (b Martin Boykan (born 1931 studied composition with Walter Piston, Aaron Copland and Paul Hindemith, and piano with Eduard Steuermann. Jacques Calonne (born 1930 in Mons) is a Belgian artist composer singer actor Logogramist and writer Niccolò Castiglioni ( July 17 1932 &ndash September 7 1996) was an Italian Composer, Pianist, and writer Aldo Clementi (born May 25, 1925 in Catania Italy) is an Italian composer Aaron Copland (November 14 1900 &ndash December 2 1990 was an American Composer of concert and film music as well as an accomplished Pianist. Luigi Dallapiccola ( February 3, 1904 &ndash February 19, 1975) was an Italian Composer known for his lyrical twelve-tone Franco Donatoni ( 9 June 1927 – 17 August 2000) was an Italian Composer. Hanns Eisler ( July 6, 1898 &ndash September 6, 1962) was a German and Austrian Composer. Karlheinz Essl (born August 15, 1960 in Vienna) is an Austrian Composer, performer sound artist improviser and composition Franco Evangelisti (born January 21, 1926 in Rome, died there January 28, 1980) was an Italian Composer specifically interested Brian John Peter Ferneyhough (born 16 January, 1943 in Coventry) is an English Composer. Irving Gifford Fine ( December 3 1914 &ndash August 23 1962) was an American Composer. Frans Geysen (born 29 July 1936) is a Belgian Composer and writer on music Alberto Evaristo Ginastera ( Buenos Aires, April 11 1916 &ndash June 25 1983 Geneva) was an Argentine Composer of classical music Lucien Goethals (born 26 June 1931 is a Belgian composer Lucien Goethals was born in Ghent, but spent his formative years in Argentina, where he studied Karel Goeyvaerts ( Antwerp 8 June 1923 – February 3 1993, Antwerp was a Belgian Composer. Glenn Herbert Gould At a young age he reportedly behaved differently from typical children at the piano he would strike single notes and listen to their long decay Lou Silver Harrison ( May 14, 1917 &ndash February 2, 2003) was an American Jonathan Harvey (born 3 May, 1939 in Sutton Coldfield) is a British composer Hans Werner Henze (born July 1 1926 Gütersloh, Germany is a German composer well known for his left-wing political convictions York Höller (born 11 January 1944 in Leverkusen) is a German composer and Professor of composition at the Hochschule für Musik Heinz Holliger (born) is a Swiss oboist, Composer and conductor. GW (Bill Hopkins ( 5 June, 1943 – 10 March, 1981) was a British composer pianist and music critic Klaus Huber (born November 30, 1924 in Bern, Switzerland) is a Swiss composer Hanns Jelinek ( December 5, 1901 &ndash January 27, 1969) was an Austrian Composer of Czech descent who is also Benjamin Burwell Johnston Junior (born March 15, 1926 in Macon Georgia) is a composer of Contemporary music in the Just intonation Rudolf Kelterborn (born September 3, 1931, Basel) is a Swiss musician and Composer. Gottfried Michael Koenig (born October 5, 1926 in Magdeburg) is a contemporary German-Dutch composer Józef Koffler (November 28 1896–1944 was a Polish Composer, music teacher Musicologist and musical Columnist. Ernst Krenek ( August 23 1900 &ndash December 22 1991) was an Austrian born (and from 1945 an American) Composer René Leibowitz (17 February 1913 &ndash 29 August 1972 was a French composer conductor music theorist and teacher born in Warsaw, Poland. Ingvar Natanael Lidholm (born February 24, 1921) is a Swedish composer Bruno Maderna ( 21 April 1920 &ndash 13 November 1973) was an Italian - German conductor and Composer Ursula Mamlok (born 1 Feb, 1928) is a German-born American Composer and Teacher. Philippe Manoury (born June 19, 1952) is a French Composer. Biography Philippe Manoury was born in Tulle. Donald Martino ( May 16, 1931 – December 8, 2005) was a Pulitzer Prize winning American Composer. Paul Méfano ( Basra ( Iraq) 6 March 1937) is a French Composer and conductor. Jacques-Louis Monod (born February 25, 1927) is an influential French-born, American domiciled Composer, Pianist and Robert Morris (born October 19, 1943 in Cheltenham, England) is an American composer and music theorist Luigi Nono ( January 29, 1924 – May 8, 1990) was an Italian Avant-garde Composer of Classical music Per Nørgård (b July 13, 1932 in Gentofte, Denmark) is one of the most important Danish composers of the twentieth century Krzysztof Penderecki (ˈkʂɨʂtɔf pɛndɛrˈɛ͡tski born November 23 1933 in Dębica) is a Polish Composer and conductor of classical Barbara Pentland (1912-2000 was one of the pre-eminent members of the generation of Canadian Composers who came to artistic maturity in the years following World War Two Goffredo Petrassi ( 16 July 1904 &ndash 3 March 2003) was an Italian Composer of Modern classical music, Michel Paul Philippot (born 2 February 1925 in Verzy, died 28 July 1996 in Vincennes) was a French Composer Walter Hamor Piston Jr ( January 20, 1894 &ndash November 12, 1976) was an American composer and music theorist Henri Pousseur (born 23 June 1929, Malmedy) is a Belgian Composer. American Composer and teacher at the University of California at San Diego Roger Reynolds was born July 18, 1934 in Detroit, Michigan Terry Riley (born June 24 1935) is an American composer associated with the minimalist school George Rochberg, ( July 5, 1918, Paterson New Jersey &ndash May 29, 2005, Bryn Mawr Pennsylvania) was an American Peter Schat ( June 5, 1935, in Utrecht - February 10 2003, in Amsterdam) was a Dutch Composer. Dieter Schnebel (born March 14 1930 in Lahr / Baden) is a Composer. Arnold Schoenberg ( pronounced ˈʃøːnbɛrk (13 September 1874 &ndash 13 July 1951 was an Austrian and later American Composer, associated with Humphrey Searle ( August 26, 1915 - May 12, 1982) was a British Composer. Mátyás Seiber ( May 4, 1905 &ndash September 24, 1960) was a Hungarian -born Composer who lived in England Roger Huntington Sessions ( 28 December 1896 &ndash 16 March 1985) was an American Composer, critic and teacher of music Nikos Skalkottas (Nίκος Σκαλκώτας ( 21 March, 1904 &ndash 19 September, 1949) was one of Roger Smalley (born 26 July 1943 in Manchester, UK) is a British- Australian Composer, pianist and conductor Ann Southam (born in Winnipeg on 4 February 1937) is a Canadian Composer. Leopold Spinner ( 26 April 1906 - 12 August 1980) Ukrainian-born British-domiciled composer and editor Igor Fyodorovich Stravinsky (Игорь Фёдорович Стравинский) ( &ndash 6 April 1971 was a Russian born Composer, considered by many to Richard Swift (b Middlepoint OH 24 September 1927; d Davis CA 8 November 2003) was an American composer and music theorist Camillo Togni (b 18 October 1922 in Gussago, near Brescia; d 28 November 1993 in Brescia) was an Italian composer Gilles Tremblay (born September 6, 1932) is a Canadian composer Wladimir Rudolfowitsch Vogel (b 17 February / 29 February 1896 in Moscow; d WikipediaWikiProject Composers#Lead section --> Anton Webern (December 3 1883 &ndash September 15 1945 was an Austrian Composer Hugo David Weisgall ( October 13, 1912 – March 11, 1997) was an American Composer, known chiefly for Opera Peter Talbot Westergaard (born 1931) is an American Composer and Music theorist. Stefan Wolpe ( August 25, 1902 &ndash April 4, 1972) was a German -born Composer. Charles Wuorinen (b June 9, 1938 in New York City is an American Composer. La Monte Thornton Young (born October 14 1935) is an American Composer and musician 2001. Aesthetics of Total Serialism: Contemporary Research from Music to Architecture. Basel, Boston and Berlin: Birkhäuser.
• Bochner, Mel. 1967. "The Serial Attitude". Artforum 6, no. 4 (December): 28–33.
• Cott, Jonathan. 1973. Stockhausen; Conversations with the Composer, New York: Simon & Schuster.
• Delahoyd, Michael. [n. d. ]. "http://www.wsu.edu/~delahoyd/20th/music.intro.html 20th-Century Music]". Author's website, Washington State University.
• Felder, David. 1977. “An Interview with Karlheinz Stockhausen. ” Perspectives of New Music 16, no. 1 (Fall-Winter): 85–101.
• Forte, Allen. 1964. "A Theory of Set-Complexes for Music. " Journal of Music Theory 8, no. 2 (Winter): 136-84.
• Forte, Allen. 1973. The Structure of Atonal Music. New Haven and London: Yale University Press.
• Forte, Allen. 1998. The Atonal Music of Anton Webern. New Haven: Yale University Press.
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• Lerdahl, Fred, and Ray Jackendoff. 1983. A Generative Theory of Tonal Music. Cambridge, Mass. : MIT Press.
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• Pousseur, Henri. 1959. “Forme et pratique musicales. ” Revue Belge de Musicologie 13:98–116. Slightly revised and expanded version, trans. into English as “Music, Form and Practice (An Attempt to Reconcile Some Contradictions) ”, Die Reihe 6 (1964): 77–93.
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• Ruwet, Nicolas. 1959. “Contradictions du langage sériel. ” Revue Belge de Musicologie 13 (1959), 83–97. English trans. , as “Contradictions within the Serial Language”, Die Reihe 6 (1964): 65–76.
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External links

• Art of the States: serial/twelve-note serial and/or twelve-note works by American composers.
• The tone row in the last movement of Mozart's Symphony No. 40. Beginning at Bar 128 on page 54, the tone row might be the following: B, C, D, Eb, F#, Bb, C#, F, G#, A, E, G -- where the exposition of the last three notes of the tone row trails into the sounding of the A major dominant chord for the d minor development section that follows. In Music, a tone row or note row ( German: Reihe or Tonreihe) also series and set, refers to a non-repetitive The first page of Mozart's Symphony No. 40 can be found at this link.

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