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In the music theory of European classical music serialism is a set of methods for composing and analyzing works of music based on structuring those works around the parameterization of parts of music: that is, ordering pitch, dynamics, instrumentation, rhythm, and on occasion other elements into a row or series in which each gradation is assigned a numerical value within that series. In its strict definition each pitch, dynamic, colour or rhythmic element should only be used in its order in the series and used only once until the series repeats. The terms total serialism, integral serialism, and multiple serialism describe music which is serial in several parameters.

Important serial composers include Karlheinz Stockhausen, Pierre Boulez, Jean Barraqué and Mario Davidovsky. Many composers wrote (and continue to write) serial pieces, and elements of 12 tone practice have been used to a greater or lesser degree by composers for whom it was not a basic trait of style, such as Benjamin Britten, Aaron Copland, Arvo Pärt, Alfred Schnittke and Dmitri Shostakovich, and a wide range of composers from 1920 forward felt it important to incorporate or respond to the use of twelve tone techniques, not just in classical music, but in Jazz as well. The use of mathematical concepts to control musical parameters has influenced composers who have not adopted strict serial methods, including Elliott Carter and Iannis Xenakis. Integral serialism was influential in the development of electronic music and synthesized music. The first serial piece may have been Nummer 2 (1951) for 13 instruments ([1]) by Karel Goeyvaerts.

Basic definition

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. Serialism is often broadly applied to all music written in the what Arnold Schoenberg called "The Method of Composing with Twelve Tones related only to one another", or dodecaphony, and methods which evolved from his methods. 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 their 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. Another term used to make the distinction is 12 tone serialism.

Serialism has been described by its practioners as an extension and formalisation of earlier methods of 'cellular' thematic and motivic unification in classical and romantic music. This extension and formalisation is seen as having been motivated by the intensifying drive towards chromatic saturation and the resulting need to unify without using tonality.

Most serial music is deliberately structured as such. 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. Composing a serial work involves continually re-rhythmicising the various reappearances of the row in its Original, Retrograde, Inverted and Retrograde-Inverted forms as these are distributed through the various elements of the texture and employed to create accompaniments and subordinate parts as well as the main themes; each of these forms may also be transposed to begin on any note of the chromatic scale.

This row or series is used in one form as the "basic set", which constitutes the "center" of gravity for the piece. Each row or series is supposed to have three other forms: retrograde, or the basic set backwards, inverted, or the basic set "upside down" and retrograde-inverted, which is the basic set upside down and backwards. 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. The most common requirement is that first half and second half of the row not be inversions of each other. The series in itself may be regarded as pre-compositional material: in the process of composition it is manipulated by various means to produce musical material.

History of serial music

The serialization of rhythm, dynamics etc 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. Twelve-tone music is regarded by some as a sub-category of serialism, and by others serialism is seen as an outgrowth of twelve-tone music.

Twelve tone music

In the early 20th century composers in the european classical tradition began searching for other ways to organize works of music other than reliance on the ordered system of chords and intervals known as tonality. Many composers used modal organization, and others began to use alternate scales within a tonal context provided by jazz. There was an increasing movement to avoid any particular chord as being central, which was described as atonal or pantonal. Composers seeking to extend this direction in music began to search for ways to compose systematically.

Just after the First World War, Schoenberg began writing pieces with 12-note motives and using a procedure to "work with the notes of the motive". He analogized this process to the contrapunctal rules of Bach, arguing that as Bach's rules produced tonality without referencing it, so his rules produced a new basic means of structuring music which was not yet understood. It is for this reason that Schoenberg is often referred to as the "founder" or creator of serialism.

While Schoenberg was concerned with the serial ordering of pitch, his student Anton Webern began to relate other aspects of music to the basic row.

The politics of Nazi Germany intruded into the development of the musical idea. With the rise to power of Adolf Hitler and the implmentation of "race laws" with regard to ownership, culture and employment, many of the main composers of 12 music were placed on a list of Entartete musik ('Degenerate Music'), the Nazi term for all music that they disapproved of. There were two reasons, one was simply the nature of the composers as "jewish", the other was the Nazi ideas of art as part of the propaganda arm of the state. Avant-garde forms of art were thus banned, even if the artist was a political adherent of Nazism. With this regime's rise, Arnold Schoenberg was obliged to emigrate, eventually to America in 1933, and his works and those of his students Alban Berg and Anton Webern were banned.

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 Oliver 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. They created the term serialism to describe what they were doing, and argued that the Twelve Tone works of Webern, Schoenberg and others were also "serial" works. To differentiate 12 tone works from those with other forms of parameterization, the term "multiple serialism" was used, and if all parameters were serially controlled total serialism. Because of the Nazi repression, some young composers took serialism to be the advancing the cause of Anti-fascism. These included Stockhausen and Boulez. Réné Leibowitz, as composer, conductor, teacher and author was also influential in claiming the Second Viennese School as being the foundation for modern music. From these figures emerged two influential schools, the School of Paris around Pierre Boulez and a German school around Stockhausen.

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, though he himself felt his ideas were being discounted. 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. In many cases older composers were influenced to adopt tone rows or other serial procedures by their students, for example, Roger Sessions began to incorporate them in 1952, influenced by Milton Babbitt who was his student.

In the late 1950's Allen Forte began working on ways to describe atonal harmony, and to combine the methods of Heinrich Schenker, who was an ardent opponent of such music, with the developments in what was then contemporary music. He made extensive use of set notation, pitch classes and families and other terms which would later become standard in the description of serial composition. 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 aleatoric music, was enormously influential in post-War 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. Declaring itself "revolutionary" and "a new tonality", serialism created an environment where experimentation with sound, in a manner similar to the exploration of pure painting in Abstract Expressionism was at the forefront of composition, which led to increased use of electronics and other applications of mathematical notation to composition, developed by theorists such as the composer and mathematician Milton Babbitt.

Other composers to use serialism include Luigi Nono, who developed similar ideas separately, Roger Reynolds, and Charles Wuorinen, the later works of Igor Stravinsky and the early works of George Rochberg. Major centers for serialism were the Darmstadt School and the "School of Paris" centered around Pierre Boulez.

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 rythmic or harmonic implications (Shatzkin: "A Pre-Canticle Serialism in Stravinsky" 1977). Because many of the basic techniques of serial compositon have analogs in traditional counterpoint, uses of inversion, retrogarde 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. Over the course of the 1950's 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 Serialism's influence cut in two diections. As with the definition of Sonata form and tonality, one of the major intellectual projects was in analyzing previous works in the light of serial techniques, for example finding use of rows in previous composers going back to Mozart. The other was the use of serial forms of analysis and structuring of compositions even by composers who were not using a row or a series as the means of structuring a work. The use of set theory, classes and parameterization is found in the post-war works of Elliott Carter, Witold Lutoslawski and even farther afield to essentially tonal composers such as Alwyn, Shostakovich and Britten.

Serialism in the present

Reactions to and against serialism

Serialism never found wide favour with classical-music audiences, even though many composers adopted it in various forms. It is no exaggeration to say that it became, in theory at least, the favored means of expression for High modernism beginning around 1950, and for the next two or three decades it continued to be regarded, predominantly in the musical academia of the USA and Germany, as the most important principle of musical construction. Some theorized that it would provide the basis for integration of electronic music and aleatoric music; though in fact the latter, making recourse to chance procedures, evolved partly as a reaction against the over-controlled nature of Total Serialism. The various reactions against Serialism became matters of controversy in musical circles, helping to produce such movements as Minimalism (music) and Neo-Romanticism.

Part of the reason for the centrality of serialism in the debate over the meaning and direction of concert music is that it was far from alone in an attempt to systematize music, and root music theory in the modern age. At the same time that Schoenberg was working on his pantonal ideas, other experimental composers were attempting to define harmony in terms of fundamental and measurable qualities, such as rhythm. This attempt to found music on a more axiomic and rigorous basis formed the background for the introduction of the theories of the late 1940's and early 1950's. It was argued that serial music raised each note to specificity, an effect called pointalistic in analogy with the painting of Seurat.

The debate was often decidedly uncollegial: serial and other forms of avant garde music were condemned as being "not music", while proponents such as Pierre Boulez argued that "music exists in the avant garde or not at all". In the words of Roger Scruton (1997), "the order that exists in [serial compositions] is not an order that can be heard, when we hear the sounds as music." Academic departments often became battlegrounds, with professors trying to tilt the balance one direction or another. Ideologies formed around what constituted progress in music, and the history of music was retold, from different viewpoints, either to support the inevitability of serialism, or conversely to ground tonality in immutable realities.

Serialism also spawned a host of other attempts to incorporate process into music, including aleatory, or chance, music, and graphical notations which provided for wide ranging improvisation on the part of musicians. This might seem counter-intuitive given the assertion by may serial composers that serialism was about control over more and more of the score, but, in fact, it arose out of the desires for greater variety and texture to music, as expressed in the arguments in the 1950's over Total Serialism.

Within the community of modern music, exactly what constituted serialism was also a matter of debate. The wide conventional usage, is that the world "serial" music 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. However, many practioners, including Roger Sessions and Allen Forte argued that serialism was an historic outgrowth of a search for a new tonality, and that both were subsets of this wider search. Other practioners of serial music argued that individual elements should not be under serial control, but instead under some form of stochastic patterning, or that the large scale of the composition should be under serial control, but individual events at the selection of the composer, or the performer.

Serialism, because of its focus on process would give birth to process musics, for example of John Cage and the early Steve Riech works such as Drumming. Some process music would retain the concern for the "liberation of dissonance" that Schoenberg declared to be essential, while other composers would select largely consonant, or non-functionally dissonant materials.

Jazz artists in the middle of the 20th century began to work with serial and 12 tone techniques to expand the pallette of jazz music. Most of these attempts were of the compositional nature such as composer-pianist Bill Evans who wrote tunes like "12 Tone Tune". More recently you have to works of American guitarist Bruce Arnold who composes and improvises with 12 tone and serial techniques.

Even 75, or 55 depending on which version of history one subscribes to, years after its creation, serial music maintains its aura of being "difficult" and archtypically "modern". Critics routinely fall into stances which praise or condemn it as a catagorey, and works composed using serial techniques are considered "daring" programming choices. However, for every assertion of uniqueness, there are also critics that argue that fundamentally the much of the music is "very late Romanticism" raised to a very high level, and that it should be played with the same eye to harmonic richness and musical esthetic.

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. According to Boulez, "Classical tonal thought is based on a world defined by gravitation and attraction, serial thought on a world which is perpetually expanding." The latter types of metaphors-- which seek to closely associate contemporary art with contemporary science-- are typical of mid-twentieth century Modern composers.

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. This "basic" row is then used to create permutations, that is rows derrived from the basic set. 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 derrived from it which is used to create a new row, these are derrived sets.

Because there are tonal chord progressions which use all 12 notes, it is possible to create rows with very strong tonal implications, and even to write tonal music using 12 tone technique, but this is not the norm. Most tone rows contain tonal cells which imply a root pitch, a composer can therefore emphasize or avoid emphasizing the tonal cell.

To serialize other elements of music, a system of quantifying an identifiable element must be created or defined. For example, if duration is to be serialized, then a durations are to be specified. If tone colour, then the separate tone colours must be identified, and so on.

The selected set or sets, their permutations and derived sets form the basic material from which the composer works. Some serial works specify as little as possible, to give the composer the maximum amount of freedom when working, other works attempt to pre-compose as much as possible, which, taken to its limit is refered to as automatism.

Composition using serial methods focuses on each appearance of the set, called an aggregate. The theoretical ideal is that in an aggregate, no element 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". A work is said to be "aggregate complete" if only one aggregate is sounding at the same time.

An aggregate is divided into complements: a subset of the series, and all of those elements of the series not part of that subset are said to be complements of each other. A subset is self-complementing if it contains half of the set, and its complement is both 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 refered to as prime combinatorial. A hexachord which is self complementing for all basic permutations - Inversion, Retrograde and Retrograde Inversion - is referred to as all-combinatorial. The concepts of combinatoriality were explored by Schoenberg and Webern, but were rigorously defined and explored in the work of Milton Babbitt.

The composer then presents the aggregate. If only the basic row is serialized, while duration, tone colour and other parameters form free variables in the presentation. 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 is achieved through the use of combinatorial devices, for example, treating of a subset of the basic set to a series of combinatorial devices. The presentation of an aggregate corresponds to units of music in common practice harmony, in that when the listener has heard all of the materials of the aggregate, the know that new presentation of the aggregate should be expected to begin, with its own combinatorial presentation. The sequence of presentations of aggregates corresponds to the cadential structure of tonal harmony, in that it forms units which are complete unto themselves.

Important composers

External links


  • Serial Music Serial Aesthetics Grant, MJ & Whittall, Arnold S, (eds) 2002
  • Structure and Sorcery: The Aesthetetics of Post-War Serial Composition and Indeterminancy Savage, Roger Caldell, John (eds)
  • Atonal Music of Anton Webern Forte, Allen
  • New Grove:Modern Masters "Stravinsky" White, Eric Walter, Noble, Jeremy
  • Structure of Atonal Music Forte, Allen 1973
  • Basic Atonal Theory Rahn, John
  • Style and Idea Schoenberg Arnold
  • Serial Composition and Atonality:An Introduction to the Music of Schoenberg, Berg and Webern Perle, George
  • Serial Composition Brindle, Reginald-Smith 1966
  • Scruton, Roger (1997). Aesthetics of Music. Oxford: Clarendon Press. Quoted in The Pleasure of Modernist Music, p.122. ISBN 1580461433.


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