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. Other composers such as Béla Bartók, Luciano Berio, Benjamin Britten, Aaron Copland, Olivier Messiaen, Arvo Pärt, Walter Piston, Alfred Schnittke, Dmitri Shostakovich, Igor Stravinsky, 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.
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 what Arnold Schoenberg called "The Method of Composing with Twelve Notes related only to one another" (Schoenberg 1975, 218; Anon. [n.d.]), 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 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. 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 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.
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.
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.]). Many composers used modal organization, and others began to use alternate scales, sometimes within a tonal context provided by jazz. There was an increasing movement to avoid any particular chord or pitch as being central, which was described as atonal or pantonal. Some composers seeking to extend this direction in music began to search for ways to compose systematically.
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. 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.
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.
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. 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, 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. 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.
Major centers for serialism were the Darmstadt School and the "School of Paris" centered around Pierre Boulez.
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). 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).
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).
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. 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). 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).
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. Likewise, the mathematical analogues in integral serialism were influential in the development of electronic music and synthesized music. 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.
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).
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.
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 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).
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). 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.