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In music, serialism is a method or technique of composition (Griffiths 2001, 116) that uses a series of values to manipulate different musical elements. Serialism began primarily with Arnold Schoenberg's twelve-tone technique, though his contemporaries were also working to establish serialism as one example of post-tonal thinking (Whittall 2008, 1). Twelve-tone technique orders the 12 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 (often called "parameters"), such as duration, dynamics, and timbre. The idea of serialism is also applied in various ways in the visual arts, design, and architecture (Bandur 2001, 5, 12, 74; Gerstner 1964, passim). The musical use of the word "series" should not be confused with the mathematical term "series".
Integral serialism or total serialism is the use of series for aspects such as duration, dynamics, and register as well as pitch (Whittall 2008, 273). Other terms, used especially in Europe to distinguish post–World War II serial music from twelve-tone music and its American extensions, are general serialism and multiple serialism (Grant 2001, 5–6).
Composers such as Arnold Schoenberg, Anton Webern, Alban Berg, Karlheinz Stockhausen, Pierre Boulez, Luigi Nono, Milton Babbitt, and Jean Barraqué used serial techniques of one sort or another in most of their music. Other composers such as Béla Bartók, Luciano Berio, Benjamin Britten, John Cage, Aaron Copland, Olivier Messiaen, Arvo Pärt, Walter Piston, Ned Rorem, Alfred Schnittke, Dmitri Shostakovich, and Igor Stravinsky used serialism only for some of their compositions or only for some sections of pieces, as did some jazz composers such as Yusef Lateef and Bill Evans.
Serialism is a method (Griffiths 2001, 116), "highly specialized technique" (Wörner 1973, 196), or "way" (Whittall 2008, 1) of composition. It may also be considered, "a philosophy of life (Weltanschauung), a way of relating the human mind to the world and creating a completeness when dealing with a subject" (Bandur 2001, 5).
However, serialism is not by itself a system of composition, nor is it a style. Neither is pitch serialism necessarily incompatible with tonality, though it is most often used as a means of composing atonal music (Griffiths 2001, 116).
"Serial music" is a problematic term because it is used differently in different languages and especially because, shortly after its coinage in French, it underwent essential alterations during its transmission to German (Frisius 1998, 1327). 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".
Serialism of the first type 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) 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 that 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. In such usages post-Webernian serialism will be used to denote works that 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. The structure of the row, however, does not in itself define the structure of a composition, which requires development of a comprehensive strategy. The choice of available strategies will of course depend on the relationships contained in a row class, and rows may be constructed with an eye to producing the relationships needed to form desired strategies (Mead 1985, 129–30).
The basic set may have additional restrictions, such as the requirement that it use each interval only once.
The series is not an order of succession, but indeed a hierarchy—which may be independent of this order of succession. (Boulez 1954,[page needed], translated in Griffiths 1978, 37)
Rules of analysis derived from twelve-tone theory do not apply to serialism of the second type: "in particular the ideas, one, that the series is an intervallic sequence, and two, that the rules are consistent" (Maconie 2005, 119). Stockhausen, for example, in early serial compositions such as Kreuzspiel and Formel, "advances in unit sections within which a preordained set of pitches is repeatedly reconfigured. . . . The composer’s model for the distributive serial process corresponds to a development of the Zwölftonspiel of Josef Matthias Hauer" (Maconie 2005, 56), and Goeyvaerts, in such a work as Nummer 4,
provides a classic illustration of the distributive function of seriality: 4 times an equal number of elements of equal duration within an equal global time is distributed in the most equable way, unequally with regard to one another, over the temporal space: from the greatest possible coïncidence to the greatest possible dispersion. This provides an exemplary demonstration of that logical principle of seriality: every situation must occur once and only once. (Sabbe 1977, 114)
For Henri Pousseur, after an initial period working with twelve-tone technique in works like Sept Versets (1950) and Trois Chants sacrés (1951), serialism
evolved away from this bond in Symphonies pour quinze Solistes [1954–55] and in the Quintette [à la mémoire d’Anton Webern, 1955], and from around the time of Impromptu  encounters whole new dimensions of application and new functions.
The twelve-tone series loses its imperative function as a prohibiting, regulating, and patterning authority; its working-out is abandoned through its own constant-frequent presence: all 66 intervallic relations among the 12 pitches being virtually present. Prohibited intervals, like the octave, and prohibited successional relations, such as premature note repetitions, frequently occur, although obscured in the dense contexture. The number twelve no longer plays any governing, defining rôle; the pitch constellations no longer hold to the limitation determined by their formation. The dodecaphonic series loses its significance as a concrete model of shape (or a well-defined collection of concrete shapes) is played out. And the chromatic total remains active only, and provisionally, as a general reference. (Sabbe 1977, 264)
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.]).
Twelve-tone serialism first appeared in the 1920s, with antecedents predating that decade. Schoenberg was the composer most decisively involved in devising and demonstrating the fundamentals of twelve-tone serialism, though it is clear it is not the work of just one musician (Whittall 2008, 1).
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.
The serialization of rhythm, dynamics, and other elements of music was partly fostered by the work of Olivier Messiaen and his analysis students, including Karel Goeyvaerts and Boulez, in post-war Paris.
Several of the composers associated with Darmstadt, notably Karlheinz Stockhausen, Karel Goeyvaerts, and Henri Pousseur developed a form of serialism that 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).
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, Gerstner 1964, Guderian 1985, Sykora 1983), specifically the paintings of Piet Mondrian, Theo van Doesburg, 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 twelve-tone 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 and Beethoven (Jalowetz 1944, 387; Keller 1955, passim). In particular, 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).
Ruth Crawford Seeger is credited with extending serial controls to parameters other than pitch and to formal planning as early as 1930–33 (Tick 2001).
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, citing theoretical claims by Boulez and Henri Pousseur, and taking as specific examples bars from Stockhausen's Klavierstücke I & II, and calling for a general re-examination of Webern's music. Ruwet specifically names three works as exempt from his criticism: Stockhausen's Zeitmaße and Gruppen, and Boulez's Le marteau sans maître (Ruwet 1959, 83, 85, 87, 93–96).
In response, Pousseur (1959) questioned the equivalence made by Ruwet between phoneme and the single note. He also suggested that, if analysis of Le marteau sans maître and Zeitmaße, "performed with sufficient insight", were to be made from the point of view of wave theory—taking into account the dynamic interaction of the different component phenomena, which creates "waves" that interact in a sort of frequency modulation—this analysis "would accurately reflect the realities of perception". This was because these composers had long since acknowledged the lack of differentiation found in punctual music and, becoming increasingly aware of the laws of perception and complying better with them, "paved the way to a more effective kind of musical communication, without in the least abandoning the emancipation that they had been allowed to achieve by this 'zero state' that was punctual music". This was achieved, amongst other things, by the development of the concept of "groups", which allows structural relationships to be defined not only between individual notes but also at higher and higher levels, up to the overall form of a piece. This is "a structural method par excellence", and a sufficiently simple conception that it remains easily perceptible (Pousseur 1959, 104–105, 114–15). Pousseur also points out that serial composers were the first to recognize and attempt to move beyond the lack of differentiation within certain pointillist works (Campbell 2010, 125). Pousseur later followed up his own suggestion, by developing his idea of "wave" analysis and applying it to Stockhausen's Zeitmaße in two essays, Pousseur 1970 and Pousseur 1997.
Later writers have continued both lines of reasoning. Fred Lerdahl, for example, outlines Ruwet's subject further in his essay "Cognitive Constraints on Compositional Systems" (Lerdahl 1988). 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). Ruwet's critique has also been criticised for making "the fatal mistake of equating visual presentation (a score) with auditive presentation (the music as heard)" (Grant 2006, 351).
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 Klavierstücke I–IV (the focus of Ruwet's criticism, they use permuted sets), as well as his Stimmung (with pitches from the overtone series, which also is used as the model for the rhythms) and Pousseur's Scambi (where the permuted sounds are made exclusively from filtered white noise).
When serialism is not equated with twelve-tone technique, a contributing problem is that the word "serial" is seldom if ever defined. Nevertheless, there are many published analyses of individual pieces in which the term is used, though examples are merely pointed out and the actual meaning is skated around (Koenig 1999, 298).
The vocabulary of serialism eventually became rooted in set theory, and uses a seemingly quasi-mathematical vocabulary 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 that 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 that 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 (timbre) is to be serialized, then 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 that is self-complementing for a particular permutation is referred to as prime combinatorial. A hexachord that 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.
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