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Six-element of rhythmic values used in Variazioni canoniche by (, 165) In, serialism is a method or technique of that uses a series of values to manipulate different. Serialism began primarily with 's, though some of his contemporaries were also working to establish serialism as a form of thinking. Twelve-tone technique orders the twelve notes of the, forming a or series and providing a unifying basis for a composition's,, structural progressions, and.
Other types of serialism also work with, collections of objects, but not necessarily with fixed-order series, and extend the technique to other musical dimensions (often called '), such as,, and. The idea of serialism is also applied in various ways in the,, and (, 5, 12, 74;, passim), and the musical concept has also been adopted in literature (, 81;, 217–19;, 37, 64, 81, 95). Integral serialism or total serialism is the use of series for aspects such as duration, dynamics, and register as well as pitch (, 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 (, 5–6).
Composers such as Arnold Schoenberg,,,,,,, and used serial techniques of one sort or another in most of their music. Other composers such as,,,,,,,,,,, and used serialism only for some of their compositions or only for some sections of pieces, as did some composers such as and. Olivier Messiaen's unordered series for pitch, duration, dynamics, and articulation from the pre-serial, upper division only—which Pierre Boulez adapted as an ordered row for his (, 178) 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 (, 92). Instead of a recurring, referential row, 'each musical component is subjected to control by a series of numerical proportions' (, 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 ' Musik' ('pointist' or 'punctual music'), then in French 'musique ponctuelle', but quickly confused with ' (German 'pointillistische', French 'pointilliste') the familiar term associated with the densely packed dots in paintings of, despite the fact that the conception was at the opposite extreme (, 451). Pieces were structured by closed sets of proportions, a method closely related to certain works from the and movements in design and architecture called ' by some writers (;;; ), specifically the paintings of,, Bart van Leck, Georg van Tongerloo, Richard Paul Lohse, and, who had been seeking to “avoid repetition and symmetry on all structural levels and working with a limited number of elements” (, 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. (, 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 (). 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 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 twelve 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 and, 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 (, 387;, passim). In particular, the orchestral outburst that introduces the half-way through the last movement of is a tone row that Mozart punctuates in a very modern and violent episode that called 'rude octaves and frozen silences' (, 400).
Is credited with extending serial controls to parameters other than pitch and to formal planning as early as 1930–33 (). Reactions to and against serialism [ ].
Main article: 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 is often used to analyze and compose serial music, but may also be used to study and nonserial atonal music. The basis for serial composition is Schoenberg's twelve-tone technique, where the twelve 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. 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 twelve notes, it is possible to create pitch rows with very strong tonal implications, and even to write tonal music using twelve-tone technique.
Most tone rows contain subsets that can imply a; 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 (; ). To serialize other elements of music, a system quantifying an identifiable element must be created or defined (this is called ', after the term in mathematics). For example, if duration is to be serialized, then a set of durations must be specified. If (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 twelve-tone serial methods focuses on each appearance of the collection of twelve chromatic notes, called an. (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 six-note segments from 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. Notable composers [ ].