Serialism

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.

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.

Related Topics:
Set theory - Tonal music

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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.

Related Topics:
Twelve-tone technique - All-interval row

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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.

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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.

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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.

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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.

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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.

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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.

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