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A twelve tone or serial composition will take one or more tone rows, called the prime form , as its basis plus their transformations ( inversion, retrograde, retrograde inversion ; see twelve-tone technique for details).
Most composers, when constructing tone rows, are sure to avoid any suggestion of tonality within it - they want their piece to be completely atonal. Alban Berg, however, sometimes incorporated tonal elements into his twelve tone works, and the main tone row of his Violin Concerto hints at this tonality:
The tone row consists of alternating minor and major triads starting on the open strings of the violin followed by a portion of an ascending whole tone scale. This whole tone scale reappears in the second movement when the choraleA chorale is a hymn of the Lutheran church sung by the entire congregation. Chorales tend to have quite simple and easy to sing tunes. They generally have rhyming words and are in a strophic form (with the same melody being used for different verses). "It is enough" (Es ist genug) from Bach'sJohann Sebastian Bach ( March 21, 1685 July 28, 1750) was a German composer and organist of the Baroque period, and is almost universally regarded as one of the greatest composers of all time. His works, noted for their intellectual depth, technical comma cantata no. 60, which opens with consecutive whole tones, is quoted literally in the woodwinds (mostly clarinet).
Some tone rows have a high degree of internal organisation. Here is the tone row from Anton WebernAnton Webern ( December 3, 1883 September 15, 1945) was a composer of classical music and a member of the so called Second Viennese School. He was born Anton Friedrich Wilhelm von Webern but never used his middle names, and dropped the von in 1918. Biogra's Concerto :
If the first three notes are regarded as the "original" cell, then the next three are its retrograde inversion (backwards and upsidedown), the next three are retrograde (backwards) and the last three are its inversion (upsidedown). A row created in this manner, through variants of a tri chord or tetrachordIn musical theory, a tetrachord is a series of four diatonic tones encompassing the interval of a perfect fourth. Two similar tetrachords, a tone apart, form the diatonic major scale. Originally tetrachord referred to the four strings (tetra chord) of Gre called the generatorIn abstract algebra, a generating set of a group is a subset S of a group G, such that every element of G can be expressed as the product of finitely many elements of S and their inverses. More generally, if S is a subset of a group G, then is the smalles, is called a derived rowIn music using the twelve tone technique a derived row is a tone row whose entirety of twelve tones is constructed from a segment or portion of the whole, the generator. Anton Webern often used derived rows in his pieces. Rows may derived from a sub- set. The tone row of many of other Webern's late works are similarly intricate.
A literary parallel of the tone row is found in Georges PerecGeorges Perec ( March 7, 1936 March 3, 1982) was a 20th century French novelist, filmmaker and essayist, a member of the Oulipo group and considered by many to be one of the most important post- WWII authors. Life Perec was born in a working class neighbo's poems which use each of a particular set of letters only once.
See also: musical set theory, operation, unified field