A twelve tone or serial composition will take one or more tone rows 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 chorale "It is enough" (Es ist genug) from Bach's 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 Webern'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 trichord or tetrachord called the generator, is called a derived row. 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 Perec's poems which use each of a particular set of letters only once.
See also: musical set theory