Tone row

In music, a tone row or note row (Reihe or Tonreihe), also series or set, is a non-repetitive ordering of a set of pitch-classes, typically of the twelve notes in musical set theory of the chromatic scale, though both larger and smaller sets are sometimes found. Tone rows are the basis of Arnold Schoenberg's twelve-tone technique and most types of serial music. Tone rows were widely used in 20th-century contemporary music, like Dmitri Shostakovich's use of twelve-tone rows, "without dodecaphonic transformations." A tone row has been identified in the A minor prelude, BWV 889, from book II of J.S. Bach's The Well-Tempered Clavier (1742) and by the late eighteenth century it is found in works such as Mozart's C major String Quartet, K. 157 (1772), String Quartet in E-flat major, K. 428, String Quintet in G minor, K. 516 (1790), and the Symphony in G minor, K. 550 (1788). Beethoven also used the technique but, on the whole, "Mozart seems to have employed serial technique far more often than Beethoven". Franz Liszt used a twelve-tone row in the opening of his Faust Symphony. Hans Keller claims that Schoenberg was aware of this serial practice in the classical period and that "Schoenberg repressed his knowledge of classical serialism because it would have injured his narcissism." Tone rows are designated by letters and subscript numbers (e.g.: RI11, which may also appear as RI11 or RI–11). The numbers indicate the initial (P or I) or final (R or RI) pitch-class number of the given row form, most often with c = 0. "P" indicates prime, a forward-directed right-side up form. "I" indicates inversion, a forward-directed upside-down form. "R" indicates retrograde, a backwards right-side up form. "RI" indicates retrograde-inversion, a backwards upside-down form. Transposition is indicated by a T number, for example P8 is a T(4) transposition of P4. A twelve-tone composition will take one or more tone rows, called the "prime form", as its basis plus their transformations (inversion, retrograde, retrograde inversion, as well as transposition; see twelve-tone technique for details).