In music, a tone row or note row (German: Reihe or Tonreihe), also series and set, refers to 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.
History and usage
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, though one has been identified in a 1742 composition of Johann Sebastian Bach, and by the late eighteenth century was a well-established technique, found in works such as Mozart's C Major String Quartet, K. 156 (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, for example in the finale of his Ninth Symphony but, on the whole, "Mozart seems to have employed serial technique far more often than Beethoven". It is clear from Schoenberg's own writings that he must have been aware of this practice.
Theory and compositional techniques
Tone rows are designated by letters and subscript numbers (ex.: RI11, also may appear 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 or serial 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). These forms may be used to construct a melody in a straightforward manner as in Schoenberg's Op. 25 Minuet Trio, where P-0 is used to construct the opening melody and later varied through transposition, as P-6, and also in articulation and dynamics. It is then varied again through inversion, untransposed, taking form I-0. However, rows may be combined to produce melodies or harmonies in more complicated ways, such as taking successive or multiple pitches of a melody from two different row forms, as described at twelve-tone technique.
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