Tonenreeksen

Tonenreeksen, often translated as tone rows, is a concept in music theory used in twelve-tone or serial composition. It refers to an ordered sequence of the twelve pitch classes (the chromatic scale) in which each pitch class appears exactly once before any is repeated. The term is commonly applied to the prime form of the row, from which other related forms are derived.

The basic forms and operations of a tonenreeksen include the prime form (P), retrograde (R, the row read backward), inversion (I, the row mirrored around a fixed pitch axis), and retrograde-inversion (RI, the combination of R and I). A row can be transposed (Tn) to start on a different pitch, producing a family of transpositions. Through these operations, a single row generates a rich set of material that can govern melody, harmony, and rhythm within a piece.

In practice, composers often employ a two-dimensional array or matrix that shows all transpositions of the row and its inversion, which helps derive related rows and manage their use throughout a work. While the method originated as a way to avoid traditional tonal centers, it does not enforce atonality by itself; tonal implications can still arise from how the row is deployed and cadences are interpreted.

History and influence: the tonenreeksen was developed by Arnold Schoenberg in the 1920s as part of the twelve-tone technique, a cornerstone of the Second Viennese School. It influenced many later composers, including Webern and Berg, and became a foundational tool in modernist and post-tonal music. Variations such as combinatorial rows exploit overlapping hexachords to create symmetrical structures within the music.