Tone Row - Theory and Compositional Techniques

Theory and Compositional Techniques

"Prime (music)" redirects here. For other uses, see Prime form (music).

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 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.

Initially, Schoenberg required the avoidance of suggestions of tonality—such as the use of consecutive imperfect consonances (thirds or sixths)—when constructing tone rows, reserving such use for the time when the dissonance is completely emancipated. 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:

This 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 Opus 24:

B, B♭, D, E♭, G, F♯, G♯, E, F, C, C♯, A

If the first three notes are regarded as the "original" cell, then the next three are its retrograde inversion (backwards and upside down), the next three are retrograde (backwards), and the last three are its inversion (upside down). A row created in this manner, through variants of a trichord or tetrachord called the generator, is called a derived row. The tone rows of many of Webern's other late works are similarly intricate.

The set-complex is the forty-eight forms of the set generated by stating each "aspect" or transformation on each pitch class.

The all-interval twelve-tone row is a tone row arranged so that it contains one instance of each interval within the octave, 0 through 11.

The total chromatic (or aggregate) is the set of all twelve pitch classes. An array is a succession of aggregates.

An aggregate may be achieved through complementation or combinatoriality, such as with hexachords.

A secondary set is a tone row which is derived from or, "results from the reversed coupling of hexachords," when a given row form is immediately repeated. For example, the row form consisting of two hexachords (one in italics and one in bold):

0 1 2 3 4 5 / 6 7 8 9 t e

when repeated immediately results in the following succession of two aggregates, in the middle of which is a new and complete aggregate beginning with the second hexachord:

0 1 2 3 4 5 / 6 7 8 9 t e / 0 1 2 3 4 5 / 6 7 8 9 t e secondary set:

A weighted aggregate is an aggregate in which the twelfth pitch does not appear until at least one pitch has appeared at least twice, supplied by segments of different set forms. First used in Babbitt's String Quartet No. 4 (Babbitt). An aggregate may be vertically or horizontally weighted. An all-partition array is created by combining a collection of hexachordally combinatorial arrays.