Tone row

Tone rows are the basis of Arnold Schoenberg's twelve-tone technique and most types of serial music.

These forms may be used to construct a melody in a straightforward manner as in Schoenberg's Piano Suite 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.

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.

This whole tone scale reappears in the second movement when the chorale "Es ist genug" (It is enough) from J.S.

Bach's cantata O Ewigkeit, du Donnerwort, BWV 60 is quoted literally in the woodwinds (mostly clarinet).

28 is based on the BACH motif (B♭, A, C, B♮) and is composed of three tetrachords: The "set-complex" is the forty-eight forms of the set generated by stating each "aspect" or transformation on each pitch class.

[17] Schoenberg specified many strict rules and desirable guidelines for the construction of tone rows such as number of notes and intervals to avoid.

In his twelve-tone practice, Stravinsky preferred the inverse-retrograde (IR) to the retrograde-inverse (RI),[21][22][23] as for example in his Requiem Canticles: Ben Johnston uses a "just tone row" (see just intonation) in works including String Quartets Nos.

"Mirror forms", P, R, I, and RI, of a tone row (from Arnold Schoenberg 's Variations for Orchestra Op. 31, "Called mirror forms because...they are identical". [ 1 ]
Tone row of Karlheinz Stockhausen 's Gruppen für drei Orchester , the registrally fixed pitches of which correspond with duration units and metronome marks. [ 3 ]
Principal forms of the tone row of Anton Webern 's Variations for piano , Op. 27. Each hexachord fills in a chromatic fourth, with B as the pivot (end of P1 and beginning of IR8), and thus linked by the prominent tritone in the center of the row. [ 10 ]
First array of four aggregates (numbered 1–4 at bottom) from Milton Babbitt 's Composition for Four Instruments , each vertical line (four trichords labeled a–d) is an aggregate while each horizontal line (four trichords labeled a–d) is also an aggregate [ 13 ]
Pierre Boulez 's Second Piano Sonata series consists of three cells: A) an ascending perfect fifth followed by a tritone and a perfect fourth , B) a descending perfect fifth followed by an ascending major second and a descending augmented fifth , and B1) B inverted . [ 18 ]
Prime form of five-note tone row from Igor Stravinsky 's In memoriam Dylan Thomas . [ 19 ]
Thirteen-note tone row from Luciano Berio 's Nones , [ 20 ] symmetrical about the central tone with one note (D) repeated.
Basic row forms from Stravinsky's Requiem Canticles : [ 23 ] P R I IR
Unordered sets from the second of Stockhausen's Klavierstücke I–IV which "retained only the rudiments of the 12-note series". [ 24 ]
Unordered sets from the third of Stockhausen's Klavierstücke I–IV [ 24 ]
Primary forms of the just tone row from Ben Johnston 's String Quartet No. 7 , mov. 2 [ 25 ] and hexachords.