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A 12-tone row has hexachordal combinatoriality with another 12-tone row if their respective first (as well as second, because a 12-tone row itself forms an aggregate by definition) hexachords form an aggregate. There are four main types of combinatoriality. A hexachord may be: Prime combinatorial (transposition) Retrograde combinatorial
This template is intended to provide a consistent and easy display for tone rows, in all forms: prime, retrograde, inverse, retrograde inversion, and inverse retrograde; and in all transpositions.
"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]In music, a tone row or note row (German: Reihe or Tonreihe), also series or set, [2] 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 ...
In music using the twelve-tone technique, derivation is the construction of a row through segments. A derived row is a tone row whose entirety of twelve tones is constructed from a segment or portion of the whole, the generator. Anton Webern often used derived rows in his pieces. A partition is a segment created from a set through partitioning.
Arnold Schoenberg - Piano Concerto, tone row melody, mm. 1-8.png 768 × 129; 17 KB Bartók - Violin Concerto No. 2, first movement twelve-tone subject.png 753 × 132; 5 KB Messiaen - Mode de valeurs et d'intensites series upper line -- Boulez - Structures Ia.png 505 × 94; 5 KB
Construction cost estimating software is computer software designed for contractors to estimate construction costs for a specific project. A cost estimator will typically use estimating software to estimate their bid price for a project, which will ultimately become part of a resulting construction contract. Some architects, engineers ...
1950 6–20: 6–20: all-combinatorial: I: 0 8 9 5 1 4 3 6 7 e t 2: P: 0 4 3 8 7 e 5 1 2 9 t 6: 4 1 5 1 4 6 4 1 5 1 4: Milton Babbitt: Composition for Four Instruments, row iii [26]
In it Babbitt for the first time employs a twelve-element duration set to serialize the rhythms as well as the pitches, [1] predating Olivier Messiaen's (non-serial) "Mode de valeurs et d'intensités", but not the Turangalîla-Symphonie (1946–1948), in which Messiaen used a duration series for the first time in the opening episode of the ...