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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
The twelve-tone technique—also known as dodecaphony, twelve-tone serialism, and (in British usage) twelve-note composition—is a method of musical composition.The technique is a means of ensuring that all 12 notes of the chromatic scale are sounded equally often in a piece of music while preventing the emphasis of any one note [3] through the use of tone rows, orderings of the 12 pitch classes.
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.
"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 ...
Row form Integers Interval classes Notation Composer: Composition Year Hexa-chord I Hexa-chord II Derivation/ Combina-toriality; P: 0 1 2 e t 9 5 4 3 6 7 8: 1 1 3 1 1 4 1 1 3 1 1
The Pyramid chord consists of every interval stacked, low to high, from 12 to 1 and while it contains all intervals, it does not contain all pitch classes and is thus not a tone row. Klein chose the name Mutterakkord in order to avoid a longer term such as all-interval twelve-tone row and because it is a chord which unites all other chords by ...
Nonetheless, a traditional twelve-tone row is used as its basis: Gruppen tone row [a] This is a symmetrical all-interval row, in which the first half consists of the intervals of a descending major third, rising perfect fourth, descending minor third, descending minor second, and ascending major second.
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.