Combinatoriality

In music using the twelve tone technique combinatoriality is a quality shared by some twelve-tone tone rows whereby the row and one of its transformations combine to form a pair of aggregates. Arnold Schoenberg, creator of the twelve-tone technique, often combined P-0/I-5 to create, "two aggregates, between the first hexachords of each, and the second hexachords of each, respectively." Combinatoriality is a side effect of derived rows where combining different segments or sets such that the pitch-class content of the result fulfills certain criteria, usually the combination of hexachords which complete the full chromatic. Combinatorial properties are not dependent on the order of the notes within a set, but only on the content of the set, and combinatoriality may exist among tetrachordal and trichordal sets, as well as between pairs of hexachords. It may also be applied to dyads.