Complement (music) - Aggregate Complementation

Aggregate Complementation

In twelve-tone music and serialism complementation (in full, literal pitch class complementation) is the separation of pitch-class collections into complementary sets, each containing pitch classes absent from the other or rather, "the relation by which the union of one set with another exhausts the aggregate". To provide, "a simple explanation...: the complement of a pitch-class set consists, in the literal sense, of all the notes remaining in the twelve-note chromatic that are not in that set."

In the twelve-tone technique this is often the separation of the total chromatic of twelve pitch classes into two hexachords of six pitch classes each. In rows with the property of combinatoriality, two twelve-note tone rows (or two permutations of one tone row) are used simultaneously, thereby creating, "two aggregates, between the first hexachords of each, and the second hexachords of each, respectively." In other words, the first and second hexachord of each series will always combine to include all twelve notes of the chromatic scale, known as an aggregate, as will the first two hexachords of the appropriately selected permutations and the second two hexachords.

Hexachordal complementation is the use of the potential for pairs of hexachords to each contain six different pitch classes and thereby complete an aggregate.