Editing Combinatoriality (section)

==Definition==
Most generally complementation is the separation of pitch-class collections into two complementary sets, one containing the pitch classes not in the other.<ref name="Whittall"/> More restrictively '''complementation''' is "the process of pairing entities on either side of a center of symmetry".<ref name="K-G">Kielian-Gilbert, Marianne (1982–83). "Relationships of Symmetrical Pitch-Class Sets and Stravinsky’s Metaphor of Polarity", ''[[Perspectives of New Music]]'' 21: 210. {{JSTOR|832874}}.</ref>

[[File:Schoenberg - Moses und Aron combinatorial tone rows.png|thumb|center|400px|Combinatorial tone rows from ''[[Moses und Aron]]'' by [[Arnold Schoenberg]] pairing complementary hexachords from P-0/I-3<ref>Whittall, 103</ref>]]

The term, "'combinatorial' appears to have been first applied to twelve-tone music by [[Milton Babbitt]]" in 1950,<ref>Whittall, 245n8</ref> when he published a review of [[René Leibowitz]]'s books ''Schoenberg et son école'' and ''Qu’est-ce que la musique de douze sons?''<ref>[[Milton Babbitt]], Untitled review, ''[[Journal of the American Musicological Society]]'' 3, no. 1 (Spring 1950): 57–60. The discussion of combinatoriality is on p. 60.</ref> Babbitt also introduced the term ''derived row''.<ref name="Christensen"/>