Generalizing Rotational Arrays

Abstract

Few theorists would deny the importance of rotational arrays in the late works of Igor Stravinsky. Probably even fewer would deny that careful study of the work of a great twentieth century composer will reveal not only the extent of his or her compositional craft, but will also indicate that craft's potential for continued use and extension by other contemporary composers. Certainly Stravinsky's adoption of the serial and twelve-tone procedures of Anton von Webern and others makes this point admirably. Since there are a number of studies' that do some justice to the late works, it is curious that, aside from articles by John Rogers and observations by Milton Babbitt,2 little seems to be written about the general nature, types and properties of rotational arrays. One reason for this neglect might be traced to the claim that rotational arrays so intimately coordinate aspects of Stravinsky's compositional style that it is very difficult to export them out of Stravinsky's musical universe without losing their context and utility. For example, the hexachords of twelve-tone rows related by transposition and rotation that form the horizontal voices of Stravinsky's arrays obviously generalize the frequent canonic textures in Stravinsky's work, especially in those compositions immediately preceding and overlapping with his last period.3 Arrays such as the one in example 0.1 provided Stravinsky with a new,