Elucidating stylistic difference in post-tonal compositions from a trichordal perspective: Commonality and individual styles in selected compositions of Milton Babbitt, Arnold Schoenberg, Ruth Crawford Seeger, and Elliott Carter.

Abstract

Trichords and hexachords are fundamental structural elements in many post-tonal compositions. A theoretical study of trichords will be used to elucidate stylistic difference between compositions that share similar ground. The dissertation is divided into two parts. Part I examines several characterizations of trichords, and discusses combinations of trichords which yield hexachords in different ways. This part includes two chapters: Chapter One discusses several categorizations of trichordal and hexachordal collection classes, Chapter Two treats the combinations of trichords, aggregate formation, and array formations. Part II discusses the role of trichords in selected compositions, using the theoretical background from Part I. This part has four chapters: Chapter Three investigates the role of trichords and hexachords in trichordal arrays and the ways they inform the underlying structure of Milton Babbitt's String Quartet No. 2. Chapter Four turns to the consideration of the role of trichords in the complexity of the musical foreground in the first sixty measures of Arnold Schoenberg's Fourth String Quartet, first movement. Chapter Five discusses the use of trichords in the second movement of Ruth Crawford's String Quartet 1931. Chapter Six treats the governing harmony in Argument from Elliott Carter's A Mirror on Which to Dwell. Trichords play rather different roles in the compositions chosen for discussion. The interactions of trichords in these different compositions occupy different corners of the twelve-tone universe. To bring these different compositions together is to compare both the commonality and individuality among their individual usages of trichords. While the seemingly different compositional strategies originate from similar areas of the twelve-tone universe, the different directions that the composers have chosen to expand, the different implications that the composers have chosen to realize in full, and the different properties that the composers have chosen to forego, constitute a large part of what we call different styles. The way that the different aspects of the trichordal relations are crucial to the composers relates closely to their respective modes of presentation, as well as to modes of continuity. The narrative roles of the trichords in chosen compositions are compared in the concluding Chapter Seven.