Describing Structural Aspects of Pitch-Sets Using Successive-Interval Arrays

Abstract

In an effort to understand the harmonic properties of non-serial atonal music-that is, the pitch and intervallic relationships among chordal or melodic segments in the music, for example, of Schoenberg or Webern-composers and theorists have developed a number of analytic tools for describing harmonic connections that might possibly prove, or have proved, significant in given compositions. In this paper my intention will be to present a means-using successiveinterval arrays-by which certain aspects of structural association may be determined. Although the specific perspective here will be somewhat different, many of the issues to be discussed have been covered in other sources. In fact, the present study derives in large part from my own efforts to understand and, to a certain degree, to synthesize other approaches of identifying intervallic and pitch relationships into terms familiar and comfortable to me. One of the most basic and familiar steps in this process toward harmonic analysis has been the construction of various means by which any combination of pitches taken from the chromatic scale may be identified. Since the number of

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