Computer-Assisted Analysis of Music in George Perle's System of Twelve-Tone Tonality

Abstract

53 Music theorists face many challenges when analyzing music written according to George Perle’s compositional theory of twelve-tone tonality, a system based on inversional symmetry. Analysts focusing on Mr. Perle’s music seek relationships among collections of notes in an effort to discover connections within and across a specific work. It is often possible to rely solely on the analytical tools of twelve-tone tonality when working with Mr. Perle’s music, but in many instances other tools have proven rather useful, such as can be found in pitchclass set theory and transformational theory. The interested reader may refer to a number of excellent resources to acquire a working knowledge of these theories (Forte 1973; Rahn 1980; Lewin 1987; Straus 2005). However, in some cases even these theories do not assist the analyst in generating meaningful results from the pitch material in a twelve-tone tonal composition. Because Mr. Perle’s music is non-tonal, it lends itself particularly well to computer-assisted mathematical anlysis. We have developed a simple computer application, Twelve-Tone Tonality Reverse Engineer, or T3RevEng, that helps determine the organization and context of the material, based on the input of pitch classes expressed as integers. In all tests thus far, T3RevEng has proven to be an essential tool for the Perlean analyst owing to its comprehensive, efficient, and accurate manipulation of data.