Interval cycles, affinity spaces, and transpositional networks

Abstract

The paper proposes a framework that coordinates several models of pitch space whose constructive features rely on the concept of interval cycles and transpositional relations. This general model brings under a focused perspective diverse pitch structures such as Tonnetze, affinity spaces, Alban Berg's "master array" of interval-cycles, and several types of transpositional networks (T-nets). This paper argues that applying incremental changes on some of the constructive features of the generic Tonnetz (Cohn 1997) results in a set of coherent and analytically versatile transpositional networks (T-nets), here classified as homogeneous, progressive, and dynamic. In this context, several properties of the networks are investigated, including voice-leading and common-tone relations. The paper also explores the music-modeling potential of progressive and dynamic T-nets by attending to characteristic compositional deployments in the music of Witold Lutosławski and György Kurtág. © 2011 Springer-Verlag.