Through Weber to Cage: the Theory of Rationality and the Solo for Piano

Abstract

The theory of rationality is a dynamic concept that evolves in relation to music. In the context of indeterminate music, where compositions are no longer grounded in harmonic structures or emotional expression, rationality emerges in the composer’s intentions and the relationships between notations and their constituent elements. Conversely, irrationality is reflected in the use of unconventional materials, multiple interpretative choices within notations, and the unpredictable nature of individual realisations. These developments suggest that Cagean indeterminacy offers a valuable framework for reinterpreting Weber’s ideas. By focusing on Cage’s expansive Solo for Piano, I wish to explore both sets of ideas and interpret them through the use of a computer visualisation programme, Gephi. Three key features are examined in relation to the theory of rationality: (i) method/methodical, (ii) function/functional, and (iii) interactivity/being interactive, all of which are recognisable in the Solo for Piano. Cage transformed random imperfections in paper into semi-determinate compositional materials by assigning function to these materials and granting performers interpretive freedoms and varied approaches to the notations. This composition thus creates a score that invites performers to actively ‘interact’ with the notations, resulting in significantly different realisations. Through a comprehensive analysis of the notations, this research employs computational methods using Gephi to uncover individual systems and the internal structure of the work, emphasising that the analyses are inherently shaped by the analyst’s understanding and the chosen metalanguage. This research investigates the complexities between rationality and irrationality in both European art music and indeterminate music and proposes a computational method for studying graphic notations, offering new insights into their interpretation and analysis.