Durational Thematicism and the Temporal Process: The Golden Ratio as a Thematic Idea in Beethoven's B-flat Major String Quartet, Op. 130, and the Grosse Fuge, Op. 133

Abstract

This thesis explores the use of Fibonacci sequences, and other rhythmic proportions corresponding to the golden ratio in Beethoven's string quartet No. 13, Op. 130, and its original finale, the Grosse Fuge, Op. 133. This provides a new angle for considering the problem of the "time-experience" in late Beethoven. The golden ratio not only forms a common thread in all of the late period quartets, but I argue that it is an essential "thematic idea" within the discourse of the whole work, one bearing implications for the unfolding of the temporal process. Firstly I outline preliminary examples of how the composer "exposes" the golden ratio at the beginnings of the Opp. 127, 130, 133 and 135 quartets. They are expressed through such means as five beats on the tonic, three on the dominant, or five beats at forte, and three at piano, or through a particular rhythmic pattern lasting five beats, and another lasting eight, and so on, each amounting to a 5:3 or 5:8 ratio, corresponding to the Fibonacci sequence, and thus to the golden ratio. In order to build a framework for durational thematicism I review literature on problems surrounding the golden ratio in Western music, the nature of rhythm, metre and pulse in tonal music, and on the "time-experience" in late Beethoven. This culminates in a brief analysis of the opening bars of the Op. 135 quartet in F major, demonstrating that the "dissociation," as the late Joseph Kerman terms it, of classical convention in the late works occurs in tandem with the "composing out" of the golden ratio itself as a thematic idea, a process common in the late quartets. I then apply this temporal process exclusively to Op. 130, suggesting that "dissociation" here performs a similar role. In the midst of this the golden ratio assumes a significance simply by being a common thread throughout these contrasting and seemingly disconnected sections. I demonstrate that the golden ratio occurs on multiple levels of musical structure, arguing that, by emphasising the golden ratio to such an extent, Beethoven sets up a thematic discourse that becomes a central subject in the whole work. Furthermore, by contradicting eighteenth-century metre (that is to say, notated time signatures), I argue that the golden ratio undergoes a sort of dialectical conflict with the latter, expressing a narrative that is retained in following movements. Chapter 4 deals with the Grosse Fuge, showing how this conflict between the golden ratio and classical metre reaches its extreme in this complex, polyrhythmic, fugal masterpiece. After a vehement battle, the music reaches a conclusion at which point the golden ratio, for the first time in the work, becomes subtly assimilated within 6/8 metre; the two finally reach a synthesis, and the dissociation referred to above reaches the point of a new "integration." I then show a similar process to underlie the alternate finale from 1826, despite its highly contrasting character.