"Numerical Composition": A Study of Pythagorean-Platonic Ideas in the Making of the Rondeaux of Guillaume de Machaut

Dissertation, Stanford University (1993)
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Abstract

My dissertation focuses on the polyphonic rondeaux of Guillaume de Machaut . I analyze the methods Machaut used in composing this 14th-century French forme fixe, and study them within a wider philosophical and aesthetic context constructed by a close reading of selections from the writings of Plato, Boethius, Johannes de Muris, and Jacques de Liege. My thesis points out the speculative and practical basis of Machaut's compositional techniques, and in this way leads to a clearer understanding of the philosophical grounding of fourteenth-century music. This study also discusses the ways in which contemporary cultural notions can be seen as being replicated in Machaut's techniques of composing rondeaux. Analysis of the rondeaux includes observations about rhythmic, modal, and contrapuntal characteristics, as well as consideration of the ways in which the formal and semantic aspect of the poetry influenced the writing of the music. ;Chapter One provides an aesthetic orientation for the analysis of Machaut's rondeaux. Ernst Robert Curtius' term "numerical composition" is used as a way to begin to define the analytical approach. Two important dialectics are explored: the concepts of ratio and sensus, constructed from the philosophies of Pythagoras, Plato, and the music theorist Boethius; and the polemic between Jacques die Liege and Johannes de Muris regarding the importance of speculation and practice in 14th-century music. ;Chapter Two outlines the historical development of the rondeau in musical literature and theory before Machaut, and summarizes modern scholarship on the subject. De musica of Johannes Grocheo and the work of Wolfgang Domling and Friedrich Gennrich are cited. ;Chapter Three creates an analytical approach using Machaut's Dame, mon cuer en vous remaint from the narrative poem Remede de Fortune as a paradigm. Chapter Four presents an analysis of the rondeaux. ;Chapter Five summarizes the theme of the project and especially points out that a numerical approach is an important addition to the analytical approach used for the 14th-century rondeau

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