Tone-Metric Analysis: A Novel Approach to the Study of Form and Performance in North German Baroque Organ Music

This dissertation studies the principles and applications of tone-metric analysis, a novel analytical approach based on the assumption that beat (or tactus) is a combinatorial set of strong and weak beats. As such, tactus can be studied using mathematical tools such as Pascal’s and Sierpinsky’s triangles, which help to quantitatively describe and model, through graphic constructs such as tone-metric waves and trees, the relationship between rhythmic, melodic, and harmonic designs as unfolding functions of the tactus’s regularity. The specificity of these functions, and their lengths and positioning within a piece, have consequences for the performance and perception of music, the analysis of which is at the core of this dissertation. Therefore, waves and trees can be used to describe phenomena such as the perception of tension and relaxation in music, and to initiate the analysis of how agogic elements can be integrated and rendered in performance. Because of its ability to describe and graphically model the elusiveness of music’s unfolding in time, tone-metric analysis is an ideal tool for the analysis, performance, and perception of repertoires that display a high degree of phrasal and formal variety, and are improvisatory in character. This dissertation studies primarily North German organ music, focusing on stylus ii phantasticus preludes and fantasias, chorale-based pieces, and fugues by Johann Sebastian Bach, Nicholaus Bruhns, Dietrich Buxtehude, Nicholaus Hanff, and Johann Pachelbel. For comparison, the dissertation also explores brief passages from later repertoires (classical, romantic, and extended tonal) by Wolfgang Amadeus Mozart, Frédéric Chopin, and Alban Berg. A major novelty of tone-metric analysis is its approach to the combinatorial and geometrical nature and features of tactus, and the consequent generation of an algorithmic basis for the analytical discourse. This approach raises questions about the nature of the relationship between tactus and other musical parameters such as melodic, harmonic, and rhythmic elements, and about their role in shaping phrasal and formal designs in music governed by a steady beat. The thesis thus recommends a new look at the fundamental nature of tactus as a conceptually combinatorial and fractal space for music.Ph.D