Author: Steffen, Ralph Martin
Title: Metalogik: The Music Theory of Walter Harburger
Institution: University of California, Santa Barbara
Begun: September 1996
Completed: June 1999
This dissertation investigates the music theory, called the "metalogic," of the German writer and composer Walter Harburger (1888-1967). The metalogic offers an alternative interpretation of rhythm and harmony in tonal music. Rooted in the familiar German theoretical tradition of Moritz Hauptmann and Hugo Riemann, it differs by embracing the rebellious spirit of the post-World War I era. The new approach to logic proposed by Edmund Husserl and his school of phenomenology is apparent in Harburger's writing, as well as the influence of new trends in mathematics and physics. Based on his idea of a logic unigue to music, Harburger reconceptualizes the primal elements of rhythm, melody, and harmony in familiar common-practice musical constructions. His unique mathematics, the "metalogic calculus," allows him to attain this goal.
In Harburger's theory, all musical structures, from the lowest level such as beats and scale degrees, to complex structures such as motives and harmonies, relate to one another through hierarchical levels of unity. In order to perceive structures on different levels, such as a single beat vs. a grouping of beats into duple or triple meters, the mind must "cross over" from one level of consciousness to another. In his metalogic equations, which resemble algebraic equations, Harburger aims to express the transformations that occur between adjacent levels of consciousness.
Die Metalogik, published in 1919, is the source for Harburer's theory. The dissertation features original translations from this book, as well as from other published and unpublished primary sources, the latter studied at the Bayerische Staatsbibliothek in Munich, Germany.
Chapters 1 and 2 survey Harburger's life in Munich and the nineteenth- and twentieth-century philosophical and scientific developments that influenced his thought. Chapters 3 and 4 investigate the metalogic in detail and Harburger's application of mathematics to music. Chapters 5 and 6 present his theories of rhythm and harmony. A concluding chapter shows how Harburger's mathematical approach foreshadows recent work in tonal music theory, especially the neo-Riemannian theories of David Lewin and Richard Cohn.
Keywords: phenomenology, mathematics, musical logic, tonal theory, rhythm, perception, Hauptmann, Riemann
Chapter 1: Harburger's Life, Work, and Critical Recognition
Chapter 2: Harburger's Philosophy and Influences
Chapter 3: _Metalogik_
Chapter 4: Harburger's Mathematical Conception of Music
Chapter 5: The Rhythmic Theory
Chapter 6: The Harmonic Theory
Chapter 7: Conclusion
Ralph Martin Steffen
P.O. Box 14103
Santa Barbara, CA 93107