Author: Byrne, David A.
Title: The Harmonic Theories of Sigfrid Karg-Elert: Acoustics, Function, Transformation, Perception
Institution: University of Cincinnati
Begun: January 2011
Completed: March 2018
This dissertation is a comprehensive study of the harmonic theories of Sigfrid Karg-Elert (1887â€“1933). The subtitle identifies the four principal components of Karg-Elertâ€™s theoretical project: the acoustic basis of its three-dimensional just intonation pitch space; its expansion of Riemannâ€™s function theory to encompass a variety of direct fifth-, third- and seventh-based relationships; its consistent system of common-tone transformations, which operates independently from function; and its presentation of the entire system as a model of harmonic perception. The appendix is a complete annotated German-English edition of Karg-Elertâ€™s treatise Akustische Ton- Klang- und Funktionsbestimmung, translated for the first time.
Karg-Elertâ€™s work synthesizes three strains of thought in late nineteenth-century German theory: a harmonic space derived from the pure fifth and major third; the concept of major-minor dualism (which Karg-Elert termed polarity), influenced especially by Arthur von Oettingen; and Riemannâ€™s theory of harmonic function. Building on that foundation, Karg-Elert introduces several new ideas, including the addition of a third pitch-space dimension, based on the pure seventh (4:7); a complete system of third transformations; and common-tone transformations that connect dominant- and half-diminished seventh chords. In total, Karg-Elert proposes 23 transformations among triads and seventh chords that retain one or two acoustic common tones. In many specific details of concept, language and notation, his transformations point forward to those of â€˜neo-Riemannianâ€™ theories, including seventh-chord transformations presented by Gollin and Childs. Karg-Elert ultimately reveals that his pitch space is a model of perception, and that we understand harmonic relations according to that model, even when pitches are sounded in equal temperament. By fully embracing the potentially infinite expanse of the just-intonation pitch universe, his work proposes that our understanding of every chord and key is shaped above all by the harmonic paths that connect them, even when those paths travel far from a centralized tonic.
Keywords: Karg-Elert, history of theory, harmony, acoustics, just intonation, function, transformation, perception
2. Sigfrid Karg-Elert (1877-1933): his career, and his theoretical writings
6. Tonality and modulation
Sigfrid Karg-Elert: Akustiche Ton- Klang- und Funktionsbestimmung
Annotated German-English edition, translated by David A. Byrne