This dissertation is the first comprehensive study of the harmonic theories of German composer and music theorist Sigfrid Karg-Elert (1887--1933), whose two major treatises date from the early 1930s. The dissertation's subtitle highlights the four principal components of Karg-Elert's theoretical project: its three-dimensional just intonation pitch space, and its acoustic derivation; its expansion of Hugo Riemann's function theory, encompassing a variety of fifth-, third- and seventh-based chord relationships; its complete and consistent system of common-tone transformations, which operates independently from harmonic function; and finally, its ultimate presentation of the entire system as a model of harmonic perception. The appendix to the dissertation is a complete annotated German-English edition of Karg-Elert's 1930 treatise Akustische Ton- Klang- und Funktionsbestimmung ("Acoustic Determination of Pitch, Chord and Function"), translated here for the first time.

Karg-Elert's treatises synthesize three strains of thought in late nineteenth-century German theory that were previously somewhat self-contained: a model of pitch and harmonic space derived from the pure intervals of just intonation; major-minor dualism (which Karg-Elert termed polarity), shaped especially by the work of Arthur von Oettingen; and the concept of harmonic function, first presented in Riemann's Harmony Simplified of 1893. Building on that scholarly foundation, Karg-Elert introduces several innovative ideas, including the addition of a third dimension to the pitch space, based on the pure or concordant seventh (4:7); a network of direct major and minor third transformations; and transformations involving the concordant seventh, which enable direct connections among dominant and half-diminished seventh chords. In total, Karg-Elert proposes 23 transformations among triads and seventh chords, all of which retain at least one common tone (conceived as a unique location in the three-dimensional just intonation space). In many specific points of language and notation, his common-tone transformation system points forward to 'neo-Riemannian' theories of the 1980s and the 1990s, including seventh-chord transformations presented by Edward Gollin and Adrian Childs.

Though Karg-Elert generates and explains his pitch space using acoustical and mathematical principles, he ultimately reveals that the space is a model of perception, and that we continue to understand harmonic relations in the pure intervals of just intonation even when pitches are sounded in a different tuning system, such as 12-tone equal temperament. In addition, Karg-Elert states that the musical imagination's ability to categorize pitches and harmonies according to their unique locations in the just-intonation space is essentially unlimited. Perhaps Karg-Elert's most fundamental contribution lies in his belief that every pitch, chord and key can exist in multiple conceptual states. By fully embracing the infinite expanse of his three-dimensional pitch universe, Karg-Elert 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.