- The Oxford Handbook of Neo-Riemannian Music Theories
- Part I Intellectual Contexts
- The Reception of Hugo Riemann's Music Theory
- “The Nature of Harmony”: A Translation and Commentary
- What <i>is</i> a Function?
- Riemann and Melodic Analysis: Studies in Folk-Musical Tonality
- Part II Dualism
- The Problem of Harmonic Dualism: A Translation and Commentary
- Harmonic Dualism as Historical and Structural Imperative
- Dualistic Forms
- Dualism and the Beholder's Eye: Inversional Symmetry in Chromatic Tonal Music
- Part III Tone Space
- From Matrix to Map: <i>Tonbestimmung</i>, the <i>Tonnetz</i>, and Riemann's Combinatorial Conception of Interval
- On the Imagination of Tone in Schubert's <i>Liedesend</i> (D473), <i>Trost</i> (D523), and <i>Gretchens Bitte</i> (D564)
- Tonal Pitch Space and the (neo-)Riemannian <i>Tonnetz</i>
- Part IV Harmonic Space
- Neo-Riemannian Perspectives on the <i>Harmonieschritte</i>, with a Translation of Riemann's <i>Systematik der Harmonieschritte</i>
- On a Transformational Curiosity in Riemann's <i>Schematisirung der Dissonanzen</i>
- Chromaticism and the Question of Tonality
- Part V Temporal Space
- Criteria for Analysis: Perspectives on Riemann's Mature Theory of Meter
- Reading between the Lines: Hugo Riemann and Beethoven's Op. 31 Piano Sonatas
- Metric Freedoms in Brahms's Songs: A Translation and Commentary
- Part VI Transformation, Analysis, Criticism
- Riemannian Analytical Values, Paleo- and Neo-
- Tonal Interpretation, Transformational Models, and the Chromatic Calls to Repent in Franck's <i>Le chasseur maudit</i>
- Three Short Essays on Neo-Riemannian Theory
- Selected Bibliography
Abstract and Keywords
This article examines the changing meaning of the Tonnetz in Riemann's writings over the course of his career. It examines how Riemann came to reconcile the literal-acoustical and the spatial-metaphorical views of the Tonnetz—how the Tonnetz as a literal matrix to represent and calculate relative frequencies of the tones in just intonation evolved in his later writings into traversable landscape of tones. This article begins by examining the table from Arthur von Oettingen's Harmoniesystem in dualer Entwickelung, which provided not only the graphic model for the table of relations in Riemann's dissertation but also shaped its underlying acoustical conception. The article then examines how two developments in the following decades were significant for Riemann's conceptual reformation of the Tonnetz. The transition from a literal to a metaphorical understanding of the Tonnetz did not simply mirror Riemann's shift from an acoustical to a psychological view of the foundation of harmony, but rather made possible the transition, providing Riemann a mechanism to mediate between the phenomenal world of musical practice and the unbounded noumenal realm of musical meanings.
Edward Gollin is Associate Professor of Music at Williams College.
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