“The Nature of Harmony”

This article provides and introduction and translation of Riemann's “The Nature of Harmony”. The translation in this article provides an easy access to an important Riemann's own theoretical evolution, which was written at the moment when a budding psychological perspective was beginning to supersede Riemann's earlier acoustical and physiological perspective. Just as Riemann attempts to place his theoretical program within a historical trajectory, the article locates his work within the wider and broader historical and intellectual discourse of nineteenth-century physics, physiology, and psychology, highlighting the implied and overt polemics with Helmholtz and others that course through its pages.

Neo-Riemannian Perspectives on the Harmonieschritte, with a Translation of Riemann's Systematik der Harmonieschritte

This article examines Riemann's discussion of the Harmonieschritte within the Skizze, locating that discussion within a nineteenth-century combinatorial tradition shaped by Riemann's conception of key. In this article, Riemann's Harmonieschritte is examined from three neo-Riemann standpoints. The first section offers a short introduction to the Harmonieschritte and examines neo-Riemann theory's embrace of these relationships, emphasizing the conflation of functional relations and root-interval transformations that this embrace has entailed. The second section discusses the development of Riemann's system of Harmonieschritte despite of neo-Riemannian theorists's acknowledgement of the system's susceptibility to interpretation as a group of transformations on the consonant triads. The third section focuses on tonal coherence, with particular interest on Riemann's recognition that Harmonieschritte might portend the sort of harmonic practice embraced by neo-Riemannians if left unchecked. The article concludes with a translation of Riemann's Systematik der Harmonieschritte, the summary of the complete “chromatic” family of triadic relations from the Skizze.

Harmonic Dualism as Historical and Structural Imperative

This article aims to provide more sympathetic readings and accounts of harmonic dualism. It makes two claims in particular: first, that the traditional attacks on harmonic dualism that focus on putative structural contradictions in the system are entirely unjustified; and second, that harmonic dualism is a good, legitimate, and useful perspective which can generate enlightening accounts of tonal pieces of music. The argument in this article is part of a broader methodological challenge that questions the means of determining the “correctness” of a music theory. The defense of dualism presented in this article is highly conscious of the modalities of Anglo-American music-theoretical discourse and makes the renewed case for dualism in the context of current argumentative strategies; in the sense, by rehabilitating Riemann's dualism, the article is also holding up the mirror to contemporary music-theoretical practices. There are three parts in this article: the first section focuses on the characteristics of the dualist theory of harmony; the second section defends the first claim presented above (that the traditional attacks on harmonic dualism that focus on putative structural contradictions in the system are entirely unjustified); and the last section defend by way of analysis the second claim—that harmonic dualism is a good, legitimate, and useful perspective which can generate enlightening accounts of tonal pieces of music.

Chromaticism and the Question of Tonality

This article examines the role of key and function as a component of Riemann's relational harmonic system. It is argued in this article that while the neo-Riemannian abstraction of Riemann's Harmonieschritte offer certain insights into the nature of chromatic relations in the nineteenth-century music, it has also resulted in a view of harmonic relations uncomfortably divorced and separated from the tonal and functional contexts in which they were conceived. In addition to examining the role of key and function as component of Riemann's relational harmonic system, and chromaticism, the article also suggests how neo-Riemannian analysis can benefit by reconnecting Riemannian harmonic relations to the functional tonal contexts in which they arose, illustrating the recovered and renewed nineteenth-century perspective with analyses of music by Beethoven, Schubert, and Wolf.

From Matrix to Map

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.

Riemannian Analytical Values, Paleo- and Neo-

This article considers Riemann's analysis of Schubert's triadic but highly chromatic Gb-major Impromptu. This article compares Riemann's own analysis of the work with neo-Riemannian view inspired by the writings of Richard Cohn, assessing the differences in analytical methodology and technology, and locating those differences with the divergent ideologies of the two approaches. In this article, the central focus is not on the analytical technologies, but rather on the assumptions and values that underlie the distinct analytical perspectives. It focuses on the analytical values, with a focus on the methodological and ethical contrasts between these two approaches. The article ends by considering the ways in which a technical rapprochement between the theories might open ethical horizons and provide new ways to value music through Riemann-inspired analytical activity.

Tonal Interpretation, Transformational Models, and the Chromatic Calls to Repent in Franck's Le chasseur maudit

This article provides an analysis of Cesär Franck's Le chasseur maudit, which serves as an extended and elegant reflection on the potential and limitations of various analytical frameworks. This article is placed with respect to notions of chromatic music, specifically on the idea that chromaticism poses analytical difficulties that Riemannian and neo-Riemannian perspectives are particularly well suited to address. After discussing the work from both linear and functional perspectives, and examining the conceptual problems that attend each, the article then demonstrates how a contextual, neo-Riemannian view can capture the work's important gestures, and offers a balance between a desire to understand the work as a reflection of an orderly and coherent relational system, and the need to engage the aural experience of the music.

What is a Function?

This article discusses Hugo Riemann's notion of a tonal or harmonic function, which he first introduced into musical-theoretical discourse, Vereinfachte Harmonielehre in 1893. Riemann's notion of a tonal function refers to either the chords or properties of chords, classified as: tonic, dominant, and subdominant. In this article, the focus is on the equation of “function” with “meaning”, because it is in this connection that the term “function” occurs for the first time, and because the equation forms the core of the later references to the idea. What follows is a critical appraisal rather than history of the concept. The aim in this article is to consider within broad but specific historical boundaries, the discursive potential of the term in Riemann's theoretical writings.

Three Short Essays on Neo-Riemannian Theory

This article presents a three-section discussion, exploring the specific interrelated themes and questions central to the transformational and neo-Riemannian enterprise. The first section discusses the natures of musical objects and relations within the transformational worldview. It asks what happens when tones and chords are imagines not as objects but as transformations. The second section delves further into the object/transformation dichotomy. It explores the structural and functional differences among dissonant and consonant trichords in a particular nonatonic cycle. It also explores how the voice-leading functional and set-theoretical implications of the cycle might be engaged by a transformational perspective as a means to impart “sensuous distinctions”. The last section examines the analytical implications of the first two sections, by examining Vaughan Williams's neo-modal triadic Fantasia on a Theme by Thomas Tallis.

The Problem of Harmonic Dualism

This article presents a key text in the transition of Riemann's argument from earlier theories and mature, psychological work. As a reference, the article also forms a link back to historical contexts already explored, and this article invokes figures such as Georg Capellen and Arthur von Oettingen—Riemann's contemporaries. In this article, Riemann is shown to summarize for one last time, the scope and ambitions of his dualistic theory and, implicitly and explicitly, he responds to his critics. As always, Riemann does not merely rework his earlier arguments but designs them in such way they adapt to the current situation and cover new ground by answering his critics.