Tonal Harmony

This chapter introduces a novel explanatory model for the tonal grammar of music from the thoroughbass era, encompassing baroque and galant practices. The framework models the internalized knowledge of a skilled continuo player improvising at the keyboard prior to Rameau’s invention of the fundamental-bass concept. It makes predictions about the tonal tendency of a chord based on the interaction of its constituent scale-degrees. The framework models something like Schenker’s “will of the tones,” predicting whether individual tones in a chord will tend to “feel” stabilized or mobilized. Stabilized tones tend to remain in place, and mobilized tones tend to move by step. These tendencies are regulated by the intervallic relations among notes in a chord, and can be expressed as two simple laws: a Law of Counterpoint that applies to generic pitch-class intervals regardless of which specific scale degrees they span, and a Law of Harmony that makes scale-degree-specific predictions.

Fundamental Bass and Real Bass in Dialogue

This article focuses on the interpretation of the fundamental bass in terms of structural modes. The aim is to develop an analytical interpretation that relates tonality and tonal form to the fundamental bass. The approach is anchored in the Ramellian tradition by considering the fundamental bass as an autonomous level of analysis. A contiguity principle is governed by the modes of the musical tetractys, or structural modes: P4–M2–P4 (first mode), M2–P4–P4 (second mode), and P4–P4–M2 (third mode). These modes consist of three-scale degrees, which are labeled tonic, subdominant, or dominant, respectively, thus creating a conceptual bridge between scale theory and functional harmony. The dialogue between fundamental bass and real bass reflects a broader dialogue between a structural approach to fundamental bass and elements from thoroughbass and partimento traditions.

Introduction to “Contributions toward a Quantitative Theory of Harmony”

James Tenney presents the introduction to his 1979 essay “Contributions toward a Quantitative Theory of Harmony.” In this introduction, Tenney discusses the history of consonance/dissonance, paying attention to the semantic problem, relations between pitches, qualities of simultaneous aggregates, and contextual as well as operational and functional senses of consonance/dissonance. He also explores the structure of harmonic series aggregates, focusing on harmonic intersection and disjunction, harmonic density, and harmonic distance and pitch mapping. Finally, he considers problems of tonality by analyzing harmonic-melodic roots and the “tonic effect,” along with harmonic (chordal) roots, the “fundamental bass,” and a model of pitch perception in the auditory system. In an epilogue, Tenney describes new harmonic resources as well as prospects and limitations of his contributions.

COLLOQUE INTERNATIONAL ET INTERDISCIPLINAIRE: RAMEAU, ENTRE ART ET SCIENCE INSTITUT DE RECHERCHE SUR LE PATRIMOINE MUSICAL EN FRANCE, BIBLIOTHÈQUE NATIONALE DE FRANCE, FONDATION ROYAUMONT AND OPÉRA-COMIQUE, PARIS, 20–22 MARCH 2014

People heard the surname Rameau with some frequency in 2014, which marked the two hundred and fiftieth anniversary of the death of the composer and theorist Jean-Philippe Rameau (1683–1764). In classrooms and on radio broadcasts, a circumscribed set of associations comes to mind with each utterance of the name. Musicologists think of Rameau's discourses on triadic harmony and his theory of the fundamental bass (basse fondamentale). Keyboardists think of music composed by a literate organist and violinist from Dijon. Singers and dancers might also think of the many forays into choral music, ballet and opera that cemented Rameau's rise to artistic prominence during the French Enlightenment.

The Harmonic Root: A Fragile Marriage of Concept and Percept

The word root, and the harmonic metabolism it helps to describe, plays a central role in how musicians think about musical structure. Vaguely implicit in some early writers' descriptions of intervals and scales, it awaited Rameau's discussions (1722/1971) of the fundamental bass to become explicit. Since then, music theorists have sought to explain its perceptual nature and causes. Their theories usually turn on some version of physical weightings, a root being the pitch class more powerfully reinforced than its companion pitch classes. After representative versions of influential explanations are reviewed, and their generic shortcomings are noted, Ernst Terhardt's "virtual pitch" theory is recognized as uniquely reasonable; it embodies a condition of pattern perception rather than physical reinforcement, thereby skirting a principal flaw of past theories. And yet, a troublesome paradox surfaces, regardless of which conceptualization one favors: empirical studies of interval perception have fallen short of confirming the phenomenal reality our concepts describe so confidently. In an attempt to outflank these empirical/phenomenal clashes, a scheme of pitch/time interaction, or "vectoral dynamics", is outlined. Its consistency with the linear perspective of vision is noted, and the model is applied to the opening of a Wolf song and to a painting by Titian.