Rameau and Musical Thought in the Enlightenment

This is the first intellectual biography of the eighteenth-century French composer and theorist Jean-Philippe Rameau. Rameau is widely recognized as the founder of tonal harmonic theory. Through his principle of the fundamental bass, Rameau was able to explicate the structure of tonal music with unprecedented concision and clarity, earning himself in his day the popular accolade "Newton of Harmony." Ranging widely over the musical and intellectual thought of the eighteenth century, Thomas Christensen orients Rameau's accomplishments in light of contemporaneous traditions of music theory as well as many scientific ideas current in the French Enlightenment. Rameau is revealed to be an unsuspectedly syncretic and sophisticated thinker, betraying influences ranging from neoplatonic thought and Cartesian mechanistic metaphysics to Locke's empirical psychology and Newtonian experimental science. Additional primary documents (many revealed here for the first time) help clarify Rameau's fascinating and stormy relationship with the Encyclopedists: Diderot, Rousseau, and d'Alembert.

TITLES IN THIS SERIES

1 Haydn's "Farewell" Symphony and the Idea

of Classical Style: James Webster

2 Ernst Kurth: Selected Writings: Lee A. Rothfarb 3 The Musical Dilettante: A Treatise on Composition by]. F. Daube: Susan P. Snook-Luther 4 Rameau and Musical Thought in the Enlightenment Thomas Christensen

CAMBRIDGE STUDIES IN MUSIC THEORY AND ANALYSIS GENERAL EDITOR: IAN BENT RAMEAU AND MUSICAL THOUGHT IN THE ENLIGHTENMENT

Portrait of Rameau engraved by].]. Benoist after J. Restout, 1771

RAMEAU AND MUSICAL THOUGHT IN THE ENLIGHTENMENT THOMAS )CHRISTENSEN Associate Profes;,;717J,;;;c, U11iversity of /o11>a

·: ... CAMBRIDGE UNIVERSITY PRESS

PUBLISHED BY THE PRESS SYNDICATE OF THE UNIVERSITY OF CAMBRIDGE The Pitt Building, Trumpington Street, Cambridge, United Kingdom CAMBRIDGE UNIVERSITY PRESS The Edinburgh Building, Cambridge CB2 2RU, UK 40 West 20th Street, New York NY 10011-4211, USA 477 Williamstown Road, Port Melbourne, VIC 3207, Australia Ruiz de Alarcon 13, 28014 Madrid, Spain Dock House, The Waterfront, Cape Town 800 I, South Africa http://www.cambridge.org © Cambridge University Press 1993 This book is in copyright. Subject to statutory exception and to the provisions of relevant collective licensing agreements, no reproduction of any part may take place without the written permission of Cambridge University Press. First published 1993 Reprinted 1995 First paperback edition 2004

A catalogue record for this book is available from the British Library Library of Congress cataloguing in publication data Christensen, Thomas Street. Rameau and Musical Thought in the Enlightenment I Thomas Christensen. p. cm. - (Cambridge studies in music theory and analysis: 4) Includes bibliographical references and index. ISBN 0 521 42040 7 (hardback) 1. Rameau, Jean-Philippe, 1683-1764 - Criticism and interpretation. 2. Music - France - 18th century - History and criticism. 3. Music theory - 18th century. 4. Enlightenment - France. l. title. II. Series. ML4 l O.R2C5 1993

To the memory ef my mother Katharine McCarroll Christensen (1923-1967)

CONTENTS

List ef illustrations Foreword by Ian Bent Acknowledgments

1 2 3 4 5 6 7 8 9 10

Introduction Rameau and the Enlightenment Rameau as music theorist Precursors of harmonic theory The generative fundamental The fundamental bass The corps sonore Mode and modulation Rameau and the philosophes D'Alembert The final years

page xi Xlll

xvn

1 5

21 43

71 103

133 169 209 252 291

Appendix 1 A note on harmonic and arithmetic proportions 307 Appendix 2 "L'Art de la basse fondamentale" and Gianotti's Le Guide du compositeur 309

Select bibliography Index ef subjects Index ef proper names

313 321 323

ILLUSTRATIONS

PLATES

1.1 2.1 3.1 3.2 4.1 4.2 4.3 4.4 5.1 6.1

6.2 6.3 7 .1 7.2 7.3 7.4 7 .5 7 .6 8.1 9.1 9.2 10.1

Portrait of Rameau engraved by J. J. Benoist after J. Restout, 1771. Reproduced by permission of the Bibliotheque Nationale frontispiece "Le Triomphe de Rameau." Engraving by C. N. Cochinfils. Reproduced by permission of the Bibliotheque Nationale page 10 Title page to the Traite de l'harmonie 27 48 Table and transposition of "scale triads" 59 Rameau's figured-bass notation for Corelli's sonata Op. 5 no. 3 Fludd's monochord 73 75 Zarlino's syntonic-diatonic division of the octave 92 Traite, 4. Rameau's string divisions Traite, 36. Rameau's demonstration of the inversional equivalence of triads 97 Nouveau systeme, 80-81. Opening ofRameau's analysis of the monologue from Lully's Armide 121 An illustration of Newton's "experimentum crucis" demonstrating the refraction oflight into a spectrum of seven colors. From Abbe Pluche, Le Spectacle de la nature (Paris, 1732), IV, 164 143 Voltaire's correlation between Newton's color spectrum and the seven notes of the diatonic scale 144 Illustration of some acoustical experiments from Abbe Nollet, Le~ons de physique experimentale (Amsterdam, 1745), III, 438 147 Generation harmonique, Plate 6 183 Generation harmonique, 43 185 Voltaire and Rameau engraved by C. de Tersan. Reproduced by permission of the Bibliotheque Nationale 188 Demonstration, Plate C 196 Demonstration, Plate M 204 Demonstration, Plate N 205 Briseux's Traite du beau, Plate 32 234 An engraving ofJean Le Rond d'Alembert; engraver unknown 254 Title page to the first edition of d'Alembert's Etemens de musique (1752) 258 Frontispiece to the Code de Musique (1760) 293

FIGURES 4.1 4.2 4.3 6.1 6.2 6.3 7.1 10 .1

Descartes's first monochord division Descartes's second monochord division Rameau's revised illustration of his monochord division Taylor's formula for the fundamental frequency of a vibrating string Modes of a string's movement when loaded by two or three weights A vibrating string at time t and t' Summary ofRameau's derivation from the corps sonore The derivation of sevenths by interlocking harmonic and arithmetic proportions

78 79 91 135 151 153 208

300

FOREWORD BY IAN BENT

Theory and analysis are in one sense reciprocals: if analysis opens up a musical structure or style to inspection, inventorying its components, identifying its connective forces, providing a description adequate to some live experience, then theory generalizes from such data, predicting what the analyst will find in other cases within a given structural or stylistic orbit, devising systems by which other works - as yet unwritten - might be generated. Conversely, if theory intuits how musical systems operate, then analysis furnishes feedback to such imaginative intuitions, rendering them more insightful. In this sense, they are like two hemispheres that fit together to form a globe (or cerebrum!), functioning deductively as investigation and abstraction, inductively as hypothesis and verification, and in practice forming a chain of alternating activities. Professionally, on the other hand, "theory" now denotes a whole subdiscipline of the general field of musicology. Analysis often appears to be a subordinate category within the larger activity of theory. After all, there is theory that does not require analysis. Theorists may engage in building systems or formulating strategies for use by composers; and these almost by definition have no use for analysis. Others may conduct experimental research into the sound-materials of music or the cognitive processes of the human mind, to which analysis may be wholly inappropriate. And on the other hand, historians habitually use analysis as a tool for understanding the classes of compositions - repertories, "outputs," works, versions, sketches, and so forth - that they study. Professionally, then, our ideal image of twin hemispheres is replaced by an intersection: an area that exists in common between two subdisciplines. Seen from this viewpoint, analysis reciprocates in two directions: with certain kinds of theoretical inquiry, and with certain kinds of historical inquiry. In the former case, analysis has tended to be used in rather orthodox modes, in the latter in a more eclectic fashion; but that does not mean that analysis in the service of theory is necessarily more exact, more "scientific," than analysis in the service of history. The above epistemological excursion is by no means irrelevant to the present series. Cambridge Studies in Music Theory and Analysis is intended to present the work of theorists and of analysts. It has been designated to include "pure" theory that is, theoretical formulation with a minimum of analytical exemplification; "pure" analysis - that is, practical analysis with a minimum of theoretical underpinning; and writings that fall at points along the spectrum between the two extremes. In these capacities, it aims to illuminate music, as work and as process.

XlV

Foreword

However, theory and analysis are not the exclusive preserves of the present day. As subjects in their own right, they are diachronic. The former is coeval with the very study of music itself, and extends far beyond the confines of Western culture; the latter, defined broadly, has several centuries of past practice. Moreover, they have been dynamic, not static, fields throughout their histories. Consequently, studying earlier music through the eyes