NUMBER TO SOUND

THE WESTERN ONTARIO SERIES

IN PHILOSOPHY OF SCIENCE

ASERIES OF BOOKS

IN PHILOSOPHY OF SCIENCE, METHODOLOGY, EPISTEMOLOGY,

LOGIC, HISTORY OF SCIENCE, AND RELATED FJELDS

Managing Editor

WILLIAM DEMOPOULOS

Department of Philosophy, University ofWestern Ontario, Canada

Managing Editor 1980-1997

ROBERT E. BUTTS

Late, Department of Philosophy, University ofWestern Ontario, Canada

Editorial Board

JOHN L. BELL, University ofWestern Ontario

JEFFREY BUB, University of Maryland

ROBERT CLIFTON, University of Pittsburgh

ROBERT DiSALLE, University ofWestern Ontario

MICHAEL FRIEDMAN, Indiana University

WILLIAM HARPER, University ofWestern Ontario

CLIFFORD A. HOOKER, University of Newcastle

KEITH HUMPHREY, University ofWestern Ontario

AUSONIO MARRAS, University ofWestern Ontario

JÜRGEN MITTELSTRASS, Universität Konstanz

JOHN M. NICHOLAS, University ofWestern Ontario

ITAMAR PITOWSKY, llebrew University

GRAHAM SOLOMON, Wilfrid Laurier University

VOLUME64

NUMBER TO SOUND The Musical Way to the Scientific Revolution

Edited by

PAOLOGOZZA Department of Philosophy and

Department of Music. University of Bologna. Italy

SPRINGER-SCIENCE+BUSINESS MEDIA, B.V.

A C.I.P. Catalogue record for this book is available from the Library of Congress.

ISBN 978-90-481-5358-9 ISBN 978-94-015-9578-0 (eBook) DOI 10.1007/978-94-015-9578-0

Printed on acid-free paper

All Rights Reserved © 2000 Springer Science+Business Media Dordrecht

Originally published by Kluwer Academic Publishers in 2000 Softcover reprint of the hardcover 1 st edition 2000

No part of the material protected by this copyright notice may be reproduced or utilized in any form or by any means, electronic or mechanical,

inc\uding photocopying, recording or by any information storage and retrieval system, without written permission from the copyright owner

Contents

Illustrations Notes on Contributors Preface & Acknowledgements

Introduction Paolo Gozza

TRADITION

1 Sounding Numbers

The Harmony ofthe Spheres

Vll

Vlll

Xl

1

Daniel P. Walker 67

"Desiderio da Pavia" and Renaissance Musical Theory Paolo Gozza 79

2 Music & Spirit

Marsilio Ficino: The Soul and the Body of Counterpoint Brenno Boccadoro 99

Music in Francis Bacon's Natural Philosophy Penelope M. Gouk 135

TRANSITION

3 Geometry vs Arithmetic

A Renaissance Mathematics: the Music ofDescartes Paolo Gozza

The Structure ofHarmony in Johannes Kepler's Harmonice mundi (1619) Michael Dickreiter

155

173

VI

4 The Uses of Experience

Was Galileo's Father an Experimental Scientist? Claude V Palisca

The Expressive Value ofIntervals and the Problem ofthe Fourth Daniel P. Walker

REASSESSMENT

5 Sound, Matter & Motion

Galileo Galilei H. Floris Cohen

Isaac Beeckman H. Floris Cohen

6 Mechanics & Affections

Marin Mersenne: Mechanics, Music and Harmony

191

201

219

233

Peter Dear 267

Moving the Affections Through Music: Pre-Cartesian Psycho-Physiological Theories Claude Victor Palisca 289

INDEX 309

Illustrations

The invention of the consonances, from Franchino Gaffurio, Theorica musice (1492) 3

The universe as a monochord, from Robert Fludd, Utriusque cosmi ... historia (1617) 5

The division of music, from Gioseffo Zarlino, Le Istitutioni harmoniche (1558) 12

Apollo and wordly music, from Franchino Gaffurio, Practica musice (1496) 16

The musician, from Franchino Gaffurio, De harmonia musicorum instrumentorum (1518) 18

Zarlino's emblem, from Giovanni Maria Artusi, Impresa dei molto R.M. GiosejJo Zarlino (1604) 39

Title page of Johannes Kepler's Harmonices mundi !ibri V(1619) 46

Title page ofRene Descartes's Compendium musicae (1683) 52

Representation of two sounds a fifth apart, from Galileo Galilei, Discourses (1638) 224

Geometrical proof of the vibrations of two sounds an eight apart, from Isaac Beeckman, Journae! (edited by De Waard) 238

The middle ear, from J. R. Pierce and E. E. David, Jr., Man's World ofSound (1958) 257

Title page ofFranz Lang's Theatrum ajJectuum humanort:m (1717) 308

Notes on Contributors

Brenno Boccadoro is 'MaHre assistant' in Musicology at the Univer­sity of Geneva. He collaborates with the Institute Louis Jeantet of the His­tory of Medicine in Geneva and Lausanne. His publications concern the theory of music in Ancient Greece ("Fonne et matiere dans la theorie mu­sicale de l' Antiquite Grecque," in Le temps et la forme. Pour une epistemologie de la connaissance musicale, Geneva 1998), in the Renais­sance and in the 18th century (see Dictionnaire de Jean-Jacques Rousseu, Paris/Geneva 1996, and Dictionnaire europeen des Lumieres, Paris 1997.)

H. Floris Cohen is Professor in the History of Science at the University of Twente, Netherlands. On the history of musical science he published Quantifying Music. The Science of Music at the first Stage of the Scientific Revolution (Dordrecht: D. Reidel, 1984). He has since published The Sci­entific Revolution. A Historiographical Inquiry (Chicago and London: The University of Chicago Press, 1994), and is currently completing a book under the working title "How Modem Science Came into the W orld. Its Conditioned Emergence; Its Threefold Dynamics."

Peter Dear is a Professor in the Departments of History and of Science & Technology Studies at Cornell University. He is the author of Discipline and Experience: The Mathematical Way in the Scientific Revolution (Chi­cago and London: University of Chicago Press, 1995).

Michael Dickreiter works in the field of professional specialization as Author and Teacher in Audition. After his book on Kepler's musical the­ory, his more recent publications concern the fields of technology of sound and recording, besides the science of instruments and scores.

ix

Penelope Gouk is a Wellcome Researcher in the History of Medicine at the University of Manchester and lectures on science, technology and medicine before 1800. Her most recent work "Music, Science and Natural Magic in Seventeenth-Century England" is in publication at the Yale Uni­versity Press. She is currently editing a comparative and interdisciplinary volume on "Musical Healing in Cultural Contexts" (Ashgate, forthcoming 1999).

Paolo Gozza teaches Philosophy of Music in the Department of Music at the University of Bologna. He has edited La musica nella Rivoluzione Scientifica dei Seicento (Bologna: il Mulino, 1989). He is the author of the chapter on music in Vol. IV of the History 0/ Science, section on 'Renais­sance Science,' for the Istituto dell'Enciclopedia Italiana Giovanni Trec­cani (forthcoming).

Claude V. Palisca is Henry L. and Lucy G. Moses Professor Emeritus ofMusic, Yale University, New Haven, Connecticut, U.S.A. His Human­ism in Italian Renaissance Musical Thought (New Haven and London: Yale University Press, 1985) won the prize of the International Musi­cological Society in 1987. His book "Music and Ideas in the Sixteenth and Eighteenth Centuries" is in publication at the Yale University Press.

Daniel P. Walker (30 June 1914 - 10 March 1985) published two col­lections of essays on music: Studies in Musical Science in the Late Renais­sance (1978), and Music, Spirit and Language in the Renaissance (1985) edited by Penelope Gouk. His "Musical Humanism in the 16th and early 17th Centuries" (The Music Review, 1941-42) is alandmark in the field of Renaissance musical theory.

Preface

Number 10 Sound: The Musical Way 10 the Scientific Revolution is a collection of twelve essays by writers from the fields of musicology and the history of science. The essays show the idea of music held by Euro­pean intellectuals who lived from the second half of the 15th century to the early 17th: physicians (e.g. Marsilio Ficino), scholars of musical theory (e.g. Gioseffo Zarlino, Vincenzo Galilei), natural philosophers (e.g. Fran­cis Bacon, Isaac Beeckman, Marin Mersenne), astronomers and mathema­ticians (e.g. Johannes Kepler, Galileo Galilei ). Together with other people of the time, whom the Reader will meet in the course of the book, these intellectuals share an idea of music that is far removed from the way it is commonly conceived nowadays: it is the idea of music as a science whose object-musical sound--can be quantified and demonstrated, or enquired into experimentally with the methods and instruments of modem scientific enquiry. In this conception, music to be heard is a complex, variable structure based on few simple elements--e.g. musical intervals-, com­bined according to rules and criteria which vary along with the different ages. However, the varieties of music created by men would not exist if they were not based on certain musical models--e.g. the consonances-, which exist in the mind of God or are hidden in the womb of Nature, which man discovers and demonstrates, and finally translates into the lan­guage of sounds.

The discourses on music of the 16th and early 17th century European intellectuals bear witness to the change in their shared conception of mu­sic. The title of the book paraphrases this change: it is the shift from a con­ception in which the object of music, i.e. sound, is thought of in terms of number to the conception in which sound is thought of in terms of move­ment. "Number does not produce sound," Marin Mersenne states; it has no separate, autonomous reality from the periodical oscillations of those sounding bodies that in some mysterious way engender the sensation of sound in man. In short, it is the transition from the 'sonorous number' to

XIl

the 'sonorous body,' from number to sound. This is a subtle but substantial change in the nature of 'music as a science,' which integrates and trans­forms the musical tradition of ancient and medieval origin.

The structure of the book makes the epistemological phases in this change clear. The metamorphosis from number (Tradition) to sound (Re­assessment) is complicated by a phase of gestation (Transition), the cogni­tion of which gave rise to the planned symmetries of the text. The outcome is a tripartite structure (the three main sections of the book.) Each section is twofold: ontological-the object of music (sound) in terms of number (Tradition: section 1), measure (Transition: section 3) and matter and mo­tion (Reassessment: section 5)-, and psychological-music as a case of the mind-body relationship in Renaissance and late-Renaissance Magic (Tradition: section 2) and in the Age of Mechanicism (Reassessment: sec­tion 6), tempered by an experimental attitude (Transition: section 4). Every heading introduces two narrative voices: those of the Authors, past and present, who take turns in telling the story. The Editor apologizes for hav­ing made use of them in this experiment. His main concern here has been to compensate for this instrumental use with the clarity of the premise and the proper design of the book. Finally, the Introduction offers the Reader the coordinates of a tradition that from ancient times reaches its fulfilment in the 18th century. In order to cover such a vast period of time, each sec­tion of the Introduction is concerned with a self-sufficient theme-each paragraph may be read on its own-, and it repeats the same time-spans: from the Renaissance to the Age of the Enlightenment, when music moves house, it abandons the Department of Exact Science and enters the De­partment ofFine Arts.

'The musical way to the scientific revolution' -the subtitle of the book-states an historical phenomenon that has not been awarded atten­tion on the part of historians: in the 16th and 17th centuries music is a model for many intellectuals in their reconsideration of the structure of knowl­edge and reality. The crisis of number leads to the reappraisal of music in relationship to other, emergent disciplines-first geometry and astronomy, then mechanics and psychophysiology-, and the mobility of music in the encyclopedia of the sciences is a clue to its epistemological changes. In virtually the same years, music leads Descartes to mathematique uni­verselle and method, Kepler to reformed astronomy, Mersenne to me­chanics and Galileo to the science of motion, to mention the most obvious cases. Music contaminates culture, it modifies knowledge and is in its turn modified by it. The contribution of Number to Sound to 'the musical way to the scientific revolution' makes two points: first, the transition from number to sound (weight) is historically tempered by measure, and, sec­ond, the new conception of sound changed the way of considering man as the enjoyer of music-two inescapable points in a tradition that alongside

xiii

David and Orpheus, the archetyp al music-physicians of the soul, places 'God, the geometer and musician,' who cuncta in numero, pondere et mensura disposuit (who arranged the whole by number, weight and meas­ure.)

Acknowledgements

I should like here to thank those people who have helped me in my work. Prof. H. Floris Cohen was very generous with suggestions and advice on all the-only too frequent-occasions I pressed hirn, which was the same fate of Dr. Penelope Gouk, who was equally helpful. I am very grateful to Prof. Claude Palisca for his uncommon availability and extraordinary professionalism. My thanks go to all the Authors, in particular the late Prof. Daniel P. Walker, whose study on the second or third floor of the Warburg Institute in London I had the chance to frequent at times way back in 1984. I also thank Dr. Carrnel Ace, Dr. Steve Jewkes and Dr. Pascal Ernst (University of Bielefeld) for their work on the translation. Finally, I thank the Warburg Institute and E. J. Brill, Edizioni dell'Ateneo, Francke Verlag and Cornell University Press for their permission to reprint the articles by D. P. Walker, P. Gouk, M. Dickreiter and P. Dear.

This book was conceived in a difficult time at horne, which prolongued its pe­riod of ge station, but is born in circumstances that look promising. I, therefore, dedicate it to litde Vincent Boccadoro, whose birth on April 6th, 1998, at 9.15 a.rn., is a token of good luck to all those who collaborated in the birth of the book and to those who will read it.

P.G.