Music and the Making of Modern Science Music and the Making of Modern Science Peter Pesic The MIT Press Cambridge, Massachusetts London, England © 2014 Massachusetts Institute of Technology All rights reserved. No part of this book may be reproduced in any form by any electronic or mechanical means (including photocopying, recording, or information storage and retrieval) without permission in writing from the publisher. MIT Press books may be purchased at special quantity discounts for business or sales promotional use. For information, please email [email protected]. This book was set in Times by Toppan Best-set Premedia Limited, Hong Kong. Printed and bound in the United States of America. Library of Congress Cataloging-in-Publication Data Pesic, Peter. Music and the making of modern science / Peter Pesic. pages cm Includes bibliographical references and index. ISBN 978-0-262-02727-4 (hardcover : alk. paper) 1. Science — History. 2. Music and science — History. I. Title. Q172.5.M87P47 2014 509 — dc23 2013041746 10 9 8 7 6 5 4 3 2 1 For Alexei and Andrei Contents Introduction 1 1 Music and the Origins of Ancient Science 9 2 The Dream of Oresme 21 3 Moving the Immovable 35 4 Hearing the Irrational 55 5 Kepler and the Song of the Earth 73 6 Descartes ’ s Musical Apprenticeship 89 7 Mersenne ’ s Universal Harmony 103 8 Newton and the Mystery of the Major Sixth 121 9 Euler: The Mathematics of Musical Sadness 133 10 Euler: From Sound to Light 151 11 Young ’ s Musical Optics 161 12 Electric Sounds 181 13 Hearing the Field 195 14 Helmholtz and the Sirens 217 15 Riemann and the Sound of Space 231 viii Contents 16 Tuning the Atoms 245 17 Planck ’ s Cosmic Harmonium 255 18 Unheard Harmonies 271 Notes 285 References 311 Sources and Illustration Credits 335 Acknowledgments 337 Index 339 Introduction Alfred North Whitehead once observed that omitting the role of mathematics in the story of modern science would be like performing Hamlet while “ cutting out the part of Ophelia. This simile is singularly exact. For Ophelia is quite essential to the play, she is very charming — and a little mad. ” 1 If in the story of science mathematics takes the part of Ophelia, music might be compared with Horatio, Hamlet ’ s friend and companion who helps investigate the ghost, discusses what may lie beyond their philosophies, sings the sweet prince to his rest, and tells his story. This book will examine some significant moments in the relationship of music to science, especially those in which prior developments in music affected subsequent aspects of natural science. By investigating this direction of influence, we question the common presupposition that, however beguiling, music is conceptually derivative or secondary compared to other modes of thought or perception — an effect, rather than a cause. The examples considered in this book show the larger intellectual and cultural dimensions of music as a force in its own right. By virtue of its special position in Greek natural philosophy, music occupied the perfect position to mediate between idealized mathematical objects and the world of experience. 2 Based on these ancient models, the continuing structures of learning mandated music ’s ensuing centrality as the “hinge ” discipline connecting arithmetic, geometry, and the sensual world. This both reflected and moved the profound alterations that surrounded the birth of the “new philosophy ” during the sixteenth and seventeenth centuries. My main contention is that, in whatever directions its interventions tended, from ancient until modern times music so deeply and persistently affected the making of science over so many historical vicissitudes that we should tell their stories jointly. Our awareness of how exactly music entered into the story can enlarge and deepen our understanding of the human and intellectual dimensions of science. In so doing, we may draw more closely together the study of “ aural culture” and symbolic structures hitherto considered separate. This rapprochement calls for an enriched exploration of the felt dimensions of scientific experience, considered as a fully human activity vividly engaged with perception, feeling, and thought. 3 2 Introduction As Horatio has ties to both Hamlet and Ophelia, music touches both natural philosophy and mathematics. Accordingly, we will examine several critical shifts of understanding in both these domains. Chapter 1 describes the most consequential move of all: ancient Greek natural philosophy connected music with mathematics and astronomy within a fourfold study, the quadrivium . This alliance involved both experiment and theory, and hence positioned music at the frontier between the worlds of physical sensation and ideal forms. During the subsequent fifteen centuries, music retained its central place among the mathematical sciences, an essential component of what became “ liberal education, ” which explicitly continued a program the Pythagoreans began, Plato systematized, and Boethius transmitted to the West. These ancient developments are important not merely as historical background, buried as hidden sediment under the surface of modernity, but as continually active and reemergent forces that shaped and continue to shape “modern ” science and mathematics. Chapter 2 considers the status of these forces as they seemed to a preeminent fourteenth- century natural philosopher. Nicole Oresme used musical concepts as important elements in his reexamination of the cosmos, its possible cycles, and their relation to arithmetic and geometry. The case of Oresme shows how significant musical issues were well before the advent of the “new philosophy” of the sixteenth century. Oresme ’s contact with the “ new music ” ( ars nova ) led him to refute the simplest versions of cosmic harmony and to propose radical new alternatives that depend on the tension between arithmetic and geom- etry. The underlying musical and cosmological considerations allow us to deduce his own unstated conclusion in favor of geometry. Disputes about the order of the planets had profound musical and cosmological implica- tions, especially on the growing controversy over whether the seemingly immovable Earth could be understood to move, as the Pythagoreans held. Though he had presented strong arguments in favor of this view, Oresme himself finally accepted the geocentric account. Chapter 3 investigates the role of music in this cosmological controversy as it came to a head in the fifteenth century. The problem of a seemingly immovable yet moving center such as the Earth parallels the musical problem of changing the usually fixed modal center of a composition. Despite its proverbial impossibility, the theorist Heinrich Glarean drew attention to just such a shift of mode in Josquin des Prez ’ s motet De profundis . If so, music might show how the immovable could move, after all. Indeed, harmony became the defin- ing issue on which Copernicus and those following him phrased their arguments about the new cosmology. Musicians followed this controversy closely; in his 1588 polemic for a revival of ancient musical practice, Vincenzo Galilei was among the first Italians to defend the heliocentric view, many years before his celebrated son Galileo took up this cause, again under the banner of harmony. Several decades before Vincenzo Galilei ’ s surprising avowal, music influenced funda- mental changes in the concept of number. Though irrational quantities had long been excluded from arithmetic and harmonics, sixteenth-century musical theory and practice Introduction 3 called for irrational and rational quantities on an equal footing. Chapter 4 discusses three central figures in this story: the German mathematician Michael Stifel, who was the first person to use the phrase “ irrational numbers ” in the course of his exposition of music, but who then hesitated to grant those numbers full reality; Girolamo Cardano, celebrated physician-polymath, who gave such quantities even greater significance in his musical writings; and Nicola Vincentino, a composer obsessed with reviving ancient Greek quarter tones who found himself in need of what he called “ irrational proportions ” to define these unfamiliar intervals. Each of these three men was involved with practical music to a degree correlated with their respective reliance on irrational numbers. Johannes Kepler, more than anyone, incorporated music into the foundations of his innovative astronomy. Chapter 5 relates his interest in musical practice to his novel approach to its theory, which moved him to reject algebraic results that contradicted musical experience. Kepler ’ s search for cosmic polyphony points to Orlando di Lasso ’ s In me transierunt as a moving expression of the “ song of the Earth, ” down to the melodic spelling of the Earth ’s song. Kepler presents both cosmos and music as essentially alive and erotically active, based on his sexual understanding of numbers. The pervasive dis- sonance of the cosmic harmonies reflects the throes of war and eros. Like Oresme, Kepler realized the essential incompleteness of the cosmic music, which may never reach a final cadence, a universal concord on which the world-music could fittingly end. Kepler treats this as an indication of divine infinitude, inscribed in the finite cosmos. Ren é Descartes began his career writing about music, which affected his innovative natural philosophy throughout its development. Chapter 6 reads his correspondence with Marin Mersenne as tracing the interaction between musical, mathematical, and philosophi-