Quantifying Music The Science of Music at the First Stage of Scienti
The soul rejoices in perceiving harmonious sound; when the sound is not harmonious it is grieved. From these affects of the soul are derived the name of consonances for the harmonic proportions, and the name of dissonances for the unharmonic proportions.
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THE UNIVERSITY OF WESTERN ONTARIO SERIES IN PHILOSOPHY OF SCIENCE ASERIES OF BOOKS IN PHILOSOPHY OF SCIENCE, METHODOLOGY, EPISTEMOLOGY, LOGIC, HISTORY OF SCIENCE, AND RELATED FIELDS
Managing Editor ROBER T E. BUTTS
Dept. of Philosophy, University of Western Ontario, Canada Editorial Board JEFFREY BUB, University ofWestern Ontario L. JONATHAN COHEN,
Queen's College, Oxford
WILLIAM DEMOPOULOS, University ofWestern Ontario WILLIAM HARPER, UniversityofWestern Ontario JAAKKO HINTIKKA CLiFFORD A. HOOKER, University ofNewcastle HENRY E. KYBURG, JR., UniversityofRochester AUSONIO MARRAS, University ofWestern Ontario JÜRGEN MITTELSTRASS, University of Konstanz JOHN M. NICHOLAS, University ofWestern Ontario GLENN A. PEARCE, University ofWestern Ontario BAS C. VAN FRAASSEN, University ofToronto & Princeton University
VOLUME 23
H. F. COHEN Technical University Twente, Department o[ Social History o[ Seien ce and Technology, Enschede The Netherlands
QUANTIFYING MUSIC The Science oi Music at the First Stage oi the Scientific Revolution, 1580-1650
Springer-Science+Business Media, B.Y.
Library of Congress Cataloging in Publication Data Cohen, H. F. Quantifying music. (The University of Western Ontario series in philosophy of science ; v.23) Bibliography: p. Includes indexes. I. Music-Acoustics and physics-16th century. 2. MusicAcoustics and physics-17th century. I. Title. 11. Se ries. ML3807.C63 1984 781'.1 84-3270 ISBN 978-90-481-8388-3 ISBN 978-94-015-7686-4 (eBook) DOI 10.1007/978-94-015-7686-4
All Rights Reserved © 1984 by Springer Science+Business Media Dordrecht
Originally published by D. Reidel Publishing Company 1984. Softcover reprint of the hardcover 1st edition 1984 and other copyright owners as specified on appropriate pages within 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, inc1uding photocopying, recording or by any information storage and retrieval system, without written perrnission from the copyright owner
The ineffably heartfelt quality of music, owing to which it flows along as an intimately known yet perpetually remote Paradise, so fully intelligible yet so inexplicable, comes from its reflecting all stirrings of our innermost Being, though quite devoid of reality and far removed from its pain. Arthur Schopenhauer (1819)
Sounds can shed more light on Philosophy than any other quality, which is why the science of Music should not be neglected, even if all singing and playing were completely abolished and forbidden. Marin Mersenne (1636)
TABLE OF CONTENTS
xi
PREFACE
xvii
ACKNOWLEDGEMENTS CHAPTER 1 / DEFINING THE PROBLEM SITUATION
1.1. The Problem of Consonance 1.1.1. Zarlino's Redefinition of the Problem 1.1.2. Objections to the Senario 1.2. The Nature of the Scientific Revolution 1.2.1. The Science ofMusic Around 1600 1.3. Outline of Chapters 2 through 7 CHAPTER 2 / THE MATHEMA TICAL APPROACH
2.1. Johannes Kepler 2.1.1. The Empirical Foundation 2.1.2. Distinguishing Consonance from Dissona
