Table Of ContentHeidelberg
Science
Library
Volume
Heidelberg Juan G. Roederer
Science
Library
liJi1odu!I!lOiJ '!O Springer-Verlag
New York
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1975
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SECOND EDITION
Juan G. Roederer
Professor of Physics
University of Denver
Denver, Colorado, 80210
Library of Congress Cataloging in Publication Data
Roederer, Juan G. 1929-
Introduction to the physics and psychophysics of music.
(Heidelberg science library: v. 16)
Includes bibliographies and index.
1. Music-Acoustics and psychophysics. I. Title. II. Series.
Ml3805.R74 1975 781'.22 75-2313
Cover illustration by J. G. Roederer. Composed using statistical
distribution histograms of time intervals between neural impulses
detected by microelectrodes implanted in auditory nerve fibers
of cats and squirrel-monkeys (Section 2.9); and oscillograms of
second order beats of a mistuned octave (Section 2.6). The
author is indebted to Dr. J. E. Rose, University of Wisconsin, for
his permission to use a collection of histograms for this purpose
(see reference Rose et a/. 1969).
All rights reserved.
No part of this book may be translated or reproduced in any form
without written permission from Springer-Verlag.
@ 1973, 1975 by Springer-Verlag New York Inc.
ISBN-13: 978-1-4615-9983-8 e-ISBN-13: 978-1-4615-9981-4
DOl: 10.1007/978-1-4615-9981-4
Dedicated to the memory of
my dear father
ABOUT THE AUTHOR
The author, Professor Juan G. Roederer, is a space scientist of
international reputation. Italian born, he spent most of his life in
Buenos Aires, Argentina, where he received his Ph.D. in physics
at the local university. He conducted research for several years
at NASA's Goddard Space Flight Center in Greenbelt, Maryland.
For ten years he was Professor at the University of Buenos Aires
and a member of its Directive Council. In 1966 he and his family
decided to emigrate to the United States, where he took the
position of Professor of Physics at the University of Denver,
Colorado. Author of several books and over 70 scientific articles,
Professor Roederer is President of the International Association of
Geomagnetism and Aeronomy, Chairman of the International
Magnetospheric Study, and a member of several committees and
panels of the National Academy of Sciences and other national
and international scientific organizations.
Professor Roederer's close and active relationship with music-
he studied organ with Hector Zeoli in Buenos Aires and Hans
Jendis in Gottingen-prompted him, several years ago, to organize
a course on Physics of Music and Psychoacoustics at the University
of Denver, of which the present book is an offspring. The teaching
of this course has switched his interest part-time to the "inner
space" of the brain functions, in particular to the study of
neuropsychological mechanisms responsible for the processing
of acoustical information.
Preface to the
First Edition
This book deals with the physical systems and psychophysi
cal processes that intervene in what we broadly call "music."
We shall analyze what objective, physical properties of
sound patterns are associated with what subjective, psycho
logical sensations of music. We shall describe how these
sound patterns are actually produced in musical instru
ments, how they propagate through the environment, and
how they are detected by the ear and interpreted in the
brain. We shall do all this by using the physicist's language
and his method of thought and analysis-without, however,
using complicated mathematics (this, of course, will neces
sarily impose serious limitations on our presentation). Al
though no previous knowledge of physics is required, it is
assumed that the reader is familiar with music, in particular
with musical notation, musical scales and intervals, that he
has at least some basic ideas about musical instruments, and
that he has experienced typical musical "sensations."
Until about 25 years ago, little attention had been paid
to the role of the brain, i.e., the central nervous system, in
the actual perception, identification, and evaluation of musi
cal sounds. The highly "mechanicistic" approach of 19th
century researchers, notably the great von Helmholz (1863),
persisted well into the first half of this century. In this
approach the perception of musical tones was regarded
mainly as a result of the conversion of certain well-defined
sound wave properties (frequency, intensity, and spectrum)
into more or less well-defined groups of neural signals
(coding information on pitch, loudness, and timbre, respec
tively). Today we know that the central nervous system does
playa far more active role; a role so essential that without
it the perception of even such basic attributes as the pitch
of musical tones would be impossible. This is why in this
viii Preface to the First Edition
book we shall refer a great deal to the discipline of psycho
physics, which in a broad sense tries to establish in a quan
titative form the causal relationship between the "physical"
input from our senses and the psychological sensations and
physiological reactions evoked in our mind and body, re
spectively. Actually, we shall try to weave a rather close
mesh between physics and psychophysics-or, more pre
cisely, psychoacoustics. After all, they appear naturally
interwoven in music itself: not only pitch, loudness and
timbre are a product of physical and psychoacoustical proc
esses, but so are the sensations related to consonance and
dissonance, tonic dominance, trills and ornamentation,
vibrato, phrasing, beats, tone attack, duration and decay,
rhythm, and so on.
Many books on physics of music or musical acoustics are
readily available. An up-to-date text is the treatise of John
Backus (1969). No book on psychoacoustics is available at
the elementary level, though. Several review articles on
pertinent topics can be found in Tobias (1970) and in Plomp
and Smoorenburg (1970). A comprehensive discussion is
given in Flanagan's book on speech (1972). And, of course,
there is the classical treatise of von Bekesy (1960). A com
prehensive up-to-date analysis of general brain processes
can be found in Sommerhoff (1974); musical psychology is
discussed in classical terms in Lundin (1967). A periodical
publishing original research articles on physics of music and
psychoacoustics is the Journal of the Acoustical Society of
America. The purpose of this book is not to duplicate but
to synthesize existing literature. The blending of physics
and psychoacoustics has been the main guideline followed
by the author.
One of the most painful parts of writing a book is decid
ing what topics should be left out, or grossly neglected, in
view of the stringent limitations of space. No matter what
the author does, there will always be someone bitterly com
plaining about this or that omission. Let us list here some
of the subjects that have been neglected or omitted-with
out venturing to attempt a justification. In the discussion of
the generation of musical tones mainly basic mechanisms
are analyzed, to the detriment of the presentation of con
crete musical situations. The human voice has been all
but left out and so have discussions of inharmonic tones
(percussion instruments) and electronic tone generation;
computer-generated music is not even mentioned. On the
psychoacoustical side, only the perception of single or mul
tiple sinusoidal tones is analyzed, with no word on noise
band or pulse stimuli experiments. Cochlear hydrodynamics
and electrophysiology, as well as a description of the neuro
anatomy of the auditory tract have had to be omitted, too.
And there is practically nothing on rhythm, almost nothing
Preface to the First Edition ix
on stereo perception, and very little on historical develop
ment. Finally, in literature references, the emphasis is on
psychoacoustical subjects. Priority was given to the quota
tion of reviews in sources of more widespread availability
to the general public; detailed references of original articles
can be found in most of the quoted reviews.
This book is an offspring of a syllabus published by the
University of Denver for the students in the Physics of
Music course, which was introduced at the university in the
fall of 1970. In addition to regular classwork, these students
are required to perform a series of acoustical and psycho
acoustical experiments in a modest laboratory. Conducting
such experiments, some of which will be described, is
essential for a clear comprehension of the principal physi
cal and psychoacoustical concepts involved. Unfortunately
for the general reader, they often require electronic equip
ment that is not readily available. We ask that the readers
trust our description of the experiments and believe that
they really do turn out the way we say they do. Whenever
possible, we shall indicate how a given experiment can be
performed with the aid of ordinary musical equipment.
The author is grateful to Professor A. H. Benade of Case
Western Reserve University (Cleveland), and to Professor
R. T. Schumacher of Carnegie-Mellon University (Pittsburgh)
for helpful comments and criticism. Sections 4.5 and 6 of
this book are based on recent, still mostly unpublished,
work done by Professor Benade and coworkers. The author
also acknowledges with gratitude the efficient secretarial
work of Norma Lanier, the expert technical drawing of
James Haworth and photographic work of David Clint, and
the careful revision of the manuscript by the author's wife,
Beatriz.
References Backus, J. 1969. The Acoustical Foundations of Music. W. W. Nor
ton and Company, Inc., New York.
Flanagan, J. L. 1972. Speech Analysis, Synthesis and Perception.
2nd ed. Springer-Verlag, New York.
lundin, R. W. 1967. An Objective Psychology of Music. 2nd ed.
The Ronald Press Company, New York.
Plomp, R., and G. F. Smoorenburg, editors. 1970. Frequency Analy
sis and Periodicity Detection in Hearing. A. W. SUithoff, Leiden.
Pribram, K. H. 1971. Languages of the Brain. Prentice-Hall, Inc.,
Englewood Cliffs, New Jersey.
Tobias, J. V., editor. 1970. Foundations of Modern Auditory Theory.
Academic Press, New York.
von Bekesy, G. 1960. Experiments in Hearing. McGraw Hill Book
Co., New York.
von Helmoltz, H. 1863. On the Sensations of Tone as a Physio
logical Basis for the Theory of Music. English translation, 1954.
Dover Pub!., New York.
Preface to the
Second Edition
Only one year has passed since the publication of the first
edition of this book. It is a gratifying sign that the first print
ing has sold out after such a short time. A lot has happened
since the submission of the original manuscript (mid-1972),
especially in the field of psychoacoustics. Also, much
thoughtful feedback has been received from colleagues and
students who have used this book in class.
The main revisions in this second edition take into ac
count important recent developments in the understanding
of complex tone pitch perception (Sections 2.7, 2.8, 2.9, and
4.8). Look at the letters of the title. Do you see contours
which actually are not physically present? Part of the revi
sions of this second edition consists of the introduction of
an auditory analog to this visual phenomenon, as a possible
explanation of the pitch perception of complex tones (see
references Terhardt 1974, Goldstein 1974, and Whightman
1973). Related to this, some new ideas on consonance and
dissonance have also been incorporated (Section 5.2). Sec
tion 2.9 is new and contains a brief description of the
principal information channels in the auditory pathway.
The specialization of cerebral hemispheres with regard to
speech and music processing is the subject of new Section
5.4. In the "physical" sections, only a few corrections or
clarifications have been made. We believe that now this
book is even more "interdisciplinary" than was its first
edition.
Many of the comments received from readers call for
more figures and more truly musical examples, and suggest
the inclusion of problems and questions for use in class.
Unfortunately, at this time it is impossible to expand this
