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Fundamentals of Musical Acoustics
By Arthur H. Benade
Dover Publications, Inc.Copyright © 1990 Virginia Benade
All rights reserved.
Preliminaries to a Study of Musical Acoustics
Starting an extensive book on a closely knit subject is akin to beginning a journey, since it carries a certain feeling of anticipation and perhaps trepidation as the author and the reader search for ways in which to work together. For the author the journey will be through territory he has visited before, most of which he has explored thoroughly. For some readers, almost everything will be new; a few may feel at times overwhelmed by the new things crowding about them that seem familiar and even trivial to those who have been there before. The author must hark back to his own first visits to the territory of his subject as he tries not to introduce too many new words and ideas all at once. His ultimate aim must be to give enough guidance on a limited number of carefully chosen subjects that the interested reader will eventually be able to explore new territory on his own. As you read on in this book, constant attention to two things can add much to the success of our travels together through the subject of musical acoustics: (1) your active participation is needed to make the joint exploration meaningful, and (2) retrospection will be encouraged as we return several times to things seen or heard earlier for closer examination from a more mature viewpoint.
1.1. Musical Acoustics: The Meeting Place of Music, Vibration Physics, Auditory Science, and Craftsmanship
This book is addressed most directly (though not exclusively) to people having a reasonable playing knowledge of music who would like to learn something of the ways in which music as an art form intertwines itself with our understanding of vibrating objects, with the study of auditory perception, and with the craft of the instrument maker. The focus of the book is on the vibrations of objects and of the air which surrounds them, but the particular manifestations of vibration physics that are chosen for discussion are those which play a significant role in actual music-making. Because music is intended to be heard, we must give considerable attention to the way in which our auditory nervous system functions as it picks out musical patterns from the complex acoustical signals that reach our ears. In the parts of this book dealing with vibration physics and practical music, I shall be quite explicit in telling how and why various phenomena take place. The perception aspects of our subject will be dealt with somewhat differently. I will tell what it is we hear when various kinds of sound are presented to our ears, but will not describe how the vibrations of an eardrum are led through the middle and inner ear to produce a myriad of nerve impulses that travel by many pathways to the central nervous system. Nor will I detail how these impulses come to act upon one another in several ways simultaneously, in a continuous process that can span a number of successive sounds to provide us with recognizable patterns of sensation. In other words, in this part of the subject we will confine ourselves to a description of phenomena, without much concern for the ways in which they come about.
The manner in which each topic is introduced, the order of presentation, and the choice of the topics themselves have all been predominantly influenced by my experience with musicians and instrument makers as we have worked together over the past two decades. Much of the material in this book is of recent origin, a considerable fraction of it being the result of my own observations and calculations, or of my analysis of the recent work of others. While I have tried everywhere to make clear the reasoning behind each assertion and to present examples of the data which support it, it must be understood that the reasons and examples shown here are merely illustrative and constitute only a small part of the basis for my conclusions. Almost everything in this book has had the benefit of extensive rehearsal in both spoken and written form. Over the years I have been blessed with a number of extremely capable students and laboratory guests. The opportunity to sharpen up the various ideas by talking with these people and with interested colleagues in physics and engineering has been immensely valuable. More recently I have had to deal with the expository problems connected with teaching various methods of adjustment to craftsmen or explaining the reasoning behind my activities as I trimmed up someone's trumpet, flute, clarinet, oboe, or bassoon. These experiences have added a certain intensity to the more relaxed classroom atmosphere of the courses and lecture series in musical acoustics I have given.
One question that immediately arises in the mind of a prospective reader of a book on acoustics written by a physicist concerns the amount of mathematical knowledge that will be required of him. If you will leaf quickly through the book you will notice that I have rigorously confined myself in the text to the simplest of arithmetic—addition, subtraction, multiplication, and division; a number may occasionally be squared or carry a square root sign. Numerical illustrations of the various calculations are supplied in almost every case, partly as a way to show what is going on and partly as a convenient way to supply ourselves with numbers for later use.
While the level of overt mathematics has been kept to the lowest possible, I do not at all wish to leave the impression that the book makes similarly low demands on your ability to follow a line of reasoning or on your ability to do a little courageous speculating. It will perhaps reassure many of you to learn that reasonably diligent efforts on the part of musician-students in my musical acoustics course have always rewarded them with a good understanding of the subject. Their greater familiarity with musical instruments seems to offset certain slight advantages possessed by their scientifically trained classmates who (except for those who are in the life sciences) are likely to be a little ill at ease with logical reasoning carried on without the help of mathematics.
Those of you who come to this book already supplied with a good knowledge of engineering acoustics or of physics and mathematics will sometimes find my presentation a little strange or at least unfamiliar. At times the strangeness comes from the fact that musical vibrations can have somewhat different properties from the vibrations with which you are familiar, or that different aspects of these vibrations come to the fore as dominant. Sometimes the feeling of unfamiliarity may come from my going quickly over something that you considered difficult because you learned it late in graduate school, and other times I will labor mightily over points that you found obvious in high school. Remember that all of this is new to my major audience, and enjoy with me the fact that what an intelligent musician finds straightforward in vibration physics is conditioned greatly by his intensive experience with things that oscillate. Remember also with me that perhaps one of the reasons he chose music as a profession is that his high-school mathematics was taught in such a way as to frighten him, whereas yours attracted you! Another reason for the unfamiliarity you may feel in this book comes from the fact that you may not be used to taking as careful account of the properties of ears as we are forced to do in a musical context.
There is one other group of prospective readers to whom I should address a note of comment and explanation—those of you who have some knowledge of modern psychoacoustics. Perhaps the main thing that will attract your attention (and maybe your concern) is the fact that I seem to attribute to the ears of musicians and musical listeners a far greater ability and achievement than might seem justified by the careful laboratory experiments in hearing that have been carried on during the past forty-five years. There are a number of reasons for this apparent discrepancy, reasons which are themselves of considerable importance to all of us as we begin our exploration of musical acoustics. In the first place, skilled experimenters measuring the properties of ears have almost always taken great pains to supply their auditory signals to their subjects' ears in the most sanitary fashion possible. This calls for the use of carefully calibrated earphones constructed in such a way as to exclude all outside sounds. This exclusion not only of noise but also of the distracting and hard-to-control reverberations of sound in the room is necessary in certain circumstances. In musical surroundings the human auditory apparatus exploits the possibility of hearing and rehearing the echoing sounds of the instrument. Musical sounds are by their very nature highly organized collections of acoustical components which are grouped into patterns by the composer and the player. The emission of sound by musical instruments is of such a nature (especially in a room) that a few missing or out-of-place pieces of sensory input have little effect on our ability to detect or recognize their relationships. A further difference between the capabilities shown by subjects of a psychoacoustical laboratory experiment and by musicians practicing their profession arises from the fact that we are comparing the performance of a heterogeneous group in unfamiliar surroundings with the accomplishments of a group of people who by talent, training, and experience have become quite expert at what they are doing. However, this is an expertise which we should not expect them to bring into the laboratory unless great care is taken to test them in musically relevant ways. Perhaps you will be stimulated to extend and clarify the nature of some of the musical-perception phenomena I describe and thus join the growing number of people who see this as an area of enquiry that promises many rewards to our understanding.
1.2. The Organization of This Book
Now that I have completed a fairly extended discussion of how various groups of my readers may find themselves reacting to this book, it is time for me to outline its general structure. It will then be possible for me to suggest some ways in which you can use the book to extract the fullest measure of understanding from it.
The general principles that governed the writing of this book may be summarized compactly in a set of numbered statements of a sort which will be used for similar purposes throughout this work.
1. Use is made of a carefully chosen minimum of technical terms beyond those commonly used in music. Most technical terms are italicized on their first appearance and defined there either in a formal way or by means of an illustrative example of their usage.
2. This technical terminology is normally identical with that used in other branches of physics or engineering. Occasionally there will be small differences, these being identified and the reasons for them explained. It has been necessary to define a very limited number of terms that are not used elsewhere; special attention is called to these and an explanation is given of why they are needed.
3. Fundamental ideas are introduced whenever possible in the setting of everyday experience (at least that of musicians), or else new concepts are developed by making use of ideas that have already been dealt with thoroughly in earlier parts of the book. Many of the fundamental ideas are initially presented in simplified form, their fuller development taking place as we go on through the book. I have tried to prevent the initial simplification from having possible misinterpretations.
4. Great care has been taken to keep a clearly marked distinction between mechanical phenomena in an instrument or in the room (which are the special province of a physicist or engineer) and the human auditory response to these phenomena (which is the primary concern of a perception psychologist). For example, the word loud is never used to denote a vigorous oscillation; the word is reserved as a description of the perceived nature of this oscillation. In similar fashion care has been taken to keep specifically musical terminology from confusing itself with terminology used for other purposes.
Let us now turn our attention to a description of the various chapters and of their relationships. While musical instruments and musical sounds are dealt with constantly in chapters 2 through 6, the main effort here is to give the reader an introduction to the way one goes about studying things acoustical and an understanding of some of the basic ideas of vibration physics and their perceptual correlates.
Chapters 7, 8, and 9 are concerned with the behavior of some explicitly musical objects (e.g., plucked and struck strings, kettledrum heads, and glockenspiels). Here we are getting ready to think about guitars, pianos, etc., by providing ourselves with some of the applications of ideas developed earlier. In chapters 2 through 9 we confine our attention to vibrations that are set in motion by impulsive excitations such as striking or plucking.
In chapters 10, 11, and 12 we begin the study of the behavior of systems that are set into motion by repetitive forces, such as when one pushes a child on a swing. This part of the book widens its concerns to include the acoustical phenomena that manifest themselves as sound in a room. These chapters deal in part with the production of sound in a room, its spread, and its detection from the point of view of physics. They also provide us with a solid foundation of knowledge about what our hearing mechanism can do as it copes with such sounds. As in earlier chapters, most of the illustrations of the various ideas are chosen from musical practice, along with a certain amount borrowed from the audio industry, with its concern with microphones and loudspeakers.
Chapters 13, 14, and 15 are devoted primarily to a description of the manner in which our ears "put together" various sounds in the comparison of pitch and of loudness. Also discussed are the ways in which the properties of certain classes of sounds allow the ear to combine them into relationships that are recognized in music. We will find that a great deal of what shapes formal music (e.g., harmonic and scale relations) is strongly influenced by the fact that we commonly listen to music in a room rather than outdoors, where as a matter of fact a musician may feel quite uncomfortable and insecure.
The rest of the book applies the principles developed earlier to an explanation of the nature and behavior of the major types of musical instruments. Chapters 16, 17, and 18 take up the keyboard instruments, which are constrained to produce tones having rigidly fixed pitch. The pipe organ is touched upon only as the simplest example of such instruments and as a means for showing the existence of certain tuning problems and how they may be dealt with. Pianos, harpsichords, and clavichords, on the other hand, are discussed in more detail; the impulsively excited vibration of their strings is described and account is taken of the way the string reacts back on the exciting hammer or plectrum, as well as of the way in which the strings "talk" with the soundboard and so also with the room. The practices of instrument makers in proportioning strings, hammers or plectra, and soundboards to one another are described and explained, with examples ranging from the latest in pianos back to harpsichords of the seventeenth century. Notice that the choice of keyboard stringed instruments as our starting point for the systematic study of instruments is a repetition of our earlier choice of impulsively excited systems as the first type to be dealt with on an introductory level.
Excerpted from Fundamentals of Musical Acoustics by Arthur H. Benade. Copyright © 1990 Virginia Benade. Excerpted by permission of Dover Publications, Inc..
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