The Structure of Musical Sound is about science from the point of view of musical sound. It is also a book about musical sound from science's point of view. First and foremost, however, it is a science text for nonscientists. You, the reader, will be introduced to the methods of science; and you will be shown how these methods are used to discover more about musical sound. You will be an active participant in both of these quests, and as a result you will become a more "scientific" person than you might have realized possible. Parts of musical sound have scientific explanations. Examples of these parts include the rules for the formation and propagation of sound waves, the operation of musical instruments as they produce their sounds, and the acoustic conditions for good listening to musical sound in rooms and halls. The Structure of Musical Sound explains all of these scientific aspects of music. Questions are included throughout the book. They will challenge you to demonstrate your understanding of the ideas just presented. The solutions, not just the answers, to these questions are provided at the end of this book.
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Willard Charles Sperry is Professor of Physics Emeritus at Central Washington University. He received degrees from Stanford University and the University of California at Davis; and has published articles about nuclear and particle physics and science pedagogy. He wrote the student notes for a musical sound science course, which have become this book.
Preface and Acknowledgements...................................................................................vAdditional Preface for Teachers................................................................................ixList of Illustrations..........................................................................................xvList of DEMONSTRATIONS.........................................................................................xviiList of Recordings.............................................................................................xixIntroduction...................................................................................................xxiCHAPTER 1. PROPERTIES OF SOUND.................................................................................3CHAPTER 2. MUSICAL SOUND.......................................................................................17CHAPTER 3. MUSICAL VIBRATIONS AND THEIR VIBRATORS..............................................................39CHAPTER 4. MUSICAL SCALES AND TEMPERING........................................................................75CHAPTER 5. STRINGED INSTRUMENTS-MAKING THE SOUND...............................................................83CHAPTER 6. SOME MUSICAL PERCUSSION INSTRUMENTS.................................................................99CHAPTER 7. WIND INSTRUMENTS-MAKING THE SOUND...................................................................105CHAPTER 8. BRASS INSTRUMENTS...................................................................................145CHAPTER 9. WOODWINDS...........................................................................................155CHAPTER 10. TWO OTHER KINDS OF WIND INSTRUMENTS................................................................159CHAPTER 11. ROOM ACOUSTICS.....................................................................................169APPENDIX A SOUND BECOMES LESS LOUD: A CLOSER LOOK AT THE STRUCTURE OF A GAS....................................211APPENDIX BCOMPUTER-CONTROLLED AUDIO ELECTRONICS................................................................235APPENDIX C SCIENCE SYMBOLS: PHYSICAL QUANTITIES, PHYSICAL OBJECTS, AND HOW THEYARE WRITTEN.....................259Answers To QUESTIONS...........................................................................................263Notes..........................................................................................................313Glossary of Technical Terms....................................................................................317Additional and Extended Readings...............................................................................331Sources of Illustrations.......................................................................................333Index..........................................................................................................335
1.1 Sound in General and a Model
We begin by studying sound in general, identifying and explaining its properties. The particular kind called musical sound has all the general properties; but, as you will see, some of them will be limited to specific values or will lie within a narrower range of the complete scope of sound.
Little experiments, or demonstrations, will show you some of the general properties. These demonstrations use apparatus that extends our ability to perceive the structure of sound beyond the information that our ears alone can provide. The apparatus will let you observe the very quick changes of very small things that are basic to sound, and show you the characteristics of air which make sound possible. Sound can pass through other media. You can hear under water, but musical sound travels mostly through air, and this will be the playing field on which our exploratory game takes place.
The demonstrations have a twofold purpose: one, to present and explain the physical properties of sound; and two, to let you develop a correspondence between what you hear and these properties. The demonstrations and the explanations that accompany them will often be suggestive rather than conclusive; but they will make sense. After several demonstrations a model of sound will be proposed. The model will be a description of a thing that has these properties, and will be our description of the physical structure of sound. Model making is one of the most speculative, important, and pleasant parts of science. Once a model of sound is suggested we will realize that if the model is correct sound must have additional properties or must behave in certain ways. More demonstrations and experiments can be mounted to check these predictions. In this way you can gain confidence, or not, that the model is correct.
I admit that the model proposed here will be the accepted model of sound, and that the demonstrations have been chosen to show its properties. Other models of sound, which looked promising, or even good but which were discarded because they finally did not agree with experiment, are not mentioned. This can tend to make science look like an arrow that always hits the bull's-eye, which is certainly not true.
The model proposed and supported by the demonstrations is that sound is a train of high and low pressure regions moving through the air.
The demonstrations will also show that vibrating objects cause these high and low pressure regions. And they will show that musical sound has unique properties. I have arranged the demonstrations in order that one suggests the next, and so they tell a story.
DEMONSTRATION I: Sound, Vibrations
Apparatus: Tuning Fork
Strike a tuning fork on a soft surface such as your knee. You will hear its soft tone. With your other hand gently touch the tines and feel the buzzy vibration. The sound ceases when the vibrations do. The conclusion is that the vibrating tines cause the tone.
It's impossible to tell in detail what's happening, though. The vibrations are too quick and too small to follow with sight or touch. Sound is also invisible. You did hear something, however, and the next demonstration adds some instrumentation, which will make some of the features of sound visible.
DEMONSTRATION II: Sound Made Visible
Apparatus: Tuning Fork, Microphone, Oscilloscope
Strike the tuning fork. Along with the sound, a pattern appears on the oscilloscope's screen. The microphone (mike) transforms the sound into a changing electric signal, which the oscilloscope (scope) displays as a graph of the signal's strength vs. time.
The oscilloscope begins the graph when the signal has a specified height and slope. In this way, if the signal has a reoccurring form the scope will continue to redraw the same graph in the same place on the scope's screen, and you will see it as a fixed pattern. Of course, the signal changes with time, but the scope waits until the signal has the right height and slope to begin graphing. If the sound does not have a repeating form the scope will begin the graph almost at random, and the display will be continually changing and impossible to read or to understand.
So, if the sound has a repeating form, the scope will be able to show it in a steady unchanging display. This is happening for the sound from the tuning fork; the display repeats a basic shape, called a cycle, about every one thousandth of a...
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