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.

The Structure of Musical Sound

By Willard Charles Sperry

iUniverse, Inc.

Copyright © 2009 Willard Charles Sperry
All right reserved.
ISBN: 978-1-4401-7507-7

Contents

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

Chapter One

PROPERTIES OF SOUND

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 second. The electric signal from the mike is weak, and the scope has amplifiers to make the display big enough to read and measure. You can adjust the display's time scale and amplification; these capabilities are built into the oscilloscope and make it one of the most useful scientific instruments for showing the properties of a large range of electric signals. Many companies make devices to change physical phenomena into electric signals that can be displayed on oscilloscopes or stored and manipulated in computers. Microphones are good examples of these devices. DEMONSTRATION II shows that they change sound into electrical signals. Another type is the fuel gauge in an automobile. It changes the level of the fuel in the tank to an electrical signal that is displayed on the dashboard. In general, devices that change purely physical phenomena into analogous electric signals are called transducers.

There might be a connection between the repetitive oscillations of the fork's tines and the cycles on the scope's display. If this is so, and it is, what is the link between them? It is the sound generated by the fork and received by the mike. This should fix your attention on what's in the space between them, but you still don't know what is happening there, or what is traveling from the fork to the mike, other than that its name is sound.

What is the microphone changing into an electric signal? A demonstration taking a closer look at the microphone will answer this.

DEMONSTRATION III: Operation of a Simple Microphone Apparatus:

Microphone

This microphone is not the best; it was chosen because it is simple and is easily taken apart. The diaphragm is a thin metal disc held in place by the attraction from the two poles of the magnet. Metals conduct electricity.

A conductor moving near a magnet will have an electric signal generated in it whose strength and polarity (the plus or minus of the signal) depend on whether the conductor is moving fast or slow and whether it is getting closer or farther away from the magnet. This is the signal the scope displays and if you remove the diaphragm from the mike there will be no display on the scope. You should gently push on the diaphragm when it is back in place and see the display change. From this evidence you can correctly conclude that the sound is moving the diaphragm, and since the electric signal has alternating polarity (it goes above and below the zero level) the sound both pushes and pulls on the diaphragm.

The demonstrations so far tell you what sound does but not what it is. Can we invent a model that does both? Yes. Try this explanation.

A. The vibrating tines create high and low pressure regions in the nearby air. By "high and low" it is meant just slightly more and less than normal atmospheric pressure. The low pressure is a partial vacuum. Appendix A describes why packing more air molecules into the same volume (such as adding air to a tire) raises the air pressure inside the tire.

B. These high and low pressure regions flow outward with the speed of sound from their original locations.

C. When a portion of these flowing regions intercepts the diaphragm they push (the highs) or pull (the lows) on it. This causes the vibration of the diaphragm.

Let's look at each of these steps in detail.

Note that this creation of successive highs and lows is taking place at the same rate that the tines are vibrating: quickly. Also note, for future use, that any vibrating object will produce highs and lows next to it. Loud speakers are probably the most common example, but they are not musical instruments. Appendix A. "Sound Becomes Less Loud: A Closer Look at the Structure of a Gas" tells how you can also change the pressure by changing the air's temperature, but this method is not used to create musical sound.

Although tuning forks are almost perfect examples of sound producing vibrators, there are lots of others; and Chapters 5 through 11 will describe musical ones. You will see that they all vibrate to produce highs and lows, and that they come in as many shapes as there are musical instruments or loud speakers.

B. An original high-pressure region will expand (excess air molecules will flow outward). This reduces the original high to normal atmospheric pressure, but creates a "halo" of high pressure around the original region.

Here is a "skin" of high pressure expanding from the original high. The fixed number of excess air molecules in the original high fills an increasing volume skin and the high pressure becomes less as the skin grows. This also explains why sound gets less loud as it moves away from its source. With an original low-pressure region just reverse the direction of the molecules' flow. They flow into the low, leaving an expanding skin of low pressure.

The result is successive skins of high and low pressure expanding from the vibrating object. These are the sound waves. How fast do they move? With the speed of sound! Your ear intercepts a part of these skins and your eardrum vibrates like the mike's diaphragm.

Do the fork's tines really vibrate this way? Do they come together and then fly apart as shown or do they both move left and then both move right in which case the highs and lows would not be formed so efficiently? A demonstration, which illuminates the tines with a high-speed strobe light, will answer this.

DEMONSTRATION IV: Making the Tuning Fork's Vibrations Visible

Apparatus: Tuning Fork, Strobe Light

Adjust the strobe's flash rate until it is about the same as the fork's rate of vibration and you will see a "slow motion" picture of the fork. It is slow enough that you can easily see the tines vibrating as described in step A.

If you understand how this slow motion effect occurs you will be well on your way to understanding the sonic phenomenon called beats. In fact the slow motion effect you are seeing are visual beats. Here's the explanation.

If the strobe's flash rate were equal to the fork's rate of vibration you would see the tines at rest because they would be in the same place each time that the strobe flashed. If these two rates are not quite equal, however, the strobe will light the tines at progressively earlier (or later) times in its cycle of vibration. This will show the tines in slightly earlier (or later) position than shown with the previous flash. As the flashes continue you see the tines slowly move through the positions of their motion.

This explanation of a sound wave propagating by means of the flow outward (or inward) of the excess air molecules is correct, but can easily lead to a misconception which must be corrected. The misconception is that the original high pressure's excess molecules continue to flow outward. In fact they go a very short distance before they collide with normal concentration air molecules. The original high pressure molecules collide with and bat the normal ones into having an excess concentration of high pressure. These in turn strike the next outer ones and the high pressure expands outward in a kind of 3-dimensional domino theory. This is impossible to see, and your ears do not sense that this is happening. However, this type of process occurs in other media. They are not air, but you can see them.

DEMONSTRATION V: Visible Traveling Waves

Apparatus: Rubber Tubing, Slinky

A rubber tube is stretched and then released. The stretch travels down the tube.

When the stretched tube is released the deformation travels across through the tube. The motion of any part of the tube is up and down as the deformation arrives and passes. None of the tube moves to the right.

Again, here is another kind of medium with deformations that are not perpendicular to the direction of their travel. A Slinky is compressed at one end and released. The compression travels down the Slinky.

In both of these examples, the stretched or compressed parts correspond to a low or a high pressure region in air. Neither the stretched piece of tubing nor the originally compressed coils travel horizontally. If you tied a piece of red yarn to the top of the original stretch, or to one of the compressed coils, it would not move across the tube or across the Slinky. The stretch or compression itself travels, and the tube or Slinky only passes on this disturbance. The air molecules in the highs or lows also don't move much at all. If they did you would feel the wind.

Did you notice in this demonstration that in order for the disturbance to travel the medium must be elastic? Is air elastic? This must be so, if the tube and Slinky results can be applied to air. Also, the elasticity of air was assumed while explaining how the vibrating tines could create high and low pressure regions; i.e., the air molecules were contained in a different volume and then sprang out of (or into) it. The required elasticity of air can be demonstrated.

DEMONSTRATION VI: Elasticity of Air

Apparatus: Large Syringe

Push down on the plunger and feel the pressure build up as the volume of air decreases. The number of air molecules didn't change (no leaks). What did change was the number of molecules per volume, i.e. the pressure inside the syringe. When the plunger is released, the increased pressure pushes it upward and the air again attains its original volume. This air is acting like a spring; it has elasticity.

High and low pressure skins (the sound's wave fronts) hit the diaphragms as shown above. The high pressure pushes the diaphragm to the right, and the low pressure lets the higher, normal atmospheric pressure push it to the left. There is no pull, just pushes from the opposite direction.

Therefore, the model of sound, being that of moving high and low-pressure regions in the otherwise still air, seems to agree with all of the demonstrations. Of course this doesn't make it right. There might be hundreds of other models of sound, which could also agree. Is there any way to test whether our air-pressure based model is wrong? Yes! According to our model, sound cannot exist where there is no air. Bring on the vacuum pumps!!

DEMONSTRATION VII: Air is Necessary for Sound

Apparatus: Vacuum Pump, Sound Source in a Bell Jar

The audio oscillator produces a cycling electric signal, which the loud speaker plays as a tone. It has dials with which you can change the pitch and loudness of the tone. As its name implies, the range of pitches it can generate is about equal to the range you can hear, i.e. audio. The vacuum pump pumps the air out of the bell jar. The valve is a little more complicated than shown. It can not only connect or isolate the pump from the bell jar, but it can let air back into the pumped bell jar.

Start with air in the bell jar and with the loud speaker playing a tone you can hear. Then, begin to pump the air out of the jar. The sound gets fainter (less loudness but no pitch change) as the air is pumped. When the air is let back in, the sound returns. Listen to the recording of this happening (Band 1).

So, air is necessary for sound. This alone does not prove our model correct, but it does add new evidence in its favor.

You should now have some confidence that the claim that sound is created by vibrating objects is correct, and that the model I have proposed is satisfactory.

QUESTIONS, such as the one below and the others that you will encounter, are an important part of this book. Don't just continue to read on when you come to them, but take time to answer them. Some will not have a unique answer. You will be required to state some answer and then defend it. A scientist who is proposing a solution to an as-yet-unsolved problem must proceed in this manner.

Other QUESTIONs will have definite answers, which are given at the end of this book. You can check these against your answers and gain confidence, or not, that you have the particular idea or technique asked about well in hand (and head). If so, you can proceed; if not, you must think some more about how to answer the QUESTION. The QUESTION below is one without a unique answer, although the hint should indicate a possible one.

(Continues...)

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