Unidade 2


The word 'acoustics' is often used to describe the way sound is conveyed in a specific environment. Concert halls are frequently characterized in terms of having 'good acoustics' or 'bad acoustics'. Although a hall with good acoustics conveys musical sound in a pleasing, or at the very least, efficient manner, these two terms can really mean any number of things. On a technical level, the word acoustics means "the science of sound". Knowing a little more about this science of sound can often enhance one's understanding of music and its effects. The relatively new field of psychoacoustics concentrates specifically on the psychological effects of musical sound and environment.

In its very dry, precise, and scientific sense, music is merely a series of highly organized air disturbances that communicate something to us. To an acoustician, the eighth symphony of Gustav Mahler is a very complex, mathematically intricate eighty-five minute air disturbance created by somewhere between 500 and 1000 musicians who are coordinating their individual disturbances. When we listen to a recording of the same piece, we are listening to a device that more or less recreates that eighty-five minute disruption to the air. If this highly objective approach squeezes the life out of a very emotion-packed piece of music, it does offer some interesting things to think about when one is listening to a live concert or a recording that seems particularly moving or inspiring!

In reality, acoustics offers some intriguing details and insights into the mechanics of the often abstract field of music. Acousticians delve into mysteries of concert halls where someone can literally drop a pin on stage (that's a straight pin, not a bowling pin) and a listener standing at the back of the auditorium can hear the tiny sound it makes. They attempt to understand why there are certain violins that you can go out and buy for $100 and why there are others that you couldn't touch for $1,000,000. They try to explain why certain singers can sing a particular note and literally shatter a piece of glass, along with other physical mysteries.

While this unit only touches the surface of a very fascinating and intricate field, it will hopefully introduce you to a little of the solid mechanics that help make up the total picture of often abstract music.


Communication by way of sound is a rather miraculous thing. For hundreds of species of birds, reptiles, fish, insects, and mammals it has become absolutely vital to survival itself.

Humans are, of course, not the only species that puts sound to work. While our use of it has taken on an incredible amount of subtlety and sophistication, many animals are sensitive to various rhythmic patterns, melodies, and tone colors in their own worlds. This evolutionary precursor to music is indispensable to social animals as they communicate basic messages to each other--such as warn others of danger, signal food, delineate one's territory, or send out a mating call (perhaps you've seen one of Gary Larson's "Far Side" cartoons which depicts a series of mating calls of several species, ending with the sound "Hey Ba-by! Hey Ba-by!" from an inhabitant of a singles' bar).

To receive and process sound involves some very elaborate steps. In spite of a complicated (and sometimes seemingly inefficient) apparatus, we are able to hear an infinite variety of sounds. We can decipher their meanings and, with a little practice, tell a great deal about what is creating them, even about the environment in which they have been created. Virtually anyone can recognize hundreds of individual voices even when they are speaking the same set of words. In addition, we can distinguish between dozens of inflections in the identical set of words delivered by each one of those speakers. We are able to recognize the distinctive patterns of thousands of other sounds, from the crashing of waves on a beach to the crashing of thunder to the roar of a jet engine (three very similar types of sound). With training, many people can recognize the tone color of musical instruments, even the distinctive sound of individual orchestras, etc. What allows us to accomplish something this marvelous?

While sound contains infinite complexities, the receiving apparatus needs to respond only to air disturbances, convert the motion to nerve impulses that show whether the air is being pushed or pulled, and how fast they are being pushed and pulled. It is then up to the brain to take care of the rest and tell us if we are hearing music, speech, noise, silence, or anything in between.

Toss a rock into a still pond and you'll have a pretty good two-dimensional model of what happens when sound is created in air. Just as the surface of the pond is pushed and pulled up and down by the waves, air pressure is also pushed and pulled by things that disturb it. As the waves spread out in a pond, so do the waves in air. If their intensity is enough to push and pull our eardrums, we say that we hear something.

In this process the first thing that happens is that the cone shaped pinna (the visible part of the ear) catches some of the sound and funnels it into the auditory canal. The sound waves then push and pull against the very thin tympanic membrane, more commonly called the eardrum. The eardrum is so thin and sensitive that we can almost--but not quite--hear the sound of individual air molecules bumping against it. These parts of the ear make up what is called the outer ear. In the outer ear, what we know as sound is still fluctuations in air pressure. The physical form of the music, speech or noise that we are listening to is about to change drastically.

In the middle ear the motion is transferred to the three smallest bones in the body--the hammer, the anvil, and the stirrup. These oscillate back and forth in the patterns of the sound just heard. The highest pitch we can hear is approximately 20,000 vibrations per second, and yes--that means that when we are hearing that sound of 20,000 cps, the bones of the middle ear are moving back and forth 20,000 times every second.

While they're obviously highly flexible and sensitive, the three bones are able to relieve a little of the intensity from very loud sudden sound shocks. Regardless of this structure, repeated or sustained loud sounds will damage the mechanism and cause hearing loss--and the damage is irreversible. Unfortunately, the rumors are true--loud music of any kind can permanently damage parts of the ear. Many rock performers have lost alarming amounts of their hearing. Even though walkman headphones or ear buds are very small and light, they can easily deliver the required volume to cause hearing damage after extended use. Heavy industrial noise will also cause hearing loss. Signs of potential damage due to intensity include a ringing sensation. The ability to detect high frequencies is usually the first thing to go. As we get older there is a normal high tonal loss due to age, but intense levels of sound can speed up the process.

Another important component of the middle ear is the eustachian tube which leads from each ear to the back of the throat. There is a tiny bit of air trapped in the middle ear and when we change altitude, the difference in pressure can cause the eardrum to bow in or out. This causes a loss of flexibility, and a slight loss of hearing sensitivity. A little air passes through the eustachian tube, equalizing the pressure. The usual sensation is where sounds seem a little muffled, and then suddenly you hear a 'pop'--and you hear better.

The sound is then transferred to the oval window, which is the parallel to the eardrum. It is a tiny membrane that connects the stirrup to the cochlea, which is the principle organ that makes up the inner ear.

Coiled like a little snail, the cochlea is filled with a fluid called perilymph that distributes what once was the sound as a series of pressure changes. Inside the cochlea is the basilar membrane. The basilar membrane is covered with tiny nerve endings that sense the pressure changes. They send messages to the brain by way of the auditory nerve (sometimes called the 'acoustic nerve').

Before we get to the final organ in the hearing process, let's pause a moment in the process and recap what has happened thus far: first, we had air pressure disturbances pushing against a small membrane. Then the membrane drove three little bones back and forth. Then the bones pushed against another membrane, creating pressure in a thickish fluid. Finally, we have this fluid disturbing thousands of little nerves that fire off electro-chemical impulses over neural paths to other parts of the body. It would seem unlikely that a device like this could handle anything but the most primitive noises, let alone the incredible detail that passes through it almost instantaneously.

If this isn't enough to boggle your mind, add the following to the list: every sound you can possibly hear is transmitted through the ear mechanism in not three, not two, but ONE-DIMENSIONAL motion. Everything--a guitar, a dog's bark, the whoosh of falling rain, a soft singer's voice, a stirring speech, industrial and mechanical noise, a horse's hooves clopping on pavement, et cetera, ad infinitum. . . That one-dimensional movement is enough to convey every piece of aural information we will ever need or be able to use.

The final organ of hearing--one that doesn't often get credit--is the brain. The brain receives two sets of nerve impulses (one from each ear), compares the patterns to ones it has encountered before, and controls the rest of the body accordingly. Did it hear the sound of soothing music, a familiar voice, or a kitten purring? The whole body 'automatically' relaxes, perhaps the person smiles and closes his eyes, overcome by a peaceful mood. Did it hear the sound of an angry dog growling, a close explosion, or a large fast-moving truck bearing down on it? Adrenalin is quickly pumped into the bloodstream, the respiration and heart rates quickly shoot up, and the body immediately gets orders to evade serious physical damage. Did it hear sounds that it deciphers as speech, specifically someone cracking a joke? It triggers yet another complex set of physical reactions culminating in laughter.

Close your eyes and have a friend walk around the room while speaking to you. You can tell his or her exact position because the brain is receiving two slightly different sets of information. Blind people tend to have a highly developed ability to gather information about their surroundings from the things they hear.

In addition to deciphering the patterns of the sound disturbances, the brain compares the impulses received from each of our two ears and gathers yet more information from the whole mix. The next time you listen to music through headphones, concentrate on the spatial direction of the sounds. Recording engineers carefully consider the locations of the instruments in a stereo mix.

For all practical purposes, the brain never goes off duty. The hearing mechanism and process remains in operation when we sleep. Otherwise we would have a really good excuse for sleeping through our alarm clocks.

Other important parts of the inner ear (not pictured in the diagram) are the semicircular canals. These have nothing to do with hearing, but are responsible for our equilibrium. They act like tiny bubble levels and are constantly sending information to the brain, telling it what our body position happens to be at the moment. If there is a conflict between what the eyes tell the brain about motion and what the inner ear tells it, dizziness or worse sets in. Astronauts getting into gravity-less space for the first time often have it a bit rough. The semicircular canals have no gravitational reference point to latch onto. As far as a visual reference point, up or down is up for grabs. An astronaut's brain is constantly pelted with confusing sensory information, resulting in 'space sickness'. Most of the time the body adapts to this in a day or so. Motion sickness drugs can also help.

Certain chemicals on gravity-bound Earth--for example, alcohol--will often cause the semi-circular canals to send grossly incorrect messages to the brain. When that happens, the eyes tell the brain that the body is motionless and the semicircular canals tell the brain that it is violently moving. At this point a very primitive protective mechanism sets in. The brain assumes that the body has ingested a toxic substance (which alcohol is), assumes it has been poisoned, and sends a message to the stomach to eject its contents, getting rid of any toxin remaining in the system.

Our range of hearing is such that the loudest sound that we can normally stand is about 1 x 1012 times the intensity of the softest sound we can hear. In non-scientific notation, that number is 1,000,000,000,000, which is a bit unwieldy.

To make things a little bit easier and avoid, numbers with ridiculous amounts of zeros, the standard unit for sound intensity, the decibel, is based on an exponential scale.

That loud sound mentioned in the above paragraph (which will cause pain) has a pressure intensity of about one watt of energy per square meter. A watt is a small amount. Our eardrums are a very small amount of a square meter--that might give you an idea how sensitive our hearing is. The decibel rating for that sound is 120 decibels. The softest sound that the normal ear can hear is assigned a level of 0 decibels.

Within this system, any increase of 3 decibels represents a doubling of sound intensity. This means that a sound at six decibels is twice as intense as one at three decibels. It also means that a sound at a level of 9 decibels is twice the intensity of 6 decibels, 12 double 9, and so on, 53 double 50, and so on. You can see that the intensity of the sound quickly rises as we go up the scale.

With a little calculation, you can figure that the a sound at 98 dB is about 65,000 times the intensity of a sound at 50 dB. You may be wondering--to a listener, is a sound of 98 dB 65,000 times as loud as the one at 50 dB? The answer is no--our scale of hearing more closely follows the exponential curve of the decibel scale than it does the straight linear mathematical scale that simple numbers would suggest.

You have just gotten a brief glimpse into the workings of a very remarkable processing system. The next step is to take a look at what it processes. . .


You probably have heard the riddle "if a tree falls in the forest and no one is around to hear it, does it make a sound?" Before we get to answer that, perhaps we should understand sound.

Imagine the surface of a pond. With nothing disturbing it, the surface remains smooth and flat. Throw a rock into the pond and some of the water will be temporarily pushed out of the way, creating waves. If the pond is large enough, these waves (disturbances) spread out from the original splash until they eventually become too weak to disrupt the surface tension of the water, and the surface of the water is smooth and flat once more. If the pond is small, some of the waves would bounce of of the shore and reflect back into the center. After a fairly short period, all will be quiet on the surface again.

If we were to have taken a closer look at each of the waves as they spread out from the source, we would find that each one consisted of a little water pushed out of the way and piling up slightly (the crest) and small spaces where the water had been pushed from, creating a little pull that will eventually be filled when the water 'snaps back' into position (the trough).

If we were to repeat the experiment with a larger rock, the splash would be a little larger, the size of the waves would be a little larger and they would travel a little farther before they died out--but they wouldn't move any faster.

Throw a very large rock into the pond, and the waves still wouldn't move any faster, but they would travel farther before dying out. The crests would rise a little higher above the normal surface of the water and the troughs would go a little farther below--because more water had been pushed out of the way.

The above few paragraphs are quite a good model for what happens in air when a sound is created. Like the surface of water, air pressure tends to remain constant until it is disturbed. Imagine a firecracker explosion, which is quite a good analogy to the rock tossed in a pond.

The rapidly expanding gasses created in the explosion slam into the molecules of air compressing them into tiny regions of higher than normal air pressure. This is referred to as the compression phase of sound and is analogous to the crests of the waves in the pond. Those molecules smack into other molecules, those hit other molecules, etc. as the sound wave travels outward from the source.

Following behind the compression wave is an area of low pressure--the region that the molecules have been bumped out of. This is a very close match to the troughs generated in the pond. As the water eventually flowed back into these regions, the air molecules will eventually snap back into the regions of lower than normal pressure, called rarefactions or decompressions.

After many thousands of rounds of molecules pushing, bumping into other ones, then snapping back, there won't be enough energy left to displace the molecules. At that point, we would say the sound had died out. If there is a building in the way, some of the molecules would reflect off the walls of the building and bounce back toward the source.

With a larger firecracker, more air will be displaced and it will take longer for the sound to die out, but the air will eventually become like the level surface of a pond. Set off a stick of dynamite--and like the large rock in the pond, you will create quite a violent 'splash' in the air pressure. The molecules will be slammed quite a bit out of their normal position, but will eventually return to a normal state. And, like the waves in the water, the sound will travel at a constant rate regardless of the intensity of the disruption.

Most sounds are obviously not quite this violent or disruptive to the normal state of air, but they nevertheless consist of quantities of air being pushed and pulled. When those compressions and rarefactions encounter a thin membrane called an eardrum, they push it and pull it--setting in motion the events described above in "THE HUMAN EAR". We have then heard a sound.

Our world is filled with many devices that disturb the air pressure. Motorcycles, doors slamming, jet engines roaring are some examples of devices that do it with little possibility for control of the disturbance.

To find devices that disturb the air in a highly controlled fashion, you need look no farther than your stereo speakers. Inside each one is a little electromagnet that receives an alternating current from your stereo amplifier. The magnet receives a positive voltage and pushes out against air molecules, which push into other ones, etc., etc. The magnet receives a negative voltage and pulls back in, creating the rarefaction which then spreads out. If you send the appropriate pattern to the speaker magnets, then they can duplicate the patterns of pushes and pulls made by virtually any sound or combination of sounds. This even includes sound of a thousand people disturbing the air in Mahler's Eighth Symphony.



Like the waves in water, sound waves can be reflected. As a matter of fact, most of the time our acoustical environment consists of a great deal of reflected sound--from the floors, the ceilings, the walls. This is why a person speaking outdoors is harder to hear than he would be from the same distance indoors. Outside, the only sound that you are hearing is the direct sound with nothing reflected.

In an environment with no reflection, the intensity of the sound dies down with the inverse of the square of the distance. This means that if you double your distance from a sound source, you will get only one-fourth the intensity. If you move to three times your distance, you will then be getting only one-ninth the original intensity. Again, this rule applies only where reflected sound is not a factor.

Far from being a problem, carefully controlled reflection of sound is what makes a great concert hall. A musician sitting on a concert stage is producing sound waves (splashes) that travel out in all directions. When the indirect waves are reflected really well back to the audience, they can hear much more detail--and more of them can hear. Don't forget that before the mid 1900s, there was no such thing as amplification. This good reflection was all they had.

Again, this reflected sound strikes our ears as being natural. Recordings that don't have any reverberation tend to sound very unnatural, even a little odd. Before the invention of electronic reverberation, musicians would often record in rooms with hard concrete walls.

Echo and reverberation are two names given to reflected sound. An echo is a reflection or a series of reflections where each can be heard distinctly. A lot of cartoons will show an echo canyon, which is a natural rock formation that will clearly reflect sounds back to the source.

Reverberation is a bit different from an echo in that you cannot distinguish between the large number of reflections. Reverberation sounds like the original sound is "trailing off" into silence. When someone creates a sound in a room with hard walls, the sound will travel outward in all directions and then be reflected back to the source in many complicated paths, each one covering a different distance, each one taking a different time. Although it sounds very much like it, playing a note on a piano with the damper pedal held down is not true reverberation.

It's possible to have too much reflection. Many older-style churches and government buildings, etc. will reflect a little too much sound, causing all sounds to be muddy. It's not uncommon for some of these places to have a reverberation time of four seconds. Hard and flat surfaces, like the marble found in the above described structures, tend to reflect most sound waves that hit them. Soft and irregular surfaces, tend to absorb the sound. Fabrics do this wonderfully.

Sometimes structures are built that accidentally reflect sound well. A famous incident took place in the U.S. Capitol when someone was quietly whispering details of a political plot. By sheer accident, he happened to be standing at a spot in the room where the sound cleanly bounced to another part of the room, a fair distance away. The person standing in the other spot heard the plotting as clearly as if it had been whispered in his own ear.

An anechoic chamber is the name given to a room built to absorb over 99.5% of all reflected sound. These places are often used to test audio equipment or other sound producing devices that need very precise analysis.


Sound passes through barriers other than air--in fact, air isn't even the best medium in a number of ways.

Often, sound travels farther and faster in solids or liquids. Whales and other seagoing mammals take advantage of this. When the water happens to be a certain temperature and pressure (due to depth), sounds can travel over many miles.

In air, sound travels just about 1100 feet per second. This speed varies just a bit with the air temperature (breaking the speed of sound, known as Mach 1 isn't quite a constant). By contrast, the speed of sound in water is a bit over 4700 feet per second. If you clank a bar of steel with a hammer, the vibration will travel over 16,000 feet per second.

To give you an example of these relative velocities, if I were to clap my hands, it would take about 1/50 of a second for that sound to travel 20 feet. In the same time it took sound waves in air to travel that distance, they would have travelled about 85 feet. In that same 1/50 of a second, they would have travelled 290 feet in steel. By comparison with the fastest thing known in the universe, in the time that it took a sound wave in air to travel 20 feet, a beam of light would have travelled almost 3400 miles.

One place sound CANNOT be transmitted is through an environment with no vibrating medium--such as the vacuum of space. When you're watching a science fiction movie and see a spaceship explode in outer space and then hear a huge explosion in the soundtrack, some sound effects person is pulling your leg. Furthermore, the walls of a ship designed to stand the rigors of a vacuum and space travel would have to be so thick that the ship would be far more soundproof than any structure that currently exists on Earth.


To suggest their product's ability to store sound, Memorex created a set of commercials that show someone sitting down, turning on the stereo, and you see his hair blown back, furniture being pushed away from the speakers, as if the music and volume was creating a powerful wind. While it makes for memorable images, and probably helped sell quite a few tapes, this is as bad of science as hearing an explosion in space.

As mentioned in the above section on sound, when air molecules are disturbed, they are pushed outward (the compression phase), and then are pulled back into place (the rarefaction phase). If they travelled all the way from the source to our ears, every time we heard a sound we would feel a breeze. The louder the sound, the stronger the breeze. . . and that obviously doesn't happen.

What is actually travelling is the wave motion. Eventually that wave motion (energy) pushes and pulls our eardrums when we hear sound. What might come a little surprise, when a noise is made--for example someone clapping his hands--you really aren't even hearing the two surfaces of skin hitting together--you are hearing the air disturbance created. To put it a little simpler, you aren't hearing the clap, you are only hearing the sound of the clap.

Going back to the model of the surface of a pond, if you have a floating object on the surface (and no wind), any waves coming along will cause the object to bob up and down, but it will remain in basically the same place. The same happens with the air molecules.

As mentioned above, there are a few differences in the effects created if one were to throw a pebble and then a boulder in the pond. The waves created by the boulder would be just a little bit bigger and travel farther before dying out than those created by the pebble.

The difference in those wave sizes is a difference in amplitude. Again, this is quite a good model for what happens in air. Let's say we hear two sounds--a handclap and then a thunderclap. An acoustician would say that the thunderclap had a greater amplitude than the handclap, meaning that the air molecules were displaced farther out of their normal positions than in the handclap. To the rest of us, our built in "air motion sensors" (better known as our ears) will pick up the difference and we will conclude that the thunderclap is louder than the handclap.

Simply put, amplitude is synonymous for loudness, and the greater amplitude a sound has, the louder it will seem.

An amplifier is an electrical device that will increase the amplitude of a signal fed into it. When you turn up the volume control on your stereo you are increasing the amount of push and pull on the air.

On occasion, a piece of music will call for a rapid change in loudness. This name for this is "tremolo". Most acoustic instruments will produce a tremolo by playing the same note over and over very rapidly. Synthesizers and vocalists do it a little differently. Many electric guitars have a tremolo bar at the bottom (sometimes called a "whammy bar"), which is incorrectly named. It changes the tension of the strings on the guitar, which produces a change in pitch, NOT a change in loudness. This effect is correctly called vibrato. Singers and most instruments use vibrato to give a musical sound warmth and help a melody line flow a little more smoothly.

Any discussion about loudness and amplitude wouldn't be complete without a mention of "the big one" which occurred on the night of August 26, 1883. Krakatoa, a small island with a big volcano near Java, was undergoing a series of eruptions. After one of them, lava cooled in the conduit, sealing the volcano. It tried to erupt but remained sealed. Pressure built up. More pressure built up. Finally the volcano exploded (taking a good bit of the island with it) creating a sound that was audible 3000 miles away. Nothing else in recorded history comes close to the volume of that eruption. I have been unable to find any account written by someone relatively close to the explosion, probably because anyone near was drowned in the tidal wave created in the event.


One of the significant characteristics about sound is the amount of order or regularity we perceive from it. When air vibrations have little or no organization or patterns in them, we usually call them "noise". Radio static, rainfall, wind, thunder, jet exhaust, etc. are some examples of what is probably the most chaotic sound we know of. The name white noise is given to this sound: noise because of the lack of order heard in it, and white because it contains frequencies from all over the audible spectrum (just as white light is a mixture of all visible light).

If we try to analyze white noise, we get no comprehendible or recognizable patterns. A term for sounds that don't have any regularly repeating pattern is "transient sounds". White noise consists completely of transient sounds. Using the pond analogy, noise is like tossing a handful of pebbles of varying size in a pond.

Obviously, there are more types of sound in our environments than types of white noise. One example of this is speech. When analyzed by a computer or seen on an oscilloscope screen, speech has a definite pattern--but little regularity (all too often in music and art regularity is mistakenly thought of as synonymous with order--they are only distantly related cousins!). Both speech and white noise contain transient sounds--that is, air disruptions that don't repeat. The difference is that speech uses these non-repeating sounds in recognizable patterns, whereas white noise has no distinct patterns at all. In essence, speech is order without regularity.

Let's go a bit further in the concept of order, patterns, and regularity. When we repeat an air disturbance at precisely regular intervals, the adjective used to describe it is "periodic".

When periodic air disturbances happen less than 16 times a second, we hear them as individual clicks, pops, or other events. An interesting thing happens, though, when those repetitions come faster than 16 times a second. There is a breakdown in the process because our nervous system can't deal with hearing more than sixteen individual events in a second, and begins to hear all of those disturbances as a single event--a musical note. The faster the disturbance, the higher pitch we hear. Over the last few thousand years, we have been building some highly sophisticated devices that disturb the air at precisely controlled rates. We normally call these devices "musical instruments." For example, if you disturb the air at a rate of 440 times a second, you will produce the note "A" above middle C.

If we increase the frequency [speed] of the vibration, our built in air motion detectors on the sides of our heads send the complex information to the brain. The brain then comes to a simple conclusion that the pitch has gone up. Slow the air vibrations down and to a listener, the pitch drops. Create a device that can create regular (periodic) air disturbances at varying speeds, make it easy to control, and you will have invented a musical instrument. Many musicians have a sense of hearing so accurate that they can tell the difference between a note at 440 vibrations per second and one sounding at 441 vibrations per second.

To our hearing mechanisms, these repeating disturbances create music only up to a point. When they disturb the air faster than 20,000 times a second, there's a part of our hearing mechanism that can't handle vibrations that fast, and we perceive silence, even though the air is still being disturbed. The average human hearing range is from 16 to 20,000 cycles per second (usually abbreviated cps, sometimes Hz, short for Hertz). As mentioned above in the section on the ear, age and repeated exposure to loud will cause the upper limit to drop.

Other lifeforms don't share our high frequency limitations. There really is no such thing as a "silent" dog whistle. It is silent to us only because it produces pitches above the 20,000 cps limit, which is still well within a dog's range of hearing. If it were truly silent, the dog wouldn't hear it either! Bats emit very high pitched squeaks to communicate and use as a type of sonar. Recording equipment can capture these sounds and slow them down to where they will make sense to our own built-in hearing equipment.

To sum up the last few paragraphs, the amount of order and pattern we perceive in air disturbances determines whether we hear noise, speech, music, or anything in between. It's likely that everyone below the age of 50 (and probably over 50 as well) has had his or her music called "noise" at some time or another by a parent or two. While "beauty is in the eye of the beholder", to a certain extent it is also true that "music is in the ear of the hearer." On a technical level, this is not always true. Unless you sit and listen to radio static, the next time someone tells you that "you're just listening to noise", gently remind them that noise is sound without any order whatsoever. The order in your music may simply not be getting across to everyone who hears it, but that doesn't qualify it as noise. Scientifically analyzed, music is as far away from noise as one can get. But then again, the lines may be blurring just a bit.

Composer Edgar Varese once defined music as "ordered sound", to which I would like to emend slightly to read as "ordered non-speech sound", even though there is a very close relationship between speech and the melodic and rhythmic elements of speech (and if you alter speech just a bit, it becomes singing which is clearly musical--well, at least in the hands of some people it does!).

Definitions such as these purposely open up the barn door as to what can be called music. There are a great deal of things surrounding us that have order. Are bird songs music? Messian, Vivaldi, and Beethoven are three in a long line of composers who thought so and created compositions using bird songs for some of the melodies. How about street sounds, such as car horns? Listen to "An American in Paris" by Gershwin. A train? Try "Pacific 231" by Honegger. The hee-haw of a donkey? Mahler, Grofe, Mendelssohn are among those that have found that sound musical enough to incorporate in their own compositions. In their own times, these compositions may have raised a few eyebrows, but today are considered staples of the repertoire.

Let's take these ideas a bit further and stray into territory that many people find a little dangerous. What about things like lawnmowers or vacuum cleaners (certainly periodic, definitely ordered)? A composer might create a composition using bits and pieces of such sounds and ultimately make a very powerful statement on a mechanized society. Another musician adept at using a sampling keyboard will take any one of the above sounds and convincingly play Bach or Mozart for you. Which one of these two examples is music? Both? Neither?

Even white noise isn't without musical value. If I told you there have been instruments invented that produce bursts of white noise and filtered white noise (filtered means that some ranges of frequencies are removed), you might laugh. That is, until you learned those instruments are commonly called "drums".

Maybe this territory isn't quite as new as it sounds. Ever since the beginning of music, we have been incorporating sounds from our environment. There isn't sufficient room on this page to list all of the musicians who have used sounds of storms to create pieces of music, but it includes Beethoven, Rossini, Wagner, and Vivaldi. Another good example would be musical instruments made from body parts of dead animals, specifically the horns--a few thousand years or so later, we began making them of metal and called them names like "trumpets" and "trombones".

Today's environment merely provides some unexpected possibilities and perhaps some unexpected riches.

How many rappers have made their own rhythm tracks by turning a record on a turntable back and forth a few inches?

Perhaps the ultimate statement made about all the organized sound that has become significant in our lives was a composition by American composer John Cage. While Cage has been called a charlatan, insane, a genius, and about everything else imaginable, he certainly will go down in history as one of the most revolutionary musical thinkers in this century. One of his compositions is entitled 4' 33", named for its length of four minutes and thirty-three seconds. When it is "performed", there is a definite starting time. Four and a half minutes later, the composition ends without the performer having played a single note. Yes, that's correct, the score consists of a four and a half minute rest. The music consists of all of the organized sounds that intrude on the silence--programs rustling, audience members coughing, distant car horns, bird songs, perhaps a vacuum cleaner on another floor, traffic noises, perhaps someone walking by with a loud boom box, etc.

When a tree falls in the forest and no one is around to hear it, does it create a sound? From what we know, it most certainly creates an air disturbance. . . To solve this old riddle, the answer lies in how we define 'sound'--if it has to be heard or not or not to be called "sound". The question really has nothing to do with acoustics or physics or any other science--it has to do with semantics. A good overview of the problem and knowledge of all factors involved will help decide the answer.

Are all of the strange sounds described above music? Are some of them? Where does one draw the line? Those are questions ultimately to be decided by each listener, but regardless of opinion, when a listener encounters something radically different, he should keep an open mind and hang on to an understanding of historical perspective. Like the above riddle about the tree falling in the forest, the real answer to the question involves understanding all parts of the problem and then making an informed decision. Choosing when all of the facts are not known really isn't much of a choice.

Is John Cage a controversial figure? Without question. And equally without question, he has helped to push the boundaries of what we consider music farther than they have ever gone.

If I haven't answered the question of what is music and what isn't, it's because there is no answer. Maybe it would be better to say there really is no one answer for everyone. We are fortunate to be living at a time where there is a great deal of experimentation and exploration, enough to challenge us for the rest of our lives. If I can't answer the question, I hope I have at least been able to show the complexity of the problem.

Finally to close all this philosophizing on music, I'll pose a riddle of my own. If John Cage falls in the forest while performing 4' 33" and no one was listening, would he create music?


As mentioned earlier, the system that does our hearing for us can move back and forth in only one dimension, but that one dimension gives all the information needed.

Primarily, there are three independent factors that are significant in making up the difference in the sounds that we hear. These three also show up on an oscilloscope screen and can be easily distinguished on a waveform diagram.

The first and most obvious of these is the aspect of AMPLITUDE, or how far the air is being pushed back and forth. The amplitude of a sound determines how far in and out our eardrums are pulled by a sound. Subjectively, we hear amplitude as loudness. Amplitude is not an insignificant factor--we might not even notice the distant (soft) burst of a firecracker while a close one (loud) will cause us to dive for cover.

A second factor that we hear is the aspect of FREQUENCY. For the most part, this applies mostly to periodic or musical sounds--sounds that repeat the air disturbances over and over. Again, to our ears, this gives us the sense of pitch. A fast periodic disturbance will cause us to call it a high pitch. A slow one will cause us to call it a low pitch. These two factors are independent of each other in our hearing--and on an oscilloscope screen or waveform diagram.

To complete a discussion of frequency, an understanding of the concept of wavelength is necessary.

If we were to create some kind of a periodic vibration on the surface of a pond, the wave peaks would travel outward from the source. If we were able to instantaneously freeze the surface of the pond, we would have a clear record of that wave disturbance sitting in front of us. A simple ruler would be the only thing needed to measure the distance from peak to peak, a reading that would give us a measurement described as "wavelength".

Again, nearly the same thing happens in air. Even if we could see the pressure changes in air, it would be going by too fast for us to see. If you think of the model of the surface of the pond, you will get the point.

Imagine an instrument is producing a frequency of 1100 cps. The sound travels outward from the source at a rate of 1100 feet per second. Let's say, like the pond water, we are able to instantly freeze the motion of the air molecules. In that one second, 1100 different vibration cycles have travelled over 1100 feet. Each individual vibration will be spread out over. . . one foot. One foot, then, will the wavelength of the sound.

Imagine another note, this time at a frequency of 550 cps. Travelling outward at the same speed, in one second these 550 vibrations are evenly distributed over a distance of 1100 feet. Each one will be spread out over. . . two feet. A pitch of 550 cps will have a wavelength of two feet.

Several things can be derived from this. First, if you raise the pitch, you also shorten the wavelength being produced. Lower the pitch and the wavelength lengthens. Among other things, this helps explain why big speakers are generally needed to produce low sounds. Larger acoustical instruments are usually necessary to produce the long, weighty low pitches--the size of the instrument is often related to the wavelengths it produces.

First, it's relatively easy to come up with the formula to determine wavelength. Wavelength = 1100/cps of the note.

Because a regular measurement is needed, transient sounds are usually not described in terms of wavelength. Only periodic sounds apply here.

The factor responsible for the most riches in the variety that we hear is the PATTERN of the air disturbances.

Instead of being a simple push-pull or a series of pushes and pulls, it is often highly complex, and in the case of music, highly mathematical.

If there is no detectable pattern of the air disturbances, we call it noise. Everything that we recognize has some kind of pattern, therefore some kind of order that we recognize. If we hear a great deal of order, we often call that sound music.

The simplest pattern of push and pull on the air is the sine tone, following the pattern of the sine function. Unless it is generated electronically, you will never hear one by itself, although the human whistle is moderately close.

Most natural sounds are complex--very complex, far more so than the sounds produced on a synthesizer.

Musical instruments produce a very unique pattern of air vibrations. The patters are very complex--but actually quite predictable and very regularly mathematical.


All of the different shades of light that we see can be broken down into combinations of the three primary colors of light--red, blue, and green (pigments in painting use a slightly different set of primary colors but the principle is the same). White light is the equal presence of all three, while darkness is the absence of all three.

It's rare that in all the shades you see every day that you will see many primary colors. Most of what we see is a mixture of hues.

In the same sense, musical sounds are also very complex mixtures, but mixtures that contain a lot of regularity in their patterns. With one exception, every single musical note you will hear is not just one simple vibration, but a combination of many different frequencies. Out of lack of anything better to call it, this concept is named "tone color." Different combinations of these vibrations are what make instruments sound distinct from each other and produce different "tone colors".

That means that even when a person plays one note on a piano or a guitar, he is producing not just one but many periodic vibrations. When we listen to this, we are hearing a very complex mixture--even though we perceive it as only one note.

There's a physical principle attached to all of this: when an object vibrates in air, or when the air itself vibrates (as in the case of the flute), it never just pushes and pulls the air in the very fundamental pattern illustrated below.

This sound, called a sine tone because it mimics the pattern of the trigonometric sine function, can only be produced electronically. Every other object or instrument that produces a tone produces the mixture. Sounds close to that of a sine are the human whistle and the test tone used for the Emergency Broadcast System.

Each tone produces a series of vibrations. The lowest pitched one of this series is called the fundamental. In most notes, the fundamental is also the loudest of all of the vibrations.

Our ears pick out the fundamental the most. To our hearing, this particular component gives us the sense of pitch. In other words, the fundamental is responsible for us hearing a note as a C, a C#, an Ab, and so forth.

Let's say I sound a note on a piano with a vibrating frequency of 110 cps. That means the fundamental frequency is pushing and pulling the air 110 times a second, and happens to be the note "A" in the first space in the bass clef.

The piano string and the soundboard are also causing more vibrations than just this one in the air.

The rest of these are called overtone vibrations, or just simply, overtones.

Overtones sound at a higher pitch than the fundamental (vibrate the air faster), and are almost always quieter than the fundamental. Our ears don't pick the individual overtones out, but react to them as a package. That package is what makes us hear the element of tone color. Overtones tell us whether we are hearing a C played on a trumpet, a piano, a violin, an oboe, or any other instrument.

Going back to the piano note 110 cps A; when played, in addition to the fundamental frequency of 110 cps you will hear additional disturbances (overtones) created at 220 cps, at 330 cps, at 440 cps, 550 cps, 660 cps, etc. Yes! All those in just that one note.

Do you notice a relationship between all those numbers? Hopefully you do. In algebraic terminology, if we say the fundamental is sounding at x cps, the overtones created are sounding at 2x, 3x, 4x, 5x, 6x, and so on.

In reality, when you play that note A, you are also hearing additional pitches that correspond to the notes in the parentheses below.

Another example--if a piano sounds a note with a fundamental frequency of 400 cps, you hear vibrations at 400 cps, 800 cps, 1200 cps, 1600 cps, 2000 cps, etc.

In both cases, we have the pattern of x cps, 2x cps, 3x cps, 4x cps, 5x cps, etc. being perfectly duplicated. The name for this special and very orderly pattern is the harmonic overtone series.

A common question--which do you hear first, the fundamental or the overtones? The answer is neither, and here, visible light can be used as a model. When you look at an object painted in orange paint you don't see first the yellow and then red! In musical sound, you don't hear first one and then the other--you hear the whole package at once.

Although this pattern might well seem that it should be a rarity in musical sound, it is not. If fact, it is the rule and any other pattern is the exception, usually sounding quite foreign to our ears.

Bells are one of the few sounds sculpted to produce an inharmonic overtone series. Many synthesizers can be adjusted to produce notes with an inharmonic overtone series--they tend to sound very unnatural and characteristically electronic. Any sound whose overtone frequencies aren't exact multiples of the fundamental frequency will probably sound strange to our ears.

When these sounds are fed into an oscilloscope, there is a curious relationship between what we see and what we hear. If the picture on the screen looks orderly and symmetrical, it will probably sound pleasing. If it looks irregular, bizarre, or out of control, it will sound accordingly. The reason for that is somewhat of a mystery. It may well be that our nervous system simply likes to process the most regular and orderly types of data.

Going a little more deeply into the effect we know as tone color: two instruments, let's say a viola and a trombone, are playing the same note. Each one is a normal harmonic overtone series. Therefore, each one is producing a fundamental at the same frequency. Each one's overtones will also be sounding at the same frequencies.

Why do they sound different from each other?

The answer here lies in not the frequency of the overtones, but the amplitude of each one.

While instruments might be producing the same overtones, they aren't producing them at the same loudness.

Take the example of color--if you mix red and yellow together, you get orange. Add a little more yellow to the mix and you get a brighter orange. Add black to the mixture and it will begin shifting toward the color brown.

Patterns differ from instrument to instrument. For example, a French horn has an overtone series that drops off quite evenly in volume as the overtone frequencies go up. A clarinet has a soft first overtone, a loud second overtone, a soft third, a loud fourth, etc.

If we could somehow make a musical instrument with overtones that could be adjusted in volume, you would have a tone color chameleon. Those instruments exist and are commonly called "synthesizers". Many synthesizers can successfully mimic the sounds of acoustical instruments because they can adjust their overtone amplitudes.

Strong upper overtones are responsible for making an instrument's sound "bright" or "piercing". If we get rid of some of the upper overtones, the sound becomes a little "darker" or "duller". If you have ever tried to talk through a pillow, the low frequencies will travel through with little problem whereas much of the high frequency energy will be absorbed by the pillow, producing a muffled sound.

To summarize the above:

  1. Each musical note produced on an acoustical instrument is a complex mixture of pure sine tones
  2. The vast majority of non-electronic instruments produce a harmonic overtone series--meaning a pattern of x, 2x, 3x, 4x, 5x, etc.
  3. The lowest pitched one is called the fundamental and our ears interpret it as the pitch of the note
  4. Frequencies higher than the fundamental are called overtones; we perceive overtones as creating "tone color"
  5. Two instruments playing the same note will sound different because their overtones will be sounding at different amplitudes.

It might seem a safe assumption that our ears and our nervous system will respond the best to the very simplest types of vibrations. As harmonic sounds seem more pleasing than inharmonic sounds, maybe the most soothing acoustical environment might be where all we hear would be sine tones.

In reality, such an environment might make the most insidious torture chamber of them all. Natural sound is a very rich mixture of overtones, transients, and little acoustical idiosyncrasies that our nervous systems have learned to know and love.


There are some mathematical relationships found in normal harmony. There are quite a few early mathematicians who have discovered fundamental links between the order found in mathematics and music, Pythagoras being among their company.

As stated above, if you take any frequency and exactly double it, you will get the frequency of the first overtone. You will also get a musical interval called an octave. You will also get a note of the same letter name as the one from where you started.

If we start on any note named "C" and double the frequency, we will get another note named "C". Furthermore, the two will sound and function quite a bit alike. A note that clashes with one C will clash with any other. A note that sounds well with any C will also sound well with any other.

The lowest note on a full size piano is an "A", vibrating at a frequency of 27.5 cps. If I double that figure, and keep on doubling it, I will name every note named A in the musical range--55 cps, 110 cps, 220 cps, 440 cps, 880 cps, 1760 cps, 3520 cps, etc. This is a mathematical progression called a geometric progression.

Another relationship--if I take any frequency (we'll call it the algebraic x), and sound the frequencies representing 4x, 5x, and 6x, it will produce a major triad (discussed at the end of Chapter Four). Any three notes with a frequency ratio of 4/5/6 will be a major chord. Tones of 200 cps, 250 cps, and 300 cps will produce that. Tones of 440 cps, 550 cps, 660 cps will do the same.

Although it sounds straight out of science fiction, these simple mathematical relationships are highly important in the normal musical sound we take for granted. As mentioned much earlier in this text, Classical Greeks considered music to be one more branch of mathematics.

However, when a loud stereo is blaring from an adolescent's room, the excuse "I'm just doing my math" still doesn't work too well. . .


When they think about it, many people might find it more than a little surprising when they realize that while a stereo system has only two speakers, more than two sounds can be produced simultaneously. LOTS more, as a matter of fact. Returning to the example of the Mahler eighth symphony with its small army of performers, those same two (or even one speaker on a small player) can reproduce the sound of those one thousand musicians. A good listener can concentrate only on the woodwinds, the strings, the brasses, perhaps one of the organs, a section of singers, or even one of the soloists--even when all of them are performing simultaneously. How can this happen?

Baron Jean Baptiste Fourier was a mathematician who lived from 1768 to 1830. He expressed the theory that any simple regular, complex regular, or irregular function could be expressed by the sums of many sines and cosines at different amplitudes and frequencies.

More simply put, Fourier stated that all regular mathematical patterns could be made from a series of sine patterns.

Mathematically speaking, when several patterns or functions are combined on a Cartesian graph, the values add. In the combination illustrated below, the positive values (above the x axis) combine to a greater positive number, and the negative values combine to produce a greater negative number. When one is positive and the other negative, they cancel out each other out somewhat.

While Fourier had only mathematical functions in mind, he created a perfect model for what happens to the airwaves as several sounds combine. It also creates an excellent model for explaining the regular patterns found in the periodic sounds generated by musical instruments. Sine tones (an air disturbance following the pattern of the sine function) are the basic building blocks for the periodic sounds we call music.

Fourier synthesis is the technique of creating complex sounds out of these sine tone building blocks. Fourier analysis is simply the reverse, examining the air disturbance patterns made by an instrument and breaking them down. Many synthesizers create their tone colors by a process called FM synthesis, which is basically Fourier synthesis under another name.

Let's go back to the graph, and this time think of them as being sounds that push and pull the air instead of mathematical functions. The positive Y values (relating to the up and down axis) represent compressions and the negative Y values represent rarefactions. The X axis (the horizontal axis) represents the passage of time. If we have two things pushing the air at the same time, the result is a combined push or compression. Ditto for a combined pull (a combined rarefaction). When one musical instrument is pushing and another is pulling, a certain amount of cancellation takes place. If you have two identical waveforms perfectly out of phase with each other (meaning that one is pushing while another is pulling), you will get zero air disturbance. In other words, silence.

So--an interesting thing happens when you hear several tones or sounds simultaneously--their compressions and rarefactions combine into a single disturbance that is the sum of their disturbances. BUT--that sum disturbance retains certain characteristics of its components. AND--very importantly, that sum disturbance pushes and pulls our eardrums in and out in the same complex manner. A good listener (it has very much to do with concentration and little to do with hearing) can pick out the individual parts.

The diagrams below start with simple examples and move into more complex sum disturbances [waveforms]. Keep in mind that if we were hearing these as sound, each component--no matter how weak--would have an effect on the sum disturbance, and thereby on our hearing.

Keep in mind that more complex air disturbances, such as the disturbances created by musical instruments, work exactly the same way. They combine into a sum disturbance, which pushes and pulls on the microphone in that same complex sum disturbance. The playback of the recording causes a speaker or two to push and pull on the air in a complex pattern.

When that complex pattern reaches our eardrums, they are pushed in and pulled out in the same pattern. When those patterns reach the brain, it tries to make sense of the pattern, comparing it to what it is already familiar with.

At that point, without consciously thinking much in the process, we conclude that we are listening to the Mahler 8th symphony, the Talking Heads, Louis Armstrong playing with a jazz band, or one of countless other sounds.

This is basically how our eardrums can move in and out in only one dimension and we can still hear everything. It also helps the process that over the years we have learned to make sense of and recognize many of those patterns.

The waveform diagram on the left shows two sine waveforms. The first is at a frequency of X and an amplitude of Y; the second with a frequency of 3X and an amplitude of 1/2 Y. The sum waveform on the right contains obvious elements of both the large structure and the small structure. We can not only see the combined effect of the two, we could easily hear it. If the low frequency tone was the note "C", the higher one would be sounding the note "G" an octave and a fifth higher.

This particular combination is much simpler than the average musical instrument's sound, but would resemble the sound of a cheap electronic organ.

The second waveform diagram is a result of four sine functions, the first at a frequency of X and an amplitude of Y; the second at a frequency of 3X and an amplitude of 1/3 Y; the third at a frequency of 5X and an amplitude of 1/9 Y; and the fourth at a frequency of 7X and an amplitude of 1/27 Y. The sum waveform on the left begins to resemble a square waveform which has a fundamental and even numbered numbered overtones (which are actually at the frequencies of 3, 5, 7, etc. times the fundamental). The slight asymmetry in the sum waveform is a result of rounding errors in the computer calculations. If the lowest tone was a "C", the second would be a "G" an octave and a fifth higher, the third would be the "E" a sixth above that, and the fourth would be a note halfway between an "A" and a "Bb" above the "E".

This waveform would sound a good deal like a clarinet.

A sawtooth waveform is theoretically the result of a fundamental and all overtones. The above diagram seems to support that conclusion. This third diagram is a result of seven waveforms--two of them are beyond the resolution of the graph but are still figured in the final calculations. The first is at a frequency of X and an amplitude of Y; the second at a frequency of 2X and an amplitude of 1/2 Y; the third at a frequency of 3X with an amplitude of 1/4 Y; the fourth with an amplitude of 4X and an amplitude of 1/8 Y; the fifth at a frequency of 5X and an amplitude of 1/16 Y; the sixth at a frequency of 6X and an amplitude of 1/32 Y; and the last with a frequency of 7X and an amplitude of 1/64 Y. If the lowest tone was a "C", the others would be (in ascending order) "C" an octave up, "G" immediately above that, the next "C", the next "E", the next "G", and ending on a tone halfway between "A" and "Bb".

This waveform would sound quite a bit like that of a string on a violin.

The final waveform diagram is an odd assortment of frequencies and amplitudes. You may have noticed that some of the waveforms ended in the middle of a cycle--at any rate, they do not conform to any particular ratio. The final result is a mess of asymmetry. It not only looks strange, but will sound very electronic and unusual. The first three waveforms are calculations involving harmonic overtones. This one makes use of inharmonic overtones.

This waveform would sound unlike anything we are used to hearing, although with a percussive envelope (amplitude change), it might sound like a bell.

Again, each of these sines in the diagrams on the left represents the separate components found in a musical sound.

The resulting waveform (the sum waveform, on the right of each diagram) is the complex waveform that actually comes from an instrument or travels through the air and drives our eardrums. Fourier analysis, in that case is only theoretical because the instrument gleefully produces that whole package of sound. Fourier analysis, however, does demonstrate that the complex is made up of a finite simpler series.

If you look carefully, you can see that each sum waveform has characteristics of all of its components. In all cases you would be able to hear the effects of all the components in the final result.

There is often a strangely close relationship between the order we can see (especially if the waveform is fed into an oscilloscope) what we can hear.

When the sine frequencies are mathematically related in what is called a harmonic pattern, they will produce a symmetry that is sometimes strikingly beautiful. Most musical instruments automatically produce harmonic patterns. They will also sound very smooth, interesting, and--natural. Remember that most of the musical sound we hear is composed of a harmonic overtone series.

When the component sine frequencies are mathematically unrelated, an inharmonic series is created. Inharmonic sounds both look and sound strange.

Fourier synthesis demonstrates that the complex periodic sounds generated by instruments have very regular, predictable, and mathematical components.

It also demonstrates that you don't need one thousand speakers to playback the sound of one thousand musicians--or need a large number of ears to catch the sounds around us.


When compared to musical sound, speech is rather chaotic, but it nevertheless contains some of the characteristics of music. With a little modification, the process becomes very musical, specifically singing.

Speech is pretty much a mixture of transient sounds and periodic sounds. Conveniently, they correspond to consonants and vowels, respectively. Singing emphasizes the vowels, which being periodic, are tailor-made for musical creations.

When we breathe, air travels from the lungs through the windpipe. If we wish to create a sound we divert some of that air through the larynx, commonly called the voicebox. The larynx is situated inside the bump on our throat, commonly called the "Adam's Apple".

A woman's larynx is typically smaller than a man's. The smallest ones, producing the highest pitches will produce a singer in what is called the 'soprano' range. If the larynx grows a little larger, she will sing in an 'alto' range.

Before puberty, there's little differance between the size of male and female larynx. At the onset of puberty, one of the changes that takes place is a drastic enlargement of the male larynx, and the voice begins to drop. Men will generally sing in the 'tenor' range, or if their larynx gets a bit larger, the 'bass' range.

The larynx contains a membrane (often mistakenly called "vocal cords"--there is no anatomical structure even resembling a cord). Those vocal membranes vibrate from the airstream, much like a reed in a saxophone or clarinet. If we want to create a loud sound, we divert a lot of air over the vocal membrane. If we wish to create a soft sound, we divert only a little through the larynx. If we wish to be silent, we shut off the detour through the larynx.

The larynx, while flexible, is connected to muscles that control the tension placed on it. When it is very loose, it will vibrate at a slow pitch. When the muscles tense on it and begin to pull it taut, it will vibrate faster. If you have ever sung, you have learned to control those muscles.

Even if we don't sing, our natural speech often contains rises and falls in pitch. Just by listening to a person's speech you can often tell if he is nervous or tense--we naturally tend to flex the muscles controlling the vocal membrane--and the pitch of our speech rises just a bit. Anyone who has ever acted is very aware of the nuances expressed through this varying tension on the membrane.

If it sounds like a complicated process, it is. But, it's something we literally can do from the instant we are born--babies cry all too easily without being taught.

Going a little further into the process, let's examine the periodic sounds--the vowels. Compare the vowel sounds "EEEEEE" and "OOOOOO". Seen on an oscilloscope screen, the "EEEEEE" sound contains many jagged lines that are very close together--a dead giveaway for high frequency sounds. The sound "OOOOOO" appears much more round, missing the sharp close points--there is a much lower proportion of high frequency sound in the total mix. Other vowel sounds fall in between these two extremes.

The vocal membrane produces a basic vibration with little variation in tone color. It is up to our mouths and sinuses, among other organs, to shape the sound into the various sounds and phonemes that make up speech.

To shape the vowel sounds, we have learned to use our upper respiratory organs as tone controls--not too unlike the tone controls on a stereo. When we want to make the EEEEEE sound, we are letting the whole spectrum of frequencies pass, allowing some of the higher ones to resonate in our sinuses. When we change that to an OOOOOO sound, we are using our mouths, our tongue, and our sinuses to damp out those high frequency components of the sound.

Again, the vowels are quite easy to sustain, something necessary for musical sounds.

Consonants are a slightly different matter. They represent non repeating bursts of sound shaped by the mouth, tongue, and sinuses. Several consonant phonemes ('s', 'f', and 'p' for example) don't even involve the larynx and are created exclusively in the mouth.

The difference between the structure of the consonants is very minute. People who have a bad headcold are often very difficult to understand because their sinuses aren't able to produce all of the frequencies we are used to hearing from those consonants. Holding your nose and talking will create nearly the same effect.

Speech tends to emphasize consonants much more than singing. Singers, especially operatic singers, are often very hard to understand because that type of singing requires a very heavy and unnatural concentration on the vowels. As it emphasizes very careful control of muscles from the diaphragm to the head, it can also result in massive amounts of sound. The type of singing employed by trained opera singers came about before PA systems were invented, when individuals had to compete with an orchestra and fill an entire hall with their sound.