Musical tones are produced by musical instruments, or by the voice, which, from a physics perspective, is a very complex wind instrument. So the physics of music is the physics of the kinds of sounds these instruments can make. What kinds of sounds are these? They are tones caused by standing waves produced in or on the instrument. So the properties of these standing waves, which are always produced in very specific groups, or series, have far-reaching effects on music theory.

Most sound waves, including the musical sounds that actually reach our ears, are not standing waves. Normally, when something makes a wave, the wave travels outward, gradually spreading out and losing strength, like the waves moving away from a pebble dropped into a pond.

But when the wave encounters something, it can bounce (reflection) or be bent (refraction). In fact, you can "trap" waves by making them bounce back and forth between two or more surfaces. Musical instruments take advantage of this; they produce pitches by trapping sound waves.

Why are trapped waves useful for music? Any bunch of sound waves will produce some sort of noise. But to be a tone - a sound with a particular pitch - a group of sound waves has to be very regular, all exactly the same distance apart. That's why we can talk about the frequency and wavelength of tones.

Figure 3.6. 

A noise is a jumble of sound waves. A tone is a very regular set of waves, all the same size and same distance apart.

So how can you produce a tone? Let's say you have a sound wave trap (for now, don't worry about what it looks like), and you keep sending more sound waves into it. Picture a lot of pebbles being dropped into a very small pool. As the waves start reflecting off the edges of the pond, they interfere with the new waves, making a jumble of waves that partly cancel each other out and mostly just roils the pond - noise.

But what if you could arrange the waves so that reflecting waves, instead of cancelling out the new waves, would reinforce them? The high parts of the reflected waves would meet the high parts of the oncoming waves and make them even higher. The low parts of the reflected waves would meet the low parts of the oncoming waves and make them even lower. Instead of a roiled mess of waves cancelling each other out, you would have a pond of perfectly ordered waves, with high points and low points appearing regularly at the same spots again and again. To help you imagine this, here are animations of a single wave reflecting back and forth and standing waves.

This sort of orderliness is actually hard to get from water waves, but relatively easy to get in sound waves, so that several completely different types of sound wave "containers" have been developed into musical instruments. The two most common - strings and hollow tubes - will be discussed below, but first let's finish discussing what makes a good standing wave container, and how this affects music theory.

In order to get the necessary constant reinforcement, the container has to be the perfect size (length) for a certain wavelength, so that waves bouncing back or being produced at each end reinforce each other, instead of interfering with each other and cancelling each other out. And it really helps to keep the container very narrow, so that you don't have to worry about waves bouncing off the sides and complicating things. So you have a bunch of regularly-spaced waves that are trapped, bouncing back and forth in a container that fits their wavelength perfectly. If you could watch these waves, it would not even look as if they are traveling back and forth. Instead, waves would seem to be appearing and disappearing regularly at exactly the same spots, so these trapped waves are called standing waves.

For any narrow "container" of a particular length, there are plenty of possible standing waves that don't fit. But there are also many standing waves that do fit. The longest wave that fits it is called the fundamental. It is also called the first harmonic. The next longest wave that fits is the second harmonic, or the first overtone. The next longest wave is the third harmonic, or second overtone, and so on.

Figure 3.7. Standing Wave Harmonics

There is a whole set of standing waves, called harmonics, that will fit into any "container" of a specific length. This set of waves is called a harmonic series.

Notice that it doesn't matter what the length of the fundamental is; the waves in the second harmonic must be half the length of the first harmonic; that's the only way they'll both "fit". The waves of the third harmonic must be a third the length of the first harmonic, and so on. This has a direct effect on the frequency and pitch of harmonics, and so it affects the basics of music tremendously. To find out more about these subjects, please see Frequency, Wavelength, and Pitch, Harmonic Series, or Musical Intervals, Frequency, and Ratio.

You may have noticed an interesting thing in the animation of standing waves: there are spots where the "water" goes up and down a great deal, and other spots where the "water level" doesn't seem to move at all. All standing waves have places, called nodes, where there is no wave motion, and antinodes, where the wave is largest. It is the placement of the nodes that determines which wavelengths "fit" into a musical instrument "container".

Figure 3.8. Nodes and Antinodes

As a standing wave waves back and forth (from the red to the blue position), there are some spots called nodes that do not move at all; basically there is no change, no waving up-and-down (or back-and-forth), at these spots. The spots at the biggest part of the wave - where there is the most change during each wave - are called antinodes.

One "container" that works very well to produce standing waves is a thin, very taut string that is held tightly in place at both ends. (There were some nice animations of waves on strings available as of this writing at Musemath.) Since the string is taut, it vibrates quickly, producing sound waves, if you pluck it, or rub it with a bow. Since it is held tightly at both ends, that means there has to be a node at each end of the string. Instruments that produce sound using strings are called chordophones, or simply strings.

Figure 3.9. Standing Waves on a String

A string that's held very tightly at both ends can only vibrate at very particular wavelengths. The whole string can vibrate back and forth. It can vibrate in halves, with a node at the middle of the string as well as each end, or in thirds, fourths, and so on. But any wavelength that doesn't have a node at each end of the string, can't make a standing wave on the string. To get any of those other wavelengths, you need to change the length of the vibrating string. That is what happens when the player holds the string down with a finger, changing the vibrating length of the string and changing where the nodes are.

The fundamental wave is the one that gives a string its pitch. But the string is making all those other possible vibrations, too, all at the same time, so that the actual vibration of the string is pretty complex. The other vibrations (the ones that basically divide the string into halves, thirds and so on) produce a whole series of harmonics. We don't hear the harmonics as separate notes, but we do hear them. They are what gives the string its rich, musical, string-like sound - its timbre. (The sound of a single frequency alone is a much more mechanical, uninteresting, and unmusical sound.) To find out more about harmonics and how they affect a musical sound, see Harmonic Series.

The string disturbs the air molecules around it as it vibrates, producing sound waves in the air. But another great container for standing waves actually holds standing waves of air inside a long, narrow tube. This type of instrument is called an aerophone, and the most well-known of this type of instrument are often called wind instruments because, although the instrument itself does vibrate a little, most of the sound is produced by standing waves in the column of air inside the instrument.

If it is possible, have a reed player and a brass player demonstrate to you the sounds that their mouthpieces make without the instrument. This will be a much "noisier" sound, with lots of extra frequencies in it that don't sound very musical. But, when you put the mouthpiece on an instrument shaped like a tube, only some of the sounds the mouthpiece makes are the right length for the tube. Because of feedback from the instrument, the only sound waves that the mouthpiece can produce now are the ones that are just the right length to become standing waves in the instrument, and the "noise" is refined into a musical tone.

Figure 3.10. Standing Waves in Wind Instruments

Standing Waves in a wind instrument are usually shown as displacement waves, with nodes at closed ends where the air cannot move back-and-forth.

The standing waves in a wind instrument are a little different from a vibrating string. The wave on a string is a transverse wave, moving the string back and forth, rather than moving up and down along the string. But the wave inside a tube, since it is a sound wave already, is a longitudinal wave; the waves do not go from side to side in the tube. Instead, they form along the length of the tube.

Figure 3.11. Longitudinal Waves in Pipes

The standing waves in the tubes are actually longitudinal sound waves. Here the displacement standing waves in Figure 3.10 are shown instead as longitudinal air pressure waves. Each wave would be oscillating back and forth between the state on the right and the one on the left. See Standing Waves in Wind Instruments for more explanation.

The harmonics of wind instruments are also a little more complicated, since there are two basic shapes (cylindrical and conical) that are useful for wind instruments, and they have different properties. The standing-wave tube of a wind instrument also may be open at both ends, or it may be closed at one end (for a mouthpiece, for example), and this also affects the instrument. Please see Standing Waves in Wind Instruments if you want more information on that subject. For the purposes of understanding music theory, however, the important thing about standing waves in winds is this: the harmonic series they produce is essentially the same as the harmonic series on a string. In other words, the second harmonic is still half the length of the fundamental, the third harmonic is one third the length, and so on. (Actually, for reasons explained in Standing Waves in Wind Instruments, some harmonics are "missing" in some wind instruments, but this mainly affects the timbre and some aspects of playing the instrument. It does not affect the basic relationships in the harmonic series.)

So far we have looked at two of the four main groups of musical instruments: chordophones and aerophones. That leaves membranophones and idiophones. Membranophones are instruments in which the sound is produced by making a membrane vibrate; drums are the most familiar example. Most drums do not produce tones; they produce rhythmic "noise" (bursts of irregular waves). Some drums do have pitch, due to complex-patterned standing waves on the membrane that are reinforced in the space inside the drum. This works a little bit like the waves in tubes, above, but the waves produced on membranes, though very interesting, are too complex to be discussed here.

Idiophones are instruments in which the body of the instrument itself, or a part of it, produces the original vibration. Some of these instruments (cymbals, for example) produce simple noise-like sounds when struck. But in some, the shape of the instrument - usually a tube, block, circle, or bell shape - allows the instrument to ring with a standing-wave vibration when you strike it. The standing waves in these carefully-shaped-and-sized idiophones - for example, the blocks on a xylophone - produce pitched tones, but again, the patterns of standing waves in these instruments are a little too complicated for this discussion. If a percussion instrument does produce pitched sounds, however, the reason, again, is that it is mainly producing harmonic-series overtones.

Music is sound that's organized by people on purpose, to dance to, to tell a story, to make other people feel a certain way, or just to sound pretty or be entertaining. Music is organized on many different levels. Sounds can be arranged into melodies, harmonies, rhythms, textures and phrases. Beats, measures, cadences, and form all help to keep the music organized and understandable. But the most basic way that music is organized is by arranging the actual sound waves themselves so that the sounds are interesting and pleasant and go well together.

A rhythmic, organized set of thuds and crashes is perfectly good music - think of your favorite drum solo - but many musical instruments are designed specifically to produce the regular, evenly spaced sound waves that we hear as particular pitches. Crashes, thuds, and bangs are loud, short jumbles of lots of different wavelengths. These are the kinds of sound we often call "noise", when they're random and disorganized, but as soon as they are organized in time (rhythm), they begin to sound like music. (When used as a scientific term, noise refers to continuous sounds that are random mixtures of different wavelengths, not shorter crashes and thuds.)

However, to get the melodic kind of sounds more often associated with music, the sound waves must themselves be organized and regular, not random mixtures. Most of the sounds we hear are brought to our ears through the air. A movement of an object causes a disturbance of the normal motion of the air molecules near the object. Those molecules in turn disturb other nearby molecules out of their normal patterns of random motion, so that the disturbance itself becomes a thing that moves through the air - a sound wave. If the movement of the object is a fast, regular vibration, then the sound waves are also very regular. We hear such regular sound waves as tones, sounds with a particular pitch. It is this kind of sound that we most often associate with music, and that many musical instruments are designed to make.

Figure 3.1. 

A random jumble of sound waves is heard as a noise. A regular, evenly-spaced sound wave is heard as a tone.

Musicians have terms that they use to describe tones. (Musicians also have other meanings for the word "tone", but this course will stick to the "a sound with pitch" meaning.) This kind of (regular, evenly spaced) wave is useful for things other than music, however, so scientists and engineers also have terms that describe pitched sound waves. As we talk about where music theory comes from, it will be very useful to know both the scientific and the musical terms and how they are related to each other.

For example, the closer together those evenly-spaced waves are, the higher the note sounds. Musicians talk about the pitch of the sound, or name specific notes, or talk about tuning. Scientists and engineers, on the other hand, talk about the frequency and the wavelength of the sound. They are all essentially talking about the same things, but talking about them in slightly different ways, and using the scientific ideas of wavelength and frequency can help clarify some of the main ideas underlying music theory.

So what are we talking about when we speak of sound waves? Waves are disturbances; they are changes in something - the surface of the ocean, the air, electromagnetic fields. Normally, these changes are travelling (except for standing waves); the disturbance is moving away from whatever created it, in a kind of domino effect.

Most kinds of waves are transverse waves. In a transverse wave, as the wave is moving in one direction, it is creating a disturbance in a different direction. The most familiar example of this is waves on the surface of water. As the wave travels in one direction - say south - it is creating an up-and-down (not north-and-south) motion on the water's surface. This kind of wave is fairly easy to draw; a line going from left-to-right has up-and-down wiggles. (See Figure 3.2.)

Figure 3.2. Transverse and Longitudinal Waves

In water waves and other transverse waves, the ups and downs are in a different direction from the forward movement of the wave. The "highs and lows" of sound waves and other longitudinal waves are arranged in the "forward" direction.

But sound waves are not transverse. Sound waves are longitudinal waves. If sound waves are moving south, the disturbance that they are creating is giving the air molecules extra north-and-south (not east-and-west, or up-and-down) motion. If the disturbance is from a regular vibration, the result is that the molecules end up squeezed together into evenly-spaced waves. This is very difficult to show clearly in a diagram, so most diagrams, even diagrams of sound waves, show transverse waves.

Longitudinal waves may also be a little difficult to imagine, because there aren't any examples that we can see in everyday life (unless you like to play with toy slinkies). A mathematical description might be that in longitudinal waves, the waves (the disturbances) are along the same axis as the direction of motion of the wave; transverse waves are at right angles to the direction of motion of the wave. If this doesn't help, try imagining yourself as one of the particles that the wave is disturbing (a water drop on the surface of the ocean, or an air molecule). As it comes from behind you, a transverse waves lifts you up and then drops down; a longitudinal wave coming from behind pushes you forward and pulls you back. You can view here animations of longitudinal and transverse waves, single particles being disturbed by a transverse wave or by a longitudinal wave, and particles being disturbed by transverse and longitudinal waves. (There were also some nice animations of longitudinal waves available as of this writing at Musemath.)

The result of these "forward and backward" waves is that the "high point" of a sound wave is where the air molecules are bunched together, and the "low point" is where there are fewer air molecules. In a pitched sound, these areas of bunched molecules are very evenly spaced. In fact, they are so even, that there are some very useful things we can measure and say about them. In order to clearly show you what they are, most of the diagrams in this course will show sound waves as if they are transverse waves.

Both transverse and longitudinal waves cause a displacement of something: air molecules, for example, or the surface of the ocean. The amount of displacement at any particular spot changes as the wave passes. If there is no wave, or if the spot is in the same state it would be in if there was no wave, there is no displacement. Displacement is biggest (furthest from "normal") at the highest and lowest points of the wave. In a sound wave, then, there is no displacement wherever the air molecules are at a normal density. The most displacement occurs wherever the molecules are the most crowded or least crowded.

Figure 3.3. Displacement

The amplitude of the wave is a measure of the displacement: how big is the change from no displacement to the peak of a wave? Are the waves on the lake two inches high or two feet? Are the air molecules bunched very tightly together, with very empty spaces between the waves, or are they barely more organized than they would be in their normal course of bouncing off of each other? Scientists measure the amplitude of sound waves in decibels. Leaves rustling in the wind are about 10 decibels; a jet engine is about 120 decibels.

Musicians call the loudness of a note its dynamic level. Forte (pronounced "FOR-tay") is a loud dynamic level; piano is soft. Dynamic levels don't correspond to a measured decibel level. An orchestra playing "fortissimo" (which basically means "even louder than forte") is going to be quite a bit louder than a string quartet playing "fortissimo". (See Dynamics for more of the terms that musicians use to talk about loudness.) Dynamics are more of a performance issue than a music theory issue, so amplitude doesn't need much discussion here.

Figure 3.4. Amplitude is Loudness

The size of a wave (how much it is "piled up" at the high points) is its amplitude. For sound waves, the bigger the amplitude, the louder the sound.

The aspect of evenly-spaced sound waves that really affects music theory is the spacing between the waves, the distance between, for example, one high point and the next high point. This is the wavelength, and it affects the pitch of the sound; the closer together the waves are, the higher the tone sounds.

All sound waves are travelling at about the same speed - the speed of sound. So waves with a shorter wavelength arrive (at your ear, for example) more often (frequently) than longer waves. This aspect of a sound - how often a peak of a wave goes by, is called frequency by scientists and engineers. They measure it in hertz, which is how many peaks go by per second. People can hear sounds that range from about 20 to about 17,000 hertz.

Figure 3.5. Wavelength, Frequency, and Pitch

Since the sounds are travelling at about the same speed, the one with the shorter wavelength "waves" more frequently; it has a higher frequency, or pitch. In other words, it sounds higher.

The word that musicians use for frequency is pitch. The shorter the wavelength, the higher the frequency, and the higher the pitch, of the sound. In other words, short waves sound high; long waves sound low. Instead of measuring frequencies, musicians name the pitches that they use most often. They might call a note "middle C" or "second line G" or "the F sharp in the bass clef". (See Octaves and Diatonic Music and Tuning Systems for more on naming specific frequencies.) These notes have frequencies (Have you heard of the "A 440" that is used as a tuning note?), but the actual frequency of a middle C can vary a little from one orchestra, piano, or performance, to another, so musicians usually find it more useful to talk about note names.

Most musicians cannot name the frequencies of any notes other than the tuning A (440 hertz). The human ear can easily distinguish two pitches that are only one hertz apart when it hears them both, but it is the very rare musician who can hear specifically that a note is 442 hertz rather than 440. So why should we bother talking about frequency, when musicians usually don't? As we will see, the physics of sound waves - and especially frequency - affects the most basic aspects of music, including pitch, tuning, consonance and dissonance, harmony, and timbre.

Most of the music books you'll find on the shelf are about Western music. From the end of the Middle Ages to modern times, composers and performers in western Europe gradually developed widely accepted standards for tuning, melody, harmony, meter, notation, form, counterpoint and other music basics. These rules are a sort of grammar for the language of music. Just as the basic rules for putting together sentences and paragraphs help people understand each other, knowing what to expect from a piece of music helps people understand and like it.

Of course, music, like language, changes through the centuries. A Bach invention, a Brahms symphony, and a Beatles song are different forms in different genres, and at first they may sound as if they have nothing in common. But they all use the same musical "language" and follow basically the same rules. They are all examples of Western music, and are all more like each other than they are like a Navajo lullaby, a Chinese opera, or a west African praise song.

Wherever Europeans went during the colonial era, they took their music with them. So, in places like Australia and the Americas, not only do most of the people speak European languages, much of their music also sounds Western. What are the rules of this European musical language? A complete answer to that question would be long and complex, since Western music, like any living language shared by many different communities, has many "local dialects". The short answer is: Western music is generally tonal, based on major or minor scales, using an equal temperament tuning, in an easy-to-recognize meter, with straightforward rhythms, fairly strict rules on harmony and counterpoint, and not much improvisation. This is, of course, a huge generalization. Twentieth century art music, in particular, was very interested in breaking down or even rejecting these rules. But because they are flexible enough to allow plenty of interesting but easy-to-grasp music, the rules are still widely used, particularly in popular music. In fact, the use of these traditional rules for Western music is now so widespread that it is sometimes called common practice. They are what makes Western music sound familiar and easy to understand.

Non-Western music is any music that grew out of a different culture or musical tradition than the European. For someone who grew up listening to Western music, Non-Western music will have a recognizably exotic sound. This comes from the use of different tuning systems, different scales, different vocal styles and performance practices, and different approaches to melody and harmony.

Much of the music that is popular today cannot really be classified as completely Western or Non-Western. Since colonial times, when European cultures came into contact with many Non-Western cultures, musicians on all sides have been experimenting with music that is a blend of "the best of both worlds." Many musical styles have been invented that mix Western and Non-Western traditions. Perhaps the oldest and most widely popular of these styles are the ones that join European and African musical traditions. These include various Latin (from Central and South America, some of which also include Native American influences) and Caribbean traditions, and from North America, many different kinds of jazz and blues. Most American popular musics also grew out of this blending of traditions.

But the process of inventing new ways of fusing Western and Non-Western music continues today in countries all over the world. The term World Music is often used as a catch-all category referring to almost any music with widespread popularity that clearly does not sound like North American popular music. This includes older blended traditions such as rumba and samba, newer but well-established blended genres such as reggae and Afrobeat, and groups with unique experimental sounds borrowing from more than one tradition. Folk and traditional music from around the world is also sometimes included, but the most popular genres in this category tend to be those, such as Flamenco, Hungarian folk, and Celtic music, that are easy for Western-trained ears to understand. African-American traditions are so basic to popular music that they are generally not included in World music, but other North American traditions, such as Native American and Cajun traditions, sometimes are.

As mentioned above, Western music has not remained static through the centuries, either. It has changed and evolved as composers experimented with new sounds, ideas, and even new or evolving instruments.

Medieval European music, like many Non-Western traditions, was modal. This means that a piece of music was not in a particular key based on a major or minor scale. Instead, it was in a particular mode. A mode may look very much like a scale, since it lists the notes that are "allowed" in the piece of music and defines the tonic of the music. But a mode is usually also a collection of melodies, melodic phrases, or patterns that are found in that mode and not others (since the various modes are more different from each other than the various scales). Modes also may imply or suggest specific moods or they may be meant to have particular effects on the character of the listener.

Different keys may also evoke different moods, but the main purpose of a key is to define the chords and harmonic progressions that will be expected from a piece of music. From the Renaissance to the present day, most Western music has tended to be tonal. Tonal music is music in which the progression of the melody and harmony gives the strong feeling that the piece has a note and chord that are its "home base", so to speak (the tonic of the key). Think of a very familiar tune, perhaps "Row, Row, Row your Boat" or "Happy Birthday to You". Imagine how frustrating it would be to end that tune without singing the last note or playing the final chord. If you did this, most people would be so dissatisfied that they might supply that last note for you. That note is the tonal center of the tune, and without it, there is a feeling that the song has not reached its proper resting place. In tonal music, just about any melody is allowed, as long as it fits into the harmonies as they wander away from and then head back to their home base. Most Western tonal music is based on major and minor scales, both of which easily give that strongly tonal feeling. Some other scales, such as blues scales, also work well within a tonal framework, but others, such as whole-tone scales, do not.

Most of the Western music that is popular today is tonal, but around the beginning of the twentieth century, composers of "Classical" or Art music (see below) began experimenting with methods of composing atonal music. "Atonal" literally means "not tonal". As the name implies, atonal music treats all notes and harmonies as equal and in fact tries to avoid melodies and harmonies that will make the piece sound tonal. One type of atonal music is twelve-tone music, which seeks to use each of the notes of the chromatic scale equally. Other pieces may even dispense with the idea that music has to consist of notes; compositions may be collections of sounds and silences. Since the music is not organized by the familiar rules of Western music, many people have trouble appreciating atonal music without some help or study.

Music can be more or less tonal without becoming completely atonal, however. Music that does not stray at all from its key is called diatonic. Many Western children's songs, folk songs, and pop songs are in this category. But composers often add some notes or even whole sections of music that are from a different key, to make the music a little more complex and interesting. Music that goes even further, and freely uses all the notes of the chromatic scale, but still manages to have a tonal "home", is called chromatic. Music that has more than one tonal center at the same time (Ives was particularly fond of this composition technique) is called polytonal.

Popular music is, by definition, music that appeals to many people. You don't have to know anything about music to like a pop tune - it's "catchy". Art music is a catch-all term for any music that is enjoyed by a smaller crowd. This can include the more challenging types of jazz and rock music, as well as Classical. Most people agree that the appreciation of art music requires some study, careful listening, or other extra effort. But it can be harder to agree on what exactly belongs in this category. This is at least partly because popular tastes do change. For example, most operas were written to be popular, middle-class entertainments, and artists such as Liszt and Paganini enjoyed rock-star-like fame and popularity in their day. Today, however, nineteenth century operas are no longer considered popular entertainment, and popular works that could technically be considered opera - except for the fact that they are written in popular musical styles - are instead grouped with musicals. As another example, ragtime was wildly popular during Scott Joplin's lifetime. It later fell out of favor and was known only to some jazz connoisseurs. Then in the 1970's it became popular again.

Classical music is a confusing term with more than one meaning. In the visual arts, the term classical refers to ancient Greece and Rome. In the 1700's, Western Europeans became very interested in the ancient classical style, which was imitated by many artists, sculptors, and architects. Art historians call that period the neoclassical ("new classical"). Unfortunately, nobody really knows what the music of ancient times sounded like. So instead of being influenced by the sound of ancient Greek music, eighteenth-century composers were influenced by the ideals of classical art. The music of Mozart, Haydn, and the early works of Beethoven are in this style, which we call classical rather than neoclassical, because the original classical music of ancient Greece and Rome is lost. (And actually, it probably would sound very exotic and Non-Western to us if we could listen to it!)

So the original classical music comes from one fairly short era. The other great composers of Western music lived during other periods: Bach and Handel were Baroque era composers, for example; Brahms and Wagner, Romantic; and Ravel and Debussy, Impressionist. But most people do not know which music is from which period. So all of the music of the great Western composers of the past (as well as modern art music that is part of the same tradition) is lumped together and called classical. The art music of other cultures is also often called classical; for example, people speak of the classical music of India.

The terms "folk music" and "pop music" also have more than one meaning. The folk music of a culture is the music that is passed down from one generation to the next, often without writing it down. It includes many different kinds of music: lullabies and children's singing games, tunes that everyone enjoys singing together or dancing to, songs for celebrations, ceremonies, and holidays. Folk music can gradually change as it gets passed along. Usually nobody remembers who originally wrote it, or who changed it, and there may be more than one version of any particular folk song. Since ancient times, folk music has been the music of ordinary people, not the ruling class or professional musicians. In every culture, children learned and remembered the music that everyone enjoyed the most, and the music that was important to their traditions.

The modern recording industry has changed things, though. In many cultures, pop music has largely replaced folk music as the music that everyone knows. Unlike folk music, it has usually been written recently and belongs to professional musicians, and new popular tunes quickly replace old ones. Even the types of music that are considered popular can change quickly. The term pop music can refer to a specific kind of popular music, as in "bubblegum pop". Popular music is also a general term for any type of music that is or has been a top seller. This includes most types of rock music and some kinds of jazz.

As the rise of recording pushed aside traditional music, some musicians made a point of recording traditional folk songs, so they would not be lost altogether. Some also wrote new songs in a "folk" style that enjoyed some popularity, particularly in the 1960's. Although these modern tunes do not fit the traditional definition, they are also called folk music.

It can be difficult to follow a discussion of music without hearing some examples. If you would like to hear some music in the categories above, or you are planning to present this lesson to a class, here are some easy-to-find suggestions. Some categories also include suggestions for where to start if you want more information.

The range of a voice or instrument is the set of pitches, from lowest to highest, that it can sing or play. A range can be described using the appropriate octave identification, for example, "from one-line c to two-line g". But it is often easiest to write the range on a staff, as the two notes at the high and low ends of the range.

A piece of music, or one performer's part in that piece, may also be described as having a range, from the lowest to highest note written for the performer in that piece. There is usually a difference (sometimes a large one) between the total range of the part and a smaller range that the part stays in most of the time (heading to the extreme highs and lows only occasionally). This smaller range is called the tessitura of the part. One can also speak of the tessitura of a performer's voice, which is the range in which it sounds the best (so that matching the tessitura of the part and of the performer is a very good idea). Notice the similarity between this second definition and the term power range, sometimes used to describe the most powerful or useful part of an instrument's range.

A register is a distinctive part of a vocal or instrumental range. For example, singers may speak of the head register, in the upper part of their range, and the chest register in the lower part of their range. These two registers sound and feel very different, and the singer may have even have two distinct tessituras, one in each register. The large range of the clarinet is also divided into distinctive registers with different capabilities and very different timbres. Even when an instrument does not have a very large variation in timbre over its range, its players may speak of the difficulty of "playing in the high register" or a "dull timbre in the low register".

Figure 2.8. Describing a Range

A typical choral arrangement divides women into higher and lower voices and men into higher or lower voices. Most voices can be assigned one of these four ranges, and this gives the composer four vocal lines to work with, which is usually enough. The four main vocal ranges are:

Arrangements for these four voices are labelled SATB (for Soprano Alto Tenor Bass). The ranges of the four voices overlap, but singers may find themselves straining or getting an unpleasant sound at the top or a weak sound at the bottom of their ranges. So although the full ranges of an alto and a soprano may look quite similar, the soprano gets a strong, clear sound on the higher notes, and the alto a strong, clear sound in the lower part of the range. But there are vocalists whose strong, best-sounding range falls in a distinctly different place from any of these four voices. The names for some of these ranges are:

Figure 2.9. Vocal Ranges

Voices are as individual as faces; some altos will have a narrower or wider range, or the sweetest and most powerful part of their range in a different place than other altos. These are approximate, average ranges for each voice category.

The same terms used to identify vocal ranges are also often used to identify particular instruments. For example a bass trombone has a lower range than a tenor trombone, and an alto saxophone sounds higher than a tenor saxophone. Some other terms that are used to describe instrument ranges are:

The ranges of some instruments are definite and absolute. For example, even a beginning piano player can play the highest and lowest keys; and even the best player cannot play beyond these. But the ranges of many instruments are, like vocal ranges, not so definite. For example, an experienced horn or clarinet player can play much higher and lower notes than a beginner. An exceptional trumpet player may be able to play - with good sound and technique – high notes that the average high school trumpet player cannot play at all.

Other instruments may be a mix of absolute and indefinite ranges. For example, on any string instrument, nobody can play lower than the note that the lowest string is tuned to. But experienced players can easily play very high notes that inexperienced players have trouble playing well.

So it is sometimes useful to distinguish between a possible range, which includes the notes that a very experienced player can get, and a practical range, that includes all the notes that any competent player (including a good younger player) can get.

Some sources even list the power range of an instrument or voice. This is the part of the range where the instrument or voice is particularly strong. It may be in the middle of the range, or at the top or bottom, but writing in the power range should guarantee that the part is easy to play (or sing), sounds clear and strong, and can be easily heard, even when many other instruments are playing.