Idiot's Guides - Music Theory
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There are lots of different definitions of the word “music,” some more poetic than practical. For example, William Shakespeare called music the “food of love,” George Bernard Shaw called music the “brandy of the damned,” and Gottfried Wilhelm Leibnitz called music “sounding mathematics.”
Interesting definitions all, but not really what we’re looking for here. Let’s try another definition:
Music is the art, the craft, and the science of organizing sound and silence in the framework of time.
Now that’s a little more helpful, but it’s still fairly broad. This definition could describe a tremendous range of activities—a mother singing a lullaby to her child, an orchestra playing a Mozart symphony, a rock group performing their latest hit, a group of Native Americans playing ceremonial drum beats, Louis Armstrong playing trumpet in a jazz quartet, a group of sailors chanting “yo heave ho,” or a nightingale warbling a serenade. You probably didn’t buy this book to learn about all these things, although all of them can be called “music.”
So we’ll use a slightly different definition of music in this book. This definition is a lot more specific:
Music is a succession of tones arranged in a specific rhythm.
Better? This definition doesn’t cover everything that’s ever been called “music,” but it probably covers those types of music that you’re familiar with—primarily, twentieth- and twenty-first-century popular music, from ragtime to reggae to rock, and everything in between.
Now to the word “theory.” In scientific circles, this word is used as the formulation of a hypothesis, such as Einstein’s theory of relativity. Although academic music theorists sometimes do formulate hypotheses in this scientific fashion, that’s not what this book is about.
In our context, we’ll use the word “theory” to mean a study of the rudiments of music—the basic things that performers and listeners need to know to produce and enjoy this marvelous art. This goes back to the root meaning of the word, which means “a way of looking.” If we broaden this definition to include not just looking, but also listening and performing, then we’re set.
Now that we’ve defined our terms, it’s time to learn the theory behind the music. Let’s go back to our definition of music, which says that music is a succession of tones, arranged in a specific rhythm. To study music, then, we have to learn about notes, and about arranging them.
We’ll get to the “arranging in a specific rhythm” bit starting with Chapter 5. That lets us focus our attention, for the time being, on tones.
Understanding Musical Tones
So what’s a tone? The definition is simple: a tone is a sound that is played or sung at a specific pitch.
When you hum (go ahead …), you’re humming a tone. When you whistle, you’re whistling a tone. When you go “aaaahhhh,” you’re sounding a tone. If you put two or more hums, whistles, or “aaaahhhhs” together, you have music.
DEFINITION
Pitch describes the specific frequency or tuning of a tone.
You can hum lots of different tones, high or low. The higher tones are referred to as higher pitched; lower tones are called lower pitched.
Here’s an exercise: hum a tone. Now hum a tone higher than the first tone.
What you’ve just hummed are two separate tones, at two separate pitches. The second tone was higher pitched than the first tone.
Different voices and different instruments produce different ranges of tones. For example, women tend to have higher voices than men; the tones most women sing are higher pitched than the tones most men sing. (There are exceptions to this rule, of course; listen to some of the doo-wop singers of the 1950s and you’ll hear some fairly high male voices!)
In the world of musical instruments, physically larger instruments tend to produce lower-pitched tones, whereas smaller instruments tend to produce higher-pitched tones. This is because bigger instruments move more air than smaller ones do, and more air means a lower pitch. This is why the small cylinder of a flute produces higher notes than the big brass tubing of a tuba, and why the thin strings on a guitar are higher pitched than the thick strings.
NOTE
Some instruments produce tones that aren’t at specific pitches. These instruments—such as drums and cymbals—are called unpitched or nonpitched instruments. The tones they produce can be high or low, but typically don’t correspond to specific note pitches.
Some instruments produce a broader range of tones than other instruments. In particular, the piano has a very broad range. From the lowest tone (the key on the far left of the keyboard) to the highest (the key on the far right), the piano reproduces more tones than just about any other instrument—and certainly a lot more than the human voice!
Time for another exercise: hum the lowest tone you can hum; then gradually raise the pitch until you’re humming the highest tone you can hum. You just hummed a whole lot of different tones. How, then, do you describe a specific tone so that someone else can hum the same tone?
NOTE
You’ll find lots of musical terms in this book, but you need to know that musicians tend to use a lot of these terms interchangeably. A conductor who says, “That note was wrong,” might mean that the pitch was wrong, or that the note value (rhythm) was wrong. That’s because the word “note” can be used in place of either more specific definition. So don’t get hung up on the differences between “tones” and “pitches” and “notes.” While there are specific definitions for each word, it’s acceptable to be a little loose on the usage. I might even substitute one word for another in this book. You’ll understand what I mean from the context.
Tones Have Value
When it comes to describing a tone, it helps to know that every tone you can sing or play has a specific value. You can measure that value scientifically, and use that value to describe the tone—or, more precisely, its pitch. If that’s too complicated, you also can assign an arbitrary name to each tone. (Go ahead: hum a note called “Bob.”)
NOTE
One good way to determine a specific pitch is with a tuning fork, which is a fork-shaped piece of metal that resonates at a specific frequency when struck. Most tuning forks resonate at 440Hz, which is the pitch A. Some people have what is called perfect pitch, in that they can hear absolute pitches in their heads. However, most people need the guidance of a tuning fork, pitch pipe, piano, or other musical instrument to fix a specific pitch.
Tuning Into a Frequency
If you plug a microphone into an oscilloscope, and then hum a tone into the microphone, the oscilloscope will measure the frequency of the tone. This is actually a measurement of how fast the molecules of air are vibrating; the faster the vibrations, the higher the pitch.
DEFINITION
Frequency is a measurement of how fast air molecules are vibrating.
These vibrations are measured in cycles per second, and there are a lot of them. (Cycles per second are often called hertz, abbreviated Hz.) If you hum the pitch we call middle C (the white key in the exact center of a full 88-key piano keyboard, or the first fret on the second string of a guitar), the oscilloscope will measure 261.6Hz—that is, the air is cycling back and forth 261.6 times per second.
So one way to identify specific pitches is by their frequency. Unfortunately, writing out even a simple melody in terms of frequency gets a tad unwieldy. For example, here’s the first half of “Mary Had a Little Lamb” (“Mary had a little lamb, little lamb, little lamb”) notated by frequency:
659Hz, 587Hz, 523Hz, 587Hz, 659Hz, 659Hz, 659Hz,
587Hz, 587Hz, 587Hz,
659Hz, 783Hz, 783Hz
Not easy to read, is it? That’s why we don’t use the frequency method to write music.
NOTE
The “standard” pitch today that most musicians tune to is the A above middle C, which equals 440Hz; all the other notes are pitched in relation to this note. In earlier times and cultures, this note had other values—as low as 376Hz in early eighteenth-century Fra
nce, and as high as 560Hz in early seventeenth-century Germany (referred to as North German church pitch).
Play by Numbers
An easier way to designate tones is to number each individual pitch. But before we start numbering, it helps to know a little bit about how different pitches relate to each other.
When you hum a pitch, you can “slide” that pitch from lower to higher and back again, which might make you think there are an infinite number of pitches available. (You can certainly see this when you look at frequencies; you have one tone at 256Hz, another at 257Hz, another at 258Hz, and so on.)
Although that might be true in theory, in practice some pitches are too close together to clearly distinguish them. For example, if you hum a 256Hz tone and a 257Hz tone, they sound almost identical in pitch because there isn’t a big enough interval between the tones.
We need to place a reasonable interval between tones, enough for our ears to notice, and then assign values to those main pitches that result. What you end up with is a series of pitches called a scale. (You’ll learn more about scales in Chapter 2.) Each scale starts on a specific tone, and ends on a higher-pitched version of that same tone.
In the Western world, we divide our scales into seven main notes—eight if you count the top note, which is the starting note repeated higher at the end of the scale. Because there are seven notes, it’s easy to number them—one through seven. Using this numbering system, here’s what the first half of “Mary Had a Little Lamb” looks like:
3 2 1 2 3 3 3
2 2 2
3 5 5
If you’re reading ahead and want to see how the numbering system applies to traditional music notation, here’s what the C Major scale looks like, by the numbers:
Numbering the notes in the C Major scale.
Now, not to be confusing here, but there are actually notes between some of these main notes—enough of them that we really have 12 pitches before they start repeating. These in-between pitches are equally spaced in what we call half steps, where the major pitches (A, B, C, etc.) have either one or two half steps between them, depending on the note. (I know, it’s getting confusing already ….)
For the time being, we’re going to focus on the seven main notes of a scale since that’s easiest to understand. We’ll leave the half steps for Chapter 2. Feel free to read ahead if you’re interested.
Do Re Mi
Another way to remember each tone is by assigning a simple syllable to each tone. Remember the song from The Sound of Music that goes “Do, a deer, a female deer”? That’s what we’re talking about here.
In this particular method, called Solfeggio or Solfège (pronounced sol-FEZH), each of the seven notes of a scale has its own name. The following table shows the words to use.
TIP
Solfeggio is a method of naming musical tones using a set of syllables—do, re, mi, and so on. These syllables come from the initial syllables of the first six words to “The Hymn to St. John the Baptist”; the seventh syllable (Ti) is derived from the name St. John, in Latin.
The Solfeggio Method
Tone
Solfeggio Name
Pronunciation
1
Do
Doh
2
Re
Ray
3
Mi
Mee
4
Fa
Fah
5
So (Sol)
So
6
La
Lah
7
Ti
Tee
8
Do
Doh
Here’s what the first half of “Mary Had a Little Lamb” looks like using the Solfeggio method:
Mi Re Do Re Mi Mi Mi
Re Re Re
Mi So So
If you’re reading ahead and want to know how the Solfeggio names apply to traditional music notation, here’s what the C Major scale looks like:
The Do Re Mis of the C Major scale.
Tones Have Names
It’s important to know that both the numbering and the Solfeggio methods are relative ways of naming musical tones. That is, the first note in a scale is always number one, and is always called Do. The second tone is always number two, and is always called Re. It doesn’t matter what actual tone you start with, these names always apply.
The problem with using relative naming is that it doesn’t tell you what precise pitch to start with. You might start your Do Re Mi on a low pitch, and your neighbor might start hers on a higher pitch, and your duet will end up sounding like two water buffaloes in heat.
And that’s not good. (Unless you’re a water buffalo, of course.)
No, what we need is a way to designate specific pitches—without resorting to the cumbersome frequency method.
Learning the ABCs
The accepted way of naming specific musical pitches uses the first seven letters of the alphabet—A, B, C, D, E, F, and G. Although the numbering method is relative (the number 1 can be assigned to any pitch), the letter method is absolute. This means that A always refers to a specific frequency. When you tell someone to sing or play an A, they’ll always sing or play the same pitch.
The only problem with this method is that you can sing or play more than one A.
Try this exercise: sing A B C D E F G A (think “Do Re Mi Fa So La Ti Do”). The first A and the second A should be the same tone, with the second A an octave higher than the first A. (You’ll learn about octaves a little later in this chapter—suffice to say it’s a way of presenting a lower or higher version of the same note.)
You can play an A with a low pitch, and an A with a higher pitch—and other As both below and above those. Now, all the As will have the same tone; they’re just higher or lower versions of the basic pitch.
How, then, do you tell which A to play or sing?
Notes on a Piano Keyboard
A good way to visualize the seven basic notes (A through G) is to look at a piano keyboard. Each white key on the keyboard corresponds to one of these seven main notes, as shown in the following figure. (And ignore the black keys, for the time being.)
The white keys on a piano keyboard.
As you can see, the black and white keys on a piano form a certain pattern. If you start in the right place, you’ll see that the black keys are arranged in groups of threes and twos. The first white key to the left of a group of three black notes is always assigned to the tone of F. The first white key to the left of a group of two black notes is always assigned to C. Once you know where F and C are, you can figure out the location of the other tones.
To figure out which A (or F or C) to play, know that the C located in the very middle of a full-size piano keyboard—directly underneath the manufacturer’s logo or pull-down door handle—is called middle C. (It’s the C in the middle of the keyboard—easy to remember.) All other notes can be described relative to middle C—as in “the F above middle C” or “the D below middle C.”
TIP
Some musicians identify the specific pitch by placing a number after the note name. Using this method (which is sometimes called scientific pitch notation), the lowest C on a grand piano is notated C1. The next C up from that is C2, then C3, C4, and so on—and the same for all the other notes. (In this notation, middle C is C4.)
Notes on a Staff
Now that you know the seven basic notes and where they lie on a piano keyboard, how do you go about communicating those notes to others? You could just spell out a song; if you used this method, the first half of “Mary Had a Little Lamb” would look like this:
E D C D E E E
D D D
E G G
Now, that’s more specific than using numbers or Solfeggio, but it’s still somewhat difficult to read. A better way to notate pitches is to do so visually, using a graphic that in some ways resembles a basic piano keyboard. This graphic is called a staff.
The basic music staff is co
mposed of lines and spaces, like this:
A blank staff.
As you can see, the staff has precisely five lines and four spaces. Each line or space represents a specific pitch. The pitches are determined by the clef at the beginning of the staff; the staff we’re looking at here uses what’s called the treble clef. (There are several different types of clefs, which we’ll discuss later in this chapter.)
The notes of a staff (treble clef).
This treble clef staff pictures the notes in the exact middle of a piano keyboard—just above middle C. (The bottom line of the staff represents the E above middle C.) The following figure shows how the notes of the staff relate to specific piano keys.
The notes on a staff and where they appear on a piano keyboard.
Back to “Mary Had a Little Lamb,” here’s what the first part of that song looks like on a music staff:
The notes of “Mary Had a Little Lamb” on a music staff.
Above—and Below—the Staff
The basic staff describes nine basic notes—five on the lines, four in the spaces. But what about all those notes either above or below these nine notes—like that last note in “Mary Had a Little Lamb”?
Notes higher than the F at the top of the staff are written in the lines and spaces above the staff. For example, the first space above the staff is the first note after F: G. The first line above the staff is the first note after G: A. You can keep adding spaces and lines above the staff to describe higher and higher notes, as shown in the following figure.