Idiot's Guides - Music Theory
Page 5
Major and Minor Intervals
When you describe intervals by degree, you still have to deal with those pitches that fall above or below the basic notes—the sharps and flats, or the black keys on a keyboard.
When measuring by degrees, you see that the second, third, sixth, and seventh notes can be easily flattened. When you flatten one of these notes, you create what is called a minor interval. The natural state of these intervals (in a major scale) is called a major interval.
Here’s what these four intervals look like, with C as the root, in both major and minor forms.
Major and minor intervals, starting on C.
NOTE
Remember, in this chapter we’re dealing with intervals within a major scale. Minor scales (described in Chapter 3) have different “natural” intervals between degrees of the scale.
Perfect Intervals
Certain intervals don’t have separate major or minor states (although they can still be flattened or sharpened). These intervals—fourths, fifths, and octaves—exist in one form only, called a perfect interval. You can’t lower these intervals to make them minor or raise them to make them major; there’s no such thing as a minor fifth or a major octave. The intervals, because of their acoustical properties, are perfect as-is.
Here are the three perfect intervals, with C as the root.
Three perfect intervals, starting on C.
Over the years, I’ve found that perfect intervals tend to confuse some beginning music students. (And some more advanced ones, too!) The fact that they don’t have major and minor forms puts them in stark contrast to the other intervals.
Now, it’s perfectly (sorry …) okay to just accept that fourths and fifths and octaves are different from other intervals and let it go at that. But it’s the why behind these unique intervals that vexes many students.
The big question I get asked is, “Why is a perfect interval so perfect?” It all has to do with frequencies, and with ratios between frequencies. In a nutshell, perfect intervals sound so closely related because their frequencies are closely related.
For example, a perfect octave has a ratio of 2:1 between the two frequencies—the octave is twice the frequency of the starting pitch (which is called the fundamental). If the fundamental is 440Hz, the octave above is twice that frequency, or 880Hz. Similarly, a perfect fifth has a ratio of 3:2; you take the starting pitch and multiply it by 3/2 to get the perfect fifth above (660Hz for a 440Hz fundamental). A perfect fourth has a ratio of 4:3; multiply the fundamental by 4/3 to get the perfect fourth (586Hz for a 440Hz fundamental).
Other intervals have more complex ratios, which makes them less perfect. For example, a major third has a ratio of 5:4, not quite as simple—or as perfect—as a 2:1, 3:2, or 4:3 ratio. And the minor third ratio of 6:5 is even less perfect.
Put into a series, each increasingly complex interval ratio forms what is called a harmonic series, and the intervals (in order) are called harmonics. The simpler harmonics of the perfect intervals sound more pleasing to our ears because they’re less complex—there’s less stuff going on, sonically.
To make a long story short, the reason we call octaves, fifths, and fourths “perfect” is because they’re simpler and more consonant—that is, they sound better and more natural than do the less perfect intervals. The nomenclature is somewhat arbitrary, admittedly, but that’s just the way things are. My advice is not to lose too much sleep over all this and just learn which intervals are which. They’re not going to change.
Augmented and Diminished Intervals
Okay, now you know that perfect intervals can’t be major or minor. That doesn’t mean that they can’t be altered, however. You can raise and lower fourths and fifths—however, the result is not called major or minor. When you raise a perfect interval a half step, it’s called an augmented interval. When you lower a perfect interval a half step, it’s called a diminished interval. So don’t call the new intervals major or minor—call them augmented or diminished.
NOTE
An augmented fourth and a diminished fifth are enharmonically the same note.
For example, if you use C as the root, F is a perfect fourth away from the root. If you sharpen the F, the resulting note (F-sharp) is an augmented fourth above the root.
Along the same lines, G is a perfect fifth above C. When you flatten the G, the resulting note (G-flat) is a diminished fifth above the root.
Here are the key augmented and diminished intervals, with C as the root.
Augmented and diminished intervals, starting on C.
Now, just to confuse things, other types of intervals can also be called diminished and augmented—and these intervals have nothing to do with the perfect intervals.
To start, you can also create a diminished interval by lowering a minor interval by another half step. For example, F to D-flat is a minor sixth; if you flatten the D-flat (yes, there’s such a thing as a double flat), the resulting interval is called a diminished sixth.
You can also create an augmented interval by raising a major interval by another half step. For example, F to A is a major third; if you sharpen the A (to A-sharp), the resulting interval is an augmented third.
Fortunately, you don’t have to deal with either type of diminished or augmented interval that often. But you still need to know what they are, just in case!
Beyond the Octave
You don’t have to stop counting intervals when you get to the octave. Above the octave are even more intervals—ninths, tenths, elevenths, and so on.
Intervals that span more than an octave are called compound intervals because they combine an octave with a smaller interval to create the larger interval. For example, a ninth is nothing more than an octave and a second; an eleventh is an octave and a fourth … and so on.
The following table describes the first six intervals above the octave.
Compound Intervals
Interval
Combines
Ninth
Octave plus second
Tenth
Octave plus third
Eleventh
Octave plus fourth
Twelfth
Octave plus fifth
Thirteenth
Octave plus sixth
Fourteenth
Octave plus seventh
Compound intervals can have all the qualities of smaller intervals, which means a compound interval can be (depending on the interval) major, minor, perfect, augmented, or diminished.
Intervals and Half Steps
It might be easier for you to think of all these intervals in terms of half steps. To that end, the following table shows how many half steps are between these major and minor intervals.
Half Steps Between Intervals
Interval
Number of Half Steps
Perfect unison
0
Minor second
1
Major second
2
Minor third
3
Major third
4
Perfect fourth
5
Augmented fourth
6
Diminished fifth
6
Perfect fifth
7
Minor sixth
8
Major sixth
9
Minor seventh
10
Major seventh
11
Octave
12
Minor ninth
13
Major ninth
14
Minor tenth
15
Major tenth
16
Perfect eleventh
17
Augmented eleventh
18
Diminished twelfth
18
Perfect twelfth
19
Minor thirteenth
20
Major thirteenth
21
Minor fourteenth
Major fourteenth
23
And take special note of those intervals that are enharmonically identical—such as the augmented fourth and the diminished fifth. What you call that particular interval depends on which direction you’re heading, and which notation is the easiest to read in a given piece of music.
Mod-12
What you’ve learned so far is traditional Western music notation—but it’s not the only way to notate musical pitches. Some educators today use what is called the Mod-12 system to teach notes and intervals. In this system, the intervals between the 12 half steps in an octave are numbered, from 0 to 11. (If you count the 0, that adds up to 12 intervals.)
For example, the interval we call unison has zero half steps between notes, and is called “interval 0.” The interval we call a minor third has three half steps, and is called “interval 3.”
The nice thing about using this system is that you don’t have to worry about enharmonics. A diminished fifth and an augmented fourth both have six half steps, and are both called “interval 6.”
You can also use the Mod-12 system to describe individual notes—based on their interval from tonic. Tonic, of course, is note 0. The minor second degree is note 1, and the major second degree is note 2. If you wanted to describe the tonic, the major third degree, and the perfect fifth degree, you’d use the numbers 0, 4, and 7.
Some people like to use the Mod-12 system to teach intervals, but I prefer the old-fashioned method presented here earlier in this chapter, for the sole reason that this is what you’ll run into in the real world. When you’re playing in a concert band or a jazz trio, you won’t hear other musicians say “play 4, 7, 11.” You will hear them say “play the major third, fifth, and major seventh.”
Still, if Mod-12 works for you, use it. It’s a perfectly acceptable way to learn the 12 tones we use in Western music—and it makes it a lot easier to deal with enharmonic notes.
Exercises
Exercise 2-1
Add sharps before each of these notes.
Exercise 2-2
Add flats before each of these notes.
Exercise 2-3
Enter a new note an octave above each of the following notes.
Exercise 2-4
Enter a new note a specified number of half steps from the previous note. (Remember to start each new note after the previous note you entered!)
Exercise 2-5
Name each of the following intervals.
Exercise 2-6
Using the first note as the root, enter a second note to create the specified interval.
Exercise 2-7
Using sharps, flats, and naturals, change the following major intervals to minor.
Exercise 2-8
Using sharps, flats, and naturals, change the following minor intervals to major.
The Least You Need to Know
The smallest interval between any two notes is called a half step. Two half steps equal one whole step.
A sharp raises the value of a note by a half step. A flat lowers the value of a note by a half step.
The intervals between any two notes are described in terms of degree. For example, the interval between the first and third notes is called a third.
In a major scale, seconds, thirds, sixths, and sevenths are called major intervals. You can create a minor interval by flattening these notes.
In a major scale, fourths, fifths, and octaves are called perfect intervals. When you flatten a perfect interval, you create a diminished interval; when you sharpen a perfect interval, you create an augmented interval.
CHAPTER
3
Scales
In This Chapter
Putting eight notes together to form a scale
Creating major and minor scales
Discovering the different modes within a major scale
Lesson 3, Track 24
In the first two chapters we discussed the seven key notes (A through G), and how they relate to each other. We also tossed around the word “scale” to describe all seven of those notes together.
In this chapter we further examine the concept of the musical scale, which (no surprise) is seven notes all in a row, in alphabetical order. (If you count the first note, repeated an octave higher at the top of the scale, it’s eight notes.)
What might be surprising is that there are so many different types of scales. You can have a major scale, a minor scale (three different types of minor scales, actually), or any number of different modes within a scale. It sounds confusing, but it’s really fairly simple once you understand how scales are constructed, using different intervals between the various notes. (What’s a mode, you ask? You’ll have to read this entire chapter to find out!)
Scales are important because you use them to create melodies, which you’ll learn about in Chapter 8. In fact, you can create a nice-sounding melody just by picking notes from a single major scale. For example, use the C Major scale (the white notes on a piano) and pick and choose notes that sound good when played together. Make sure you start and end your melody on the C note itself, and you’ve just written a simple song.
Eight Notes Equal One Scale
A scale is, quite simply, eight successive pitches within a one-octave range. All scales start on one note and end on that same note one octave higher.
For example, every C scale starts on C and ends on C; an F scale starts on F and ends on F; and they all have six more notes in between.
The eight notes of a scale; C Major, in this instance.
The first note of a scale is called the tonic, or first degree, of the scale. Not surprisingly, the second note is called the second degree, the third note is called the third degree, and so on—until you get to the eighth note, which is the tonic again.
The major exception to the eight-note scale rule is the scale that includes all the notes within an octave, including all the sharps and flats. This type of scale is called a chromatic scale, and (when you start with C) looks something like this:
The C chromatic scale. The top staff shows the scale using sharps; the bottom staff shows the scale using flats.
Now, any given scale has specific relationships between the different degrees of the scale. That’s how you can describe different types of scales: a major scale has different intervals between specific notes from those you’ll find in a similar minor scale. These different intervals give each type of scale its unique sound.
TIP
When you’re playing a piece of music, you typically stay within the notes of the designated scale. Any notes you play outside the scale are called chromatic notes; notes within the scale are said to be diatonic. For example, in the C Major scale, the note C is diatonic; the note C-sharp would be chromatic. Even though chromatic notes might sound “different” than the normal scale notes, they can add color to a piece of music. (That’s where the term comes from, by the way; chroma means “color.”)
The most common scale is called the major scale. Major scales are happy scales; they have pleasant and expected intervals at every turn. (Just sing “Do Re Mi Fa So La Ti Do” and you’ll hear this pleasant quality.)
The mirror image of the major scale is the minor scale. Minor scales are sad scales; the intervals between the notes sound a little depressing.
WARNING
Most musicians don’t capitalize the word “minor,” or any of its abbreviations. Major chord notation is (almost) always capitalized, and minor chord notation is (almost) always lowercase.
Both major and minor scales can start on any note—from A-flat to G-sharp. No matter which note you start with, each scale has its own specific combination of intervals between notes.
The following sections go into more detail about both major and minor scales.
Major Scales
What makes a major scale major are the specific intervals between the notes of the scale. Every major scale uses the same intervals, as shown in the following table.
; The Intervals of the Major Scale
Note
Half Steps to Next Note
Tonic
2
Second
2
Third
1
Fourth
2
Fifth
2
Sixth
2
Seventh
1
Put another way, the intervals in a major scale go like this: whole, whole, half, whole, whole, whole, half.
If you start your major scale on C (the C Major scale), you end up playing all white keys on the piano. C Major is the only major scale that uses only the white keys; all the other scales have black keys in them.
To make things easier for you, the following table shows all the notes in the 15 major scales.
The 15 Major Scales
Scale
Notes
C Major
C-sharp Major
D-flat Major
D Major