Go the Distance
Defined as the distance from one note to another, intervals provide the basic framework for everything else in music. Small intervals combine to form scales. Larger intervals combine to form chords. Intervals aid in voice leading, composition, and transposition. There are virtually no musical situations that don't use intervals (barring snare drum solos). Even in some of the extremely dissonant music of the twentieth century, intervals are still the basis for most composition and analysis.
There are five different types of intervals:
You will learn all about the five types of intervals in this chapter, but before you go any further, you need a visual helper, like a musical slide rule: the piano keyboard. Intervals can seem like an abstract concept; having some visual relationships to reference can make the concept more concrete and easier to grasp. FIGURE 2.1 shows the piano keyboard.
FIGURE 2.1 The Piano Keyboard
This image will be repeated at different times throughout this book, but earmark this page for reference because you're going to need it.
The keyboard shows you the location of all the notes within one full octave. It also shows you all the sharps and flats on the black keys.
Notice how C# and D occupy the same key. This situation, in which one key can have more than one name, is called an enharmonic. This occurs on all black keys. The white keys have only one name, whereas the black keys always have a second possibility. This will be explained further along in this book.
The first interval to look at is the half step. It is the smallest interval that Western music uses (Eastern music uses quarter tones, which are smaller than a half step), and it's the smallest interval you can play on the majority of musical instruments. How far is a half step? Well, if you look at a piece of music, a great example of a half step is the distance from C to C# or D sound the same. FIGURE 2.2 shows the half step in a treble staff.
FIGURE 2.2 Half Step
Now that you have been given a rudimentary explanation of a half step, go back to the piano. Stated simply, the piano is laid out in successive half steps starting from C. To get to the next available note, you simply progress to the next available key. If you are on a white key, like C, for example, the next note is the black key of C#/D You have moved a half step. Move from the black key to the white key of D and you've moved another half step. When you've done this twelve times, you have come back around to C and completed an octave, which is another interval.
Now, this is not always a steadfast rule. It is not always the case that you will move from a white key to a black key, or vice versa, in order to move a half step.
As you can see in FIGURE 2.3, the movement between E and F and the movement between B and C are both carried out from white key to white key, with no black key between them. This means that B and C, and E and F, are a half step apart. This is called a natural half step, and it is the only exception to our half-step logic. The good news is that if you keep this in mind, all intervals will be much easier to define, not just half steps.
Why is there a half step between B and C and E and F when everywhere else it takes a whole step to get to the next letter name? The answer is simpler than you think. The sound of the C major scale (C–D–E–F–G–A–B–C) came first. The scale happened to have a half step between E and F and B and C. When the system of music was broken down and actually defined, that scale was laid out in white keys and had to fit the other half steps between the other notes. It really is arbitrary and provides another argument for the fact that sounds come first and then they are named or explained.
A whole step is simply the distance of two half steps combined. Movements from C to D or F# to G# are examples of whole steps. If you are getting the hang of both whole and half steps, you can take this information a bit further. You could skip to scales, which would, in turn, lead you to chords.
The intervals between E and F and B and C are still natural half steps. FIGURE 2.4 gives an example.
A whole step from E ends up on F# because you have to go two half steps to get to F#, passing right by F to C.
Now that you have gone through half and whole steps, the next step is the C major scale to see some of the other intervals out there.