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acquainted with all of the modal scales. Each of these is named for the medieval church mode which has the same interval pattern, and each can be used with a different chord within the key. Dorian is included here only to explain the common jazz reference to the "dorian minor" and to give notice to students that the jazz approach to scales can be quite different from the traditional classical approach.

Figure 4.29. Comparison of Dorian and Minor Scales

You may also find it useful to compare the dorian with the minor scales from Figure 4.26. Notice in particular the relationship of the altered notes in the harmonic, melodic, and dorian minors.

Solutions to Exercises

Solution to Exercise 4.4.1. (Return to Exercise)

Figure 4.30.

Solution to Exercise 4.4.2. (Return to Exercise)

A minor: C major

G minor: B flat major

B flat minor: D flat major

E minor: G major

F minor: A flat major

F sharp minor: A major

Solution to Exercise 4.4.3. (Return to Exercise)

Figure 4.31.

Solution to Exercise 4.4.4. (Return to Exercise)

Figure 4.32.

4.5. Interval*

The Distance Between Pitches

The interval between two notes is the distance between the two pitches - in other words, how much higher or lower one note is than the other. This concept is so important that it is almost impossible to talk about scales, chords, harmonic progression, cadence, or dissonance without referring to intervals. So if you want to learn music theory, it would be a good idea to spend some time getting comfortable with the concepts below and practicing identifying intervals.

Scientists usually describe the distance between two pitches in terms of the difference between their frequencies. Musicians find it more useful to talk about interval. Intervals can be described using half steps and whole steps. For example, you can say "B natural is a half step below C natural", or "E flat is a step and a half above C natural". But when we talk about larger intervals in the major/minor system, there is a more convenient and descriptive way to name them.

Naming Intervals

The first step in naming the interval is to find the distance between the notes as they are written on the staff. Count every line and every space in between the notes, as well as the lines or spaces that the notes are on. This gives you the number for the interval.

Example 4.5.

Figure 4.33. Counting Intervals

To find the interval, count the lines or spaces that the two notes are on as well as all the lines or spaces in between. The interval between B and D is a third. The interval between A and F is a sixth. Note that, at this stage, key signature, clef, and accidentals do not matter at all.

The simple intervals are one octave or smaller.

Figure 4.34. Simple Intervals

If you like you can listen to each interval as written in Figure 4.34: prime, second, third, fourth, fifth, sixth, seventh, octave.

Compound intervals are larger than an octave.

Figure 4.35. Compound Intervals

Listen to the compound intervals in Figure 4.35: ninth, tenth, eleventh.

Exercise 4.5.1. (Go to Solution)

Name the intervals.

Figure 4.36.

Exercise 4.5.2. (Go to Solution)

Write a note that will give the named interval.

Figure 4.37.

Classifying Intervals

So far, the actual distance, in half-steps, between the two notes has not mattered. But a third made up of three half-steps sounds different from a third made up of four half-steps. And a fifth made up of seven half-steps sounds very different from one of only six half-steps. So in the second step of identifying an interval, clef, key signature, and accidentals become important.

Figure 4.38.

A to C natural and A to C sharp are both thirds, but A to C sharp is a larger interval, with a different sound. The difference between the intervals A to E natural and A to E flat is even more noticeable.

Listen to the differences in the thirds and the fifths in Figure 4.38.

So the second step to naming an interval is to classify it based on the number of half steps