Solutions to Exercises in Chapter 4 (Understanding Basic Music Theory)

## Solutions to Exercises

### Solution to Exercise 4.1.1

### Solution to Exercise 4.2.1

### Solution to Exercise 4.2.2

Figure 4.59: If your answer is di erent, check to see if you have written a di erent enharmonic spelling (Section 1.1.5) of the note in the answer. For example, the B at could be written as an A sharp.

### Solution to Exercise 4.3.1

1. Major

2. Major

3. Minor

4. Major

5. Minor

### Solution to Exercise 4.3.2

Notice that although they look completely di erent, the scales of F sharp major and G at major (numbers 5 and 6) sound exactly the same when played, on a piano as shown in Figure 4.61 (Enharmonic Scales), or on any other instrument using equal temperament (Section 6.2.3.2: Equal Temperament) tuning. If this surprises you, please read more about enharmonic (Section 1.1.5) scales.

Enharmonic Scales

Figure 4.61: Using this gure of a keyboard, or the ngerings from your own instrument, notice that the notes for the F sharp major scale and the G at major scale in Figure 4.60, although spelled di erently, will sound the same.

### Solution to Exercise 4.4.1

### Solution to Exercise 4.4.2

1. A minor: C major

2. G minor: B at major

3. B at minor: D at major

4. E minor: G major

5. F minor: A at major

6. F sharp minor: A major

### Solution to Exercise 4.4.3

### Solution to Exercise 4.4.4

### Solution to Exercise 4.5.1

### Solution to Exercise 4.5.2

### Solution to Exercise 4.5.3

### Solution to Exercise 4.5.4

### Solution to Exercise 4.5.5

### Solution to Exercise 4.5.6

1. Diminished sixth

2. Perfect fourth

3. Augmented fourth

4. Minor second

5. Major third

### Solution to Exercise 4.6.1

1. The ratio 4:6 reduced to lowest terms is 2:3. (In other words, they are two ways of writing the samemathematical relationship. If you are more comfortable with fractions than with ratios, think of all the ratios as fractions instead. 2:3 is just two-thirds, and 4:6 is four-sixths. Four-sixths reduces to two-thirds.)

2. Six and nine (6:9 also reduces to 2:3); eight and twelve; ten and fteen; and any other combination that can be reduced to 2:3 (12:18, 14:21 and so on).

3. Harmonics three and four; six and eight; nine and twelve; twelve and sixteen; and so on.

4. 3:4

### Solution to Exercise 4.6.2

Opening both rst and second valves gives the harmonic series one-and-a-half steps lower than “no valves”.

### Solution to Exercise 4.7.1E at major (3 ats):

• B at major (2 ats)

• A at major (4 ats)

• C minor (3 ats)

• G minor (2 ats)

• F minor (4 ats)

A minor (no sharps or ats):

• E minor (1 sharp)

• D minor (1 at)

• C major (no sharps or ats)

• G major (1 sharp)

• F major (1 at)

### Solution to Exercise 4.7.2

### Solution to Exercise 4.7.3

• A major adds G sharp

• B major adds A sharp

• E major adds D sharp

• F sharp major adds E sharp

### Solution to Exercise 4.7.4

• B minor adds C sharp

• F sharp minor adds G sharp

• C sharp minor adds D sharp

### Solution to Exercise 4.7.5

• E at major adds A at

• A at major adds D at

• D at major adds G at

• G at major adds C at

### Solution to Exercise 4.8.1

Figure 4.75: This whole tone scale contains the notes that are not in the whole tone scale in Figure 4.48 (A Whole Tone Scale).

### Solution to Exercise 4.8.2

Figure 4.76: The ats in one scale are the enharmonic equivalents of the sharps in the other scale.

Assuming that octaves don’t matter – as they usually don’t in Western music theory, this scale shares all of its possible pitches with the scale in Figure 4.48 (A Whole Tone Scale).

### Solution to Exercise 4.8.3

If you can, have your teacher listen to your compositions.

Basic Music Theory

**Read more…**

- Harmony and Form: Chapter 5 – Form (Understanding Basic Music Theory)
- Harmony and Form: Chapter 5 – Cadence (Understanding Basic Music Theory)
- Harmony and Form: Chapter 5 – Beginning Harmonic Analysis (Understanding Basic Music Theory)
- Harmony and Form: Chapter 5 – Naming Other Chords (Understanding Basic Music Theory)
- Harmony and Form: Chapter 5 – Consonance and Dissonance (Understanding Basic Music Theory)