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By Root 977 0

circle of fifths gets its name from the fact that as you go from one section of the circle to the next, you are going up or down by an interval of a perfect fifth. If you go up a perfect fifth (clockwise in the circle), you get the key that has one more sharp or one less flat; if you go down a perfect fifth (counterclockwise), you get the key that has one more flat or one less sharp. Since going down by a perfect fifth is the same as going up by a perfect fourth, the counterclockwise direction is sometimes referred to as a "circle of fourths". (Please review inverted intervals if this is confusing.)

Example 4.10.

The key of D major has two sharps. Using the circle of fifths, we find that the most closely related major keys (one in each direction) are G major, with only one sharp, and A major, with three sharps. The relative minors of all of these keys (B minor, E minor, and F sharp minor) are also closely related to D major.

Exercise 4.7.1. (Go to Solution)

What are the keys most closely related to E flat major? To A minor?

Exercise 4.7.2. (Go to Solution)

Name the major and minor keys for each key signature.

Figure 4.59.

Key Signatures

If you do not know the order of the sharps and flats, you can also use the circle of fifths to find these. The first sharp in a key signature is always F sharp; the second sharp in a key signature is always (a perfect fifth away) C sharp; the third is always G sharp, and so on, all the way to B sharp.

The first flat in a key signature is always B flat (the same as the last sharp); the second is always E flat, and so on, all the way to F flat. Notice that, just as with the key signatures, you add sharps or subtract flats as you go clockwise around the circle, and add flats or subtract sharps as you go counterclockwise.

Figure 4.60. Adding Sharps and Flats to the Key Signature

Each sharp and flat that is added to a key signature is also a perfect fifth away from the last sharp or flat that was added.

Exercise 4.7.3. (Go to Solution)

Figure 4.58 shows that D major has 2 sharps; Figure 4.60 shows that they are F sharp and C sharp. After D major, name the next four sharp keys, and name the sharp that is added with each key.

Exercise 4.7.4. (Go to Solution)

E minor is the first sharp minor key; the first sharp added in both major and minor keys is always F sharp. Name the next three sharp minor keys, and the sharp that is added in each key.

Exercise 4.7.5. (Go to Solution)

After B flat major, name the next four flat keys, and name the flat that is added with each key.

Solutions to Exercises

Solution to Exercise 4.7.1. (Return to Exercise)

E flat major (3 flats):

B flat major (2 flats)

A flat major (4 flats)

C minor (3 flats)

G minor (2 flats)

F minor (4 flats)

A minor (no sharps or flats):

E minor (1 sharp)

D minor (1 flat)

C major (no sharps or flats)

G major (1 sharp)

F major (1 flat)

Solution to Exercise 4.7.2. (Return to Exercise)

Figure 4.61.

Solution to Exercise 4.7.3. (Return to Exercise)

A major adds G sharp

E major adds D sharp

B major adds A sharp

F sharp major adds E sharp

Figure 4.62.

Solution to Exercise 4.7.4. (Return to Exercise)

B minor adds C sharp

F sharp minor adds G sharp

C sharp minor adds D sharp

Figure 4.63.

Solution to Exercise 4.7.5. (Return to Exercise)

E flat major adds A flat

A flat major adds D flat

D flat major adds G flat

G flat major adds C flat

Figure 4.64.

4.8. Scales that aren't Major or Minor*

Note

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Introduction

Sounds - ordinary, everyday "noises" - come in every conceivable pitch and groups of pitches. In fact, the essence of noise, "white noise", is basically every pitch at once, so that no particular pitch is heard.

One of the things that makes music pleasant to hear and easy to "understand" is that only a few of all the possible pitches are used. But not all pieces of music use the same