8.20 The circle of fifths

Theory

You've learned 12 major scales and 12 minor scales, each with their respective numbers of sharps or flats. How can you remember them all? There is a solution to this: the circle of fifths. In this chapter, you'll learn about the circle of fifths. In Chapter 8.21 Applying the circle of fifths you will learn how to apply the circle of fifths.

1. What is the circle of fifths?

The circle of fifths is a diagram showing the keys with their respective number of sharps or flats. Using the circle of fifths, you can calculate the number of sharps or flats in a scale. You can also use the circle of fifths to determine the key of a piece of music. Don't let the circle fool you. It could also have been a straight line or a square. It's all about the fifths. There is a circle of fifths for major scales and a circle of fifths for minor scales. Five fifths circle tips:

Tip 1. to understand the circle of fifths you need to know what a perfect fifth is.
Tip 2. to properly apply the circle of fifths, you must be able to make perfect fifths on all notes, both on and under a note.
Tip 3. you only need to know the circle of fifths for the major scales. For the minor scales, there is a handy trick.
Tip 4. do you never play scales with many sharps or flats? Then you don't need to learn them (for the time being). And then you don't need to learn the whole circle of fifths either.
Tip 5. the circle of fifths is a useful diagram, nothing more and nothing less. It will be particularly useful if you play pieces of music with 3 or more sharps or flats.

2. Major scales with sharps

We're going to place all of the major scales with sharps in an scheme, starting with zero sharps up to and including seven sharps.

major scale

(C#)

number of sharps (#)

(7#)

Examples

One can see that the distance from one scale to the next is always a perfect fifth higher.

3. Major scales with flats

We're going to place all of the major scales with flats in an scheme, starting with zero flats up to and including seven flats.

major scale

(Cb)

number of flats (b)

(7b)

Examples

One can see that the distance from one scale to the next is always a perfect fifth lower.

4. All major scales

We will merge the scheme with sharps and the scheme with flats, with C in the middle.

(Cb)

(C#)

(7b)

(7#)

One can see that the scales with six accidentals are F sharp major and G flat major. On the piano, the F sharp tone and G flat tone are the same key. This means that the F sharp major and G flat major scales share the same tonic and keys; only the names of the tones differ. Notes with the same pitch but different names, as F# and Gb, are called enharmonic. The F sharp major and G flat major scales have the same tonic, the notes are just called different. And since they are both major scales, would all the notes be enharmonic? If you played both scales on the piano, would you play the same keys?

The F sharp major scale is comprised of the notes: F# G# A# B C# D# E# F#.

The G flat major scale is comprised of the notes: Gb Ab Bb Cb Db Eb F Gb.

The answer is yes, F sharp major and G flat major are enharmonic. On the piano, you play the same keys for both scales. And not only F sharp major and G flat major are enharmonic, but also C sharp major with 7 sharps and D flat major with 5 flats are enharmonic, and C flat major with 7 flats and B sharp major with 5 sharps.

5. The circle of fifths

With the F sharp major and G flat major scales, the scheme of the major scales with sharps and the scheme of the major scales with flats overlap each other. This scheme can be represented by a circle, called the circle of fifths.

Do you see that the scales with six accidentals are on the same point? And that the scales with five sharps and seven flats and the ones with seven sharps and five flats are also on the same point? Here the scales with sharps and flats overlap.

To use the circle of fifths, it is important to be able to make perfect ascending and perfect descending fifths.

One half of the circle has scales with sharps: C - G - D - A - E - B - F# - (C#).
The other half of the circle has scales with flats: C - F - Bb - Eb - Ab - Db - Gb - (Cb).

6. Circle of fifths and minor scales

We can also make a circle of fifths for the minor scales. The half of the circle with sharps starts at A, adding consecutive ascending perfect fifhs, the half of the circle with flats starts at A counting consecutive descending perfect fifths. That is the origin of the following scheme:

(Ab)

(A#)

(7b)

(7#)

There is always a pair of major and minor scales with the same key signature. Major and minor scales that have the same key signature are called parallel keys. One example of parallel scales are the scales of C major and A minor. Both scales have no accidentals. Another example are the scales of F major and D minor. Both scales have one accidental, B flat.

Luckily, it is not necessary to learn the circle of fifths for the minor scales by memory. It is simpler to make use of the circle of fifths for major scales and parallel scales. A parallel minor scale is always a minor third lower than a major scale.

For example: do you want to know which minor scale has two sharps? Then first look up the major scale with two sharps, this is D major. Then go down a minor third from the D, and you'll end up on the B. So the minor scale with two sharps is B minor.

There are also major and minor scale with the same tonic. Keys with the same tonic are called relative keys. An example of relative keys are the scales of C major and C minor. Both scales have the same tonic but different key signatures. The C major scale has no accidental, the C minor scale has three flats, B flat, E flat, and A flat.

You can also use the circle of fifths very well if you want to transpose or modulate. Changing a melody or chord progression into a different key is called transposing . This is a common practice in singing. If a song is too high or too low for a particular voice, you can transpose to a key lower or higher. For example, if a piece is in G major and it needs to go down a fifth, you transpose to C major. Modulation is the process of changing from one key to another. Read more about it at Wikipedia.

7. Practise

Harmony exercise 8v: practise determining the keys of scales using the circle of fifths.

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8. Tonality

Music written in a particular key is called tonal. Music that uses major and minor scales is tonal music. Tonal music includes all music up to the 20th century and almost all pop music, blues and jazz. Music that uses scales other than major and minor, such as church scales is also tonal. These scales are discussed in Chapter 8.22 Alternative scales. An important characteristic of tonal music is that it has one tonic.

There is also music that deviates from this. For example, music with more than one key at the same time or music without a particular key. Music in which more than one key occurs simultaneously is called polytonal.

In the piece Festive Dance, the melody is played in A major and the accompaniment in F sharp minor.

Music without a particular key is called atonal. In this music, all twelve chromatic notes in the octave are equally important.

An important composer of atonal music is Arnold Schonberg. As the founder of twelve-tone music, he is counted among the most influential composers of the twentieth century. Together with his students Anton Webern and Alban Berg, they form the Second Viennese School.

Listen to an example of atonal music by Anton Webern: Variations, Op 27 (1936).

8.20 The circle of fifths

Theory

1. What is the circle of fifths?

2. Major scales with sharps

Examples

3. Major scales with flats

Examples

4. All major scales

5. The circle of fifths

6. Circle of fifths and minor scales

7. Practise

8. Tonality

Summary

Circle of fifths

Practise