Relationships Between Scales - Circle of Fourths and Fifths

Circle of Fourths and Fifths is the very foundation of Western music theory. It's also the best tool in the kit for deciphering musical concepts.

You may be interested to learn that Pythagoras invented the Circle of Fourths and Fifths. In fact he is legendary for his discovery that musical notes could be translated into mathematical equations.

Major Scale Revision

In the previous lesson, we constructed the major scale by determining the lower and upper tetrachords, both of which share the same 2-2-1 patterns. It follows then that the upper tetrachord of one major scale can represent the lower tetrachord of another major scale. Lets look at an example so that we can visualise this idea.

The C major scale can be constructed by first deriving the lower tetrachord

Lower Tetrachord Construction

Next, we move up one whole-step to G

Tetrachord Link

And finally construct the upper tetrachord

Complete Scale

Now, the upper tetrachord of the C major scale becomes the lower tetrachord of the G major scale.

G Major Lower Tetrachord

We can then determine the starting note of the upper tetrachord of the G major scale by moving up one whole-step from the last note of the lower tetrachord

G Major Lower Tetrachord

Finally derive the upper tetrachord of the G major scale

G Major Lower Tetrachord

This relationship exists between all the major scales and when continued will reveal the following cyclic pattern

Circle of 5ths

Circle of Fifths

When we follow this pattern in a clockwise direction, it is known as the Circle of Fifths ,
as the 5th note of each major scale becomes the 1st note of the next major scale in the sequence.

Circle of Fourths

When we follow this pattern in a counter clockwise direction, it is known as the Circle of Fourths ,
as the 4th note of each major scale becomes the first note of the next major scale in the sequence. For example:

The fourth note of the C major scale is F

4th note of C major is F

The fourth note of F major is Bb

4th note of F major is Bb

The fourth note of Bb major is Eb

4th note of Bb major is Eb

Foundation in Stone

Understanding and memorising the Circle of Fifths/Fourths helps us understand and describe musical relationships. It will become an essential part of your musical foundation, helping you with composition, harmonisation and chord building.