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The circle of fifths is a handy tool that can seem obscure and confusing if you do not understand how it is built and used. The circle of fifths is like a musical color wheel. It is a way to arrange all twelve tones logically and progressively so that one can identify and understand their relationships and use them in creative ways to make new and interesting chord progressions and melodies.

## What is a fifth?

To start, let’s figure out what a fifth is.
In music theory, the distance between any two notes is called an interval. Intervals are measured in half steps, like feet are measured in inches, or pounds are measured in ounces.

One half step is the distance from one note to the next highest or lowest note. For example, the distance from C to C♯ is one half step higher. The distance from D to D♭ is one half step lower.

The interval of a fifth is equal to seven half steps. This concept may seem a little counter-intuitive; you might think a fifth should be five half steps, right? Let’s look a little closer.

Think about it like this. There are twelve notes in the musical alphabet:
C, C♯/D♭, D, D♯/E♭, E, F, F♯/G♭, G, G♯/A♭, A, A♯/B♭, and B

Even though there are seven half steps from C to G, G is only five letters away from C (C, D, E, F, G). Anything that is a distance of 5 letters apart is referenced in terms of a fifth. The same goes for the other intervals, but we will save that rabbit hole for another time.

## Using the circle in your songwriting

Before diving further into all this theory, you may be wondering how I can use these patterns in my songwriting? Can’t we just skip to the fun part?

One way to apply  the circle of fifths in your songwriting is to fit the chord progressions you like onto the circle and then graft that same pattern onto a different location in the circle.

For example, take the chord progression from the beginning of “Smell Like Teen Spirit” by Nirvana: F5 – B♭5 – A♭5 – D♭5. How does this pattern fit on the circle? Let’s look into how the circle is constructed and see if we can answer that question. You can do this with any song or chord progression you like.

## Using fifths to build the circle

Now that you understand that a fifth is equal to seven half steps, you can use this knowledge to build the circle of fifths.

The first step is to draw a circle and place 12 evenly spaced dots around the outside, like the numbers on a clock. Draw the letter ‘C’ at the top of the circle like this:

Moving clockwise around the circle, the following note will be a fifth up from C. Count up seven half steps from C, and you reach G. Mark G at the one o’clock position on the circle like this:
Continuing clockwise, count seven half steps up from G, and you will reach D. Count seven half steps up from D, and you will reach A. Seven half steps above A is E, seven half steps above E is B, seven half steps above B is F♯, and seven half steps above F♯ is C♯. Take a minute to absorb that; there was a lot of math in a quick moment. Now your circle should look like this:

## Key signatures and enharmonic equivalents

One of the main pieces of information contained in the circle of fifths is the progression of key signatures. Key signatures are another way to organize groups of pitches based on the number of sharp or flat notes in the set.

For example, the key of C major at the top of the circle does not have any sharps or flats. When we move clockwise around the circle, we add sharps to the key signature. Thus the key of G major has one sharp, the key of D major has two sharps, the key of A major has three sharps, etc.

This pattern continues until we reach the key of C♯ major, which has seven sharps. At this point, all the notes in the major scale are sharp, so if we wish to continue, we will need to add double sharps. Double sharps are sort of challenging to think about quickly, so most people will switch to flat keys here using the concept of enharmonic equivalents.

Enharmonic equivalents are two notes that share the same pitch. For example, C♯ and D♭ are the same pitch but are different notes. G♭ and F♯ are different notes but the same pitch. These notes are called enharmonic equivalents.

## Using enharmonic equivalents to complete the circle

Backtrack a few steps to the B note on the circle. Can you think of the enharmonic equivalent of B? If you play a keyboard instrument, look one key to the right of B. Otherwise, move one note to the right in the musical alphabet, and then add a flat.

C♭ is the enharmonic equivalent of B. Mark C♭ on the inside of the circle like this:

Now, we can continue clockwise around the circle with the flat keys. Count up seven half steps from C♭ , and you find G♭. Count up another seven half steps, and you will reach D♭. Another seven half steps bring you to A♭. Seven half steps above A♭ is E♭, seven half steps above E♭ is B♭, seven half steps above B♭ is F, and finally, seven half steps above F brings us back around to C. Now your circle should look like this:

Congratulations! You have successfully constructed the circle of fifths!

## Some basic patterns on the circle

We learned previously that the key of C major at the top of the circle does not have any sharps or flats and that the key of C♯ major has seven sharps. It follows then that the key of C♭ major will have seven flats. If we connect these three points on the circle, we create a triangle that looks like this:
There are many patterns like this on the circle. For example, take a simple chord progression like C – F – G, one of the most common chord progressions of the last 100 years. If you connect C – F – G on the circle, it forms a narrow triangle like this:
Imagine the pattern that would form on the circle if you connected all possible I – IV – V chord progressions? It would look like a beautiful, fractal mandala.

## Picking up where we left off

Now that you see how the circle is constructed let’s finish analyzing the Nirvana song from earlier. Remember, the chord progression is F5 – B♭5 – A♭5 – D♭5.

Beginning on the F chord, move one step counterclockwise to B♭. Then, you jump to A♭ and move one step counterclockwise to D♭. See if you can trace this pattern on your circle, it should be pretty straightforward to see. Now let’s mess around with it.

Can you construct this same pattern beginning from D? The pattern would be D – G – F – B♭. Now, vary the tempo, change the quality of chords to minor or major, or add extensions like the 9th or 11th, so the progression does not sound too similar. Simple, right?

You can take this approach with just about any song. You will find that most popular chord progressions fit nicely on the circle of fifths.