For the past week or so, I've had the Circle of Fifths on my mind. In fact, it's been a bit of an obsession. This is partly because the School of Music Theory is now offering Grade 5 Theory online (which you can read about HERE), but it's also because the Circle of Fifths is so beautiful and complete in its fifth-ness!
Let me show you what I mean.
The Circle of Fifths is like a clock face
The Circle of Fifths is like a clock face. It is a graphic that shows key relations within the functional diatonic system of harmony. (You can read more about that idea HERE and HERE.)
C major is at 12:00. As you travel around the circle you will find that every point is fifth-related. C major at 12:00 moves up a fifth to G major at 1:00, which moves up a fifth to D major at 2:00, and up a fifth to A major at 3:00, etc.
When I say fifth-related, I am referring specifically to perfect 5ths. What are perfect 5ths? And why are they "perfect"? For this, we need to review a small point of acoustics. (Or you can read more in-depth about it HERE.)
Whenever you play a note, you are hearing more than just that note. You are hearing the note plus all of the overtones above it. These are overtones:
When this low G is struck, plucked or bowed, you are mostly hearing the low G (called the fundamental). But you are also hearing the G an octave above, and then the D a perfect 5th above that G, and then the G above that, and so on. This is called the harmonic series, and each overtone of the harmonic series becomes progressively weaker. Which means that the first few overtones are strongly present in the sound you hear. The perfect octave and the perfect 5th represent the first two overtones in the harmonic series, so they resonate strongly with the fundamental.
So the Circle of Fifths represents an important relationship found in the very acoustics of sound! That is one reason it is so exciting. It also represents the flowering of a harmonic system that developed around this notion of pure consonance, and that is another reason it is so exciting!
Moving clockwise around the circle - moving up by perfect 5th
As you move clockwise around the Circle of Fifths, you move up a perfect 5th, and in doing so add a sharp to the key signature at each point along the circle. Moving from C major at 12:00 -
- to G major at 1:00, we add an F# to the key signature.
Moving up another 5th from G -
- we keep the F# and add a C# to the key signature.
Moving up another 5th from D -
- we keep the F# and C# and add a G# to the key signature.
This additive process continues as we move clockwise around the circle.
Even the sharps are fifth-related!
The scales themselves are not the only fifth relations. The order of sharps added to the key signature at each point on the circle are also fifth related.
F# -> up a fifth to C# -> up a fifth to G#
You can see how this is illustrated on the Circle of Fifths.
This process repeats around the circle all the way to 7:00 - C# major, where every note of the scale is sharp.
Moving counter-clockwise around the circle - moving down by perfect 5th
As you move counter-clockwise around the Circle of Fifths, everything is reversed. You move down a perfect 5th, and in doing so add a flat to the key signature at each point along the circle. Moving from C major at 12:00 -
- down to F major at 11:00, we add a Bb to the key signature.
And like the sharp key signatures, the order of flats added to the key signature at each point on the Circle of Fifths, moving counter-clockwise, are also fifth-related.
Bb -> down a fifth to Eb -> down a fifth to Ab
This process repeats counter-clockwise around the circle all the way to 5:00 - Cb major, where every note of the scale is flat.
What I love most about the Circle of Fifths
What I love most about the Circle of Fifths is that once you understand the underlying principle of it (fifth relations), you can reconstruct it easily. I know there are mnemonics for remembering the order of sharps and flats, and those have their place as reinforcement and memory aides for those who respond well to them. (Personally, I often have trouble remembering the special sentence for the mnemonic!). But if you understand the concept of the Circle of Fifths, you don't need extraneous aides for memorisation. Instead, you have a deep understanding of harmony and the way it works, and you can recall and reconstruct this graphic representation of key relations, key sgnatures and how harmony moves.
I use the Circle of Fifths as a guiding concept in all of my teaching, at every level. From the earliest piano beginners, where I seed the idea of fifth relations using finger numbers, to Grade 5 Theory students, who need these concepts to understand the Grade 5 Theory exam, through to advanced theory students, who use the idea of fifth relations to understand structure in music and to realise their compositional ideas, the Circle of Fifths is a marvelous tool for understanding the core principles of western harmony.
Circle Harmony
I'm such a big Circle of Fifths nerd that I made some learning resources based on it! If you would like to study the Circle of Fifths or use it as a teaching resource for your own students, have a look at my new curriculum, called Circle Harmony. In it, you will find lesson slides, worksheets and piano activities all designed to develop a full understanding of the Circle of Fifths.
Click HERE for Circle Harmony 1 - Scales and Chords Around the Circle of Fifths. Part 3 of this curriculum includes a very handy checklist of activities for students to play in every key around the circle at three different technical levels!
Click HERE for Circle Harmony 2 - Minor Keys Around the Circle of Fifths. The minor mode has its own quirks. In fact, there are three different versions of minor, so I dedicated a whole separate ebook to dive deep into the minor mode.
Click HERE for the Circle Harmony Workbook, which is filled with music theory activities to apply everything from the Circle Harmony curriculum.
And if you really want to dive in deep, you can buy all three of these resources for 30% off the price HERE.