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What is the theory behind the circle of fifths?
How do we use it?
Improve your music theory skills with our deep dive!
You have about two-thirds of a great piece of music, but that won’t be enough. You can tell it needs to go somewhere, but you don’t know where. Now might be the time to whip out the trusty circle of fifths, a tool utilized by composers since the early Baroque era, to figure out how to chart a compelling modulation.
The circle of fifths is an arrangement of key signatures and their tonal centers by perfect fifths. It is laid out so that keys located closer together in the circle are more closely-related, which makes it a useful tool for charting modulations.
In this article we explore the circle of fifths and its uses, helping you take out the guesswork out of modulation in your next project.
Let’s Talk Theory
There are just a few elements of music theory worth reviewing before we get into using the circle of fifths as a tool; think of these as the assembly instructions breaking down the patterns utilized in the formation of the circle of fifths. For the music theory heads out there who already know their way around the circle of fifths, feel free to skip to the next section. But then again, you might find this a helpful review.
Put most simply, a key signature defines a set of pitches that relate to one another in a pattern of half-steps and whole-steps. The major and minor modes are the most common in western music, so the circle of fifths is almost exclusively set up to outline how major and minor key signatures relate to one another.
In the case of a major scale, the interval relationships between scale degrees follow the pattern W – W – h – W – W – W – h, where W = whole-step and h=half-step. The minor scale, on the other hand, separates scale degrees by the pattern W – h – W – W – h – W – W. For more on these scales, see our deep dive articles on the major scale and the three minor scales.
Keys are named for the starting pitch (also known as the tonal center or root) and the pattern or interval relationships between scale degrees (major or minor for the purposes of explaining the circle of fifths).
The accidentals (sharps and flats) identified in key signatures are alterations of specific pitches that maintain the modal interval relationship patterns. A major scale beginning on D, for example, requires two pitch alterations, F-sharp and C-sharp, in order to maintain the pattern of W – W – h – W – W – W – h, so the key signature for D Major will indicate these two sharp pitches.
Major And Minor Keys
Major and minor keys follow different patterns of pitch relationships, but these pitch relationships are related to one another. Essentially, re-ordering a major scale so that the root is centered on the sixth scale degree will give you a minor scale. This is the relative minor of the major scale you used to derive it. These scales will utilize the same key signature but a different root.
Because the relationship between the major and relative minor is constant, the process used to find the relative minor is also constant. The reverse is also true, meaning that the relative major of a minor key centers its root on the third scale degree of the minor scale, and both keys will utilize the same key signature. A few examples of relative keys include C Major and A minor, D Major and B minor, and B♭ Major and G minor.
Modulation is the movement from one key area to another. Short-term or incomplete modulations are often referred to as tonicizations, which is the treatment of a pitch other than the overall tonic as a temporary tonic.
In music, modulation can be a useful technique for heightening drama and making a clear distinction between sections of a piece of music. It is often a clearer marker of change and movement than simple chord changes that never leave a single key signature. The circle of fifths is very useful in mapping modulations and tonicizations as it will help you choose the most appropriate key to shift to.
Sharps and Flats
With the circle of fifths, the tonal centers of the keys move in perfect fifths from one key to the next, but the key signatures move just one accidental at a time. For example, C Major and A minor are typically listed at the top of the circle of fifths. As we move to the right (clockwise), we add one sharp with each key, so the next keys are G Major/E minor, the keys with one sharp.
Moving one more key to the right we land on D Major/B minor, with two sharps. The process continues, with each new key adding an additional sharp and centering the root a perfect fifth above the root of the previous key.
If we return to C Major but then move to the left (counter-clockwise), we land on a key signature with one flat, F Major. F is a perfect fifth below C. If we move one step further to the left we land on B-flat Major, with two flats. This pattern continues as well, with each additional step to the left landing us an additional flat in our key and centering our root one perfect fifth lower (or one perfect fourth higher) than that of the previous key.
This is an important distinction to note: moving clockwise around the circle of fifths results in ascending by perfect fifths (C – G – D – A – E – B – F♯ – C♯). Moving counter-clockwise, however, results in descending by perfect fifths or ascending by perfect fourths, depending on your perspective (C – F – B♭ – E♭ – A♭ – D♭ – G♭).
The perfect fifth is the inversion of the perfect fourth, meaning that a movement in one direction will be inverted in the opposite direction. In this way, the circle of fifths could be conceived as the ascending circle of fourths if read counterclockwise, or the descending circle of fourths when read clockwise.
Each of the major keys has its own arrangement of sharps or flats, and the order in which accidentals is added follows a pattern: the order of sharps is F♯, C♯, G♯, D♯, A♯, E♯, B♯, whereas the order of flats is the reverse of this pattern: B♭, E♭, A♭, D♭, G♭, C♭, F♭.
Why A Circle?
Thus far we have detailed the circle of fifths in a somewhat linear way: move to the right and add a sharp (or remove a flat) and move to the left to add a flat (or remove a sharp). So why do we lay key relationships out as a circle? The answer is clearer at the bottom of the circle, as we see the overlapping keys of D♭/C♯ Major, G♭/F♯ Major, and C♭/B♯ Major.
While we could conceive of key relationships in a linear way, from seven flats to seven sharps and all of the keys in between, we would then miss out on the fact that several of the keys at the extreme ends of the gradient are enharmonically-related, meaning that they are the exact same keys simply spelled differently. For that reason, we lay the keys out in a circle and think of harmonic motions as moving counter-clockwise and clockwise around the circle as opposed to leftwards or rightwards on a line.
We are of course already familiar with musical pitch being cyclical – once we reach the next octave, the notes in a scale repeat an octave higher.
Closely (And Distantly) Related Keys
Part of the art of crafting music is balancing similarity and difference. Too much sameness can make for boring music, whereas too much difference can make it difficult for an audience to find their footing.
We see this dichotomy repeat throughout the practice of composing music. Whether it be in utilizing inversions to take advantage of common tones and maximally smooth voice leading or the use of melodic and rhythmic motives that return frequently enough to help ground the listener’s attention but not so frequently as to bore them.
Part of what makes the circle of fifths one of our most useful resources for composition is that it is essentially a roadmap connecting key areas in terms of how closely they relate to one another. Keys that neighbor one another, for example, share every pitch except for one, meaning that they are very closely related. Keys located directly across from each other on the circle share no common pitches, meaning that they are very distantly related. In the next section, we will go into why this is so useful.
The Circle Of Fifths Beyond Key Relationships
Some theorists will point to the use of the circle of fifths in theoretical questions unrelated to key signatures, such as building triads. While the arrangement of pitches in perfect fifths does make it possible to map relationships other than those between key areas, the circle of fifths is a fairly clunky tool for doing theoretical work beyond just mapping key relationships. For a useful tool in constructing triads and visualizing their relationships, look into the tonnetz.
Even for the work of mapping key relationships it starts to lose some of its handiness when it comes to modulations that are not based on perfect-fifth relationships, such as those initiated through diminished pivot chords. For these modulations, the best the circle of fifths can do for us is to show us that they are distantly-related; it cannot do anything to tell us why the modulations seem somehow to work.
It is situations like these in which a music theory tool is not a particularly effective means of explaining why something sounds good. So we have to be on our guard that the analytical tool does not take on the role of a gatekeeper. Music theory and all of its limitations should never take precedence over making good music.
A Helpful Reference Tool
The circle of fifths is a collection of patterns that can be a tremendous help in keeping track of where the patterns intersect. For example, given one variable, such as the name of a key, and the understanding of how sharps and flats are ordered in the circle of fifths, it is possible to determine how many sharps or flats make up that key.
Inversely, given the number of sharps or flats in a key and the understanding of how roots progress up a fifth for every step in clockwise motion and down a fifth for every step counterclockwise, it is possible to determine the name of a key.
Just like any tool for making and dissecting music, the more one uses it the less one needs to reference it, but the circle of fifths can prove invaluable early on in making sense of music theory.
Modulations: Where Do We Go From Here?
Whether we’re building a modulation path that traces the circle of fifths exactly or simply moving to the dominant key area before a predictable return to the tonic, the circle of fifths has a lot to offer us in presenting key areas in a way that clarifies the degree to which they are related to one another.
The following compositional techniques draw directly from the circle of fifths, but the list is far from exhaustive. I encourage you not only to make use of these techniques but also to think outside of the box and find other ways to approach the circle of fifths beyond the standard uses.
Modulation To A Relative Key
The first technique we will explore has nothing to do with perfect fifths; rather, the relationship between a major key and its relative minor. With both key areas sharing the same key signature, this makes the modulation from a major key to its relative minor, or vice versa, a fairly smooth transition. In western art music, the transition from a major key to its relative minor key is often cued with a raised leading tone in the minor key area. Other than that, there is no alteration of the key signature, since relative keys share the same key signature.
One example of the modulation to a relative key can be heard in “One” by U2, in which the verse is in A minor but the chorus has a chord progression set in C Major.
Modulation To The Dominant
A dominant key relationship exists between any given key and the key found one step clockwise on the circle of fifths. A modulation to the subdominant does not require much preparation, since both the tonic key and the dominant key each share six of their seven pitches. A particularly transparent example of a modulation to the dominant key area can be heard in Queen’s “Save Me,” in which the song begins in G Major, but modulates to D Major for the chorus before modulating back to G Major.
I say this modulation is transparent because there is something of an abrupt pause before we hear the first chorus in the dominant key. Knowing Queen’s style, this is by design and meant to heighten the drama. For anybody hoping to approach the dominant key area more smoothly, however, there is the secondary dominant.
The secondary dominant is the dominant chord of the key you are approaching, which helps to reinforce the modulation by serving as a sort of middleman helping to introduce the new tonic.
If, for example, you were hoping to modulate to the dominant of C Major, which is G, you could use the V chord in G to reinforce the arrival of G as the tonic of a new key area. This would be a D Major chord, which is distinct from the ii chord in C, D minor, because it features an F-sharp, the leading tone in G Major, as its chordal third. This arrival of the F-sharp implies a resolution upwards by step to G and thus helps to prepare the arrival of the new tonic in the modulation.
This use of the secondary dominant is not limited to modulations to the dominant; in fact, a secondary dominant can be used with varying degrees of smoothness in any modulation.
Modulation To The Subdominant
A subdominant key relationship exists between any given key in the circle of fifths and the key found one step counterclockwise. Much like in the case of a modulation to the dominant, both the tonic key and the dominant key each share six of their seven pitches, thus there are relatively few steps required to get from one to the other. One particularly well-known example of a modulation to the subdominant can be heard in the bridge section of The Beatles’ “I Want To Hold Your Hand.”
While the rest of the song is in G Major, the bridge moves to C Major, as is made clear through the D minor chord that begins the accompaniment to the phrase “And when I touch you.” The F-natural in the D minor chord does not belong to the key area of G Major, but it fits right into the key of C Major.
Don’t Shoot The Pianist recently put out a new cartoon entitled “How Composers Modulate” in which the first example features Bach proceeding from the “old” key through an arch labeled “circle of fifths” to the “new” key. The implication is that Bach moves through much of the circle of fifths via an ascending or descending fifths progression in order to arrive at a new key.
The way the descending fifths progression works is to begin with a chord built on any tonic, then progress to the chord built on the pitch a fifth below the original tonic (the key area one step counterclockwise), then repeat the process from the new home chord, until you have reached your destination. It is possible to travel all the way around the circle of fifths this way until you reach your original home chord or to get off the ride a bit early through either a chromatic alteration to speed the process of returning home. It is also possible, as in the example from the comic, to arrive at your “new key” destination.
The ascending fifths, or ascending fourths, progression is essentially the same with a clockwise motion through the circle of fifths as opposed to the counterclockwise motion.
The example below is not Bach but Purcell, yet for fans of Wes Anderson it might be more familiar as the theme quoted by Benjamin Britten as part of The Young Person’s Guide to the Orchestra, which Anderson used to frame the soundtrack to Moonrise Kingdom (2012). At any rate, Purcell places a descending fifths progression prominently after the first few seconds of the piece.
There are countless examples from Baroque music in which this is an accurate depiction of how composers modulate, but one need not go back so far to find the descending fifths progression. One well-known example is “I Will Survive,” a tune first popularized by Gloria Gaynor but later reinterpreted by Cake and Demi Lovato, among others. The chord progression for this tune is another classic descending fifths progression.
The Circle Of Fifths: Your New Favorite Toy
The circle of fifths will not make music for you, but it can serve as an invaluable reference tool and perhaps even the source of your next creative spark. Much like someone stricken by wanderlust spinning a globe, closing their eyes, and setting about to figure out how to arrive wherever their finger lands, the circle of fifths can offer both a challenge and an opportunity to anyone who treats it as a roadmap to a modulatory destination.
The circle of fifths is one of these resources that is scaleable. From the student looking to get better acquainted with the flat keys to the master challenging herself to modulate through each of the flat keys within one composition, the circle of fifths has the potential to offer something to any musician.
It is worth reiterating, however, that the circle of fifths should always be thought of as a tool, and never a rule. There is endless possibility when it comes to any facet of music, thus we as creative musicians should never stop ourselves short of finding the next great sound just because it doesn’t fit neatly in the frameworks we have for understanding music.
Finally, make sure you check out our other articles on music theory if you want to learn more: