In recent years, this elegant musical utility has been no more than the poster child for crusty old music teachers imbibing about Beethoven and proper voice leading. How passé! Wrong. The musical establishment doesn't own the circle of fifths anymore than artists can own chord progressions.
The Greek philosopher Pythagoras is credited with inventing the mathematical foundation for the circle, with his ubiquitous Pythagorean Theorem. It wasn’t until the 1670s that the modern circle was introduced by Nikolay Diletsky.
Essentially, the circle of fifths is a system that organizes musical keys by placing the most closely related keys next to one another. Instead of organizing the keys in sequential or “chromatic” order (such as C, C#, D, D#, etc.), the circle orders the keys according to the number of accidental “sharp” or “flat” notes they contain. When arranged in this pattern, the distance between each key is a perfect fifth (C, G, D, A, etc.), hence the name, “circle of fifths”.
This system of ordering musical keys is most intuitive because it follows a consistent pattern. Each consecutive key gains one sharp note (when moving clockwise) or one flat note (when moving counter-clockwise).
The circle of fifths is like garlic or onion, it can be used as the basis of myriad musical dishes and serve up some killer flavors! If you’re still on the fence or feeling the slightest bit intimated, here is a list of benefits to mastering the circle.
Build more interesting chord progressions
Learn about borrowed chords
Understand how to properly change keys (modulate)
Quickly identify harmonic relationships
Quickly identify musical keys when reading or analyzing sheet music
Get better at spelling chords
Improve your musical vocabulary
Get better at identifying intervals and chords while ear training
All Western music can be mapped to the circle, from harmony to melody and structures of improvisation in jazz and post-modern classical music. Think of it as a Swiss-army knife of musical adaptation. Or as a compass to help you build a more useful road map of the relationship between various scales, keys, chords, and progressions.
The circle is first and foremost a method of organizing musical keys, represented by key signatures in a manner that makes the most practical sense. There are 15 key signatures in total, representing 12 musical keys. Major/minor keys share the same key signatures, which is why there are fewer than you might expect, with the possibility of a major and minor key being constructed on each note. For instance, C major and A minor are enharmonic or relative keys, meaning they share the same notes. If a piece or song uses A minor as the tonic chord, that song would still be notated in the key of C.
The 15 key signatures, including relative minor keys
The key signature can be found in the center of the ToneGym circle of fifths above.
Key signatures are made up of either sharp or flat notes, called accidentals. These represent visually the song’s key. As we move right on the circle, each consecutive key gains one sharp note, while keys gain one flat note when moving left. At the bottom of the circle, the keys overlap. Again, these are called enharmonic key signatures, meaning they sound the same, but can be written differently. Kind of like the differences in spelling of American English and UK English words, color and colour, favorite and favourite, theater and theatre.
Flat keys tend to be preferable for jazz, theater, and American songbook arrangements, as they often call for horn arrangements or were written with horns in mind. Horns read in flat keys, as the note C on many brass and woodwinds is in fact sounded as “Bb”.
Learning to recognize keys at a glance will greatly speed up your reading, analysis, and general knowledge of theory. It’s like learning to read, you don’t read individual letters, you recognize whole phrases and words quickly.
The circle is (unsurprisingly) organized in perfect fifths. A perfect fifth is the most stable musical interval after the octave and serves as the building block of many musical chords. There is something magical about a perfect fifth. So much so that rock&roll is quintessentially built on them (power chords on a guitar, which use just a root and fifth). Fifths are neither major nor minor (although there is a compelling theory about this by famed musicologist and artist, Jacob Collier… worth watching for anybody wishing to stretch the boundaries of imagination and theory).
In the harmonic series, which western harmony is constructed from- the further away you go from the perfect octave, the less stable the intervals are. And the perfect 5th comes right after the perfect octave!
The circle begins on C and then moves to G (a perfect fifth), then from G to D (another perfect fifth). This pattern continues ad infinitum. When moving counter-clockwise, the circle gives us something called the “cycle of fourths”. Intervals invert when the notes are switched, which is why the clockwise fifths become counter-clockwise fourths!
The first key signature in the circle, “C”, contains no sharp or flat notes or accidentals. The next sharp key, “G”, contains one sharp, the note F#. If you look at the circle, you can see that this F# is taken from two spaces back on the circle. When we move to the next sharp key, D, there are two sharps, F#, and C#. Noticing a pattern? Again, the sharp notes come from further back on the circle (skip the last note and add the rest beginning on F). From D we move to A, which contains three sharps (F#, C#, G#).
We refer to these accidental notes as scale degrees, from 1 (one) through 7, the pattern of notes that constitute the major scale. Scale degrees simply describe where a certain note is placed within a sequence of notes as in a musical scale.
C major = 1 2 3 4 5 6 7 8
C Dm Em F G Am B* C
When moving counterclockwise around the circle (descending order of flats) each consecutive key gains a flat note. This also follows a pattern, with the flat note coming from further ahead on the circle.
Given that the circle of fifths is constructed geometrically, it serves as a helpful tool, similar to a compass, that can be used to generate everything from chord progressions to modulations.
When constructing a chord progression, it is possible to use the circle as a cheat sheet for finding the corresponding chords in each musical key. For example, when using a progression, all you need to do is locate on the circle the chord you're using as the (tonic), and you’ll find the chord to the left and the chord to the right. If you added a chord to the progression (as in countless popular songs), you would only need to move 90 degrees from the tonic, which in the key of “C”, would be “A minor”.
This same pattern could be applied elsewhere on the circle, generating the chords needed to plug into a progression in any key. Simply rotate the circle and voila! You have a set of chords in the new key. This is an especially useful tool for transposing songs quickly, whether you’re on a gig or in the studio.
Let’s talk about modulation, or more simply, a key change. The circle shows us which keys are most closely related, and therefore which keys work best together when modulating between them. The closer two keys are located on the circle, the more in common they have, making them harmonious and/or complimentary. Modulating up by a whole step or major 2nd is a common tool used in a lot of pop, rock, and Broadway tunes. As you can see, C and D are only two spaces apart on the circle.
F# however, couldn’t be further from the key of “C”. This makes a C to F# modulation more difficult, unpleasant, or altogether unwise.
Rules are made to be tested and at times broken, but as far as tried and true songcraft, keys that stick together win (Grammys) together.
The further you hopscotch away from these close-knit musical relationships, the more unstable and dissonant the relationships become. If you want to experiment with adding some dissonance to your sound, try leaping to the other side of the circle.
It’s also possible to modulate between parallel keys, like C major into C minor (A major). This can be done because both keys share the same dominant chord. The parallel key can be found 90 degrees away from the tonic.
Using the circle to find keys that share common chords makes modulating a breeze, as you can use the common chord as the pivot point for switching to the new key.
Finally, modulating stepwise by a half step is also very common. “Love on Top” by Beyoncé for instance, modulates upwards in half-steps. Even though C and C# are about as far away as can be on the circle and have nothing in common, this modulation still functions because EVERY note in the key is moving upwards at the same rate. It’s almost as if they have so little in common it works. Like a negative and a positive, or celery and peanut butter. Total opposites attract…
One final system of modulating is the common tone system, which uses a common tone even if that tone doesn’t produce the same chord in each key. For example, we could modulate between F major and Ab major by using the shared Bb tone in both keys. This chord would be major (IV) in the key of F and minor in the key of Ab (ii). By using this shared tone as the turning point when changing keys we can often disguise the key change and make it relatively smooth. Typically this note would be sustained, while the rest of the notes shift. You can hear this used in Mozart’s Fantasia in C minor.
The circle can also be used to generate systems for complex improvisation, as in John Coltrane’s legendary “Giant Steps”. This is a concept for another article entirely, but to introduce the idea, here is an example of the “Coltrane Matrix” mapped to the circle…
The Coltrane matrix moves in mediant and submediant relationships (thirds/sixths).
“Giant Steps” is so named because the piece modulates constantly by giant intervallic steps. As you can see on the circle above, the song’s key leaps around the circle in a wide triangle pattern.
So how can we put this into practice? Well with ToneGym of course. Check out our interactive circle of fifths to hear all of this in action. The circle will display the diatonic chords in each key, and allows you to playback not only the triad chords but also the 7th chords associated with each scale degree. You can also map the keys to each musical mode. Try experimenting with this particular feature to find more exciting chord substitutions and sounds.
The interactive circle on ToneGym also allows you to switch between scalular and intervallic views, so you can view either the roman numeral and classical nomenclature, or intervallic labeling.
Wowza. Did you make it to the end? We’re not surprised, just proud. Congratulations on expanding your horizons and getting to know the circle of fifths a bit better (or for the first time!). When put into practice, the circle of fifths is actually pretty darn cool.
Don’t stop here, keep learning and flexing those muscles in ToneGym!
Okay, so I lied about the end. If you still have some brain power left after all of the above… feel free to read on. The following bonus section is not at all necessary to understand the circle or put it to use in most contexts, but for those of us who love diving deep into the arcane and stretching the boundaries of music’s fundamental structure, you might find this interesting.
In 1953, jazz theoretician George Russell published Lydian Chromatic Concept of Tonal Organization, a book that fundamentally challenged using the C major (Ionian) mode as the Circle’s tonic center. He instead suggested that the C Lydian mode should be used as the tonal center of the circle, because the first 7 notes traveling clockwise on the circle form the Lydian scale when compressed into the space of an octave (C D E F# G A B C).
Russell actually suggested that all of music’s tonal gravity revolves around the Lydian mode, with a great deal of merit.
This theory formed the basis of modal jazz pioneered by musicians like Miles Davis and John Coltrane. Many of these pieces, such as those recorded for Kind of Blue and Giant Steps, are analyzed using the Lydian Chromatic Concept. The title track of Coltrane’s opus, which I mentioned earlier, actually moves through three Lydian chromatic scales (C, Ab, and E).
The Lydian Chromatic Concept is actually taught in varying degrees at major conservatories and university programs. Many jazz musicians still incorporate this theory into their improvisational toolkit.
Pianist, musical artist, and theoretician Jacob Collier postulates that fifths are actually major and fourths are actually minor (when properly extended).
As you likely already know, fourths and fifths are “perfect” intervals, meaning they are typically neither major or minor (like thirds, sixths, seconds or sevenths).
When a fourth or fifth is altered it’s either diminished, or augmented, but never ascribed a major or minor tonality.
Collier supports his theory by playing the first five notes on the circle of fifths in ascending order, C G D A E
This cycle of fifths results in a C 6/9 or C major add 6th add 9th chord. Coincidentally, it is also the C major pentatonic scale.
Now if you were to play the notes moving left on the circle in fourths, you would get C F Bb Eb Ab, a C minor 7th 11th b13th chord.
It’s incredibly interesting to apply Jacob’s theory for yourself and hear the results. The fifths expand outward, while the fourths contract. Just as major is an inversion of minor, fifths mirror fourths, providing starkly different sounds when the cycles are extended and played in unison.
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