Circle of fifths, part 2: Origins and uses


Last time we surveyed the rich culture that surrounds music’s circle of fifths: the posters, gadgets, apps, clocks and t-shirts, and the almost endless variants of the iconic diagram. But apart from the human fondness for zodiacs, mandalas and other circular things, what are the secrets of its success?

This time I’ll be looking at the origins of the circle of fifths, and some of its musical uses. Next time, a lesser-known but fascinating application of the circle.  After that, I’ll look into the theory behind the circle of fifths, why it is so useful, and why it exists at all.

First, let’s sort out the terminology. Circle of fifths, cycle of fifths, circle of fourths?

I try to say ‘circle’ when I mean the diagram, and ‘cycle’ when I am describing a chord progression or referring to the abstract concept behind the diagram. But I often default to ‘circle’.

Fifths or fourths? For my money, circle (or cycle) of fifths is the one, because it is universally used and understood. We do not need two names, or two diagrams. The step between C and G can be read as either a fifth or, in the other direction, a fourth. So the circle of fifths is also a circle of fourths.

Which way is up? The diagram is usually drawn with C at 12 o’clock, E at 3 o’clock, F#/Gb at 6 and Ab at 9. But it can be rotated into any orientation, or reflected in a mirror, and it will still work.  You might reasonably draw the diagram differently when you are illustrating the relationships between chords in a key other than C. In an app, this is an easy and natural thing to do.


The earliest example of a circle of fifths diagram is in a book by the Ukrainian musician Nikolai Diletsky, published in 1679.
Diagram from Diletsky’s ‘Idea grammatiki musikiyskoy’ (Идея грамматики музикийской, “An idea of musical grammar”). The manuscript is held by the Russian State Library. Public domain,
A few years ago the illustrator Josh Wells revived Diletsky’s design, adding a dash of J R R Tolkien. The resulting image has spread on the internet, often unattributed. You can buy it as an 11″x17″ (279x432mm) poster for US$8.00, or on a hoodie for US$32.00, from Odd Quartet. Marvellously, Josh’s design retains Diletsky’s coolest feature: the circular stave.

The circular stave, adorned with key signatures, vividly conveys the way each key morphs into the next, by changing just one tone at a time. It would be perfect, if only the transition from ‘sharp’ keys to ‘flat’ keys could be handled a bit better.

In the short step from Db to F# major, it looks as though the scale is completely rejigged: five flats are cancelled and six sharps are applied. In fact, of course, only one tone changes: the C in Db major drops to B in F#. The other six tones don’t change pitch. Only their names change. (In modern equal temperament this is exactly true. But even in historic tunings, the pitches are very close.¹)

Could we make this continuity of pitches more obvious? One way would be to interlace the stave with itself, at the point where the circle closes, so that each stave line turns into a space and each space into a line. The 6 o’clock position on the circle would be occupied by two equivalent keys, Gb and F#, and the stave would do something like this (though possibly the other way up):

All those sharps and flats disguise the fact that these two keys have the same notes. Here the staves are offset so that the pitches match one-for-one.
I think M.C. Escher would have understood what is happening here.
1960s fabric print found on and inspired by Escher’s ‘Day and Night’ (1938)
Johann David Heinichen (1728) drew a circle of 24 keys, designed as a practical guide to modulation. The major keys form a circle of fifths, and next to each major key appears its relative minor.
Heinichen’s circle of 24 keys: a guide to modulation, for 18th-century musicians
David Kellner (1737) rearranged this into what is essentially a modern circle of fifths, with relative minors on an inner ring. The outermost ring describes key signatures just as we would: ‘two sharps’ is written in glorious gothic script above D major and B minor. And look! There is a Diletsky-style circular stave. This is peak Circle of Fifths. It doesn’t get better than this.
David Kellner, 1737: a modern arrangement of major and minor keys, plus a Diletsky-style circular stave.

Circle of fifths diagrams were invented and popularised because the concept of a cycle of fifths was in the air at that time. The old church modes were on the way out, replaced by the new concept of major and minor keys. Musicians had begun to think about a series of transpositions or modulations that would return to its starting point after going through a number of keys.

How many keys? Twelve major, plus twelve minor, seemed to do the trick². And twelve pitches in each octave were sufficient to build twelve seven-note scales, because each pitch could be re-used in several keys.

There were a few tuning glitches, ‘wolf’ intervals and the like. Harpsichord and organ tuners struggled with these issues for years, using both the concept and the diagram of the circle of fifths. I’ll come back to that and other specialised uses later, after considering the circle of fifths in its most familiar guise, as a mnemonic for key signatures.

A key to key signatures

This is quite possibly the diagram’s most important single use. It does the job well, until we reach the more extreme key signatures with six or more accidentals. The closed circle clearly asks us to accept that F# and Gb are the same key. But this is an additional fact that has to be learned. You would never guess it from the way key signatures are written.

There is a bit of a disconnect here. Music is taught on the basis that there are 12 pitches per octave, 12 major keys and 12 minor keys. It’s a closed, finite system. And though keys are clearly different in the way they interact with instruments, voices and ears, all keys are theoretically equivalent and there is certainly no one key that is special.

By naming seven pitches with the letters A to G, and treating all other pitches as modifications of those seven, our notation makes one tonality – C major – look special. C isn’t special. It’s just lucky.

Because all pitches other than A to G must be notated with sharps and flats, we soon encounter pitches where there is a notational choice: A# or Bb? F# or Gb?

In any given context, does it matter whether we write Bb or A#? Yes, but mainly because it is helpful to have some rules to keep written music intelligible. One rule is to use each letter-name (and thus, each stave position) exactly once in each seven-note scale. In an A major scale, we agree to call its third degree C# rather than Db or, lord help us, B##. The idea is to get an alphabetic sequence (A, B, C#, D, E, F#, G#, A) rather than something like A, B, B##, D, E, Gb, G#, A which identifies the correct piano keys but is utterly confusing.

It’s a pain having to learn those notational conventions. Much of what is taught as music theory is really a set of rules for operating in a 12-tone, all-keys-are-equal world, while using a notation which seems to describe a completely different universe. A universe where monks were the musicians, God was the audience, harmony was just a glint in melody’s eye, key-changes didn’t happen, seven stave positions per octave seemed sufficient, and seven names for pitches looked like all we’d ever need. Happy days.

If you can see past the notational fog of sharps and flats, the circle of fifths is telling us something fundamental about Western music. Whatever major scale you start with, you can always sharpen the fourth or flatten the seventh to make another major scale. It is this that allows us to arrange 12 major scales in a circle.

Not all scales have this property. Take a melodic minor scale, for example. There is no way you can alter a single tone and still have a melodic minor scale. I’ll have more to say about the peculiar properties of diatonic scales in a future post.

The circle of fifths as a practice aid

Whether it’s scales, arpeggios, 2-5-1s or Charlie Parker licks, jazz students are always told to practise in all twelve keys. The circle of fifths, as a map of tonalities, provides a systematic way of doing this.

For scales, licks or complete tunes, stepping around the circle either clockwise or anticlockwise can be helpful. Moving in fifths, up or down, ensures that changes in the tonal palette (the key signature, basically) are as gradual as possible. On the piano, your hands will be making shapes which change only gradually as you progress through the keys.

Piano students are often taught to practise 2-5-1s (cadences) in the cycle C, Bb, Ab, Gb, E, D, C. That means moving down by whole steps, equivalent to two fifths at a time. Why? Well, it sounds musical; it minimises hand movement; and it is good preparation for tunes like Victor Young’s Stella By Starlight where 2-5s are chained. Basically this is the route tunes take when they want to get home in a hurry, with no harmonic fuss.

The last line of Stella has the chords E-7b5, A7, D-7b5, G7, C-7b5, F7, Bbmaj7. That’s three chained minor 2-5s, followed by a major resolution. Though only three tonalities (D, C and Bb) are implied, we’ve got seven consecutive chord roots there in circle-of-fifths sequence. Another example: the bridge of Clifford Brown’s Joy Spring contains three complete, major 2-5-1s in the sequence G, F, Eb – part of a six-key cycle that most jazz piano students have practised.

For a full 2-5-1 workout you must include the alternate cycle: G, Eb, Db, B, A, G.  It is also wise to practise 2-5-1s and 2-5s moving in half steps – for tunes like Strayhorn and Ellington’s Satin Doll, Benny Golson’s Stablemates and John Coltrane’s Moment’s Notice. In fact you have probably got a book, an app or a teacher telling you to cycle through technical exercises in other patterns such as minor thirds, and in random patterns so you are ready for anything.

Tessitura Pro, from mDecks Music, makes a pretty thorough job of this. The whole app is based on the circle of fifths as a device for visualising and comparing ‘structures’ (scales and chords). Choose a structure, and the app can generate a variety of practice exercises, from simple scales and arpeggios to complex patterns. Be aware that the notes shown on the circle are actual notes, not keys or tonalities. The screenshot shows the five notes which make up the C minor pentatonic scale, and an exercise generated from them.

tessitura exercise
Tessitura Pro knows hundreds of scales, chords and modes, and presents them visually on the circle of fifths. From any chosen scale it can generate a variety of practice exercises.

Harmonic progressions

Harmonic progressions which move in descending fifths are common, and easily traced on the circle diagram. In any key, the standard root movement is 4-7-3-6-2-5-1, though it can go in the reverse direction. 4 to 7 is a tritone so this is really a semicircle of fifths.
CoF progression
Arrows show the circle-of-fifths progression that is used in songs like Autumn Leaves. Apart from the tritone F to B, the progression moves in descending perfect fifths. The diatonic chords of C major / A minor are shown, plus a couple of secondary dominants. E7 is a secondary dominant in C major, and the actual dominant of A minor.

Note that we are no longer using the circle as a chart of tonalities. We are tracking root movement. The diagram above shows how circle-of-fifths progressions operate within a single key, or within a pair of relative major and minor keys. The complete sequence cycles through the full range of diatonic chord qualities. Autumn Leaves, normally regarded as a minor tune, starts with a major cadence (D-7, G7, Cmaj7) before moving into the minor part of the cycle (B-7b5, E7, A-7).

In the B section of the tune, the cadences come in reverse order, minor leading into major, giving the whole section a major feel. It’s just a question of where you start on the loop, and where you finish.

Notice how the chord quality changes progressively during the in-key circle-of-fifths progressions of Autumn Leaves. If you like to think in modes, these progressions go through all seven diatonic modes, from the darkest (locrian) to the brightest (lydian), and then back to locrian.

This contrasts with our earlier examples from Stella by Starlight and Joy Spring, where the tonality changes progressively while the chord qualities (and corresponding modes) follow a simple repetitive pattern. To sum up the differences:

In-key circle of fifths progression

  • root movement in descending diatonic fifths – mostly perfect fifths, with one tritone
  • confined to a semicircle of the full circle of fifths
  • stays within one key, or a relative minor/major pair
  • may cycle through all four diatonic, seven-note chord qualities: -7b5, -7 (3 times), 7, maj7 (twice)
  • correspondingly cycles through all seven diatonic modes
  • on the full cycle, chord quality gets progressively brighter, then darkens again

Through-the-keys circle of fifths progression

  • root movement in descending perfect fifths
  • potentially covers the entire circle of fifths
  • short repeating cycle of chord qualities e.g. (-7, 7), (-7, 7, maj7) or simply (7)
  • correspondingly, a short repeating cycle of three or fewer modes
  • moves rapidly through keys, adding flats or cancelling sharps
  • sense of homecoming or darkening tonality (though this is obviously relative, and no key is intrinsically darker than any other)
Some tunes, including Autumn Leaves and Fly me to the Moon, are built almost entirely on circle-of-fifths progressions  But the real challenge for the songwriter is how to break away from this and do something original. Many jazz tunes include a leap into a distant key, and then rely on circle-of-fifths progressions to navigate back to the home key of the piece.
Chord Wheel iOS
The Chord Wheel app, zoomed in on the triangle of diatonic chords for C major or A minor. The app also highlights the secondary dominants D7 (bottom right) and E7 (out of picture). The inner coloured ring shows chords in circle-of-fifths order. Can anyone explain why the second ring isn’t also in circle-of-fifths order?

In the previous post I mentioned the Chord Wheel, a rotary device based on the circle of fifths. This also exists as an app for iPhones and iPads, with the big bonus of hearing the chords as they would sound on a guitar or piano.

The Chord Wheel is sold as a tool for analysing progressions and creating your own. Its circle-of-fifths layout is ideal for key changes and transpositions. When it comes to exploring chords within a key, you will notice that the seven diatonic chords have been pulled together into a triangular cluster which conceals the fifth relationships between them. Sure, you can tap out the Autumn Leaves sequence, but your finger has to hop around a bit. Perhaps that is no bad thing. If it was too easy to reproduce Autumn Leaves, you might find it correspondingly harder to compose something original.

My next post will describe how the circle of fifths has given 300 years of service in the tuning of keyboard instruments such as the harpsichord, the piano and their electronic successors. It’s a specialised, even geeky subject, but I’ll attempt a not-too-geeky treatment. It will give me a chance to show you some of the most amazing infographics I have come across in the whole field of music.

In the fourth and final article of this series I will investigate why the circle of fifths works, and why it even exists. What is the source of its magic? This leads into deep and still-open questions in music theory. I shall look behind a few doors that most music teachers – very understandably, if you ask me – prefer to leave closed.

(1) It is not just a matter of tuning. The physicist Herman Helmholtz seems to have objected to the abstract idea of circular modulation. “Although B# has very nearly the same pitch as C, and can even be improperly identified with it, the hearer can only restore his feeling for the former tonic by going back on the same path that he advances,” he wrote in The Sensations of Tone (1863). Certainly an expert musician might notice when modulations do not return to their starting point by the same path. Even an untrained listener might have some inkling of this. But does that make it bad to return to the home key by unexpected routes? Jazz, I need hardly say, does this all the time. Modern theorists tend to be less judgmental than Helmholtz: they analyse what musicians do. They do not tell them what to do.
(2) I am glossing over a huge subject here. The 12-note octave is not an automatic choice. Non-octave structures, and octave structures with more than 12 pitch classes, occur in some musical traditions and in the work of modern microtonalists. This article only relates to 12-note musics such as jazz.
The circle of fifths assumes a palette of 12 pitches at roughly equal intervals, but emphatically it does not assume equal temperament or any other specific tuning. Whether it is Miles Davis bending a long note, or Ellington’s horn section locking together in a harmony more exact than anything you can play on a piano, performers are by no means restricted to equally tempered pitches.

Further reading

Each jazz textbook or web resource has its own approach to the subject of circle-of-fifths progressions.

The Berklee Book of Jazz Harmony, by Joe Mulholland and Tom Hojnacki, refers to ‘cycle 5’ progressions. The authors introduce the in-key (diatonic) version in their first chapter, before they have explained minor harmony, so initially they can offer no role for the -7b5 chord. In chapter 2 they introduce the ‘II-V progression’ (major version only) and ‘extended dominant strings’, both of which are examples of through-the-keys cycle-of-fifths progressions.

In Jazzology, Robert Rawlins and Noor Eddine Bahha approach the subject by way of the ii-V-I cadence. They give many examples of in-key and through-the-keys progressions. They cover ‘ii-V chains’ thoroughly, including those which depart from circle-of-fifths root movement. ‘Backcycling dominants’ (chains of dominant 7th chords descending in fifths) are treated separately in the next chapter.

Mark Levine’s Jazz Theory Book states concisely: “You should use the cycle when you practice because it approximates real life. Most chord movement within tunes follows portions of the cycle. For instance the roots of a II-V-I progression follow the cycle.” Chained dominants are introduced as “V of V”. Levine’s book is an easier read than the previous two, because it does not try to fit (force?) everything into the theoretical framework of functional harmony. His survey of other common progressions reminds us that not everything follows the circle of fifths.

The Jazz Piano Site is a useful web resource, with a good page on circle-of-fifths progressions. Three main types are identified.

For details of the the origin of the circle of fifths and the modern key system, an important source is Between Modes and Keys: German Theory, 1592-1802 by Joel Lester.

Leave a Reply

Fill in your details below or click an icon to log in: Logo

You are commenting using your account. Log Out /  Change )

Facebook photo

You are commenting using your Facebook account. Log Out /  Change )

Connecting to %s