The Circle of Fifths, Drawn and Played

Take any note and go up a perfect fifth. Do it again from where you land. Keep going, and after twelve steps you are back on the note you started from, having passed through every one of the other eleven exactly once. That is the circle of fifths, and it is not a chart to memorize: it is the reason the scales you play have the notes they have. Five steps round it make a pentatonic. Seven make a major scale, and which of the seven you call home is the mode. The keys next to each other on it share six of their seven notes, and the chord changes you hear most often are a step round it.

This page draws that and lets you hear it. The figure follows the text. The wheel in the middle is the twelve notes by semitone, home on top — the ordinary view, the wheel every set on this site is drawn on. The outer ring is the same twelve notes by fifths. The capsule holds a run of consecutive fifths, the wheel lights the scale that run makes, and a line joins each note on the ring to its place on the wheel. Tap a note in the run to make it home. ♪ plays the run round the ring, then round the wheel.

The circle of fifths

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CD♭DE♭EFF♯GA♭AB♭B

C

Twelve fifths, every note once

Start on C and go up a fifth: G. Again: D. Again: A. Each step is seven semitones, and seven shares no factor with twelve, so the steps never land on a note they have already used until every note has been used. Watch each new note find its place on the wheel as the run grows — four, six, nine, all twelve — the lines from ring to wheel crossing more and more, because the two rings hold the same notes in different orders, and never a note twice. Step by fourths instead and you walk the same circle the other way — the circle of fourths is this one read counterclockwise. No other interval does it: steps of a whole tone close after six notes and miss the other six; steps of a major third close after three.

So the circle is not one arrangement of the twelve notes among many. It is the only one where the neighbors are a fifth apart, and the fifth is the interval that matters most.

Why the fifth

Two notes a fifth apart are the second and third harmonics of one string — the ratio 3:2, the simplest relationship two different notes can have short of the octave. Their sound waves line up every two cycles, which is why a fifth sounds open and stable, why a power chord works, and why it is the first interval the app teaches you to hear. The harmonic series page draws the waves. What matters here is the consequence: two notes next to each other on the circle are as closely related as two different notes can be, and every step you take away from a note is a step toward notes that sound less like it. The circle is a map of relatedness, and distance on it is what your ear hears as distance. (Strictly, twelve pure 3:2 fifths overshoot seven octaves by a quarter of a semitone — the Pythagorean comma — and the circle only closes because equal temperament trims each fifth by two cents. Nothing on this page depends on it.)

Five in a row: the pentatonic

Light five consecutive fifths — C G D A E — and look at the wheel. Sorted into pitch order they are C D E G A: the major pentatonic, the scale you can hum without having learned it. Five notes that are all a fifth from a neighbor, and none a semitone from any other — that is what makes it impossible to play a wrong note in. The semitone, the interval that grinds, is five steps round the circle — B to C, say, is C G D A E B read backwards — and a run of five is never five steps wide.

Any of the five can be home, and each choice is a mode of the same five notes. Home on the first note of the run is the major pentatonic. Home on the fourth is A C D E G, the minor pentatonic, the scale under most of the blues and rock solos ever played. Same notes, different center: the circle makes the relative minor a change of which note you stand on, not a new scale. The major triad is inside too — the run's first, second and fifth notes, C G E — and the minor triad, A C E, is the run's fourth, first and fifth. One run of five, two chords, two scales.

Seven in a row: the major scale

Add a fifth at each end — F below and B above — and you have seven notes that sort into C D E F G A B, the major scale. The two new notes are the ones the pentatonic left out, and they are where the semitones come from: B is five steps round from C and F five steps from E — the distance that is a semitone — and a run of seven is the first that is wide enough to hold two such pairs. That is the whole difference between the pentatonic and the major scale: two notes, and with them the two semitones that give the scale its pull toward home.

Where home sits in the run is the mode, and the circle puts the seven modes in an order no other picture does. Home on the run's first note is lydian, the brightest; home one step in is the major scale; then mixolydian, dorian, aeolian — the natural minor — phrygian, and home on the last note is locrian, the darkest. Read along the band and the modes go from bright to dark, because each step moves home one fifth up the run, leaving one more note below it on the circle — and compared with the major scale, each of those is one more flattened degree: mixolydian flattens the 7th, dorian the 7th and the 3rd, aeolian adds the 6th, phrygian the 2nd, locrian the 5th. Lydian, with nothing below home, sharpens the 4th instead. The modes on guitar page plays them on a neck; here you can see why they sound the way they do.

Three pentatonics inside every scale

A run of seven has three runs of five inside it: the first five, the middle five and the last five. Each is a major pentatonic on its first note and a minor pentatonic on its fourth, and it holds one major and one minor triad — so a major scale contains three major pentatonics, on its IV, I and V, and three minor ones, on its ii, vi and iii, and the six triads with the same roots. Those are the six chords of the key and the six scales you solo with over them, and the circle shows why the F major pentatonic works over an F chord in C major: it is the same seven notes, five at a time, with the window moved one step. The nesting page draws the same idea on the instrument, and the app's harmony games are built on it.

Next door: keys that share six notes

Shift the whole run one step clockwise — C major to G major — and six of the seven notes stay: watch one note leave the capsule and one join. F drops off one end and F♯ comes on the other. That is why G major has one sharp: every step clockwise from C adds one, every step counterclockwise adds a flat, and the key signatures are nothing more than distance from C round the circle. It is also why a song can drift from C to G without anyone noticing the join, and why a change to a key far round the circle — C to F♯, six steps, sharing only two notes — sounds like a door opening onto a different room.

Harmony travels the circle

The most common chord change in Western music is one step round the circle: the V chord going home to I, G to C, a fifth down. The most common three chords are the neighbors — IV, I and V, three adjacent points on the circle, the same three the pentatonics sit on. The jazz standard cadence ii–V–I is three points in a row walked counterclockwise: D to G to C. A long chain of that motion, every chord a fifth below the last, is the cycle of fifths progression, and it works because each step is the most consonant move a root can make. When you pick roots in the app, you are learning to hear this: which of the key's six chords is sounding, and how far it stands from home.

What NoSheet does with this

The app teaches scales in the order the circle builds them. Root and fifth first — one step. Then the pentatonic, five steps, the safe scale you can't play a wrong note in. Then the major scale, seven, and the modes as the same seven with a different home. Every set on the site is drawn on the same wheel you see in the middle of this figure, so when you meet a new scale you can see where it sits on the circle and which older, smaller set it grew from. Play a run of fifths once and the circle stops being a diagram: a scale is a handful of neighbors, a key is a place, and a chord change is a short walk.