Fun with the Circle of Fifths

Fun with the Circle of Fifths, part 1

This is the Circle of Fifths, you may have seen it before:

Some people think it should look like this:

And there are people who call it the Circle of Fourths.

None of those differences really matter because it all comes down to the same thing. We will use the circle from the first picture.

You can find a large portion of music theory in this mysterious circle, and I’ll show you some of these fun facts in this article.

Just like a clock, the circle has 12 “dials” because there are twelve unique tones in the musical alphabet. The C is on top, or in the 12 o’clock position.

Going clockwise

It is called the Circle of Fifths because if you go in the clockwise direction, the tones are a perfect fifth interval apart.

An interval is simply a fancy name for the distance between two notes. There are many possible intervals and a “perfect fifth” is one of them.

It’s called a perfect fifth (or just “fifth”) because the distance between one tone and the next is five steps along the major scale.

Let’s start on the C, which is on top of the circle. The next note clockwise is G. Guess what? If you play the C major scale and start at C, then you’ll play five notes, C-D-E-F-G, until you hit G.

Another way to look at intervals is at the number of “half-steps” they encompass. A half-step (or “semitone”) means: go one key on the keyboard to the left or right. A whole step (or whole tone) means: skip a key.

Suppose we start at middle C. A half-step up from C is C# but a whole-step up from C is D. A half-step down from C is B but a whole-step down from C is Bb. And so on…

A perfect fifth is a distance of 7 half-steps. If you start at the middle C on your piano and then count 7 half-steps up, again you end up at G.

Try it for the other notes in the Circle of Fifths. Go clockwise from G to D. Again that is 5 steps along the major scale — of course, this time you’ll have to use the major scale of G, not C — or 7 half-steps up.

From D to A is again 5 steps, this time in the major scale of D. And so on… After stepping through all twelve possible notes, we’re back at C.

Clockwise is also called the “dominant” direction. In chord terminology, G is the dominant of C.

Going counterclockwise

In the counterclockwise direction, tones are a perfect fourth apart. That is why people sometimes call it the Circle of Fourths.

You can probably already guess by now that a “fourth” means: go to the fourth note in the major scale. Going counterclockwise from C means going to the fourth note in the C major scale, which is… F.

You can also count 5 half-steps. If you go all the way counterclockwise you end up at C again.

Going counterclockwise is also called the “subdominant” direction because F chord is the subdominant of C chord.

Upside-down

So far we have counted four or five steps upwards when we played a scale, but we can also play the scale backwards. If you go backwards from C to G on the C major scale, you’ll play C-B-A-G.

That’s only four steps, so from C to G is now a perfect fourth interval while not too long ago I told you it was a perfect fifth… What’s going on here?!

The same thing happens when you go counterclockwise but play the scale backwards: from C to F you now play C-B-A-G-F, which is a perfect fifth and not a fourth.

It is all a matter of perspective. In the end it doesn’t really matter if you call it a fourth or a fifth. That’s because these two intervals are “complementary“: going up a fourth is the same as going down a fifth, and going down a fourth is the same as going up a fifth.

Confused? No matter, they are just numbers.  You don’t really need to know this in order to make practical use of the circle, but I wanted to tell you about it anyway.

Key signatures

The Circle of Fifths describes the 12 major scales and the relationships between them. The closer keys are together on the circle, the closer is their relationship.

In the clockwise direction, each step adds a sharp (#) to the key signature:

• C major scale has no sharps
• G major scale has one shars
• D major scale has two sharps
• . . . and so on until…
• C# major scale has seven sharps

Counterclockwise, each step adds a flat (b) to the key signature:

• C major scale has no flats
• F major scale has one flat
• Bb major scale has two flats
• . . . and so on until . . .
• Cb major scale has seven flats

If you remember our picture of the clock, you can see the relationship between the number of sharps and flats and the numbers of the “clock”, at least on the right side of the circle.

On the left, you would have to subtract the “time” from 12. The key of Eb, which is at 9 o’clock, has 12 – 9 = 3 flats.

Note that the left side of the circle mirrors the right, but with flats instead of sharps.

At the bottom of the circle we see three items with a double name: Db and C#, F# and Gb, and B and Cb. We call these key signatures “enharmonically equivalent”.

That means they have different names, and different numbers of sharps and flats — Db has 5 flats while C# has 7 sharps — and therefore their notes have different names BUT they sound exactly the same.

If you were to transpose a piece in Db major to C# major, it would sound exactly like before… though it may be harder to read. That’s why composers and arrangers prefer the key of B over the key of Cb: it’s easier to write and easier to read.

You could go even further and create the key of Fb, which is enharmonically equivalent to the key of E, but that would be madness!

Fun with the Circle of Fifths, part 2

If you ever wonder what the order of sharps or flats is in the key signature, then you can look at the Circle of Fifths.

In the previous post we saw that the key of C major has no sharps or flats. The key of G major has one sharp, the key of D major has two, and so on.

You can find the tones that are made sharp by starting on F and then going clockwise through the circle.

Which means the order of sharps in the key signature is: F – C – G – D – A – E – B

See how it works in practice:

• C major scale has no sharps, so that’s easy.
• G major scale has the same tones as C major scale, except for F, which now becomes F#.
• D major scale has the same tones as G major scale, except for C, which now becomes C#. Its two sharps are F# and C#.
• A major scale has the same tones as D major scale, except for G, and so on…

In other words, F is the first tone that is made sharp, C is the second tone that is made sharp, G the third, and so on clockwise around the circle.

You can also find the flats using the same picture but now we start on B and work backwards.

The order of flats in the key signature is: B – E – A – D – G – C – F

Let’s apply it:

• C major scale has no flats.
• F major scale has the same tones as C major scale, except for B, which now becomes Bb.
• Bb major scale has the same tones as F major scale, except for E, which now becomes Eb. Its two flats are Bb and Eb.
• Eb major scale has the same tones as Bb major scale, except for A, and so on…

Did you notice that each time you take the next step, which tone changes?

• If we go clockwise, for example from the key of C to the key of G, the tone that changes is F, which becomes F#. F is directly to the left of C. So you can look to the left (or rather, counterclockwise) of your starting key to see which tone has to be raised.
• If we go counterclockwise, it works slight differently: the tone to the left is now the one that has changed. Say we go from the key of C to the key of F. One step left from F is Bb, which means the B tone was flattened to become Bb.

So you can look in the circle to see which tone you have to change.

You can also remember which scale step to raise or lower:

• Clockwise, raise the 4th note from the scale. From C to G, we first find the 4th note from the C major scale, which is F. We raise F to get F#. The note that has changed will also be the 7th note of the new scale.
• Counterclockwise, lower the 7th note from the scale. From C to G, the 7th note from the C major scale is B. We lower B to get Bb. The note that has changed will also be the 4th note of the new scale.

What if you quickly want to know which tones need to be sharpened for a particular key signature? Look up the key in the circle, let’s say the key of A. Go counterclockwise one step (we skip this one). Then all the tones counterclockwise back to F must be sharpened. So in this case we skip D (this one doesn’t change) and sharpen G, C and F.

Getting the flats is a little harder. You move counterclockwise one step from your key signature and then go back clockwise again until you reach Bb. So in the key of Ab, we first go to Db and then back to Bb: Ab, Eb, Bb. So the key of Ab has four flats: Db, Ab, Eb, Bb. A little tricky, this one.

There is another method. Go directly across the circle from your key signature, then count clockwise to B and flat all these notes. From Ab across the circle gets us at D, then clockwise we meet A, E and finally B. We flatten these notes to find the four flats: Db, Ab, Eb, Bb. Still a little convoluted, but hey, it’s possible!

If you know which notes are flattened, how do you determine the key? The name of the key is the second-to-last flat in the list. For example, in the picture below the flats are: Bb – Eb – Ab – Db – Gb. The second-to-last is Db, so the key must be the key of Db major.

Or you could just count the number of flats and go counterclockwise that many steps in the circle, starting from the top.

For sharps it is even easier: Take the last sharp in the list and go up a half-step to find the name of the key. In the picture below the sharps are: F# – C# – G#. To find the key, raise G# by a half-step, which results in: the key of A major.

Of course, here you can also count the number of sharps starting from the top, but this time we go clockwise.

It is easy to see that the circle goes F – C – G – D – A – E – B clockwise. These are all names without sharps or flats. But because B is enharmonically equivalent with Cb, it continues Cb – Gb – Db – Ab – Eb – Bb clockwise. Do you notice, with the exception of F, that this is the same as the first list but simply with added flats?

To find the notes in the current key, read the five notes clockwise and the one note counterclockwise. You can also simply go one position counterclockwise and then read seven notes going clockwise.

So from G we go left once to find C, then we go six times clockwise to find G, D, A, E, B and F#. Put these in alphabetical order and you have the notes from the key of G.

This works for all keys, although sometimes you’ll have to turn flats into sharps for it to make sense. Applying this formula to the key of D would give you G, D, E, A, B, F#, Db but you should obviously turn that Db into a C#.

Phew! That’s a lot of crazy things you can do with the circle and key signatures.

Fun with the Circle of Fifths, part 3

Ready for more fun with the Circle of Fifths? Here we go!

Minor keys

There is also a circle for minor keys:

I put the names of the minor keys on the inside of the circle. This is because each major key has a relative minor key.

If you don’t have this handy picture around, you can still find the relative minor key. Draw a 90 degree angle from the major key through the center of the circle. The leg will point to the relative minor.

Or: Rotate the circle so the major key is at 12 o’clock. Its relative minor is now at 3 o’clock.

Or: Skip two keys in the clockwise direction. Start at Bb, skip F, skip C, then the relative minor is Gm.

You can also remember that the relative minor is the 6th tone from the major scale, or simply go 3 half-steps down. Or go three steps clockwise.

It also works the other way around: each minor key has a relative major key.

Ways to find the relative major scale:

• Draw a 90 degree angle the other way around.
• Rotate the circle so the minor key is at 12 o’clock. Its relative minor is now at 9 o’clock.
• Skip two keys in the counterclockwise direction.

You can also remember that the relative major is 3 half-steps up. Or three steps counterclockwise.

Chords and the circle

Chords that are close together in the circle sound good together in a song.

Every major key has three primary chords: the I (tonic), IV (subdominant) and V7 (dominant) chords. These are easy to find in the circle.

Go to your key, for example C. Go one step clockwise and we find the V7 chord, in this case G7. One step counterclockwise from C is the IV chord, in this case F.

The V7 chord is the dominant 7th chord. It uses the 1st, 3rd, 5th, and 7th notes from its own major scale, but the 7th tone is flattened.

For example, the tones of the G7 chord are: G – B – D – F. Note that F is not part of the G major scale; it is “borrowed” from the key one step counterclockwise: the key of C.

If you know the V7 chord, then what key are you in? Look counterclockwise one position in the circle. For example, you can tell this way that the C7 chord belongs to the key of F. The tones of C7 are C – E – G – Bb, and that Bb comes from the scale of F.

The following picture shows the 7 “diatonic” chords that can be used in the key of C (without borrowing “accidental tones”). Note that the major chords are neatly grouped together, as are the minor chords.

Chord progressions

Chords like to move counterclockwise in the circle. The G7 chord provides the strongest pull towards the C chord. The D7 chord, in turn, provides the strongest pull towards G.

In songs in the key of C, it is common to see a chord progression such as A7 – D7 – G7 – C.

The chords are not always dominant 7ths, they could also be Am – Dm – G7 – C or Am – D7 – G7 – C. However, they do tend to follow the circle counterclockwise back to the home chord.

You may have heard of the famous ii-V-I chord progression, or 2-5-1. That’s simply a trip counterclockwise around the circle.

In key of C, ii-V-I is Dm – G7 – C. Extended versions of this chord progression exist too, like the vi-ii-V-I or 6-2-5-1 (also called a 1-6-2-5). We already saw that above: Am – Dm – G7 – C.

You can go even further and add Em in the mix to get a 3-6-2-5-1. All these chords come straight out of the circle, and the principle works just the same in any of the other major keys.

Tritone substitution

A “tritone” is an interval of three whole tones. There is a concept in jazz music called the “tritone substitution”, or the “flat 5″ substitution. You can use this technique for substituting dominant-7 chords.

For example, you could replace a G7 chord with a Db7 chord. You can do this because G7 and Db7 have 2 tones in common: the B and the F. These two tones just happen to be a tritone (i.e. three whole tones) apart. It may sound a little weird at first, but jazz cats like it.

There are several ways to figure out what the tritone substitution chord is, but you can also look into the circle. The substitution chord is the one directly across. Draw a line from G through the center of the circle and you’ll end up at Db. And that’s your tritone chord.