Fun with the Circle of Fifths, part 1

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

Circle of Fifths

Some people think it should look like this:

Circle of Fifths, reversed

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.

Circle of Fifths as a clock

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.

Circle of Fifths with key signatures

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.

Circle with number of sharps and 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”.

Bottom of the circle

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!

More about the circle next time…

Read more articles on Piano Clues:

Basic Theory


Chords and Harmony


The Circle of Fifths


Arrangement, Improvisation and Composition


Reading Music and Sheet Music


How to Record Piano


Software and Virtual Instruments


Scales and Exercises


Digital Pianos


Links and Other Stuff


Comments

  1. Joan says:

    Thanks so much for this site. I’m getting it slowly, but I’ll need to keep coming back until I absorb it fully. A big help as I struggle to teach myself to play the piano.

  2. mb says:

    thanks, at least now i can impress my piano teacher!

  3. Marcel Tchaou says:

    Thanks a million!

  4. anonymousv says:

    OMG. thx soooo much! i hav an upcoming theory test and i didnt understand a thing! you totally saved me!!! :)

  5. Bruce says:

    This is great! It is by far the best explanation of the “Circle” I have seen. Thanks!

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