The circle of fifths

The circle of fifths (also called cycle of fifths) gives us a handy overview of the different scales and how they are related to each other.

How to form the circle of fifths

In the lesson ‘How to form a major scale’, I explained that starting from the C major scale, every time we take a major scale a fifth higher, the scale gets one extra sharp note. And, starting from C major, every time we go a fifth down (or a fourth up, which is basically the same), we get one more flat note in the major scale.

We could now display all the roots (starting notes) of the major scales in a row with C major (no sharps, no flats) in the middle. At the left of C, all the major scales with flats. Every step to the left would mean a fifth down (or a fourth up) and thus an extra flat note in the scale. At the right of C, all the major scales with sharps. Every step to the right would mean a fifth up (or a fourth down) and thus an extra sharp note in the scale.

Gb      Db      Ab      Eb      Bb       F        C        G        D        A        E        B        F#

It is important to realize that the most left scale (Gb) and the most right scale (F#) are actually the same scale, since Gb and F# are the same note, only written differently: they are enharmonic equivalent.

So that means that we could display this row with scales in a circle, as follows:

circle of fifths major

At the right side we have the major scales with sharps, on the left side the major scales with flats.

Every step clockwise in this circle (this would correspond with a step to the right in our row above) means a fifth up (or a fourth down). And every step counterclockwise a fifth down (or a fourth up). That’s why we call this circle the ‘circle (or cycle) of fifths’. Since a fifth up corresponds with a fourth down and vice versa, this circle is sometimes also called the ‘circle (or cycle) of fourths.

The minor scales in the circle of fifths

Since a natural minor scale has exactly the same notes as its relative major scale, we can also put the natural minor scales in our circle of fifths. So, for example: since the A minor scale and the C major scale share the same notes, we can put them in the same place in the circle of fifths:

circle of fifths major minor

And see here our circle of fifths, which gives us a quick overview of the number of sharps and flats in every major and minor scale, plus an overview of relative minor/major relationships.

Why would I need a circle of fifths?

As mentioned above, the circle of fifths gives a good overview of sharps/flats and relative minor/major.

The circle of fifths is among other things very handy for example in transposing a song (I’ll come back on this in a later lesson).

The circle of fifths also quickly shows us why the major scales that start on a black key on the piano are mostly written with flats instead of with sharps. Let me illustrate this with the Eb major scale, which has 3 flats.

Eb is enharmonic equivalent with D#, so let’s look how the D# major scale looks like. First of all, in the circle of fifths, from F# I will go on clockwise to C#, G# and then to D# (so every step a fifth up). You can see that D# major has 9 sharps (wow!).

circle of fifths D# major 9 sharps

Let’s, for fun, see how the D# major scale looks like (see also the lesson ‘How to form a major scale’):

From D#, a whole tone (W) up to E#

From E#, a whole tone (W) up to F## (or Fx)

From F##, a half tone (H) up to G#

From G#, a whole tone (W) up to A#

From A#, a whole tone (W) up to B#

From B#, a whole tone (W) up to C## (or Cx)

From C##, a half tone (H) up to D#

So the D# major scale is:

D#  E#  F##  G#  A#  B#  C##  D#

As you can see: a total of 9 sharps (don’t count the D# twice)!

Compare this with the Eb major scale:

Eb  F  G  Ab  Bb  C  D  Eb

Now, my question to you is: “Which scale do you prefer, the Eb major scale, or the D# major scale?” I think I know the answer… 🙂

 

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Martin Cohen
 

Martin Cohen is a science and piano teacher. He is also a jazz musician and composer.

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