The Circle of 4ths and 5ths

How to work out Keys and Major Scales

So far we have been concentrating on the C Major Scale, as it contains no sharps or flats. It's the only Major Scale which doesn't contain any. All other Major Scales/Keys contain a number of sharps or flats.

So where does the Circle of 4ths and 5ths enter into this?

The circle allows you to cycle through the keys, calculating how many sharps or flats are in each key. Although there are 12 notes, by doing this, we actually end up with 15 Keys! However this is due to enharmonic relationship (notes which are made up of the same frequencies but have different names e.g. F# and Gb. Both F# and Gb are the same note, but depending on what Key we're playing in there have different names)

So, how do we go about working out sharps/flats in the other Keys/Scales?

All keys are derived from the C Major Scale.

The cycle of 4ths tells us the keys that contain flats.

The cycle of 5ths tells us the keys that contain sharps.

The Cycle of 4ths

If we start with the scale of C Major:

KEY I II III IV V VI VII
C C D E F G A B

The cycle says we start on the 4th Degree of the scale, in this case an F and flatten the 4th degree, turning it from B into Bb. This gives us the key of F which contains one flat (Bb)

KEY I II III IV V VI VII
C C D E F G A B
F F G A Bb C D E

We then repeat the process, but now the 4th degree is Bb, so that's where we start and flattening the 4th changes the E to Eb. So the Key of Bb contains two flats they are: Bb and Eb.

KEY I II III IV V VI VII
C C D E F G A B
F F G A Bb C D E
Bb Bb C D Eb F G A

This process is then repeated until we evenntually end up with all Flats! ...but hold on a minute, there are only 5 black keys on a keyboard, so what gives with the 7 flats?

Take the example of the Key of Cb, it contains 7 flats: Cb, Db, Eb, Fb, Gb, Ab, Bb. Now let's look at the keyboard:

Notice that there's no black key between B & C and E & F? Yet we have 7 flats? Well it's comes down to 'Enharmonics'. Cb is actually just another name for B and Fb is another name for E. They are the same notes, but called different names. The notes of Cb and B are said to be 'Enharmonic', as they are actually the same note, but have different names depending on which key we're playing in. The same is true for Fb and E.

The reason we don't just calle Fb an E and Cb a B is because each note can only be contained within a Key once, therefore we must call these notes by other names to fit into the pattern.

The Cycle of 5ths

The cycle of 5ths work slightly differently from the cycle of 4ths, in that we now start on the 5th and sharpen the seventh. So starting with C Major, we start on the 5th degree, in this case a G and sharpen the seventh, in this case F becaomes F#. So the key of G contains one sharp; F#.

KEY I II III IV V VI VII
G G A B C D E F#
C C D E F G A B

If we then take the 5th degree of G, we get D as our starting note and we sharpen the 7th, in this case C becomes C#.

KEY I II III IV V VI VII
D D E F# G A B C#
G G A B C D E F#
C C D E F G A B

The Cycle

Here's the entire cycle of 4ths and 5ths for reference...

KEY I II III IV V VI VII
C# C# D# E# F# G# A# B#
F# F# G# A# B C# D# E#
B B C# D# E F# G# A#
E E F# G# A B C# D#
A A B C# D E F# G#
D D E F# G A B C#
G G A B C D E F#
C C D E F G A B
F F G A Bb C D E
Bb Bb C D Eb F G A
Eb Eb F G Ab Bb C D
Ab Ab Bb C Db Eb F G
Db Db Eb F Gb Ab Bb C
Gb Gb Ab Bb Cb Db Eb F
Cb Cb Db Eb Fb Gb Ab Bb

Why 15 keys when there are only 12 notes?

You will notice we've ended up with 15 keys! BUT there are only 12 notes! However, the key of Db sounds exactly the same as they key of C#, the key of Gb sounds the same as the key of F# and the key of Cb sounds the same as the key of B.

T,T,S,T,T,T,S

You may also notice ALL of the notes in each key follow the pattern of Tone, Tone, Semitone, Tone, Tone, Tone, Semitone. Therefore, regardless of which note you start on, as long as you follow this pattern you will construct a Major Scale.