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Start with the key of C major (which is a neutral key in
that it needs neither sharps nor flats to maintain the correct
formula). Write out:
Key of C major:
C D E F G A B C
And then calculate the intervals between each note (T=Tone,
S= Semitone):
C [T] D [T] E [S] F [T] G [T] A [T] B [S] C
Notice that, without alteration these notes already conform
to the major scale formula. So we say that the key of C major
has no sharps. A line of music written in this key would start
like this:
Now count up four steps (because we are following
the circle of fourths):
C D E F
This gives you F major as the next key in
the circle. Write out the letters for F:
F G A B C D E F
And then calculate the intervals between each note (T=Tone,
S= Semitone):
F [T] G [T] A [T] B [S] C [T] D [T] E [S]
F
Now compare this to the major scale formula (T,T,S,T,T,T,S)
and we see that the B note is wrongly positioned (too close
to the C and too far from the A).
We fix this by turning the B into Bb. So the notes in the
key of F major are:
F G A Bb C D E F
And we say that the key of F major has ONE FLAT:
Bb
The start of a line of music written in this key would like
this:
The flat sign is placed on the middle line where the note
B would be found.
Now count up four steps again.
F G A Bb
This gives you Bb major as the next key
in the circle. Write out the letters for Bb:
Bb C D E F G A Bb
And then calculate the intervals between each note (T=Tone,
S= Semitone):
Bb [T] C [T] D [T] E [S] F [T] G[T] A [S] Bb
Now compare this to the major scale formula ( T,T,S,T,T,T,S)
and we see that the E note is wrongly positioned.
We fix this by turning the E into Eb.So the notes in the
key of Bb major are:
Bb C D Eb F G A Bb
And we say that the key of Bb major has TWO FLATS:
Bb and Eb
The start of a line of music written in this key would like
this:
The new flat sign is placed on the fourth space up where the
note E would be found.
Now count up four steps again.
Bb C D Eb
This gives you Eb major as the next key
in the circle. Write out the letters for Eb:
Eb F G A B C D Eb
And then calculate the intervals between each note (T=Tone,
S= Semitone):
Eb [T] F [T] G[T] A [T] B [S] C [T] D [S] Eb
Now compare this to the major scale formula ( T,T,S,T,T,T,S)
and we see that the B note and the A note are wrongly positioned.
We fix this by turning the B into Bb the A into Ab. So the
notes in the key of Eb major are:
Eb F G Ab Bb
C D Eb
And we say that the key of Eb major has THREE FLATS:
Bb, Eb and Ab
The start of a line of music written in this key would like
this:
The new flat sign is placed in the second space up where the
note A would be found.
At this stage it is worth pausing to see what the pattern
is that develops as we work round this circle of fourths.
If we retrace our steps we can see that we are following these
rules:
1. The new key in the circle is based on the note four
steps above the previous key.
2. Each key in the circle keeps the bs that were added in
all previous keys.
3. One new flat is added at each step in the circle and
this new flat is always note 4 in the key.
4. The new flatted note actually becomes the next key in
the circle.
So lets see if we can speed up the process by using these
three rules as shortcuts:
We were up to the key of Eb major so according to rules 1.
and 4. the next key will be Ab major.
Rule 2. tells us that the notes B, E and A will all be flatted
and rule 3. says that D will be flatted as well (D is note
4 in the key of Ab).
So, by applying the rules we calculate that the key of Ab
major comprises:
Ab Bb C Db
Eb F G Ab
Let’s just check by examining the intervals between
each note:
Ab [T] Bb [T] C [S] Db [T] Eb [T] F [T]G [S] Ab
T T S T T T S which checks out against our major scale formula.
So we know the system works!
The new flat sign is placed on the fourth line where the
note D would be found.
We can predict that the next key in the circle will be Db
major and that this will have 5 flats:
Db Eb F Gb
Ab Bb C Db
The new flat sign is placed on the second line up where the
note G would be found.
Something a bit strange happens with the next key in the
circle. The fourth note in the key of Db major is Gb so Gb
major is our next key and as well as the five flats
inherited from Db major, if we follow our rules we will want
to add in Cb
Gb Ab Bb
Cb Db
Eb F Gb
At first this seems confusing because there isn’t a
Cb is there? In fact Cb is just another name for B. But remember
the rule: only one of each letter allowed in a major scale.
We can’t have B and Bb in the same key. So we use Cb
as a name for the note that sounds like B.
The new flat sign is placed on the third space up where
the note C would be found.
Then we come to the key of Cb major with its 7 flats:
Cb Db Eb
Fb Gb
Ab Bb Cb
This time we have the weirdly named Fb which sounds just
like the note E, but we can’t call it E in a key that
has the note Eb.
The new flat sign is placed on the first space up where the
note F would be found.
If we move on to complete the circle of fourths we bump into
the mysterious world of keys with double
flats!
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Key
Signatures
