Introduction

By now you will have come across a fair number of keys and scales, so now it's time for a reminder of them all, and to fit them together into a bigger picture.

Perfect fifths

As you create each new key by adding a sharp, what do you notice about the interval between the tonic of each successive key?

The tonic notes of each key created by adding sharps

Each of these tonic notes is exactly a perfect fifth above the previous tonic note, allowing for octave jumps.

There is a similar process at work for flats. Here are the successive tonic notes:

The tonic notes of each key created by adding flats

Now you can see that each of these tonic notes is exactly a perfect fifth below the previous tonic note, again allowing for octave jumps.

Therefore, you can tell that the tonic of the major key with - for example - 5 sharps is exactly 5 perfect fifths above C, in other words, B major:

The tonic of the major key with 5 sharps is exactly 5 perfect fifths above C: B major

Similarly, with flats, we run down perfect fifths. For example, let's try to find the tonic of the major key with 4 flats:

The tonic of the major key with 4 flats is exactly 4 perfect fifths below C: A flat major

Minor keys

The same goes for minor keys - they also run in perfect fifths, up for sharps and down for flats, starting on A (the relative minor of C major).

Therefore we can quickly tell that the tonic of the minor key with, say, 3 flats is exactly 3 perfect fifths below A: in other words, C minor:

The tonic of the minor key with 3 flats is exactly 3 perfect fifths below A: C minor

In reverse

This system also works in reverse; to know how many sharps there are in F sharp major, simply work out how many perfect fifths you have to jump back down in order to arrive at C:

We need to jump 6 perfect fifths down from F sharp to C, and therefore there are 6 sharps in the key signature of F sharp major

That's a total of 6 perfect fifths, and therefore there are 6 sharps in the key signature of F sharp major.

Remember that if you are dealing with flats, you would see how many perfect fifths up you will have to go in order to arrive at C.

And if you are trying to find a minor key signature, you should aim to arrive at A instead of C.

Remembering the order of flats and sharps

You now have a fool-proof method of knowing the major or minor key with a given number of flats or sharps.

But if you have to write down the key signature of - say - F sharp major, and you know that there are 6 sharps, how do you remember which notes are sharps and what order they are written in the key signature?

Look again at the key signature for F sharp major:

The key signature and scale of F sharp major

Once again, perfect fifths come to help us. If you can remember that the first sharp is F sharp, then the subsequent sharps follow in perfect fifths rising from F sharp, and that you will need the first six:

Rising 6 perfect fifths above F sharp gives us the first 6 sharps in the key signature

Likewise, if you can remember that the first flat is B flat, then the subsequent flats follow in perfect fifths descending from B flat. So, to get the first six flats:

Falling 6 perfect fifths below B flat gives us the first 6 flats in the key signature

Related keys

We have already looked at related keys in some depth, so here is a quick reminder of three types of relations between keys:

• Enharmonic keys: Keys with tonics that are enharmonic equivalent, major/major or minor/minor. For example, C sharp major and D flat major.
• Parallel keys: Keys with the same tonic, major/minor pairs. For example, C major and C minor.
• Relative keys: Keys with the same key signature, but a different tonic, major/minor pairs. For example, D major and B minor.

Key signatures reminder

We have encountered every key up to 7 flats or sharps now. Here is a quick reminder of each of these keys:

Sharps / flats	Major key	Minor key	Key signature
0	C major	A minor
1 sharp	G major	E minor
2 sharps	D major	B minor
3 sharps	A major	F sharp minor
4 sharps	E major	C sharp minor
5 sharps	B major	G sharp minor
6 sharps	F sharp major	D sharp minor
7 sharps	C sharp major	A sharp minor
1 flat	F major	D minor
2 flats	B flat major	G minor
3 flats	E flat major	C minor
4 flats	A flat major	F minor
5 flats	D flat major	B flat minor
6 flats	G flat major	E flat minor
7 flats	C flat major	A flat minor

The cycle of fifths

This leads us to what is known as the cycle of fifths (or sometimes also the "circle" of fifths), which is a profound part of the diatonic system used in Western music.

As summarised above, we can construct the major keys by progressively transposing C major by perfect fifths upwards or downwards, and that at each stage upwards one sharp is added, and that at each stage downwards one flat is added, and the process is similar for minor keys.

We have also seen that it is impractical to go beyond 6 sharps or flats, and that it is possible to use enharmonic keys instead.

So: what if we carry on the process of progressing upwards by perfect fifths, switching by enharmonic equivalence at 6 sharps (F sharp major) to 6 flats (G flat major)?

G flat leads up a perfect fifth to D flat (5 flats in the key signature), which leads to A flat (4 flats in the key signature)... This is looking familiar!

In fact, we arrive back at C major after exacty 12 steps, and after going through every single key. It is no coincidence that the chromatic scale also has 12 notes.

Likewise, if we progress dowards by fifths from C major - to generate the keys with flats in their key signature - at 6 flats we can swap to 6 sharps by an enharmonic shift, and we will arrive back at C major after going through each of the sharp keys.

It is possible to imagine this cycle of fifths as a circle with 12 segments, much like a clock face, as shown here:

The cycle of fifths

The "cycle of fifths" might help you to remember the order of the keys and the number of sharps and flats in each. It can also help you quickly remember the order in which sharps and flats appear in the key signature: flats appear in the anti-clockwise order starting from B flat, and sharps appear in the clockwise order from F.

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