Major Keys and Key Signatures

In this article, we will discuss an easier way to identify key signatures using the circle of fifths as well as discuss notating pitches in a performed melody.

What is a Key Signature?

In the previous article, we discussed building a key using the formula of whole and half steps. While this is a valid approach to building a key, it can be kind of tedious after a while. And, it can be limiting in the depth of knowledge you attain by simply following a formula.

Let's introduce a new way of thinking about major keys. First, we must discover what a key signature is.

Firstly, if a particular major or minor scale is used prominently throughout a piece of music, and the tonic of the scale is asserted to be the central pitch of the piece, then we can say that the piece is "in the key" that corresponds to that scale. For instance, if a piece uses the pitches of F major, and the pitch F feels like home for the music (i.e. it resolves to F), then the piece can be said to be "in the key of F major."

 F major has the following notes:

F G A Bb C D E F

Now, let's compare this key to the key of C major:

C D E F G A B C

We can see that overall, the pitch collections used in the two scales are very similar. Note that pitch collection is simply a collection of pitches, not implying any tonic/home-base relationship or any other relationships within the collection. Anyway, the two collections are similar, but there is one small difference. The key of F introduces one accidental into the mix: B turns to Bb. Thus, if a piece of music is in the key of F major, the subdominant note that is played will be Bb for a majority of the time.

If we want to build a key signature for a given key, we simply need to specify which accidentals that key has. For example, the key signature for the key of F contains one accidental, Bb. It looks like this:

If a given note appears within a given key or scale, then we can say it is diatonic to that key. Otherwise, it is said to be chromatic. For example, the note B is diatonic to C major but chromatic in F major.

If we can derive a key signature, then, it should be easy to write out all of the notes in that key. Simply write the letter names starting and ending with the tonic, then apply the accidentals that are specified in the key signature.

For example, let's write out the notes in the key of A major, given the following key signature.

First, we will write out all of the pitches from A to A.

A B C D E F G A

Then, we will apply the sharps specified in the key signature.

A B C# D E F# G# A

Thus, we have the key of A major! Feel free to check that it fits the formula we learned previously.

The Circle of Fifths

So this is all fine and dandy, but in order for this to be useful, we need an easy way to remember the key signatures. To do this, we can use a nifty chart called the Circle of Fifths.

Wow! That looks busy. Let's break it down to show how we can derive a given key signature.

Going around the circle, we can see that we add a sharp every time we go to the right, and add a flat each time we go to the left. Also, the order in which sharps are added to the key signature (F-C-G-D-A-E-B) is also the same order in which the keys are laid out on the circle but displaced by 2. The same goes for flats, but they are displaced by one in the opposite direction (B-E-A-D-G-C-F).

So, using the circle we can determine 1) how many sharps or flats are in the key signature, then 2) use the circle again (but displace the starting note by 1 or 2 depending on sharps/flats) to derive which accidentals are in the key.

We can use a mnemonic to help us remember the order of the sharps and flats on the circle of fifths. Here are a couple of options for you to choose:

For sharps:
Father Charles Goes Down And Ends Battle
Fast Cars Go Dangerously Around Every Bend
Fat Cats Get Dizzy After Eating Birds

For flats:
Battle Ends And Down Goes Charles' Father
Big Enchiladas Always Drip Gooey Cheese First
BEAD-GCF

Note that the order for flats is just the order of sharps but reversed (and down a half step since they are all flatted). The first option is easy to remember and shows this relationship clearly.

Guided Practice

That method may seem overly complicated, but let's do an example to illustrate.

Let's derive the key signature for A major.

The first step is to find how many sharps are in our key signature. For sharps, simply start at -1 with our mnemonic and add one for each step. Father (-1) Charles (0) Goes (1) Down (2) And (3). Thus, the key of A has 3 sharps.

The next step is to find out the order of the sharps. This is simply the first 3 steps in the mnemonic: Father, Charles, and Goes. Thus, the key of A has the accidentals F#, C#, and G#.

One trick to double check your work in sharp keys is that the last accidental you add should be a half step below the tonic. Indeed, G# is a half step below A.

Once we have the key signature, we can simply write the key as we did above.

Let's do one more to hammer it home: Gb major.

To start, we need to find how many flats are in the key. We can start at C and count going to the left on the circle. C (0) - F (1) - Battle (2) - Ends (3) - And (4) - Down (5) - Goes (6). We hit the key of Gb, so it must have 6 flats.

Next, we will find the order of these flats. For this step, we should start with the first flat that is introduced, which Bb: Battle, Ends, And, Down Goes, Charles'. So, the key of Gb has the accidentals Bb, Eb, Ab, Db, Gb, and Cb.

One trick to double check your work for sharp keys is that the second-to-last accidental you placed should be the tonic. Indeed, Gb is the tonic.

Practice

Practice writing out the notes for the following keys:

Even though this method may seem longer at first, the idea is that with practice, these steps will become much faster than the formula method. Plus, you now have been introduced to the circle of fifths, a diagram that will be fundamental to your learning in music theory going forward.