Key signatures are designed to simplify music notation by indicating the key. Without them, composers would be forced to write accidentals (sharps and flats) every time they're used, which would greatly complicate reading music.
Because each key signature indicates two keys (one major and one minor), key signatures are a common point of confusion for music students. (In fact, each key signature can designate any of the seven modes in music, one of which corresponds to major and another to natural minor, which are the only two modes in common use.)
While you can memorize a Key Signature Chart, key signatures are easy to learn if you follow the Circle of Fifths. Remember that a sharp raises a starting note by a half step. In other words, sharps go up. Similarly, each subsequent sharp encountered in a key signature goes up, by a fifth to be exact.
To learn all the key signatures with sharps, let's start with C major, which has zero sharps (or flats):
(Each major key has an associated relative minor, which will be detailed in a separate lesson. To keep things simple we'll stick with the major keys for this lesson. The minor keys are each a minor third lower than their relative majors; e.g., A minor is the relative minor of C major.)
The next key clockwise along the Circle of Fifths is G major, which has one sharp (F-sharp):
The second key going clockwise is D major, with two sharps:
Now we have F-sharp and C-sharp. Notice that C-sharp is a perfect fifth higher than F-sharp.
Going clockwise along the Circle of Fifths, the next key is A major, which has three sharps. These are F-sharp, C-sharp and now G-sharp:
The next key, a fifth higher, is E major. It adds D-sharp, which is a fifth higher than the G-sharp of our previous key signature:
Are you starting to see the pattern? Going around the Circle of Fifths clockwise to the next key, we reach B major:
B major has all the sharps of the previous keys, with the addition of A-sharp. B is a fifth higher than our last key of E major, and A-sharp is a fifth higher than D-sharp.
Going up a fifth, we reach F-sharp major. This adds E-sharp—a fifth higher than A-sharp:
Finally, going up a fifth and adding one more sharp, we arrive at C-sharp major. In this key, all seven scale degrees have a sharp. The last sharp—a fifth higher than the E-sharp we added last—is B-sharp. Here is the key signature of C-sharp major:
To summarize, if we start with C major (with zero sharps) and remember that the first sharp we encounter is F-sharp, all we have to do is go up a fifth for each subsequent key and sharp.
The same holds for the flats, except that we go counterclockwise along the Circle of Fifths, and flats go down by a fifth. (The system is perfectly logical if we remember that sharps raise notes and flats lower them.)
Starting again at C major with zero flats, we go down a fifth and reach F major with one flat, B-flat:
Going down another perfect fifth from F major, we arrive at B-flat major. The key signature for B-flat major has two flats, B-flat and E-flat:
E-flat is a perfect fifth lower than B-flat. This brings us to our next key going counterclockwise along the Circle of Fifths, E-flat major, with three flats:
The third flat is a fifth lower than the previous flat we encountered (also E-flat, not to be confused with the key of E-flat major). This third flat is A-flat.
The next key, A-flat major, is a fifth lower than the previous key. It has four flats, and the fourth one is a perfect fifth lower than A-flat. This fourth flat is thus D-flat:
Going down another fifth we reach D-flat major, with five flats. The fifth flat is G-flat, and it's down a perfect fifth from D-flat:
The next key going counterclockwise along the Circle of Fifths (i.e., a fifth lower than the last key) is G-flat major. It has six flats, and the sixth one is C-flat:
The final flat key is C-flat major with seven flats. The last flat is F-flat:
As long as you remember the rule of fifths, it will be easy to learn all the key signatures. Sharps raise notes, and the order of the sharps goes up by fifths: F-sharp, C-sharp, G-sharp, D-sharp, A-sharp, E-sharp, B-sharp.
Flats lower notes, and the order of the flats goes down by fifths: B-flat, E-flat, A-flat, D-flat, G-flat, C-flat, F-flat.
If you remember the first sharp (F-sharp) and the first flat (B-flat) encountered in key signatures, along with the rule of fifths, you can easily build any key signature.
There's one more detail to know before we conclude this lesson:
Each major key has a relative minor associated with it. (Conversely, each minor key has a relative major.)
To find the relative minor of any major key, simply go down a minor third. A minor third down from C is A—thus, A minor is the relative minor of C major.
Another way to find the relative minor of any major scale is to take the sixth scale degree (the sixth note) of the scale. For example, the sixth scale degree of C major is A, so A minor is the relative minor of C major.