On the link I gave to the circle (which may set off some malware alarms but it's an ok link), you may have noted that it has the number of sharps and flats noted in parentheses. What does that mean?

Most every scale has certain notes that will either sharped or flatted. The reason is because if we don't sharp or flat the notes, the scale will be out of tune. That doesn't mean that note will ALWAYS be played that way in that scale. Sometimes, it will be played natural and will be specially designated for that purpose but it is otherwise to be played flat or sharp depending on the scale.

The scale degrees are simply numbered 1-8 with 1 and 8 being a full octave (12 half-steps). So the D major scale has two sharps according to that chart. Why? Let's lay it out: D (1), E (2), F# (3), G (4), A (5), B (6), C# (7) and D' (8). Notice that there are half-steps between 3 and 4 and also between 7 and 8. The rest are whole steps. That's how a major scale is laid out. So in D major, there are two sharps—F# and C#.

Now the equivalent minor of D major is B minor (remember, we move up three note designations clockwise on the circle). Why do we tie it to D major? Because it uses the same notes. The difference is that while a major scale has half-steps at 3 and 4 and also at 7 and 8, the minor scale has half-steps at 2 and 3 and also at 5 and 6. Let's lay it out: B (1), C# (2), D (3), E (4), F# (5), G (6), A (7) and B' (8). Notice that B minor has the exact same notes sharped in its scale—F# and C#.

Now you may ask why we go from B to C# in the above example. Why not to C? Because at 1 and 2, we need a whole step. B to C is a half-step. If you look at a keyboard, you'll see that between B and C there is no intervening black key. The same is true of E and F. A white key and black key next to each other is a half-step. But if there is no black key, then the two white keys at the point are a half-step apart. All the other white keys are whole steps apart.

Let's try another scale: Eb major which has three flats according to that chart. Which notes in that scale are flatted? Eb (1), F (2), G (3), Ab (4), Bb (5), C (6), D (7) and Eb' (8). So there are our flats in Eb major—Eb, Ab, Db.

Now we count up three notes on the circle clockwise to get the equivalent minor of Eb major and we see it is C minor. It should have the same notes as Eb major. Let's see: C (1), D (2), Eb (3), F (4), G (5), Ab (6), Bb (7) and C' (8). Once again, the same flats—Bb, Eb and Ab.

So to keep from having to write flats in front of every B, E and A in a piece, we use a key signature.

The order of the sharps in the key signature is FCGDAEB while the order of the flats in the key signature is BEADGCF so one is simply the reverse of the other. The thing to keep in mind is that if, say, D is flatted in the key signature then so are B, E and A. D will never be flatted by itself. The only note that can be flatted by itself in the key signature is B and this order must always be followed. Same goes for the sharps. If A is sharped in the key signature, then so are F, C, G and D. Only F can be sharped by iself. The reason is that, once again, the scale would be out of key if we didn't do this.