The circle of fifths is very often talked about but may seem like a mystery to many. On the surface the circle lines up sharp keys on the right and flat key on the left. While this is true the value in the circle goes far beyond a basic diagram of keys. If you plug in the chords of a key you can visualize the flow of common chord progressions.
The upper diagram is the common view of the circle as it is related to keys. The lower digram shows how chords commonly move (by 4ths) in the key of C major. To visualize another key all you have to do is rotate the chords to the appropriate key. The pattern will move to the new tonic.
