The Circle of Fourths

Hi guys...would you please explain the concept of the circle of fourths to me? Thanks..

The circle or Fourths is the circle of 5ths backwards.
Ex...F to C to G to D etc.

and every key has one flat note more than the previous one...

Thanks, Chris. I read that the circle of 4ths can be used to create long, good-sounding chord progressions...how can I do this in the key of C for example?

Cycle of fourths and Cycle of fifths are interchangeable, in that you can go up the cycle of fourths by going down the cycle of fifths, and vice versa. Classical musicians tend to refer to it as the circle of fourths, jazz and rock players tend to refer to it as the cycle of fifths. A good example of a progression based on the cycle of fiths (as I call it) is the tune made famous by Hendrix; Hey Joe. The chords are all major chords going clockwise around the circle starting on C and ending on E. So the chords are C, G, D, A, E. As you can hear, although these chords are not all in the same key, the progression sounds really smooth. This is because there is only one note's difference from one chord to another in the cycle of fifths. The smoothest way of changing from one key to another is to follow the cycle which is why it is so common for a pop song to go from C to G.

Sherif...What your referring to is known as "back-cycling", like Bardsley said it's usually done using the cycle of 5ths, but I'm sure 4th's would also work.
What you do is pick a chord (we'll say C just to keep things simple). Now instead of going directly to the C chord in the progression you would approach it from a 5th away. Ex; G C
Now you can take this sequence as far back as you wish.
Ex; D G C or Ex; A D G C or Ex; F# B E A D G C
You can mess around with the tonalities of the chords to make it more interesting, but if you make them all Dominant 7th chords you can't go wrong, then resolve to the C major.

Like previous posts noted, the Circle of fourths is essentially the same as the circle of 5ths. The only difference is how you move about on the circle. For example, if you were to take a Major scale and play it in the key of C and then move that scale to the key of G to D to A to E ...etc you would be moving the key up a 5th every time you changed keys (ergo the name Circle of 5ths). If you were to change keys in the opposite direction, you would be moving up a 4th every time you change keys: C to F to Bb to Eb, etc... (Circle of 4ths). It's really a matter of semantics. You could also look at changing keys from C to F to Bb to Eb, etc... as moving DOWN a 5th or moving from C to G to D to A, etc as moving down a 4th.

As for using the circle to create nice chord progressions, for an interesting application of this concept, check out the song "Chestnuts Roasting on an Open Fire." If I remember correctly, this song in its full form actually changes through all 12 keys at different points in the song. (I may be thinking of the wrong song, so if someone else knows what I'm talking about, please correct me)

The Christmas Song doesn't quite make it through all 12 keys ( Eb Ab G Gb & F) and mainly changes keys through decending 2 5's. Not sure of any song that does.

If that's not the one then I'm not really sure which one it is. I'm pretty sure it was a christmas-type song though. It's something that someone had pointed out to me a long time ago.