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Circle of Fifths - Free Tutorial
The Circle of Fifths is a concept that will help you to better understand the idea of intervals, and in turn, will heighten your understanding of chord progressions, as well. But before you can understand the Circle of Fifths concept you must be able to fully understand what an 'interval' is first.
An 'interval' is a relative movement from one tone to another, relative because the same measurement of interval motion applies, no matter what note you begin with.
As you can see from the diagram below, if you move from note C to note D, the interval is a second. From note C to note E is a third, C to F is a fourth, and so on.

The same intervals apply if you begin on any other note of any scale. Just like moving from note C to note E is a third, E to G is also a third, F to B is a fourth, and so on. Remember, intervals are just a measurement of relative movement between notes and have nothing to do with which notes are being moved between. This is a critial concept. Reviewing the Major Scales and their corresponding scale degrees will be of value to you.
In the diagram below the numbers inside the circle indicate how many sharps or flats there are in each of the keys surrounding the circle.
Different musical styles utilize certain common chord progressions/movements. Rock music and jazz both make use of patterns in which the chords move in intervals of fourths. The diagram below is the aforementioned Circle of Fifths. In a clockwise direction, if you choose any note in the circle, the note directly to its right is the interval of a perfect fifth. In a counter-clockwise direction, the note immediately to the left of any other note is the interval of a perfect fourth.

Take a look at the key of Eb (E flat). According to the diagram, in the 7 notes contained in the key of Eb (refer to Major Scales Tutorial), 3 of them are flatted, or lowered. Therefore, the key of Eb contains 3 flats. How do we know which of the notes should be lowered?
There are 2 mnemonic devices, that can be used in figuring out what notes are flatted or sharped in any key. They're just silly phrases that are so odd you actually remember them. If you do have trouble, make up your own phrases using the same letters.
For the sharp keys:
Fat Cows Go Down Around Every Barn
For the flat keys:
Boiled Eggs Are Darn Good Clean Fun
Since we were looking at the key of Eb, again, notice that there are 3 flats. Using your mnemonic device for the Flat keys, the first three words are "Boiled Eggs Are". Thus, the flatted notes in the key of Eb are Bb, Eb, and Ab. Practice this device in all 12 keys until it comes to you effortlessly. The 12 keys and the 7 notes (plus Octave) each of them contain can be reviewed on the Major Scales Tutorial page.