The Circle of Fifths: Circular Reasoning. A Key to Learning Music.

What is a Circle of Fifths diagram? It is a visual representation of the major and minor key signatures arranged in order of ascending and descending perfect fifths. On the Circle, the addition or subtraction of a sharp or flat to any key signature creates a new key that is either up a perfect fifth (in the case of addition of a sharp or flat), or down a perfect fifth (in the case of subtraction of a sharp or flat) from the original key. For example, the key of D Major has two sharps (an F and a C). Add an additional sharp (a G) to D major, and the key becomes A major -- which is up a perfect 5th from the original D Major. Take away a sharp from D Major, and the key becomes G Major, which is down a perfect fifth from the original key of D.

Logically, the Circle of Fifths diagram is circular in shape, much like an analog clock. When a sharp is added, the new key is placed clockwise on the diagram. When a sharp is removed or a flat is added, the new key is placed in a counterclockwise position relative to the previous key. Major and minor keys with the same number of sharps and flats are placed together.
The Circle of Fifths Diagram has many possible uses. The first and most obvious is to allow the student to determine the key of the music he or she is playing. If a piece has two sharps, a quick glance at the circle tells the student that the music may be in one of two possible keys: either D major, or b minor. If, instead, the music has four flats, the possibilities are either A-flat Major or f minor.

Another use of the circle is to help the student memorize scales. When learning scales, the student can use the circle to determine how many sharps and flats there are in any given key, and thus which notes must be "raised" or "lowered." He or she can also determine from the diagram how the keys are related. For instance, if the student memorizes that C major (and also A minor) has no sharps or flats, he or she can easily determine the key signature of any major or minor key simply by counting how many perfect fifths such key is away from C major (or, if minor, from A minor) -- or from any other reference key. For instance, suppose the student must determine how many sharps or flats there are in A Major. Moving clockwise, adding a fifth to C gets us to the key of G major. Then, a perfect fifth away from G yields D Major. Finally, a perfect fifth up from D Major yields A Major. (Intervals are counted including both the first and last note along with all notes in between). This represents three clockwise leaps of perfect fifth intervals away from C; thus, A major must have three sharps. (Had the student tried moving counterclockwise --or down sets of perfect fifths-- he or she would have encountered F, then B-flat, then E-flat, from which it would be impossible to ever reach A.)

A third good use of the Circle of Fifths diagram is to determine the relative major of any minor key -- since these are placed together on the circle and have the same key signature. Similarly, the dominant chord of any key is one clockwise step away from the tonic, and the subdominant (or IV chord), is one step counterclockwise removed from the tonic. Seeing these chords represented on a diagram can help the student understand basic harmony.

Of course, not every circle of fifths diagram is created equally. And, certainly, these concepts (that are rather cumbersome to describe in writing) are simply intuitive on well designed Circle.
I encourage every teacher and student to use the Circle of Fifths diagram to help with understanding of key signatures and with basic harmony.