Circle of Fifths

So far we've really only talked about C Major and A minor, which are composed of the 7 white keys per octave on the piano. But scales can be built upon any of the 12 tones in the chromatic scale. We know the whole-half patterns of the major and minor scales, so we can figure out what notes any scale has, but what about the interrelation between scales? This is where the circle of fifths helps to keep things in perspective.

Let's look at the scales of F Major, C Major, and G Major:

F  - G  - A  - Bb - C  - D  - E  - F
C  - D  - E  - F  - G  - A  - B  - C
G  - A  - B  - C  - D  - E  - F# - G

F and C Major differ by only one note (C Major has a B while F Major has a Bb). Similarly, C and G also differ by one note (F vs. F#). Let's look at the whole-half patterns:

                  w    w    h    w    w    w    h
               F  - G  - A  - Bb - C  - D  - E  - F

   w    w    h    w    w    w    h    w    w    h    w    w    w    h              
C  - D  - E  - F  - G  - A  - B  - C  - D  - E  - F  - G  - A  - B  - C

                       w    w    h    w    w    w    h
                    G  - A  - B  - C  - D  - E  - F# - G

The whole-half pattern from F to F in the key of C Major is w-w-w-h-w-w-h. If we flatten the 4th note, the B, we get w-w-h-w-w-w-h - the major scale pattern.

The whole-half pattern from G to G in the key of C Major is w-w-h-w-w-h-w. If we sharp the 7th note, the F, we get w-w-h-w-w-w-h - the major scale pattern.

Remember that F is a fifth below C and G is a fifth above. We notice that if we change the key by moving in fifths, only one note changes. While no two major scales will have different tonic notes but identical sets of notes, some scales are more inter-related or harmonic than others.

The circle of fifths lists keys in 5ths, which is useful to determine how interrelated any two keys are.

The full circle only consists of the 12 tones, which can be arranged like the hours on an analog clock. The points opposite each other (12 vs. 6, 3 vs. 9, 11 vs. 5, etc.) are the least related, while the points nearest each other (12 and 1, 1 and 2, etc.) are most related. As we go right or clockwise, we sharp the 4th of the current key to get the next key. For example in C Major, sharping the 4th (F) gives us the scale of G Major. As we left or counter-clockwise, we flatten the 7th of the current key to get the next key. For C Major, we flat the B to get F Major.

Let's find all 12 tones in order of fifths, going both ways from C:

                             C
                         F - C - G
                    Bb - F - C - G - D
               Eb - Bb - F - C - G - D - A
          Ab - Eb - Bb - F - C - G - D - A - E 
     Db - Ab - Eb - Bb - F - C - G - D - A - E - B
Gb - Db - Ab - Eb - Bb - F - C - G - D - A - E - B - F#

F# is the same pitch as Gb, which means we've completed the circle. If we keep going, we still get unique key names, but the pitches will match other keys already in the circle. For example, continuing left (counter-clockwise), we reach Cb, which is the same as B. Going right (clockwise), we reach C#, which is the same as Db.