Common Chord Progressions: Major Keys

People with a lot of time on their hands have analyzed tons of music to find out why and how things work. One thing that came form this study of music is the Common Chord Progression Chart. This chart shows how chords often move from one to the other. When one chord is played it has tendencies that pull it toward other chords. This is why you can play so many songs with the same few chords, or why many songs have similar chord progressions.
Here is what the chord chart looks like:

So, what does this mean?

If we take a key like C Major and think about the chords we get this pattern...

C   Dm  Em   F    G7   Am     Bo
I     ii     iii     IV  V7    vi       viio

The chart tells us (starting with the I chord on the far right side) that

• The I chord can go anywhere.
• The iii chord tends to go the the vi chord
• The vi chord tends to go to the ii or IV chord
• The ii or IV tends to go to the V or viio
• The V or viio tends to go to the I 
• The I chord can go anywhere...

So how might this look in the key of C Major?

C could go to Dm which might go to G7 which could go to C

I                      ii                                  V7                               I

What kind of patterns can you come up with?