subject: Guitar Lesson -- The Circle Of Fifths [print this page] Music keys are actually organized in a very precise, mathematical way. This organization is called the Circle of Fifths -- Also called the Circle of Fifths and Fourths.
We can't draw a circle here, but let's show it this way:
Gb Db Ab Eb Bb F C G D A E B F# C#
We are going to start with the key of C. The key of C has no sharps or flats.We know this because of the formula for constructing major scales 1+1+1/2+1+1+1+1/2:
C D E F G A B C
Now here's where the "Fifth" of the Circle of Fifths comes into play. Let's construct another major scale starting from the 5th tone of the C major scale (G)
G A B C D E F# G
Note that the key of G has 1 sharp (F#).
Now let's construct another major scale from the 5th tone of this scale (D):
D E F# G A B C# D
Note that this key has 2 sharps (F#,C#)
Continuing on, let's construct another scale from the fifth tone (A)
A B C# D E F# G# A
Note that this key has 3 sharps (F#, C#, G#)
Are you starting to see a pattern here? Here's the rest. Keep using the 5th tone to get to the next scale:
E F# G# A B C# D# E (4 sharps F#, C#, G#, D#)
B C# D# E F# G# A# B (5 sharps F#, C#, G#, D#, A#)
F# G# A# B C# D# E# F# (6 sharps F#, C#, G#, D#, A#, E#) E# is the same as F (E raised 1/2 step)
C# D# E# F# G# A# B# C# (7 sharps F#, C#, G#, D#, A#, E#, B#) B# is the same as C (B raised 1/2 step)
Do you see what is happening here? We pick up one 1 sharp each time we "go up a 5th".
I could continue on if I wanted,but I would end up having to "sharp the sharps". This is necessary because we cannot violate one of the rules of constructing a major scale -- You must use every letter. But if I were to do so, I would eventually end up back at the key of C (B# would be how you would see it.) Hence, the circle. We start at C and eventually end up at C.
Not only do we see that the number of sharps increase by 1 every time we do this, but have you noticed which sharps it increased by? Go back to the depiction of the circle and check it out.
By the way,these 5ths are not ordinary 5ths. These 5ths are what are called perfect 5ths. A perfect 5th is equal to 7 half steps. Each one of the 5th iterations are perfect 5ths.
Now let's go in the other direction from C (No sharps or flats). But this time let's go up a 4th from the root:
C D E F G A B C
The 4th of C is F
F G A Bb C D E F (1 flat Bb)
Continuing on:
Bb C D Eb F G A Bb (2 flats Bb, Eb)
Eb F G Ab Bb C D Eb (3 flats Bb, Eb, Ab)
If I continued on all the way though the eventual double flats, I would again end up in the key of C. You would see it as Dbb). There's the circle again.
And these 4ths are not ordinary 4ths either. They are perfect 4ths. A perfect 4th is defined as 5 half steps. Note also the organization of the flats.
Let's look at this thing again:
Gb Db Ab Eb Bb F C G D A E B F# C#
You can use this construct to find common progressions in any key.
For example, a common chord progression in the key of C is C-F-G-C. Note the position of the letter names in the circle. Another in the key of A is A-D-E-A. In the key of Eb: Eb-Ab-Bb-Eb.
Another common chord progression in the key of C is C-Dm-G-C. Again note the positioning in the circle..
What you want to do here is take a good look at this circle and try out chord progressions based off of the circle. What you will find is that many songs that you hear do precisely that.
It's amazing how mathematically precise an emotional language such as music actually is. Understanding the Circle of Fifths will take a lot of the mystery out of this language.
