Here's what I take away from the circle:
It's a pictorial representation of tone/key movement.
Just to make sure we're all on the same page, look here:
Poster I made Thank you Cameronj, this is great!
Pick one of the Major scales
Move one position counter clockwise.
Now, moving clockwise without altering any scale tones,
the next 3 Major and the next 4 minor name the triads in the original Major scale you chose.
Example: F Major
1 position counterclockwise is Bb
In the F Major scale you will find a Bb Major triad, F Major triad and a C Major triad.
There's a G minor triad, D minor triad, A minor triad and an E minor triad.
This is the same for 7th chords with 2 exceptions:
The furthest clockwise on the Major ring would have a flat 7th to give you the dominant,
and the furthest clockwise on the minor ring would have a flat 5th and seventh to give you a half-diminished.
Next, the circle shows one way to modulate (change keys) from one Major key to a 'near by' Major key.
A common progression in Jazz is the 2-5-1 (usually written ii7-V7-I7 meaning "the second degree of a Major scale, which is a minor chord - the fifth degree of a Major scale, which is a Dominant chord - the first degree of a Major scale, which is a Major chord").
The 2 chord implies movement to the 5 which moves to the 1 which implies rest. If you're modulating to another key, you'll postpone the 1 chord.
Stay with me here...
so, if you play a 2-5 and change the 5 to a 2 it modulates to another key. You can go around the circle, counter clockwise by doing this.
Example:
In the key of F Major, the 2-5 would be
G-7 (read 'G minor 7) - C7.
G Bb D F - C E G Bb
Change the C7 to a minor by flatting the third degreee of the chord. C Eb G Bb which is the 2 chord in the key of Bb Major.
C Eb G Bb - F A C Eb (C-7 - F7) is the 2 - 5 chord progression in Bb Major.
Make the F7 (the 5 chord) minor by flatting the 3rd degree of the chord. F Ab C Eb. This is the 2 chord in Eb Major.
F-7 - Bb7 is the 2-5 in the key of Eb Major.
Keep doing this and you'll go counter clockwise around the entire circle.
Near the bottom, you'll need to re-name the chords and scales to their enharmonic name.
If this is really confusing you, take it to a piano. It's the best visual representation there is for this kind of thing.
If I can help further, please PM me.
Whew! Thank you Tony King!