Lets begin by taking a look at the modes for the key of C. If we assume that each mode is merely a major scale pinched from another key, and then play the major chord for the corresponding major scale, we get a really nice sounding chord progression, which is instantly Spanish in it's appeal:
(Forwads:) C, C#, D#, F, G, G#, A#, C
(Backwards:) C, A#, G# G, F, D#. C#, C.
Before you try to figure out what scale this might be, I can tell you that it is simply a G# major scale (or an F minor, as they are relative). And if you look again at the circle, you will see that a G# major scale is the phrygian mode in the key of C. So, Phrygian mode is a kind of "anti" major scale, easily found by playing the major scale at 8 'o' clock in relation to the key in question, or by mirroring the mode names for your key as in the previous article on the circle of fifths and modes.
So the scale of G# contains all of the root notes from the different modes for the key of C. And if you switch between C and G# major chords, you get a nice enlightening sound, similar to that when you switch between keys that share the same diminished chord.
Speaking of which, do you want to know which keys share the same diminished chord? Well that's easy. Just draw a cross shape in your circle. That will point to four different notes. Those are the keys that share a particular diminished chord, which can be named after any of the four chords you are pointing to!
And how do you find out what the notes are that diminished chord? Simply rotate your cross one place anti-clockwise. Likewise, you can draw a cross in your circle to identify the notes of a diminished chord and then rotate one place clockwise to identify the four keys that use that diminished chord. See the page on diminished chords for more info.
Wow!
I wonder if there will ever be an end to these little peculiarities.