The Circle of Fifthsis a useful tool on a number of different levels.  You can find scale patterns, geometrically interesting chord shapes, and map out chord progressions.  When I’m learning a new song, I always map out the chord progression on the circle which gives me a frame of reference for that song’s particular chord progression.

The most basic observation which we discussed here, involves why the V7 chord wants to resolve to its tonic I (Key of C: G7 to C).   Another useful post explained the role of the I-IV & V (V7) chords in songs and how these chords lay out on the circle.

This leads us to today’s exploration of The Rolling Stones’ You Can’t Always Get What You Want.  The song is a basic I-IV-I which is what gives it that melancholy feel.

Verse
I I saw her today at the re  IV ception
I A glass of wine in her IV hand
I I knew she was gonna meet her IV connection
I At her feet was footloose IV man etc.

The chorus of the song does the exact same thing until that wonderful moment when the II shows up!
The song then returns to the IV and then back home to the I.

Chorus
You I can’t always get what you IV want
You I can’t always get what you IV want
You I can’t always get what you IV want
But if you II try sometimes well you IV might find
You get what you I need

The way I memorize a song is to log the chord progression in mind by mapping it on the circle of 5ths.

Since I’ve already trained my ear to hear a I to IV change and a IV to II change, when those changes come around in a tune I can recognize them and know where to go musically.  I use the circle as a visual re-enforcement.