When we play the C for example as a C7 chord it in turn becomes unstable, it assumes to our ear the role of Overtone No.3, and resolves to its Fundamental tone a perfect fifth down, the F.

The F in turn as an F7 chord resolves a fifth down to Bb.

Bb7 resolves a fifth down to Eb, and so on.

Continuing this process from chord to chord we eventually return back to our starting point.

This circle is called the Circle of Fifths.

The Circle of Fifths is sometimes also referred to as the Circle of Fourths.

For moving a perfect 5th downwards (from G down to the C below) is the same as moving a perfect 4th upwards (from G up a 4th to the C above).

Applications and Exemples

Just about every Jazz Standard, exhibits the same principle.

Here a few examples :

Fools Rush In                             All of Me                         Heart and Soul

• “Fools Rush In” by Johnny Mercer and Rube Bloom starts with :

Fmaj7 – Bm7b5 – Em7 – Am7 – Dm7 – G7 – Cmaj7 –

• “All of Me”  by Simons and Marks contains this progression :

Cmaj7 – E7 – A7 – Dm7 – G7 –

• “Heart and Soul” by Hoagy Carmichael (similar to I Got Rhythm by George Gershwin, Oleo by Sonny Rollins, and several other Jazz Standards) goes :

F – Dm – Gm – C – F – Dm – Gm – C –

• The three chords for the 12 bar Blues also are three adjacent members on the Circle of Fifths :Blues in C : V = G , I = C , IV = F

Blues in F : V = C , I = F , IV = Bb

Blues in A : V = E , I = A , IV = D

etc.

Source: JazClass from Michael Furstner, who developped a very comprehensive Jazz Class course. Thanks to him.