The Circle of Fifths is one of the great Conversations in music history, endlessly copied and cited by composers over the centuries. As one musicologist observed:
“Corelli’s harmonies were the most appreciated quality appreciated by his contemporaries and posterity alike. On the one hand, it is the clarity and regularity of progression, the musical escalator known as the “circle of fifths,” in which a segment of melody is repeated in keys either five notes higher or four notes lower than the original statement (called a “sequence”). On the other hand, it is the audacious harmonic surprises of the sustained slow movements that conveyed the melancholy of what Hawkins calls “pathetic.” The passing excursions from major to minor and back raised and lowered the spirits of the listeners with suspensions (sustained notes which at first create harmonic instability–dissonance– against changes of harmony) that release the momentary tension they create by resolving, much to the relief of the listener.”
Bruce Lamott
Here is Corelli’s Christmas Concerto, in which the Circle of Fifths can be easily discerned. Just listen for that progression of chords, each one based on part of the last.
Arcangelo Corelli, Christmas Concerto:
The Circle of Fifths has been used by many composers over the years. Billy Roberts wrote a classic song that starts with a C Major chord, followed by G Major, etc., until it comes to rest on an E Major chord, before repeating the cycle. You probably haven’t heard his version. But you have heard Jimi Hendrix’s. The first GSOD tune to be repeated here:
The Jimi Hendrix Experience, Hey Joe:
You can hear it intuitively—the Circle of Fifths is so damn satisfying to hear. But here is a video that distills it for you: https://www.youtube.com/watch?v=yLMuhajFk7A. Other songs to use the Circle of Fifths include are such diverse offerings as “I Will Survive” (Gloria Gaynor), “You Never Give Me Your Money” (The Beatles), “Wild World” (Cat Stevens), and “Moon River” (Henri Mancini). Gershwin wrote one that went around the circle backwards, but that’s getting ahead of myself. That’s a tune for another day.
A Gertus History of Music 