The circle (or cycle) of fifths is a memory aid in music theory. It is usually represented as a wheel or circle around which the 12 notes of the scale are placed in a particular order. Each note, going forward (clockwise) on the wheel is an interval of a fifth (the distance between C and G) away from the preceding one. More here:
The circle has a variety of uses, and one of them is in constructing chord progressions. Let's have a look at the cycle written out:
F C G D A E B Gb Db Ab Eb Bb (then back to the start) F C G etc
You can remember the sequence with a mnemonic, for example Fanny Crosby Goes Daffy After Eating Bananas (with the Goes Daffy up to the end repeated and flats added).
Remember that Gb=F# and so on. If you look at where G is in the cycle, you will notice that the three most important chords in the key of G, are grouped together with the subdominant © on one side and the dominant (D) on the other. The same applies to any other key, for example, C, in which key the most important chords are F, C and G.
In the beginning of the jazz era, it was also discovered that the cycle of fifths led to some pretty interesting, and at the time, novel chord progressions. The idea is to start on the tonic chord of the key you're in (let's say it's C) and jump as many times forward as you want around the cycle to another chord, let's suppose we decided it would be A. Now you follow the cycle backwards (making it a cycle of fourths) and you get, for example,
C | A7 | D7 | G7 | C|
I don't know if that sequence is familiar to you, but it turns up in lots of songs, for example:
Don't Get Around Much Anymore
Missed the Saturday [C]dance, heard they crowded the [A7]floor
Couldn't bear it with[D7]out you, [G7] don't get around much any[C]more.
Sweet Georgia Brown
[G] [E7] No girl made has got a shade on sweet Georgia Brown
[A7] Crazy feet that dance so neat has sweet Georgia Brown
[D7] they all sigh and wanna die for Sweet Georgia Brown
[D7] I tell you just [G] why [D7] you know I don't [G] lie
Notice that sevenths are used for the run back to the start, and this is often (but not always) the case. In these examples we jumped three steps forward on the wheel, but you can jump just two, or as many as you want. The longest jump in a cycle-of-fifths progression of this type I have seen is in another standard, "Someone to Watch Over Me." Also in the key of C, where the song jumps five steps to B(7) before making its way round the circle backwards to C:
Someone to Watch Over Me
[C]Although he [F]may not be the man some
Girls think of as [C]handsome
To [B7]my heart he [E7] carries the [A7]key [D7] [G7] [C]
An interesting point about these progressions is that you can write melodies around them without ever leaving the diatonic scale of the tonic key (C, in this case). Another way of saying this is that although the chords themselves may contain notes that are not in the key of C, the melodies they accompany often use only the notes in the C scale.
The common progression C-Am-Dm-G-C used in innumerable 60s hits (eg the Four Seasons' Sherry) is also a variation on the cycle of fifths, using minor chords instead of sevenths for the A and D.
Once you know about this common progression, you start seeing variations on it everywhere and you begin to see how prevalent it is in 20th century popular music. This can help when trying to work out chord progressions by ear. The cycle is something you can try when all else fails. Eventually you become familiar with the sound of a cycle-of-fifths progression. But beware. They don't all sound the same by any means. Depending on how far you jump and whether you use sevenths or minor chords to get back, and how often you do it, these progressions can sound surprisingly different from each other, which is probably one reason why they became so popular. Almost every major pop and rock composer, including the Beatles, used the cycle of fifths to generate chord progressions.
Some other examples:
Dancing Cheek to Cheek Gmaj7 E7 Am7 D7 Gmaj7
Crazy C A7 Dm G7 C
All of Me G B7 E7 Am B7 Em A7 Am7 D7 G
Paul McCartney, not without precedent, radically changed the nature of the progression by going from the tonic, not to the chord three steps away but the chord based on the note a semitone below, then stepping up a half-tone to the cycle before continuing, in this song:
Honey Pie
[F]Honey Pie, you are making me [Db]crazy, [D7] I'm in love but I'm [G7lazy [C7] So won't you please come [F]home.
