The Circle of Fifths

A Demonstration of the Circle of Fifths
by Frank Kirschner

We hear the term, “Circle of Fifths” used often (“Barbershop harmony uses the circle of fifths”), and some of us wonder what it means. Here is an explanation that shows some of the underlying math. Don’t worry, though, you don’t need to understand math to follow the explanation.

Remember the mnemonics we use to identify the key of a song from the key signature? For sharps, it’s “Good Deeds Are Ever Bearing Fruit Constantly.” That is, the key names for sharps are as follows:

Notice that each time we add a sharp (i.e., move one place to the right in the table), we go up a fifth, that is, five notes. So from G to D (G – A – B – C – D) is a fifth, or five notes, including the notes at each end of the interval. Each time we subtract a sharp (i.e., move one place to the left in the table), we go down a fifth.

We have the same thing with flats: Fat Boys Eat Apples During Gym Class. (We’ll reverse the table so right and left stay the same.)

Each time we subtract a flat (i.e., move one place to the right in the table), we go up a fifth, that is, five notes. So from B„ to F (B„ – C – D – E – F) is a fifth, or five notes, including the notes at each end of the interval. Each time we add a flat i.e., move one place to the left in the table), we go down a fifth.

Let’s put all these key names in a line, with C (no flats or sharps) in the center:

scale

Each move to the right goes up a fifth and subtracts a flat (or adds a sharp), and each move to the left goes down a fifth and adds a flat (or subtracts a sharp).

“Well, so what?” the astute barbershopper asks. Here’s the “so what:” In most traditional melodies (the kind that make good barbershop harmony) the implied harmony (the chords you’d sing if you were woodshedding) moves one step at a time on this line most of the time, and most of the moves are to the left, going down a fifth and subtracting a sharp or adding a flat. In fact, simple folk melodies often have only three chords, and they are adjacent on this line, for example “Oh, Susannah.” We can start anywhere on the line we want (the starting point depends on the melody of the song and our best vocal range), and move one place to the right or left at a time to play all the chords of the song. Let’s pick D as our starting chord (it’s also the key of the song), and show the chords with the words:

D                                                                                 A
It rained all night The day I left, The weather it was dry
D                                                                 A            D
The sun so hot, I froze to death. Susanna, don't you cry
G                         D                         A
Oh, Susanna, Oh don't you cry for me. For I
D                                                        A        D
come from Alabama With my banjo on my knee.

Look up in our line of keys above, and you’ll see that G, D, and A are adjacent. You’ll also notice that in this song, we only move one step right or left at a time. In simple harmonies, there are no “jumps.” We could start anywhere in the line, and move one step right, one step left, etc., and we’d have the correct chords for the song. It’s the pattern that determines the harmony we hear.

Here’s a more complicated harmony: “Five-Foot Two.” We’ll start with a C chord (the song is in the key of C), and jump to the right to an E chord. The distance we jump determines the “pull” we feel that makes us want to return to the original chord. Then we move one step to the left at a time until we get back to C. Here’s a demo:

Notice that instead of tonic chords, we’ve made them dominant sevenths (or barbershop sevenths) to make it sound a bit better. Also, any time we hear a barbershop seventh chord, we want to resolve it by moving one step to the left on our chart, above. If the chorus sang a seventh chord, and was instructed to “resolve” the chord, we would instinctively change to the chord one step to the left on the chart.

What we have is a “line of fifths”:

line

Where does the “circle” part come in? Notice that on a piano, the B key is the same as the C„ key, the F# key is the same as the G„ key, and the C# key is the same as the D„ key. (We say they are “enharmonic.”) So we can wrap the line into a circle and put these enharmonic keys in the same spot, as follows:

circle

We can imagine a pointer on the circle, something like the minute hand of a clock, and create the pattern of harmony by moving around the circle. The jumps we make determine the harmony, and the starting point determines the key of the song.

For fun, you might look at a book of folk songs that has the chords specified. Look at the pattern the chords make on the circle of fifths. More complicated harmonies also have minor, diminished, augmented, and other kinds of chords, but these are the basics.