Understanding the Circle of Fifths

Review of the Major Scale

Previously, we talked about the major scale. We constructed a C major scale, which happens to contain no sharps and no flats. Then we created some other major scales based on the same exact scale formula; that is, with the same exact type of steps as the C major, but starting from a different note other than C.

The C Major Scale

Let’s take the fifth note in the scale of C major (the tone “G”) and use that note to make a new scale. What will the names of the notes be? From G we will apply the formula of whole and half steps, using the chromatic scale as our source: wh, wh, h, wh, wh, wh, h. The result is G A B C D E F♯ G.

The G Major Scale

When writing notation, will we always write a sharp when F appears? That seems annoying. So the standard practice is to declare it at the beginning of a piece of music, called a key signatureA marking used at the beginning of a piece of written music to indicate the key; normally, which notes will be sharp or which notes will be flat. (But not both) (pictured). This symbol indicates that, until otherwise specified, all “F” will actually be “F♯”. Notice that the sharp is placed squarely over the line of the treble clef note F. This key signature will represent the key of G major.

While useful in understanding notation, key signatures are also valuable even if we never read music. This is because they are an effective way of visualizing music.

A New Major Scale

Let’s re-examine the G scale. What if we spell a new major scale from the fifth of G? The fifth note of G is D. Applying the formula once again to the note D, we will produce the notes D E F♯ G A B C♯ D. A pattern has emerged. Every time we start a new scale on the fifth of a key, a single sharp is added to the old key signature, resulting in the new key signature.

We’ve seen how a single sharp can be added to a key. What about flats? Flats work the same way. If we start again from our neutral C major scale, and spell a major scale out from the fourth degree, F, the results are: F G A B♭ C D E F—one flat is added to the key. This pattern can be plotted into a visual diagram called the circle of fifthsA commonly used method of arranging various keys (or major scales) so that they can be organized by number of sharps or number of flats.. It is so predictable that musicians studying music theory frequently use it to memorize the key signatures.

Summary: C, G and D Scales

From any major scale: start a new scale on the 5^th degree, and the new scale will be the same as the old scale but with one additional sharp. The sharp will be in the position of the seventh note of the new scale.

The C Major Scale

No sharps.

The G Major Scale

A new major scale (whole, whole, half, whole, whole, whole, half) starting from the 5^th note of C major must have one additional sharp: F♯.

The D Major Scale

A new scale, started from the 5^th note of G major. In addition to the F♯, it has another new sharp: C♯.

The Order of Sharps

Suppose that we continue this process until we’ve arrived at a key with five sharps: B major. How do we remember which five notes will be sharp in this key? Thankfully, since the sharps are cumulative when the scales are arranged this way, the sharps always appear in a fixed order, which the circle of fifths will confirm: F♯, C♯, G♯, D♯, A♯, E♯, B♯. A key with three sharps will have the first three. A key with five sharps will have the first five, and so on. One easy way to remember the order of sharps is to use a mnemonic, such as: “Father Charles Goes Down And Ends Battle.”

The Order of Flats

What about the flats? What order do they appear in? They also appear in the reverse order: B♭, E♭, A♭, D♭, G♭, C♭ , F♭. A key with two flats will have the first two of these in its key signature. To remember this, we can even reverse our mnemonic: “Battle Ends And Down Goes Charles’ Father.”

The Circle of Fifths (or Wheel of Fourths)

Key Tasks

As the creator of Hub Guitar, Grey has compiled hundreds of guitar lessons, written several books, and filmed hundreds of video lessons. He teaches private lessons in his Boston studio, as well as via video chat through TakeLessons.