Circle of fifths: it is a circular graph that takes its name from the arrangement of the tones and the distance between the tones. It also allows us to see which scales are relative to each other and which alterations they have. Each diatonic scale is a subsystem made up of seven of the twelve notes of the chromatic scale. The circle of fifths is a graph used to show the relationships between the twelve notes that make up the chromatic scale. Every time you pass from fifth to fifth, a # is added to the seventh of the fifth found. The circle of fifths is defined in this way because the fundamental note of each scale is the fifth note of the scale to its left.
To illustrate all these relationships between twelve notes we refer to the following illustration, where the notes starting from C are inserted clockwise in a succession of perfect fifths in a clock face. In this way all twelve notes are represented. In a clockwise direction each note is adjacent to its dominant, while in an anti-clockwise direction each note is close to its subdominant (in the case of C: F is subdominant and G is dominant).
To determine the number of sharps or flats that are inserted in the key for a given key, move clockwise for sharps and counterclockwise for flats.
For example, starting from C major, which has no alterations in the key, we move to G which has a sharp in the key (F♯), then we move to D major which has two sharps (F♯ and C♯) and so on.
In the other direction, moving to F major we have a flat key (B♭), B♭ major has two (B♭ and E♭) and so on.
Building basic chords with Circle of Fifths
The circle of fifths is not only useful for finding flats and sharps in every key. It provides an easy way to build even basic chords. If, however, we consider the names of the notes as chords, they can help to visualize the harmonic movements of a typical progression such as the so-called second-fifth-first (often represented as II-V-I, i.e.: minor second – dominant major fifth – tonic). For example, starting from G, the typical G-7 / C7 / F progression appears counterclockwise.
The main chords are built on the root note the major third and the perfect fifth. Since we’re looking at the circle of fifths, the perfect fifth will be adjacent to its root note clockwise from your root. Let’s build a C major chord. The circle of fifths says that the perfect fifth of C is G. So we have two notes in the C major chord: C and G. Simply move diagonally down from your perfect fifth to find the third note in your major triad to find the major third, an E. Your C major chord is: C – E – G.
Building minor chords is simple. The construction scheme is a little different. For this example let’s construct a C minor chord. Minor chords begin with the root note and its perfect fifth, clockwise. The note adjacent to the C note is a G. We found 2 notes in the C minor chord: C and G. The third note in the minor chords is a minor third. To find the minor third on the circle, simply draw a line diagonally and down from the perfect fifth. So in the case of C minor, it’s M♭. There it is, your C minor chord is: C – E♭ – G
Circle of fifths is very important because it clearly represents the enharmonic bridge.
The enharmonic bridge is a phenomenon generated by the succession of a series of scales (or tones) different in name but equal in the succession of sounds, therefore they are scales of equal pitches but with different names. These shades are:
C# Major which is equal to D♭Major
F# Major which is equal to G♭Major
B Major which is equal to C♭Major
A# Minor (relative of C# Major) which is equal to B♭Minor (relative of D♭Major)
D# Minor (relative of F# Major) which is equal to E♭Minor (relative of G♭Major)
G# Minor (relative of B Major) which is equal to A♭Minor (relative of C♭Major)