The circle of fifths is a diagram that shows the relationship between the 12 semi-tones in the chromatic scale and the relative major/minor pairs that are used in WESTERN music.

It is called the circle of fifths because when moving around the circle in a CLOCKWISE direction, each note on the circle is a perfect fifth apart from the next one. 

A perfect fifth is an interval that consists of seven semi-tones or half-steps.

 For example, C and G are a perfect fifth apart, because there are seven semi-tones between them.

The circle of fifths can help us with many aspects of music theory, such as key signatures, chords, scales, and modulation (changing key).

 By using the circle of fifths, we can quickly and easily find out how many sharps or flats a key has, what chords belong to a key, what scales we can use for improvisation or melody writing, and how to change keys smoothly within a song.

To build the circle of fifths, we start with C at the top of the circle.

 The key of C has no sharps or flats in its key signature.

 We then move clockwise around the circle, adding the appropriate cumulative amount of sharps to each key. 

Moving clockwise round the circle starting from F gives us the order of sharps, which are – F, C, G, D, A, E, and B. 

To help you remember this, you may wish to use the mnemonic – 

Frets Can Grind Down After Excessive Bending, or you can make up your own mnemonic).

For example, the key of G has one sharp (F#), the key of D has two sharps (F# and C#), and so on.

To build the circle of fifths counter-clockwise, we start with C again and move counter-clockwise around the circle, adding the appropriate amount of flats to each key. 

Note that when we move round the circle of fifths in a counter-clockwise direction we could equally call the circle of fifths the “circle of fourths” because each consecutive note on the circle is a perfect 4th apart.

A perfect fourth is an interval that consists of five semi-tones or half-steps.

Moving round the circle counter-clockwise starting from Bb gives us the order of flats, which are – B, E, A, D, G, C, and F. 

To help you remember this you may wish to use the mnemonic –

 – BEAD Guitars Create Feedback, or you can make up your own mnemonic.

For example, the key of F has one flat (Bb), the key of Bb has two flats (Bb and Eb), and so on.

The 3 major keys at the bottom of the circle and their relative minor keys can be written with EITHER sharps or flats.

These are: 

The keys of F#/D#m (6 sharps) and Gb/Ebm (6 flats) are enharmonic equivalents, which simply means they sound the same but have different names. 

The keys of C#/A#m (7 sharps) are enharmonic equivalents of the keys of Db/Bbm (5 flats).

 The keys of B/G#m (5 sharps) are enharmonic equivalents of the keys of Cb/Abm (7 flats).

The circle of fifths also shows the relative minor keys for each major key.

 The relative minor key has the same key signature and notes as its major counterpart but starts on a different note.

 To find the relative minor key for a major key, we go down a minor third from the tonic (or root note) of the major key.

 A minor third is an interval that consists of three semitones or half steps. 

For example, A minor is the relative minor of C major, because A is three semi-tones below C.

The relative minor keys are shown in the inner circle of the diagram.

 For example, inside C major we have A minor, inside G major we have E minor, inside F major we have D minor, etc.

The circle of fifths is a powerful tool for music theory and composition.

 Here are some ways you can use it:

To find out how many sharps or flats a key has, just look at its position on the circle.

 The more clockwise a key is from C major, the more sharps it has. The more counter-clockwise a key is from C major, the more flats it has.

To find out what chords belong to a key, just look at the notes that surround the key on the circle.

 The chords that belong to a key are usually built on the first (tonic), fourth (subdominant), and fifth (dominant) degrees of its scale. 

These chords are also called I-IV-V chords. For example, in C major, the I-IV-V chords are C-F-G. In G major, they are G-C-D. In F major, they are F-Bb-C and so on.

To find out what scales you can use for improvisation or melody writing in a key, just look at the root or its relative minor key on the inner circle.

 The relative minor key has the same notes as its major counterpart but starts on a different note.

 For example, in C major you can also use the A minor scale (also called the “natural” or “relative” minor scale, (or AEOLIAN mode)).

To change key smoothly within a song (also called modulation), just move to an adjacent key on the circle.

 The adjacent keys have only one sharp or flat difference from each other, so they sound similar enough to avoid abrupt changes in mood or tone. 

For example, if you want to modulate from C major to G major you can use a G chord as a pivot chord because it belongs to both keys (it is V in C major and I in G major).

 If you want to modulate from C major to F major, you can use an F chord as a pivot chord because it belongs to both keys (it is IV in C major and I in F major).

You can also use the circle of fifths to show you which chords you can “borrow” from its parallel minor key to spice up your chord progressions.

The circle of fifths is a great way to visualize and memorize musical relationships between tones and keys. 

It can also inspire you to create new melodies and harmonies by exploring different keys and scales.