<<<<<<< back to Chord Functions  Circle of 5ths  Chord Boxes It is very easy to get over wrought with theory about the Circle of 5ths. It is a fascinating subject. Scholars derive all sorts of interesting and helpful diagrams the Circle of 5ths: chromatic circles, coordinate systems,  and more. BUT! We’ll use only a diatonic Circle of 5ths diagram that relates major and relative minor keys and shows how the accidentals of keys are determined. The Circle of 5ths is helpful in arranging because it lays out a diagram that shows important chord relationships.  Click here to see the Diatonic Circle of 5ths.  The circle is constructed like a clock face with the key of C at noon. Each successive key is a 5th above the preceding key. So the clockwise progression around the clock face is: C G D A E B F# and so forth. Starting with C and moving counter-clockwise the interval is a 4th. The progression then becomes C F Bb EB Ab and so forth. Note also that each progressive key in the clockwise motion adds one sharp to the key signature. In the counter-clockwise motion each progressive key adds one flat to the key signature. The circle of 5ths also shows reliable modulation steps between keys. The Circle of 5ths is also used in designing string instruments. The first five tones on the Circle of 5ths running clockwise are C G D A E. Running from low pitch to high pitch, here are the tuning systems of some common instruments. ♦  Violins and mandolins are tuned: G D A E  ♦  Violas and Cellos (and octave lower) are tuned C G D A ♦  Double Bass Violins are tuned E A D G ♦  Guitar is tuned E A D G [B E] Okay, so that two highest strings don’t follow the pattern. Accordions commonly use a linear arrangement of the Circle of 5ths for the bass note keys. Choose any key on the Circle of 5ths as a starting point. Let’s look at D. Note that the next clockwise chord is A – the dominant chord in the key of D. The counter-clockwise chord is G – the subdominant chord in the key of D. So, the circle is a diagrammatic way of expressing the chord progressions previously discussed.

The Circle of 5ths diagram can be made more useful by showing both the major keys and their relative minor keys. Click here to see this added relationship. A relative minor key is the Aeolian mode of a key. The scale is built upon the 6th tone of the major key. So the relative minor key of C major is A minor. The scale in A minor is A B C D E F G A. That is the same collection of tones as the key of C, but the arrangement is different.    The relative minor chords work with the major chords to build the kinds of chord progressions previously discussed. These relationships can be seen by shrinking the Circle of 5ths down to one key. When this is done, the result is a chord box showing relationships among chords in a given key. Click here to see the diagram and to read about chord relationships and what makes a chord progression. The Chord Box for the key of D   D G A Bm Em F#m   or using chord numbers   I IV V vi ii iii   The Chord Box for the key of D G C D Em Am Bm   or using chord numbers   I IV V vi ii iii

Notes to Those Who Love Detail Strictly speaking the circle of 5ths is not a circle but a spiral. When formed by the pitches of the diatonic scale, the octave is imperfect. A SMALL gap shows up between the expected and the actual octave. Using a justly tempered scale and moving upwards in pitch by intervals of perfect fifths for seven octaves, this difference shows itself as a flaw of 23.46 cents. The resulting pitch is higher than it should be. This small difference is called “The Pythagorean Comma” in honor of the Greek philosopher, Pythagoras, who completed the original work on harmonic theory. The equally tempered scale attempts to make the circle complete by averaging out the pitch error over an octave. The equally tempered scale was a huge invention in music. Bach loved it so much he composed a series of fugues and preludes to make use of the new tuning.  On to Diatonic Modes, Chords and Progressions >>>>>>>

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