Keys and the Circle of 5ths
One of the most useful devices to help understand the relationships among chords is called the Circle of 5ths. German musician Johann David Heinichen invented the term “circle of 5ths” in 1728 to describe a chart showing all 12 pitches arranged so that any pair of adjacent pitches is at the interval of a perfect fifth.
The chart is helpful in determining key signatures and relationships among keys and chords.
The number of sharps or flats in a key can be determined by moving clockwise around the circle. The key of “C” has no sharps or flats. The key of “G” has one sharp. The key of “D” has two sharps. The key of “A” has three sharps and so forth. The first sharp to be added in the “G” key signature is F#. Successive sharps are always a 5th above the preceding sharp. So, the order of sharps is F#,C#, G#, D#, and so forth.
Each new sharp is the leading tone (that’s the 7th tone of the diatonic scale) of the new key. In the key of C, the leading tone is B. That tone does not require any accidental to make the do re me scale work. So the key of “C” has no accidentals in its key signature. In the key of “G” the 7th tone is F#. So the key of “G” adds F# to the key signature. In the key of “D”, the leading tone is C#. So the key of “D” adds C# to the already present F# to make the key signature have two sharps.
Moving counter-clockwise around the circle of 5ths requires the addition of flats rather than sharps. The key of “F” has one flat. The key of “Bb” has two flats. They key of “Eb” has three flats and so forth. Also note that moving clockwise we move in 5ths but moving counter-clockwise we move in 4ths. Flats are added using the interval of the perfect 4th. The order of flats is: Bb, Eb, Ab, Db, and so forth.
Most string instruments, like the hammer dulcimer, play in sharp keys. Many wind instruments play in flat keys. Most music played on the hammer dulcimer will be in the keys of “D”, “G” and sometimes “A”. Occasionally a “C” tune or “E” tune will appear. For the most part dulcimers play in keys with one or two sharps.
A unique relationship exists between the tonic tone and the 6th above it. These pairs of tones create a relative major and minor pair. So, the key of D major has a relative minor key of B minor. For the key of G major the relative minor is E minor. If the circle of 5ths diagram is expanded to show these relationships by putting the relative minors inside the circle, we create a machine that helps us to analyze and build chord progressions.
Study the diagram of the circle of 5ths. You should memorize how to create it. For dulcimer music you will need to recall the keys of “C”, “G”, “D”, “A” and their relative minors.
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 difference is called The Pythagorean Comma. “Correcting” the Pythagorean Comma was an obsession for centuries. If a melody stays within an octave or two, the Pythagorean Comma is not noticeable. But, when a symphony orchestra goes to work, its range of musical sound is so great, the Comma becomes evident. Event the eighty-eight key piano has trouble with the Comma. There are many resources to read if you want to explore the subject of temperament in scales. One particularly good text is: Temperment: How Music Became a Battleground for Great Minds of Western Civilization by Stuart Isacopff.
The equally tempered scale we play attempts to make the circle complete by averaging out all the pitch differences in an octave.
