Key Signatures & The Circle of Fifths

                A key signature is a collection of seven pitches that a diatonic piece of music is composed of.  One could think of it as the pitch ingredients within the recipe of a song.  As mentioned in my Musical Alphabet and Musical Intervals posts, there are 21 pitches in music.  This is a result of a seven letter musical alphabet in which each letter can be either sharp, flat or natural. 

A#     B#     C#     D#     E#     F#     G#
A       B       C       D       E       F       G
Ab     Bb    Cb     Db     Eb     Fb     Gb            
               However, diatonic music selects seven of these 21 pitches as the pitch framework for a particular song.  A nonmusical illustration of this would be a person selecting four crayons from a box to make a drawing.  The box may contain many colors, but the drawing will only contain the four colors that the person selected.  Diatonic music is limited to one type of each letter in the musical alphabet.  There is only one type of A, B, C, etc. in a diatonic piece of music.  If a song contains a second version of a particular letter (example: A and A#) the extra pitch is chromatic and outside of the key.  Modern forms of a-tonal music are based off of other pitch systems that differ from the customary diatonic keys.  However, in this discussion we will focus on customary diatonic music.

                The key signature of a piece of music is usually indicated at the beginning of each staff (just after the clef) by listing the flat or sharp letters included within the given collection of seven.  Sharp or flat signs are placed on the line or space that illustrates the appropriate letter.  This one label signifies that every instance of that letter (regardless of register) will be a sharp or flat version.  Letters that are not mentioned within the key signature are assumed to be natural.  The key signature displayed here lists the sharps F# and C#.  A piece of music containing this key signature would be composed of the pitches circled in the following illustration.  Every key signature can result in either a major or minor key depending on the tonic that is established by the music.  The tonic is the primary pitch or harmony that the music is both centered around and resolves to.  The letter of the tonic pitch also acts as the name of the key.

                It is important to note that the existence of a sharp or flat within a key signature does not guarantee the occurrence of that pitch within the song.  Some simple songs contain less than seven different pitches within their structure.  However, the song is still based off of a particular collection of seven.  For example, a song in the key of G major (with an F# in the key signature) may not contain any F's.  However, if it did, the F would be sharp. 

                Due to enharmonic equivalence, every sharp can also be called by a flat name and every flat can be called by a flat name.  To avoid confusion, key signatures do not mix sharps with flats.  They are either a list of sharps or a list of flats.  The order in which sharps or flats are added to the list is determined by a mathematical component of music called the circle of fifths. 

                The key of C major or A minor contains no sharps or flats, so this key signature acts as the starting point of the circle of fifths.  If we travel up a fifth from there (counting C or A as one) we reach the key that contain one sharp (G major or E minor).  Continuing up in fifths will reveal the tonic for two sharps, three and so on.  Traveling down a fifth from C or A will reveal the tonic of the key with one flat (F major or D minor).  Continuing down in fifths reveals the other flatted tonics.  This circle of fifths diagram graphically depicts the order of the cycle.  Major keys are listed in the outside circle and minor keys are listed in the inside one.  At the bottom of the circle, we reach a point where additional sharps or flats would be inefficient.  Once the number of flats or sharps in a key signature exceeds six the resulting key overlaps the opposite side of the circle.  For example, the key of C# major which contains 7 sharps is the enharmonic equivalent to Db major which contains only 5 flats.  For this reason, the circle of fifths diagram usually only depicts the simplest form of each key signature.  For a more in-depth discussion on the circle of fifths, please refer to my blog posts from 5/28/14 and 6/4/14.  Please also refer to the included video for more insight into this discussion on key signatures.