In Music, Half Of Seven Is…?

Historically, music theory has been divided into two major groups, Eastern and Western.  I don’t mean Country Western.  The term refers to the music theory that came from Western Europe as opposed to Eastern Europe and Asia.  One of the main differences is that Western music is composed of scales/key signatures that contain seven notes.  The seven letters of the musical alphabet are A, B, C, D, E, F and G.  Each one can be sharped, flatted or remain natural.  However, a particular key signature will consist of only one type of each letter which results in a scale of seven pitches. 

The existence of the seven pitch scale causes me to raise the question, “How does one musically divide seven in half?”  Music has many mathematical components, and this one creates an interesting occurrence within the element of harmony.  There is no interval (harmonic distance) between the major third and the perfect fourth, so there is no musical way to represent the interval of three and a half. 

Why is the bisect point of the musical alphabet even important?  This distance can be used as the building block for chords.  Since an interval of 3.5 does not exist in Western Music we are forced to build harmonies by stacking either thirds or fourths.   In the popular forms of modern day music this creates two different styles/characters of harmony. 

Trishal harmony (built off of thirds) has a more straight and tight sound.  All simple triads (three note chords) are built from the first, third and fifth scale degrees.  These types of chords create the characteristic sound of most rock and pop music.  If you invert the order of the pitches, you have a triad that consists of one fourth and one third (a mixture of the two intervals).  However, when you are limited to these three pitches (1^st, 3^rd and 5^th) it is impossible to create a chord (in a close voicing) that consists of all fourths.  Even basic seventh chords (adding the 7^th as an additional pitch) cannot be voiced as pure stacks of fourths.    

Quartal harmony (built off of fourths) has a more lose and opened sound.  The only way to achieve pure quartal harmony is to build chords consisting of more pitches.  Seventh chords are also stacked in thirds within their root position.  The extra pitch does allow us to create additions combinations of thirds and fourths within the harmonic intervals.  As you add additional pitches to the harmony (color tones and upper extensions) you finally achieve the ability to construct cords built only of fourths. 

These seventh chords with additional pitches are characteristic of the sound of jazz, blues, gospel and r&b music.  So, it can be said that the more fourths are used to build the chords of a particular type of music the more the characteristic sound of that music leans towards jazz.  In addition, the more thirds are used the more the characteristic sound leans towards rock or pop.  I find it interesting that this inability to evenly split the seven note scale causes a split in modern musical styles.