Musical Numerology

I'm always fascinated by the connection between music and math. Music is full of mathematical relationships. And it seems to be the case that many people who have an affinity for music also have an affinity for math, and vice versa.

There is also a connection between music and numbers themselves. I'm calling this "Musical Numerology."

Many spiritual and philosophical teachings have discussed the importance of certain numbers in our cosmos and in creation. For example, the philosopher/teacher G.I Gurdjieff talked about the "rule of three" and the "rule of seven" as playing a large part in our solar system and in the organization of many aspects of life on earth.

There are three numbers which play an important role in music: three, five, and seven.

Three:
There are many instances of three in our culture, such as the Trinity in Christianity. In Western music, three can be seen in the construction of the most basic chord, a triad, consisting of three notes. In triads and in "expanded" chords, such as seventh and ninth chords, each tone is always separated by the interval of a third.
Many of our forms that larger pieces use are three-part forms. The most common of these is known as an A-B-A form, which consists of a first section (A) followed by a contrasting section (B), followed by another A section, which can be an exact repeat, or somewhat altered. One of the most enduring forms in our music is Sonata Form, which uses this ABA form on both a macro and micro level. Most symphonies, sonatas, concertos, and many of the large-scale pieces from the last three centuries or so have three movements (although many composers deviated from this and had anywhere from two to four movements); the first, in the original key, was often fast; the second movement often slower, and in a contrasting key, and the third movement again in the original key. The first movement itself is in "Sonata Form" which consists of three parts, an Exposition, a Development, and a Recapitulation.
This three-part form has proven to be so satisfying to both the composer and the listener that we just don't seem to be able to abandon it.

Seven:
There are many instances of the importance of 7 in religion and philosophy, probably starting with the Creation Story of 7 days. This of course is why we have seven days in our week.  In Western music we have a basic building block, the scale, consisting of seven tones. Composers have experimented with other options, but none of these have taken hold. There is something about the 7-tone scale that seems cosmically right. It is believed that the Greeks took the "distance" between a given tone and the tone that vibrates at exactly twice the frequency of  the first tone, and the division of that distance into 7 tones ensued from that. (They are not equal divisions of the octave, however.)That distance is referred to as the "octave." (There is quite a bit more complexity to this which goes beyond the scope of this post.)

Five:
The importance of five in music is one of my favorite things to talk about. Many cultures (not ours, however, as explained above) have based their music on a 5-tone, or pentatonic, scale. As an example, just about every Spiritual you can find has a melody based on 5 tones.
In Western music the importance of five can be seen in the Circle of Fifths. On the most surface level, this is a picture of the relationship of the tonalities to each other. The key of C Major has no sharps or flats; go up 5 tones (in that scale) and you get G Major with one sharp. The significance of this is that the most closely-related key or tonality is five tones away. On a deeper level, music tends to want to move by the interval of a fifth. This is seen in the roots of chords as they progress from one to another. The most common cadence (or ending) is V to I. (We use Roman Numerals when we refer to the degree of the scale.) The next most common is IV to I (which can be heard in the "Amen" of almost all religious music). It should be noted, however, that IV to I is also the relationship of a fifth, but going the opposite direction around the Circle of Fifths.  This is not just true of Classical music; in jazz, the most common progression is II-V-I; the II is five away from V, so II-V-I is a "chain" of fifths.

This post just scratches the surface of understanding Musical Numerology. There are hundreds of books and articles written on this subject. I always have felt that music is somehow an auditory representation of our cosmos, closely related to physics, math and astronomy. Hopefully this piques your interest to find out more about this amazing connection.