Read part 3 here.

At this point, I was positive that the major/minor system of modern tonal music was developed by individuals whose ideas were similar to those of the Ionian School of natural philosophy. In fact, a lot of the great thinkers of the Middle Ages and the Renaissance considered themselves Pythagorean or at least showed great reverence to the ancient cult figure.



Additional reading on this subject revealed that the 17th Century German mathematician and astronomer Johannes Kepler was, in fact, trying to prove the existence of The Harmony of the Spheres mathematically. In so doing, he discovered an intriguing fact about our solar system.





Kepler proceeded to assign actual notes to each of the planets at aphelion and perihelion and found that when he built with Saturn (the lowest note) at aphelion, the result was a durus scale, a major scale. With Saturn at perihelion the result was a mollis scale, a minor scale. Planetary motion apparently did involve both type of scale. Using other planets as the starting note produced the different modes used in ancient music and church music.



-Kitty Ferguson (The Music of Pythagoras)







Having done this research, it became clear to me that my discovery of the geometric structure in the functional harmony was in fact, the model of Harmonia Mundi. This reminded me of a fact about Scriabin that I had learned in Western music history class. He was trying to discover the mystical chord, which held the universe together (and apparently he did, but who knows with a guy who also told everyone he could levitate). However, what he failed to understand was that Harmonia Mundi cannot be a single chord. A single chord is just a static sound, which does not reflect the constant changes of the world. One must realize that it has to be a model that uses a geometry that mimics the greater universe to which one is connected. Therefore, it makes perfect sense that the true model of Harmonia Mundi lies within the function of the tonality, which deals with the regulated (mathematical) distances of tones that are in motion.





God is a geometer and employs geometry in all his works.



-Plato (The Republic)

To be continued