Can Sacred Geometry Produce Musical Harmony?
Geometric Frequencies
Is there a direct correlation between geometry and frequency? Were ancient civilizations given a key to connect mathematics, geometry, and sound?
Eric Rankin believes so in his documentary revolving around an interconnectedness between geometry and frequency. Sonic Geometry focuses on harmony found when the sum of the angles of all shapes is played as frequencies.
The basis of Rankin’s theory dates to the ancient Sumerian culture, roughly 5,000 years ago. The Sumerian civilization in Mesopotamia oft referred to as the Cradle of Civilization, spawned the first written language and mathematical system. The Ancient Sumerians wrote that the information that is the basis for their systems came from ‘sky gods,’ known as the Annunaki. They relied on a system of mathematics based on the numbers 12 and 60. We still retain some of the Sumerian’s mathematical system in how we calculate time, measurement in inches, and in geometry.
Pythagorean Tuning
We’re all familiar with the Pythagorean theorem in geometry, but the Greek philosopher/mathematician is not as commonly known to have applied his focus to music. Pythagoras applied geometry to music when he noticed how dividing a string in half would double its pitch. He created the Pythagorean scale based on harmonic fifths, which is now used as a root in modern music.
But according to Rankin, Pythagoras’ scale led him to stumble upon the number 432, maybe without knowing its synchronistic implications. The number happens to appear on his scale of fifths, which became the keystone for tuning frequency until the 20th century.
The sum of the angles of the basic geometric shapes, when played as frequencies, increases in octaves as you add additional sides. When combining these frequencies starting with a triangle, all the way up to an octagon, they create perfect harmony in a three-part major chord of F#. This pattern works with three-dimensional shapes as well as sacred geometric patterns to create harmonies.
The Mayan Equinox
The Ancient Mayan civilization was astronomically in tune and knew about the Earth’s axial precession. The Mayans calculated the time it took for a complete rotation of the Earth’s wobble on its axis to be 25,920 years, with one month being 2160 years. It happens that the diameter of the moon is 2160 miles. When this number is divided simply, you get some interesting results…
2160/2 = 1080 – the angle sum of an octagon
2160/3 = 720 – the angle sum of a hexagon
2160/4 = 540 – the angle sum of a pentagon
2160/5 = 432 – the Pythagorean frequency key tone
2160/6 = 360 – the angle sum of a circle and square
Rankin presents evidence of the recurrence of the number 432 as being found in multiples of measurement of time and distance, from the moon and sun to the speed of light. He believes there is some connection that is hidden within this number, that could have possibly been gifted to the Ancient Sumerians by the Annunaki and has remained embedded in many aspects of how we measure our world.
A Change in Frequency
In the early 1900s, there was a shift away from the 432hz frequency to 440hz. Almost all music since then has been recorded in this frequency, which does not have the same numerical synchronicity. To those who have alternated between the two frequencies, there is a noticeable difference.
Some theorize that the frequencies were changed as a sinister plot by the Nazis as a way of subversively increasing aggression or agitation on a large scale. It has been shown that different sound frequencies affect everything from water molecules to living organisms at different levels, so a plot to change the frequency of music sent to the masses seems like a plausible tactic of disruption. However one must judge for themselves — is the difference in frequencies big enough to manipulate human consciousness?
Cosmic Cycles of 432
Joseph Campbell found the number 432 intriguing in his studies, particularly as it recurred across different religious contexts. One instance is of an ancient Babylonian priest who wrote an account of the history of Babylonia in which a flood destroyed everything after 432,000 years.
In the ancient Hindu timeline, cosmic cycles are measured in multiples of 432,000 years. The Kali Yuga is 432,000 years, followed by the Dwapara Yuga at 864,000 years, the Treta Yuga at 1,296,000 years and lastly the Satya Yuga at 1,728,000 years.
There is even reference to cosmic cycles of 432,000 in the Icelandic Eddas, recounting Norse mythology. In one book describing Odin’s hall in Valhalla, there are 540 doors with 800 warriors coming through each door representing our time cycle. Those numbers multiplied, of course, equal 432,000.
With the interrelation of mathematics and nature as seen in such instances as the Fibonacci Sequence, it would come as no surprise that there would be an intrinsic relationship between geometry and sound frequency. What other inherent connections have we yet to discover in the nature of our existence?
What are Fractals?
If you look around you right now, depending on where you are, you’re likely to see to two distinct types of shapes: 1) blocky, linear and smooth if you’re in a manmade environment; or 2) branching, uneven and irregular shapes if you’re in a natural one. Why is there such a difference between the appearance of manmade and natural spaces? Why does one tend to look smooth, while the other looks rough? It comes down to one word: fractals.
A Brief History of Fractals
At the beginning of the 20th Century, mathematicians Pierre Fatou and Gaston Julia discovered fractal patterns while looking at complex mathematical systems. Back then, these objects defied linear analysis; they were considered aberrations or scary mathematical monsters, with infinite depth and complexity. They weren’t very popular and were forgotten until the late Belgium mathematician Benoit Mandelbrot discovered them again while working at IBM labs in Armonk, New York in 1980.
Fractals Contain Imaginary Numbers
To distinguish fractals from ordinary objects, you should know that fractal sets are created by algorithms that, in addition to ordinary integer numbers, also contain so-called “imaginary numbers”. This allows fractals to behave in much more complex ways, and describe more complex systems than ordinary numbers.
The Behavior of Fractals
Mandelbrot was the person who coined the word fractal. He used it to describe the behavior of financial markets and telephone line noise. The word fractal is derived from the word Greek “fractus,” meaning “fractured.” Mandelbrot noticed that telephone line noise is similar, whether you look at it over the course of an hour, a minute, or a second: you still see the same wave-form shape. In this sense, you can describe telephone line noise with a numerical dimension that applies at any time scale. The dimension defines the visual “roughness” of the signal; in other words, the dimension translates to how choppy it looks.
This is a very different type of geometrical logic than the one we were taught in school, where objects have a definite length and size. This is because, in school, we’re dealing with abstract objects that we imagine are perfectly linear and smooth. Nothing in the real world really looks like that!
If you take a look at almost anything natural under a microscope, you’ll see it’s full of fissures, pits and holes.
That’s because natural things are seldom perfectly flat beyond a certain scale. The closer you look, the more defects you’ll see.
