Can Sacred Geometry Produce Musical Harmony?
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.
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?
Sound Shows Evidence of a Hidden Structure Throughout Universe
Sound is a powerful force, and as humans, we know this intuitively from the day we’re born. Even for those born deaf, sound can be felt physically, such that it can still evoke a response.
When we think about sound at its most basic definition, it seems relatively simple — acoustic vibrations resonating as waves through some medium. But the way sound makes us feel is more complex, nuanced, and often ineffable.
Sound can elicit chemical changes in our brain and take us into transcendent states of euphoria; it alerts us to impending dangers or opportunities in our environment; it can distract or focus our minds on a task at hand, and it can even drive us to the brink of insanity if used nefariously.
Sound is also one of the major tools we use to manifest material reality and bring our ideas to fruition — in fact, verbal communication is like magic when you consider the impact it can have on others.
The etymology of every magician’s favorite utterance, “abracadabra,” is ambiguous and contested, but many believe its roots come from ancient Hebrew or Aramaic where it means, “I will create as I speak,” or “I create like the word.”
In nearly every religion, the origin story of the universe begins with sound. In Eastern philosophy, “aum” was the primordial reverberation that sparked existence; in Christianity, God spoke the universe into existence; in Jewish mysticism, creation texts like the Sefer Yetzirah, stress the significance of specific Hebrew letters and powerful root words used to create the universe.
And beyond contemporary religion, this concept of a “sound of creation” was even taught in ancient Egyptian schools with Ptah, the god who gave life to all through his heart and tongue.
When we consider the physics of sound, these creation stories actually make a lot of sense, as sound and matter are intrinsically connected. Because sound is unable to travel through the vacuum of space, some physical medium is necessary to not just generate it, but to propagate its waves — whether that be a solid, liquid, gas, or plasma.