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?
About the Author
What Are the Platonic Solids, Pillars of Sacred Geometry?
Platonic solids are highly symmetrical three-dimensional geometric figures that have fascinated mathematicians, philosophers and mystics for centuries. They are considered the fundamental building blocks of creation in the universe, representing essential elements and profound spiritual concepts. In this article we explore what Platonic solids are, their origin, their spiritual significance and their connection to sacred geometry.
Table of Contents
- What Are Platonic Solids?
- Where Does the Name of Platonic Solids Come From?
- One by One: The 5 Platonic Solids
- Platonic Solids in Sacred Geometry
- History and Origin of Platonic Solids
What Are Platonic Solids?
Platonic solids are five geometric figures: the tetrahedron, the hexahedron (cube), the octahedron, the dodecahedron and the icosahedron. Each of them has equal faces, edges and angles, which gives them perfect symmetry. These geometric shapes were studied by the Greek philosopher Plato, who associated them with the fundamental elements of nature.
These solids are not only mathematically interesting, but also have deep significance in sacred geometry. They are believed to be the basic patterns that form the structure of the universe, from subatomic particles to galaxies. The symmetry and balance of Platonic solids reflect the inherent harmony of the cosmos.
In the series Sacred Geometry: Spiritual Science available on Gaia, Dr. Robert J. Gilbert explores how Platonic solids are essential to understanding the structure of the universe and our own inner energies. Through his teachings, he reveals how these geometric shapes can be used in spiritual and meditative practices to enhance spiritual awareness and connection.
Where Does the Name of Platonic Solids Come From?
The name “Platonic solids” comes from the Greek philosopher Plato, who described them in his work “Timaeus”. Plato linked each of these solids to the five classical elements: earth, air, fire, water and ether. According to Plato, these elements formed the basis of all matter in the universe, and the Platonic solids represented the perfect structure of each of these elements.
Plato was not the first to discover these forms, but he was the one who popularized them and gave them philosophical and cosmological significance. His association of solids with the fundamental elements influenced philosophy and science for centuries, highlighting the importance of geometry in understanding the physical and spiritual world.
One by One: The 5 Platonic Solids
The five Platonic solids are the tetrahedron, hexahedron (cube), octahedron, dodecahedron and icosahedron. Each of these solids has equal faces, edges and angles, which gives them perfect symmetry.
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The Tetrahedron
The tetrahedron has four triangular faces, six edges and four vertices. It represents the element of fire and is associated with the solar plexus chakra. This solid symbolizes transformation and dynamic energy, and is used in meditative practices to manifest desires and promote mental clarity.
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The Hexahedron (Cube)
The hexahedron, better known as a cube, has six square faces, twelve edges and eight vertices. It represents the earth element and is related to the root chakra. The cube symbolizes stability and solidity, providing a firm and secure foundation on both the physical and spiritual planes.
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The Octahedron
The octahedron has eight triangular faces, twelve edges and six vertices. This solid is associated with the air element and the heart chakra. It represents balance and harmony, and is used to improve communication and promote mental and emotional clarity.
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The Dodecahedron
The dodecahedron has twelve pentagonal faces, thirty edges and twenty vertices. It represents the ether or the universe and is associated with the crown chakra. This solid symbolizes connection with the cosmos and exploration of the mysteries of the universe, encouraging spiritual expansion and higher consciousness.
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The Icosahedron
The icosahedron has twenty triangular faces, thirty edges and twelve vertices. It represents the water element and is related to the sacral chakra. This solid symbolizes fluidity and adaptability, promoting creativity and emotional expression in spiritual practices.
Platonic Solids in Sacred Geometry
In Sacred Geometry, the Platonic solids are considered the most basic and fundamental forms that make up the structure of the universe. These geometric forms, with their perfect symmetry and proportions, are seen as the building blocks of the cosmos, used at various levels of creation, from microscopic to macroscopic structures. Their symmetry reflects the harmony and order inherent in nature.
Each platonic solid has unique properties that make them powerful tools in meditation and energy practices. For example, the tetrahedron can be used to focus intention and manifest desires, while the cube helps to stabilize and ground energy. The octahedron promotes mental and emotional clarity, the icosahedron enhances fluidity and creativity, and the dodecahedron facilitates connection with the divine and expansion of consciousness.
The application of Platonic solids in sacred geometry is not only limited to spiritual practices; they are also found in art, architecture and science, demonstrating their relevance throughout the ages. These forms serve as bridges between the physical and the spiritual, providing a solid foundation for exploring and understanding the energies that surround us and the structures that make up our universe.
History and Origin of Platonic Solids
The history of Platonic solids dates back to ancient Greece, where they were first studied by the followers of Pythagoras and later described in detail by Plato in his dialogue “Timaeus”. Plato related each of these solids to the fundamental elements of the universe, attributing deep cosmological meanings to them and using them to explain the structure of matter and the cosmos.
In addition to Plato, other Greek mathematicians and philosophers, such as Euclid, also studied and formalized the geometric properties of these solids. Euclid, in his work “Elements”, defined and proved the properties of the Platonic solids, establishing a solid basis for geometry that would influence mathematics for centuries.
During the Renaissance, interest in Platonic solids resurfaced, especially through the work of the astronomer Johannes Kepler. Kepler used these solids to explain planetary orbits in his “Mysterium Cosmographicum”, proposing that the distances between the planets were related to the Platonic solids. Throughout history, these geometric shapes have continued to inspire scientists, artists and mystics, establishing themselves as symbols of harmony and perfection in the structure of the universe.
