If you had to send an interstellar message to an alien civilization across the cosmos, what language would you use?
Our man-made languages wouldn’t work - we need a universal code that transcends all cosmic barriers.
Fortunately, there is one such language, and it is made up of the 3 most fundamental pillars of creation: Mathematics, Geometry, and Sound.
In this final blog of our series, we show you how there is a divinely mirrored relationship between numbers, shapes and sound. This relationship has existed since the beginning of time and can be seen all around us. All we have to do is pay attention in the right places.
In our previous blogs, we have uncovered the secrets of healing sound frequencies, numerology, sacred geometry, and vortex math. In case you’re not familiar with these topics, we highly recommend perusing through these blogs first. These concepts will give you the foundational knowledge needed to fully appreciate the learnings shared with you today.
Scroll down to find out the relationship between these three concepts, and how it permeates throughout the universe.
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The Founding Fathers: Pythagoras & Plato
The sacred relationship between numbers, geometry and sound was known to many ancient cultures thousands of years ago. However, two individuals have had the biggest impact in shaping these ideas in their current form - the Greek Philosophers Pythagoras and Plato.
There’s a reason why Pythagoras was called the ‘Father of Music’, ‘Father of Geometry’ AND the ‘Father of Mathematics'. He was one of the first people to clearly establish the relationship between mathematics, geometry and music. He discovered that plucking strings of specific lengths produced a harmonious sound, which led to the discovery of the physics of intervals - or the distance between musical notes, which created the foundation for the primary harmonic system - a system we still use today!
Born a few decades after Pythagoras’s death, the Athenian philosopher Plato was heavily influenced by the former’s teachings. He built upon that knowledge to introduce the concept of the Platonic solids - one of his most significant contributions. According to Plato, these five 3-dimensional geometric shapes were the most fundamental structures of the universe - and we see how in the following sections.
Understanding The 3 Pillars Of Cosmic Harmony
Before we begin explaining the divine relationship between numbers, shapes and sound, let us do an individual recap of all 3 concepts:
Numbers hold much deeper meanings than merely the quantities they represent. Mathematics existed way before humanity ever did - and it forms the underlying blueprint or divine intelligence that governs the order and structure of all matter in the cosmos - living or non-living.
The ancient sciences of numerology and vortex-based mathematics teach us this qualitative relationship between numbers, and how certain repeating numerical patterns are found in the design of all matter.
The structure of seashells, snowflakes, flower petals to spiralling galaxies - all are astonishing examples of sacred geometry in plain sight! If numerology and vortex math study the mathematical code governing the order of all creation, then sacred geometry is the visual manifestation of the divine intelligence that guides this order.
Sacred geometry reveals design patterns with certain ratios and proportions in which energy organizes itself all across the universe. These geometrical patterns can be seen all around us and everywhere in the cosmos.
From Nikola Tesla to Albert Einstein to Pythagoras himself, people ahead of their time agree that everything in the universe can be understood in sound frequencies. If you zoom into any object that appears solid, you’ll find that it is all made of vibrating energy or frequency!
And that’s not all - Pythagoras discovered that certain sound frequencies such as the 432Hz frequency are more in harmony with nature and have healing properties for living beings, as only something truly natural can.
Photo by Pawel Czerwinski on Unsplash
Understanding the Harmony Of Sacred Triangulation
The previous section must have heavily hinted towards this old truth known to ancient cultures for thousands of years - there is a divine, consistent pattern running through numbers, geometry and sound that brings all three together in harmony. It’s a pattern as old as the universe itself, and one that reveals the inherent interconnectedness of everything we’ve ever known and are yet to know.
Let’s uncover it together below:
Mathematics ~ Sacred Geometry
We will begin with establishing the relationship between numbers and the primary geometric shapes.
As you may already know, the basic 2-dimensional shapes known to us are defined by a certain number that is the sum of all the angles relative to that shape.
For example, the triangle is a 3-sided shape where the sum of the 3 angles is always 180. The corresponding number for the 4-sided square is 360. Similarly, it’s 540 degrees for the pentagon, 720 for the hexagon and so on.
Now, let’s take a look at the digital room of these numbers (read about digital root here):
180, 360, 540
1 + 8 + 0 = 9
3 + 6 + 0 = 9
5 + 4 + 0 = 9
7 + 2 + 0 = 9
This goes on - no matter which geometric shape you take. If you take the digital root of the sum of all its angles, the answer is always 9. If you’ve read our blog on vortex math, you will know that the number 9 is known as the mathematical fingerprint of God!
Across cultures, this number is considered divine and perfect. It is an omnipotent symbol representing consciousness and enlightenment. This is not a coincidence and points to the fact that the fundamental structures of the universe all follow a harmonious pattern. And we’re only getting started.
Photo by Michael Dziedzic via Unsplash
- Sacred Geometry ~ Sound
Next, let’s explain the divine connection between geometric patterns and sound frequencies, and we will do that both by using 2D geometric shapes and the 3D Platonic solids.
Once again, let’s focus on our 2D primary geometric patterns. But this time, instead of taking the digital root of the sum of the angles contained, we will take that sum and focus on the corresponding Hz sound frequency it emits.
For example, the sum of all 3 angles in a triangle is always 180 degrees. So we will listen to the tone produced by 180 Hz frequency, and identify which musical note it is on the harmonic scale.
We will repeat this process with other 2D geometric shapes too in the following fashion. Here is what we find:
- Triangle | 180° | 180 Hz = An F# note
- Circle/ Square | 360° | 360 Hz = F# one octave higher
- Pentagon | 540° | 540 Hz = C# a perfect harmonic fifth of F#
- Hexagon | 720° | 720 Hz = F# one octave higher
- Septagon | 900° | 900 Hz = A#
- Octagon | 1080° | 1080 Hz = C# one octave higher than the pentagon
If you notice, the resultant notes - F#, C# and A# - are ALL part of the F# major chord. This means that these notes are in perfect 3-part harmony.
Here is what an F# major chord sounds like:
Image Source: Wikipedia
This harmonious 3-part harmony is not only produced with 2D geometric shapes, but also with platonic solids. Plato introduced the concept of Platonic solids to the world 2500 years ago, saying that these were the fundamental 3-dimensional structures from which all matter was formed. So again, let’s find the sum of all angles in each platonic solid, and find the corresponding Hz tone produced by that number.
- Tetrahedron | 720°| 720 Hz = F#
- The Cube | 2160° | 2160 Hz = C#
- Octahedron | 1440° | 1440 Hz = Perfect F# one octave higher
- Icosahedron | 3600° | A#
Once again, the F#, C# and A# notes all form a perfectly harmonious F# major chord.
As you can see, the pattern is crystal clear - geometry has seamlessly expressed itself in sound frequencies that are in absolute harmony within themselves.
Mathematics ~ Sound
Finally, let’s tie this cosmic knot together by showing you the divine relationship between numbers and sounds via the Fibonacci sequence.
As you may know, the Fibonacci sequence is a numerical pattern created by adding the preceding number to the current number. For example, if we start with the number 1, the preceding number to 1 is 0.
So, 0 + 1 = 1 | 1 + 1 = 2 | 2 + 1 = 3 | 3 + 2 = 5 | 5 + 3 = 8 | 8 + 5 = 13 and so on
This gives us a sequence of 1,1,2,3,5,8,13, and so on.
Now, the human ear cannot listen to sound frequencies with a single-digit Hz value, so let us apply the Fibonacci principle to our primary geometric shape - the triangle.
We know that the sum of the 3 angles of a triangle is always 180°.
Let us now create a Fibonacci sequence where the starting number is the sum of all angles of a triangle, ie. 180 degrees. We will get the following sequence:
180, 180, 360, 540, 900….
Now, let’s listen to the tones that each of these numbers produces:
- The 180 Hz is our root note
- 360 Hz is a perfect octave higher than the root.
- 540 Hz is the harmonic fifth note of the original tone.
- 900 is the major third note of the original note.
And yet again, we get a geometrically perfect, 3-part major chord!
Here’s another awe-inspiring finding: no matter which numerical digit you start with, the first 6 digits of its Fibonacci sequence will always create a perfect 3-part major chord where all notes are in complete harmony with each other.
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Mathematics ~ Sacred Geometry ~ Sound: The Tri-Part Harmony
Numbers in harmony with geometry in harmony with sound - the findings shared in this blog all point to a clear message to humanity - that harmony and self-organisation form the very essence of all creation. This sacred triangulation between mathematics, geometry and frequency is the underlying blueprint of our reality. These divine patterns are repeated endlessly, all throughout our universe - from the smallest atoms to the largest galaxies.
And while we are still yet to find out the true nature of the intelligent force that guides the order of all things, the knowledge of this sacred triangulation reveals the sacred principles put in motion by this intelligent higher force - and that in itself is no mean feat.
References & Interesting Reads:
Dear Ms. Knight, I read your article on Math,Freq. and Form and found it engaging – well thought-out. I discovered your review while working on the application(s) of triangulation of geodetic-geometric points on the planet by the Ancients.