The language of the universe is expressed through mathematics, geometry, energy patterns and frequency. Geometry and math hold the key to the nature of all existence. In 6th century BC, on the Greek island of Samos, famed mathematician Pythagoras led a school of thought that married philosophy, mathematics, music, and of course geometry. Pythagoras discovered that when a taut string was plucked it would create a tone, and when the string was divided in half it would make the same tone, only twice as high in pitch. Pythagorus came up with a numerical ratios based on harmonic fifths, and this led to the creation of the musical scale found at the root of most modern music.
According to Pythagorus, all musical notes were found by mathematics and were given number values in a master grid. By doubling the lowest octave of A, he found that A was manifested in frequencies of 27, 54, 108, 216, 432, and so on. Many ancient instruments, from Tibetan bowls to Native American flutes, produce tones that also vibrate at 432 cycles per second. Why does A 432 pervade in music throughout time and space on Earth? In my article Universal Tuning and the 440 Conspiracy, I used some examples to show how 432 miraculously appears in the mathematical analysis of universal intervallic relationships, beyond music and into the form and function of the nature of the universe itself. Here I will introduce another fascinating fact using 432 as a bridge:
The first four basic geometric shapes are a triangle, square, circle, and pentagon. The sum total of a triangle’s interior angles is 180. For a circle and square, it is 360. For a pentagon, it is 540. As you can see, these numbers are all in the same numerical neighborhood as 432, and their digits all add up to 9, just like 432:
1+8+0 = 9
3+6+0 = 9
Moving forward, we will translate these interior angle sums into sound cycle frequencies (a musical tone is measured in Hz: frequency per second). So,
180 degrees of a triangle, when applied to audible frequency, generates a perfect F# (180 Hz)
360 degrees of a circle and square, in audible cycles per second, is a perfect octave up from the triangle = F# (360 Hz)
540 degrees of a pentagon is the perfect harmonic fifth of the first two figures = C# (540 Hz)
720 degrees of a hexagon is another F# (720 Hz)
900 degrees of a septagon is A# (900 Hz), which is the perfect harmonic third of F#
1080 degrees of an octagon is C# (1080 Hz), which is another perfect harmonic fifth of F#
Essentially, the first seven basic geometric forms make a perfect three part major chord in the key of F# tuned to A=432 Hz!
Not too long after Pythagorus made his initial discoveries about music and geometry, Plato began to recognize that nature, whether expressed as a tone, the spiraling design of a seashell, a succulent or the petals of a flower, seemed to follow a three dimensional mathematical pattern. He became obsessed with trying to find the simplest three dimensional shapes — now are known as the platonic solids — which represent the most elemental construction blocks found in both human made and natural forms.
Let’s take the same method prescribed to our two dimensional shapes and find out what tones our platonic solids create:
The tetrahedron, a three sided pyramid comprised of 4 interlocking triangles, has an interior angle total sum of 720 (F#)
The cube, comprised of six 360 degree squares, totals 2160 (high C#, perfect harmonic fifth of F#)
The octahedron, comprised of 8 triangles, totals 1440 (F#, one octave above tetrahedron)
The icosahedron, comprised of 20 triangles, totals 3600 (A#, perfect harmonic third of F#)
The basic two dimensional and three dimensional forms that comprise everything we see in our known physical universe create music in perfect harmony within itself — this is beyond a miracle. It is evidence that life itself is music. Like Master Pooh said, “Music And Living? The Same Thing!”
The Tao of Pooh, Bejamin Hoff, Penguin Books, 1982
Sonic Geometry: The Language of Frequency and Form: www.youtube.com/watch?v=FY74AFQl2qQ
Photo By Krzysztof Mizera, changed by Chagler and MathKnight (Based on File:Rozeta Paryż notre-dame chalger.jpg) [GFDL (http://www.gnu.org/copyleft/fdl.html) or CC BY-SA 4.0-3.0-2.5-2.0-1.0 (http://creativecommons.org/licenses/by-sa/4.0-3.0-2.5-2.0-1.0)]