Frequency Root

Definition

The Frequency Root (FR) is a normalized composite number that collapses numeric frequencies across octaves into a single dimension, allowing for greater insight into numbers and words.

The concept of polarity is a fundamental tenet within the universe, and there can be no polarity without a third center point. This center point provides a reference for polarity to be expressed, and so trinity is a core universal concept.  Numbers are a fractal of the universe and therefore also adhere to the triadic nature of the universe. This means that numbers can be grouped into sets of three for deeper analysis and insights.  In practical terms this means reducing a number to value between 1 and 999, which is the first octave, the first grouping of three digits. This normalization of numbers to the first octave of three digits is known as the Frequency Root.

Frequency Root: method

To determine the Frequency Root of a number, we must collapse all octave (group of three digits) frequencies into a single composite waveform. This collapsing is achieved through multiplication, addition, and subsequent reduction.  

For example, the number 123,456,789 is comprised of three main frequencies or waveforms at different scales or octaves. 

123,000,000               3rd octave 
        456,000               2nd octave 
                 789               1st octave 

 First we multiply the number groups, we then sum these, and finally we reduce the number to between 1 and 999. 
(A) Multiplication: 123 x 456 x 789 = 44,253,432 (composite frequency at a higher scale) 

(B) Addition: 44 + 253 + 432 = 729 (normalized frequency) 
The FR of 123,456,789 is 729, which represents the energy of the combined waveforms (123,000,000; 456,000; and 789). 

(C) Reduction: If, after the Addition method, the FR was greater than 999, then 999 would be subtracted repeatedly until a number of 3 or less digits was derived, or we could also sum the numbers before and after the comma separator.  

For example, if we have a starting number of 456,789, then: 
Multiplication: 456 x 789 = 359,784 
Addition: 359 + 784 = 1,143 
Reduction: (1,143 – 999 = 144) or with a simpler method: (1 + 143 = 144) 

Frequency Root (simplified): method

When we initially observe a number we may also assume that the number is already in its multiplicative state, meaning that numeric multiplication has already taken place (step A of the Frequency Root method. What remains are the addition and reduction steps. For this reason, this method is referred to as Frequency Root (simplified). We can then analyze a number using both the Frequency Root and Frequency Root (simplified) methods. 

For example the number 123,456,789 can be viewed as the result of parent numbers that have already been multiplied. We can then simply add and reduce the numbers. 
Addition: 123 + 456 + 789 = 1,368 
Reduction: 1 + 368 = 369 

Word Analysis 

The Digital Root method has long been employed to analyze words, which is accomplished by reducing words to a single digit between 1 and 9.
With the English alphabet we have twenty six letters with numbers assigned to each letter: a = 1, b = 2 … z = 26 

For example the word world has number equivalents of w = 23, o = 15, r = 18, l = 12, d = 4. 
To reduce world to a single digit we can follow these steps:
23 + 15 + 18 + 12 + 4 = 72; we can then reduce the number 72 further: 7 + 2 = 9 or  
5 + 6 + 9 + 3 + 4 = 27; we can then reduce the number 27 further: 2 + 7 = 9 

The word world has a Digital Root of 9, which coincidentally indicates completeness in our 1 to 9 scale. 

The challenge with traditional Digital Root analysis is that there are only 9 possibilities and so only 9 archetypal energies exist. While this is sufficient for some insights, deeper insights are not possible with Digital Root analysis on its own. 

The Frequency Root method and its simplified version are better suited for understanding numbers and the numeric vibration of words. Certain words and numbers have FRs that are associated with geometry and specific sound vibrations 

Computing the Frequency Root of the word world yields: 
world: 23 15 18 12 4 which are combined as: 231518124 and grouped into threes as 231,518,124 using the thousands separator.
Multiplication: 231 x 518 x 124 = 14,837,592 
Addition: 14 + 837 + 592 = 1,443 
Reduction: 1 + 443 = 444 

The Frequency Root of the word world is 444.  

The Frequency Root (simplified) can be computed as:  
world: 23 15 18 12 4 which are combined as: 231518124 and grouped into threes as 231,518,124 using the thousands separator.
Addition: 231 + 518 + 124 = 873 
Reduction: the 873 is already within the 1 to 999 first octave and so no further reduction is required. 

The Frequency Root (simplified) of the word world is 873.  

Frequency Root calculator 

A Frequency Root calculator is available to simplify the analysis of words and numbers; however, I would suggest that you also use your trusty calculator to better understand number dynamics. I performed thousands of calculations using a basic calculator, which allowed for deeper insights when multiplying and adding numbers. 

Interestingly, after calculating the Frequency Roots of over 400,000 words, the top three most common Frequency Roots of these words are 999, 333, and 666 in this order and comprising 11% of all words. A random distribution would see these three numbers only accounting for about 0.3%.

Coherency: Pythagorean theorem 

While the Frequency Root method may seem mathematically arbitrary, it is far from it. The following section demonstrates that the Frequency Root method is coherent with a foundational mathematical geometric principle, namely the Pythagorean theorem. 

 The Pythagorean theorem is a fundamental principle in geometry that relates to right-angle triangles. The theorem states that the squared length of the hypotenuse is related to the sum of the squared lengths of the adjacent and opposite sides.  

Applying the Frequency Root method yields: 
C: 169 x 169 = 28,561 => 28 + 561 = 589 
A: 119 x 119 = 14,161 => 14 + 161 = 175 
B: 120 x 120 = 14,400 => 14 + 400 = 414 

589 = 175 + 414 

When we apply the Frequency Root method to the Pythagorean theorem the resultant Frequency Roots of the three squared side lengths are aligned with this foundation mathematical principle. This adds further weight to the applicability of the Frequency Root method as a tool to further analyze numbers and elucidate patterns.