In this article we are discussing some of the numeric underpinnings to the solfeggio frequencies. Its not meant to serve as an introduction to these tones as there is a great deal of information available throughout the web. My intention here is to provide an overview of some of the aspects of this subject that are not often discussed. To get at some of the mathematical underpinnings of this subject we will look at number sequences, vortex based mathematics, the nonagon and the relationship between Herzt frequencies and our measurement of time.
Music and the term Solfege
The term solfege is a word originally used to represent the letter note names in an earlier form of music notation; do, re, me, fa so, la and ti. The solfege (note names) represents the intervals of a scale rather than a specific note or frequency. Whatever the fundamental frequency we choose for our tuning, the solfege represents the scale degree in relation to the fundamental.
This is one of several misconceptions around this subject that has been a source of confusion for many people. The solfeggio frequencies don’t make an interval system that corresponds with any of the temperaments that we would use to create a musical scale. Its not a scale, but rather a mathematical code containing an information archive.
The 9 and an Information Archive
This subject is more complex and more meaningful than number gymnastic – but it is a bit of that to. To truly understand and appreciate it requires an investigation into the esoteric nature of numbers, and its relationship to geometry. Esoteric number theory, like practices taught in the western mystery schools, Pythagoreanism, neo-platonism, and Qabalah for example, consider numbers as representing underlying principals of nature abstractly. This school of thought considers numbers and their properties to be a kind of code that embodies the mathematical code of nature. In exploring them in a particular way, we are able to recognize those principals, unraveling the deeper layers of insight that they contain.
Its this philosophy that originally lead me to experiment with the solfeggio tones some 20 years ago and continues to inspire my work with music. Music is after all, an expression of mathematics, and mathematics is the universal language of the kosmos. When we weave together the several threads innate to this subject within an integral understanding, what initially seems to be series of disjointed details becomes a golden braid. Its often the case that a low resolution understanding of the esoteric sciences presents as a superstitious new age beliefs system, we have to really put on our thinking caps going deep enouph into it that we can locate its hidden treasures.
One of the ways to approach this subject is through the study of the ennead or the nonagon – the numbers 1 through 9 and their geometric expression. The term ennead means nine. The nonagon which is a nine pointed polygon has been a source of wisdom for many cultures, even giving rise to a personality typology system called the enneagram.
1-9 are esoterically considered to be the only numbers that actually exist. All higher numbers being a further iteration of the original nine. Zero is considered a non-state, or non-integer because zero is thought to be everywhere and nowhere. 0 is considered to be the thing that is expressed in every number, so in the number sequence zero is dropped.
On the tree of life, a form in the western esoteric practices representing the irreducible pattern of the life process, there are 9 nodes or sephirot. Each node represents an aspect of the divine law. The 10th node, called the “Kingdom”, represents the consolidation and summation of the preceding 9. For the Qabalists, the nine sephirot, provide the basis for all structures and activities of the universe.
Three Number Sequences
In examining number sequences, and how a series of numbers is formed, we can notice that there are three major types of counting sequences. In seeing how number sequences develop, extending the number 1 into the higher integers, we are given clues to the code that underlies the patterns of nature.
The sequence we’re most familiar with is the pattern F(n) = F(n)+1 where we count by 1, adding one to each consecutive integer to get 1 – 2 – 3 – 4 – 5 – 6 – 7 – 8 – 9.
But, we can also count by adding the last two numbers to get the next, like in the fibonacci sequence. 1 1 2 3 5 8 13 21 34 55 89 144 233 and so on. F(n) = F(n) -1 + F(n) – 2
Lastly, we can count by the doubling series 1 2 4 8 16 32 64…. where each proceeding number is twice the former one. This series of numbers has the greatest symmetry in harmonic terms because each integer has a 2 : 1 ratio relationship to the proceeding one. The doubling and halving aspect of this series makes it so that each number is harmonically proportionate to each of the other numbers in the series. This is significant in the context of music since music is an expression of harmonics.
Esoteric number theory shows that the formative patterns of nature each follow one or more of these three kinds of sequences depending on the domain and scale of our observation. Plants, animals and humans at the meso scale, for example often reveal the fibonacci sequence, seen in the golden ratio which makes up the algorithm underlying the growth processes and anatomical patterns that organic life follows.
Biological organisms, at the micro scale of cells in meiosis and mitosis, for example, take form through the doubling pattern. This is seen in the process of cellular division where 1 cell divides to become 2, the 2 divide to become 4, the 4 become 8 and so on. Everything that respirates and reproduces has this pattern governing its development.
To understand the ennead, and how its connected to the solfeggio tones we will examine the doubling series. Besides illustrating the process of cellular growth, this series highlights the code underlying the patterns of harmonics, electromagetism, and more generally, the vorticular motion itself. Since each of these types of activities operate through oscillations of spiraling force our ennead series brings into view an illustration spin dynamics.
To illustrate, I want to point out the work of Marco Rodin and the “fingerprint of God” pattern from Vortex Based Mathematics.
With the sequence 1 2 4 8 7 5, we see the doubling pattern. When taking the digital root of the bigger two digit numbers; 16, 1 + 6 = 7 and the digital root of 32, 3 +2 = 5, we see that the doubling sequence continues on indefinitely. As large as the number gets, its digital root always reduces to the pattern 1 2 4 8 7 5.
16 = 7
32 = 5
64 = 6+4=10 , 1+0=1
128 = 1+2+8 = 11 , 1+1=2
and so on…
We can think of this “doubling circuit” as a current of flow oscillating between poles of force, like the positive and negative poles of a battery. The 3 6 9 triad between them then, is a neutral and equilibrating force that holds the positive and negative poles together. Much in like the neutron of an atom holds together the + proton and the – electron, the 3 6 and 9 are a central axis around which the positive and negative poles circulate. This pattern, according to Rodin, is a numeric underpinning of the spin dynamics in operation throughout the universe. Wherever there is a whirling motion, this numeric pattern is in operation.
This idea begins to make sense when we consider that everything is in motion, from the electrons spinning around the nucleus of an atom, to the spiraling motion of the planets and milky-way galaxy itself. There is an outgoing and incoming force, a flux and reflux of energy that is circulating around a central axis. Sound vibration behaves in the same way. A tone is a pressure wave with a positive and negative pole rotating around a neutral axis. Even the action potentials of the electrical circuitry of the nervous system are enacting this pattern.
The activity that governs electricity and magnetism also describes the behavior of light, and sound. From Gamma rays, to x rays, to ultraviolet light to, to the visible light spectrum, to infrared light, to microwaves, and finally radio waves are each different octaves of the electromagnetic force in operation, all of which are governed by the mechanics of spin.
These three components make up the law of vibration and is in operation throughout the cosmos. From atoms, to molecules, to cells, to organisms, to ecosystems and celestial bodies. Everything vibrates, everything moves.
When we examine the integer series of the ennead and the doubling circuit representing spin dynamics, we can see that both the harmonic series and the doubling pattern share a common attribute. The principle of doubling.
In a harmonic series we find the overtones and undertones by doubling or halving the fundamental frequency. And, in the doubling circuit we find the next integer by doubling the previous. This doubling pattern reveals something universal and fundamental about the nature of force and flow in general.
The solfeggio number family comes to life in the nonagon. When we take an equilateral triangle and rotate it around the circle, we get 9 3 6, 1 4 7, 2 5 8 and 3 6 9, 4 7 1, 5 8 2, 6 9 3, 7 4 1, 8 5 2, but we can also reverse their order to get 7 1 4, 5 2 8 and so on. These three integer combinations make up the tones that are generally called the solfeggio tones.
If we permute out the ennead, allowing for each of the integers, to be paired with each of the other integers we get 81 three digit numbers.
In this grid pattern we can see how each column and row sums to 3, 6 and 9 in succession, pointing back to the ennead triangle in our finger print circle.
(81 number group grid)
Since 9 is a triplicity of 3, it presents a kind of harmonic symmetry. It is a higher order unity that mirrors the lower one in a similar way that an overtone is a higher harmony of its fundamental.
So we can see that the doubling circuit and the ennead are closely linked to wave dynamics through the law of vibration by the principal of doubling. The number families that we can see through this line of inquiry behave in peculiar ways that reveal an underlying harmony of the original 9 numbers.
This symmetry and higher unity is awesome to see, but what has it got to do with the solfeggio tones?
Herzt and Time
Numbers aren’t frequencies right? Putting a hz on the end of 3 digit number is an arbitrary assignment of a sound vibration to the number.
To get at this answer we need to look a what the hertz frequency is and what time is. A hertz frequency is a wave oscillation measured in cycles per-second. 1hz means that the wave form moves between its positive and negative poles 1 time every second. So Hertz and seconds are 1 : 1. Meaning they are in unison or mathematically equivalent.
But what is time? Why is the second 60 units of a minute, and why are their 60 minutes in an our and 24 hours in a day? How are the units of measurement for time not merely arbitrary. We could divide the minute into 80 units or 100 units or divide the hour into 80 or 100 units and have a completely different unit of measurement. A smaller unit of measurement would make it so that a cycle per second was experientially faster and therefore higher in pitch. Since pitch is relative to the perception of sound, whatever unit of measurement we use for time would have no impact on the actual speed of the sound waves. Right?[embedyt] https://www.youtube.com/watch?v=inWnhZp_A-M[/embedyt]
For numbers themselves to have direct correspondence to pitch, the measurement of time would need to be innate rather than arbitrary. To measure time we use what is called the imperial base 12/60 counting system or the Sexagesimal system. This system first came into effect according to record, in ancient Summeria. This system is ideal for quick computations using your fingers because we have 3 knuckles on each finger that we can count with our thumb. 3 x 4 giving us 12, 12 x our 5 fingers gives us 60. As it turns out the base 12/60 provides us with a system that gives us the maximum number of divisors possible. It has 12 divisors; 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, and 60, 3 of which are prime.
Everyone in the world uses this system for calculating time. It also gives us our system of geometry, providing us with the 360 degrees in a circle. Its so perfect an enumeration of both time and space that even after thousands of years of mathematicians and cosmologists studying the nature of things, no other system has been thought of as being anymore accurate. Its in our clocks, our maps, and our geometry, its in even in our anatomy.
The 12/60 system for measuring time is not just man’s invention but is a fundamental mathematical structure of space-time itself. Man merely stumbled upon it as a result of looking at the structure of our own form, which itself is a microcosm of the macrocosm. The structure of space-time itself is an organization of units that correspond to the 12/60 counting system. A deeper investigation into the fundamental geometry of creation reveal this perfect harmony and symmetry.
Since the ennead and the organization of space-time are directly related, conveying the solfeggio number family group in audible tones is not merely arbitrary. Numbers as abstract units and sound vibration are in fact two different modes of the expression of the same thing. This doesn’t mean there are any special powers or supernatural properties to the solfeggio tones, but it does mean that the solfeggio frequencies are directly related to the spin dynamics of electromagnetism and the fundamental ground of space-time.
Because of this auspicious correspondence, it has occurred many researchers and experimenter to apply this mathematical formula to music. Considering that the human body and brain are governed by the law of vibration through electro-chemical oscillations, it stands to reason that tuning ourselves to these oscillations can have a beneficial effect. We are each a vibrational instrument, a highly complex spectrum of frequencies. We can be more or less in tune with ourselves, and more or less in tune with the Kosmos.
The possibility of bringing about a higher order harmony between ourselves and the underlying code of time-space motion is an interesting proposition. Neuroscience has concluded that harmonic coherence throughout the various regions of the brain is responsible for the optimization of cognitive functions. Using brainwave entrainment programs has been shown to help bring about global brain coherence.
To bring about brainwave coherence at frequencies corresponding to the underlying numeric fabric of space-time itself is a worthwhile experiment. As obscure and esoteric a proposition as this truly is, in order to really get at its merits, we’d need to do the experiment to see for ourselves. We’d need to work with the brainwave patterns entraining ourselves to alpha, theta and delta brainwave correspondences, really immersing ourselves in them, building new neural network connections cued to these frequencies.
When we do, its my experience that not only do we get the cognitive benefits of everything that comes along with global brain coherence and a state training practice, but we also align ourselves with that information archive encoded in the fabric of the kosmos. An attunment of this kind, I strongly suspect to be significantly catalytic to our evolutionary process. As the gross, the subtle and causal states of our inner most sense making capabilities harmonically integrate with the informational archive of the cosmic code we are more available to the influx of insights from the higher mind. We are closer to the actualization of those faculties involved in the apprehension of the esoteric nature of things.
Whether this translates into any specific benefits to our healing or not I can not say. As someone who’s used these tones with neuro-acoustic meditations for many years, I can say I find them incredibly psycho-active. To get at empirical data and specifically identify the effects, we’d need to do hard science. But as a sonic mystic and musician its my privilege and responsibility to experiment. And that’s what I’ve done, most recently with level 1 Solfeggio Algorithms mediation series. This series uses binaural beat frequencies tuned to these intriguing numeric structures, embedding them within a background of ambient music.
My intention is to offer these programs as a supplemental tool for state training and spiritual development. For beginners to the practice of state training please check out our free e-course of the science of brainwave entrainment.
If you’re a more advanced student of western esotericism and would like to go a bit deeper into the ennead code check out this informative video from Abulafia Thought.