JonnyRadar
The Living Force
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For a few years now, I’ve been fascinated with the work of Reginald Brooks (_http://www.brooksdesign-ps.net/). During that time, and while revisiting Gurdjeff’s Enneagram as explained in ISOTM, I began to see similarities in the structure of the enneagram to Brooks’ music/color wheel.
This is a visual study of those relationships - an attempt to bring together what I’ve been learning into one coherent piece. I have a number of hand-drawn versions I had been working on and picking up now and again, and eventually decided to do it on the computer (in Adobe Illustrator) so I could examine the exact proportions. At first, it was just an effort to help myself understand the material, but I just recently came to a certain point with it and wanted to share this version here and (hopefully) receive some feedback on possible errors and faulty thinking.
As a precursor, some of the things Gurdjieff said specifically about symbols and the enneagram that piqued my curiosity to look further into it…
That last quote is very important, IMO - to not consider the symbol as something that will automatically or magically impart knowledge. In order to really grok it, the student must delve into it.
So, I’d like to explain some of the connections I saw in an effort to clarify the illustration.
The music/color wheel is based on 16 equal sections of a circle, and the enneagram on 9 equal parts. The first common multiple of 16 and 9 is 144, so the circle is split into 144 sections, each comprising 2.5 degrees of rotation, to allow a visual examination of the relationships between the different sections. The music/color wheel’s 16 sections each comprise 22.5 degrees, and the enneagram’s 9 sections comprise 40 degrees.
The Enneagram
I am still working on my understanding of G’s Enneagram of Foods, but to my current understanding, one proceeds from the first do-re-mi on the “food” octave through the octave back to do, at which point that do becomes the second do of the triangle (at 120 degrees), the air octave (breathing). Then the re-mi-fa-sol etc. shifts according to the new position of do. The same shift of do is repeated for the third octave, impressions, when the do begins at 240 degrees.
Along the process of the enneagram, there are shocks. These manifest in life or the universe as external shocks that come from an outside force. One, between mi and fa, and one between sol and la, which “should be” between si and do. This took a while for me to wrap my head around, and at present I think Gurdjieff placed the shock in the “wrong place” as a sort of alchemical diversion for those who would not delve into the symbol itself. I.e., without doing the work to study the symbol, one would not know why the shock is apparently in the “wrong place.”
When the notes of the c-scale are plotted on the wheel, the half-steps of the scale (E-F, B-C) begin at 120 and 315 degrees. The first mi-fa shock occurs at the 120 degree mark, and in G’s illustration of where the second shock “should be”, he shows it at this position of 315 degrees.
Where it “should be”
Where it “shouldn’t be”
G says this about the placement of the second shock (ISOTM p.291):
There's definitely a clue in the fact that G’s implied “correct” place for the second shock coincides with the second half-step of the scale. In ISOTM, G also gives his ratios between the frequencies of the notes do-re-mi-fa-sol-la-si-do, where he explains the nature or mathematical position of the second “hidden” shock - I’ll revisit that after touching on the music/color wheel aspect.
The Music/Color Wheel
The music/color wheel is based on the Newtonian color wheel, and constructed in such a way that one can find the dominant and sub-dominant complements (4ths, 5ths) and other harmonics of a scale at specific points on the circle by shifting the tonic to the top position. If you haven’t, I highly recommend reading Reginald Brooks’ paper The Geometry of Music, Art and Structure ... Linking Science, Art and Esthetics - (_http://www.brooksdesign-ps.net/Reginald_Brooks/Code/Html/Gomas/gomas09.htm).
Brooks writes about a correlation between the ratios of the frequencies of the musical notes to the wavelengths of the colors. The colors themselves can also be shifted to find complementary (neutral) colors at the same points of the musical resonant harmonics.
Also worth noting, in Brooks’ calculations, he includes three different tuning systems: Equal Temperament, Just Intonation, and Geometric. The frequencies of each of these tunings fall within a certain range of each note when plotted on the circle. So it's not like 240 degrees of rotation is exactly x hertz, it changes slightly depending on the tuning. This caused me a lot of trouble at first, when I was trying really hard to make the A-432hz tuning fit onto the circle, and F and A were falling about 8 degrees off. I think the overall point is that the ratios of all three tuning systems apply closely enough for horseshoes to make an interesting argument that the ISL ratios have a valid relationship to the frequencies.
These are the ratios of each note to the tonic (1) resulting from the ISL:
Regarding G’s ratios of the notes in the do-re-mi scale (that I mentioned earlier), this is what he gives in ISOTM, p.125:
And this is how he explains the semitones that occur in the scale at “fa” and “si” :
I can’t help but notice that the discrepancy between the ISL ratios and G’s ratios occurs at the point of the first shock on the octave. The ISL wheel states that F ("fa" musically) is 11/8, while G states that it's 4/3. The difference is very slight, as 11/8=33/24 and 4/3=32/24, but it's there nonetheless.
And interestingly, what should be a second discrepancy between their ratios does not exist, much like the “hidden” second shock which is in the “wrong place.”
This quote seems to imply further the deep connections between the enneagram, the law of octaves, and the unequal 8-part music/color wheel (ISOTM, p.124):
With that in mind, I began to see some other interesting similarities.
Densities
The concept of 7 densities appears to fit symbolically into the sections of the wheel. Each of their “natures” seems to be reflected in Gurdjieff’s different levels of creation, as well as reflecting the cyclical nature of reality, or the “Grand Cycle.”
There is one correlation that I find very interesting. When considering reincarnation, or alternatively stated: 3rd density death, 5th density contemplation, 3rd density birth, etc., Gurdjieff’s explanation of the the gap between mi and fa, contains some interesting points. ISOTM p. 291:
When looking at the circle, one might place 5th Density directly on the 5th note, G, which lies between fa and sol. So, paraphrased, fa (3rd density death) acquires the property of sol (5th density), to accumulate the energy to pass into the note mi (3rd density birth). This is just my own interpretation of how densities may fit onto the circle and tie in with G’s explanations of the shocks and passages.
Alchemical Steps
The 7 steps of Alchemy and their associated metals and symbols also seem to tie into the progression of the enneagram, the musical scale, and the densities themselves. When looking closely at the symbols of the alchemical steps and their components (shown in the legend), one can see that the concepts match up with the concepts or nature of each density. I tried to put that as succinctly as possible into the image itself, so I’ll spare the long-winded explanation.
The Ketogenic Diet
This is explained in a side note on the image, I just think it's interesting that while ketones are the ideal source of fuel for the body, their basic chemical structure reflects the positions of the 3 "Do's" with "The Absolute" at the top.
Eiriu Eolas
This is also explained in a side note - interesting that the in-6, rest-3, out-9 count of the breathing program also coincides with the positions of the 3 "Do's", and their numbers on the enneagram; as well as the Vagus nerve connecting the brain and the gut - symbolically connecting octave 3 (impressions) to octave 1 (food) through octave 2 (breath). Also interesting but perhaps a bit of a stretch, is that the other counts of EE, 12 and 30, are factors of 360...
The Visible Spectrum and Our Reality
This is just one other correlation that jumped out at me. While reading John Keel’s Operation Trojan Horse, I came across this about UFOs on p. 62:
According to Brooks’ work with frequency ratios, C and Red exist on the same point of the circle because of the relationships of their frequencies to each other, in hertz and in nanometers. I find this color relationship with Keel’s UFO entry and departure fields quite interesting, as if the “UFOnauts” are utilizing the law of octaves to pass in and out of our reality.
There are so many other relationships that can be drawn from the enneagram alone, not to mention when we begin to combine it with other symbols and systems and see their similarities. For me to go on with examples would be long-winded and superfluous.
This illustration is just my own study that resulted in something interesting that I wanted to share here… As I said, I do not think I fully understand the actual technical details of Gurdjieff’s enneagram and the cosmic law of octaves quite yet, but it has been a mind-expanding study and I hope to learn more.
I can also say it's been fascinating during this process to see so clearly that the work of the Chateau crew, of the School, is a direct manifestation of G's three levels of food - Diet, Breathing, and Study. :)
Edit: wrong reference to "mi-fa" corrected
