Why 7

[RflctnOfU]

whitecoast~ the numbers themselves are relatively arbitrary, since we're looking at a specific octave in the range of 24 vibrations to 48 vibrations (it could be anything, but these values allow us to look at the intervals in terms of WHOLE number values).

DO - increase of +0 - 24 vibrations
RE - increase of +1/8 - 27
MI - +1/4 - 30 (that is, +6 on the tonic DO of 24)

and so on; fa +1/3, sol +1/2, la +2/3, ti +7/8, do +1 ... or you could look at it in terms of re +9/8, mi +5/4, etc.

rflctnofu~ I'm fairly familiar with Smith's work and have even dusted my copy off from storage. While I appreciate his contributions I certain do not swallow it whole. Perhaps you can help me digest something which I cannot seem to wrap my head around in regard to the "cosmic rumple." The whole foundation of his house is built upon the Creation as being a lengthening of one stopinder and a shortening of another (verily, Beelzebub says as much). He then illustrates how by doing this (moving the note FA from 3/7 to 1/3), it creates a "rumple" in the fabric of space which then causes the notes RE and MI (1/7 and 2/7) to displace to 1/8 and 1/4. The actual geometry of this "rumple" is, of course, drawn in such a way that it conforms to his theory, but what exactly dictates that it would "rumple" in such a way? As you say this topic is a minefield, so let's take our steps very carefully.

I think that a grain of salt must be applied to the illustration of the "rumple". My opinion is that this presentation is symbolic, and not to be understood in a literal sense. The 'Holy Sun Absolute' can be viewed as a 'region' of infinite vibration/no vibration, or the 7th density - unity of all - a geometric point, if you will. The rumple, as it were, is a separation of the no vibration from the infinite vibration (while paradoxically still remaining unified), or a geometric point expanding into a circle while simultaneously maintaining itself as the center, with the entire spectrum of vibration 'all to nothing' resulting. 'Emanation of the Holy Sun Absolute'. It is this 'created', in potential, lower energy density (any area within the circle) from which physical matter crystallizes. Thus the "rumple". Does this make sense?

I have really struggled putting my thoughts on this matter into words, and doing so has clarified some of these concepts for me.

For what it is worth, I agree with you in that I don't necessarily swallow the whole banana. However I am quite impressed by what was derived (in reality) from the analysis of scales within scales - RNA, DNA, periodic table, Etc...

Kris

 

[Martfotai]

I do believe, however, that Smith does take the illustration literally, as it's his explanation for the ensuing mathematical placement of notes MI and RE. In the exercise he gives at the end of the chapter (with the elastic band) he says that (and I apologize to those that do not have this book in hand -- also, the following emphasis in bold is mine) "if you push the top end of the paper strip down to the force line at (1/3) 56, you will produce a close facsimile of the cosmic rumple. It identifies that the resulting new positions of MI and RE are also in perfect alignment with the diatonic scale, by virtue of a perpendicular line drawn back to the plane of the poster board."

My sense is that there is some clever, but not intentional, slight-of-hand at work. The rumple caused by this displacement could really take any number of possible forms, changing the perpendicular placement of these notes relative to the 'plane' of the original autoegocratic octave. It's certainly convenient and it allows him to advance to further theories (which again, I appreciate) but considering this is the foundation upon which the rest of the book is built, I have to preserve my disbelief until it is absolutely clear. There may indeed be something very significant here in this rumple, as to the nature of the properties of etherokrilno.

[quote author=RflctnOfU]I have really struggled putting my thoughts on this matter into words, and doing so has clarified some of these concepts for me.[/quote]

I agree, it has been the same for me. I appreciate the dialogue and am glad we can explore these ideas together.

[quote author=RflctnOfU]For what it is worth, I agree with you in that I don't necessarily swallow the whole banana. However I am quite impressed by what was derived (in reality) from the analysis of scales within scales - RNA, DNA, periodic table, Etc...
[/quote]

Yes, it's a valuable contribution. The danger comes when we take another's word for the Truth without verifying it for ourselves. For instance, there are many roads that lead to Rome, and my work for the last five years has been on the purely mathematical interpretation of the enneagram and the Laws. Here's an example.

We are familiar enough with the repeating decimal of .142857 and it's permutations of sevenths. We are also told that this is a representation of the Law of Octaves, represented mathematically, and that octaves are inherently doubling and halving of vibrations. Can we find this doubling and halving within this numeric representation. Indeed we can.

For all intents and purposes this repeating series seems to consist of 6 numbers; 1, 4, 2, 8, 5 and 7. Upon closer inspection, we can break this down to an infinite additive series, where at each step we multiply by 1/50th, or .02:

.14 +
.0028 +
.000056 +
.00000112 +
.0000000224 + ...
_______________
.1428571424 ...

As you can see, the 'doubled' values (14 to 28, 28 to 56, etc) compound, so that the first 7 in the series is actually the combined value of 6 and 1. Interestingly, one must begin at 'the other end of Infinity' to successfully carry-the-1, as in our above example the last 4 is an incomplete value. I would like to draw special attention here to the value of 5/7ths, .714285, as one can begin the doubling from 7 (or rather, 7/10ths) and progress in the same way. It's interesting to me that in our enneagrams of processes, the 7th step is often where the thing in itself has become actualized, for instance, in our kitchen enneagram, 7 is where the food has been created, but not yet served.

There is another way to create this repeating series which involves the property of 3, which I think is quite relevant to our current exploration. We'll begin with 1/10th (.1) and add, at each step, a multiplication by 3/10ths (or .3):

.1 +
.03 +
.009 +
.0027 +
.00081 +
.000243 +
.0000729 +
.00002187 +
.000006561 +
.0000019683 +
.00000059049 +
.000000177147 + ...
_________________
.142857066937 ...

This is really just the tip of the iceberg! I couldn't begin to post all my work on this matter but suffice it to say, the musical interpretation is but one way to see the Laws. In ISOTM G says:

The principle of dividing into eight unequal parts the period, in which the vibrations are doubled, is based upon the observation of the non-uniform increase of vibrations in the entire octave, and separate 'steps' of the octave show acceleration and retardation at different moments of its development.

In the guise of this formula ideas of the octave have been handed down from teacher to pupil, from one school to another. In very remote times one of these schools found that it was possible to apply this formula to music. In this way was obtained the seven-tone musical scale which was known in the most distant antiquity, then forgotten, and then discovered or 'found' again.

The seven-tone scale is the formula of a cosmic law which was worked out by ancient schools and applied to music.

 

[MusicMan]

It would be interesting to see how you apply these rules to the current musical scale, say on the piano, with its 88 keys consisting of eight octaves.
Each Octave consists of 13 semitones (the 13th being the double of the first, and the beginning of the next octave).
Each semitone is separated from the previous one by a factor of the twelfth root of two, which (from memory) is 1.05496. These make up all the black and white notes.

If you only use the white notes then you have the seven notes of the Octave which you speak of.
As you said, it's a minefield.
And this is using the middle (C) semitone set by convention at 440Hz.

 

[RflctnOfU]

It's interesting to me that in our enneagrams of processes, the 7th step is often where the thing in itself has become actualized, for instance, in our kitchen enneagram, 7 is where the food has been created, but not yet served.

. Serving the food would be the 8th step, completing the octave. The purpose for which the food was made - Do.

One thing that has bothered me, in regards to the literature about the enneagram relating to G's teaching, is what I perceive to be a misunderstanding about the 'incompleteness' of the symbol as given by G. I have yet to see the completion talked about, as I understand it. It is missing the lines 8-1, 2-5, and 4-7. This would show the inner structure of three octaves simultaneously, rather than just one, however, the symbol of seven within the enneagram would need to be understood in a three fold/layered manner. (Does this make sense?) I have to dig up my notes on this, but I remember charting out a flow of the three fold circuit, and as I remember it, there was a beautiful symmetry expressed in the 'dance' of movement - with 8-1/1-8, 2-4/4-2, and 5-7/7-5 ... This seems to 'ground', or give balance to, the process. Each of the points 3,6,9 representing a Do.

Kris

 

[Martfotai]

It's interesting to me that in our enneagrams of processes, the 7th step is often where the thing in itself has become actualized, for instance, in our kitchen enneagram, 7 is where the food has been created, but not yet served.

. Serving the food would be the 8th step, completing the octave. The purpose for which the food was made - Do.

I mean to say the food has been served (7th step), but not yet eaten (the 8th step). I would have corrected it if this forum would allow me to do so, but I suppose I need another 20ish posts for such privilege? To be honest, I was hoping to hear your thoughts on the new material I posted and not the one, very small, misstep which I took. Take a look at some other processes and I think you'll see what I mean about the 7th step containing the thing in itself.

[quote author=RflctnOfU]One thing that has bothered me, in regards to the literature about the enneagram relating to G's teaching, is what I perceive to be a misunderstanding about the 'incompleteness' of the symbol as given by G. I have yet to see the completion talked about, as I understand it. It is missing the lines 8-1, 2-5, and 4-7. This would show the inner structure of three octaves simultaneously, rather than just one, however, the symbol of seven within the enneagram would need to be understood in a three fold/layered manner. (Does this make sense?) I have to dig up my notes on this, but I remember charting out a flow of the three fold circuit, and as I remember it, there was a beautiful symmetry expressed in the 'dance' of movement - with 8-1/1-8, 2-4/4-2, and 5-7/7-5 ... This seems to 'ground', or give balance to, the process. Each of the points 3,6,9 representing a Do.[/quote]

Please dig up your notes and scan or make some images to accompany your thought -- I would appreciate your doing so and it would help clarify in terms of discussion. Here are my personal findings on the 'three octaves simultaneously' in regards to the mathematics of .142857 and it's relation to three, or thirds. Remember, we are instructed to look at a symbol from many different perspectives.

First take a progression by 1, in a straight line, repeating again after 9 (imagine the closed circle of the enneagram, following the outside circle):

123456789123456789 ...

Now, create another progression beneath this line, except shift by a value of 3, so that 4 is beneath 1, 5 beneath 2, and 6 beneath 3:

123456789123456789
456789123456789123

Repeat this one more time, again shifting by 3:

123456789123456789
456789123456789123
789123456789123456

Now take 9 (any 9!) to be our center, the axis around which we'll look at the other 8 numbers (it will be the same in every context of 9). As you can see, we have every number 1-9, centered around the 9, derived from three separate 'octaves':

567
891
234

Here's the same arrangement, colored different to illustrate the separation of triads; 147, 258 and 369:

567
891
234

Now begin with 1 and move in a clockwise fashion around the 9, 'skipping' 3 and 6. We once again find our repeating decimal of sevenths; 142857. Additionally, you can see how it's been constructed from 3 independent octaves or totalities.

 

[Martfotai]

(perhaps there is no error here, but a matter of the difficulty of communicating in text and not in person -- I presume you weren't actually nitpicking, so I apologize if that's the case. This is a good reason for the 2nd line of Work to occur in person -- it's difficult to communicate enough as it is, let alone through computers! But we make due with what we have.)

I think the above illustration may address what you were speaking about, as the 1-8 line is part of the 'green' octave, the 2-4 line part of the 'blue,' and the 5-7 part of the 'red.' Is this what you were speaking of?

 

[MusicMan]

Just to correct a typo in my previous post.
The twelfth root of two is 1.05946, being the separation in the octave of the 13 semitones, from Do to Do.

 

[RflctnOfU]

I mean to say the food has been served (7th step), but not yet eaten (the 8th step). I would have corrected it if this forum would allow me to do so, but I suppose I need another 20ish posts for such privilege? To be honest, I was hoping to hear your thoughts on the new material I posted and not the one, very small, misstep which I took. Take a look at some other processes and I think you'll see what I mean about the 7th step containing the thing in itself

My thought process on reading the material you posted went something like as follows: (honestly) "well, duh. [though not in a condescending sense]. That makes total sense that would be the case." (Marko Rodin came up with a somewhat similar idea, leading to his 'Rodin coil'. [he made use of the binary expansion sequence in place of division by 7]) My general attitude has come to expect connections/relations between three and seven.

(perhaps there is no error here, but a matter of the difficulty of communicating in text and not in person -- I presume you weren't actually nitpicking, so I apologize if that's the case. This is a good reason for the 2nd line of Work to occur in person -- it's difficult to communicate enough as it is, let alone through computers! But we make due with what we have.)

I think the above illustration may address what you were speaking about, as the 1-8 line is part of the 'green' octave, the 2-4 line part of the 'blue,' and the 5-7 part of the 'red.' Is this what you were speaking of?

Regarding bolded, thank you! Text is one dimensional, and this has frustrated me quite a bit over the years. And no worries. FWIW, I wasn't nitpicking :).

And, specifically, that isn't what I was talking about, though a possible connection between your thoughts and mine wouldn't surprise me.

Unfortunately, I don't have a scanner, and I have a stupid phone.

But, perhaps I can elucidate in part what I meant regarding 'three-fold/layered'. 0/9-3-6 each are a 'Do', and each has it's own "1-4-2-8-5-7" pattern, i.e. 3 functions as [0/9] , and it's "1-4-2-8-5-7" follows 4-7-5-2-8-1, with 6 as [0/9], the 7 pattern follows the 7-1-8-5-2-4 route. These 'circuits', as I visualize it, flow simultaneously. The symmetry between the 'circuits' paths is aesthetically pleasing, as well as suggestive regarding the process of DOing ;)

Kris

 

[Martfotai]

My thought process on reading the material you posted went something like as follows: (honestly) "well, duh. [though not in a condescending sense]. That makes total sense that would be the case." (Marko Rodin came up with a somewhat similar idea, leading to his 'Rodin coil'. [he made use of the binary expansion sequence in place of division by 7])

I've actually had the opportunity to spend some time with Marko and further develop the work he was doing. For those not familiar, the 'binary expansion sequence' that RflcnOfU is speaking about is based on a 'digitally compressed' (think of numerology; 13 = 4 because 1+3=4, or 25=7, etc) doubling sequence relative to our base 10 counting system. In much the same way that 142857 is a repeating series using the numbers excluding 0936, the doubling sequence is 124875 (same numbers, different permutations). 1 doubles to 2, 2 to 4, 4 to 8, 8 to 16 (reduces to 7), 16 to 32 (reduces to 5), and 32 to 64 (back to 1).

[quote author=RflctnOfU]My general attitude has come to expect connections/relations between three and seven.[/quote]

Well, they are certainly there! I'm personally driven by the 3rd-Obligolnian-striving, "to know ever more and more concerning the Laws of World-creation and World-maintenance." I consider it part of my being-parktdolg-duty not only to know the laws in their finest detail, but to understand the mechanics (geometric relationships expressed through time) and to reflect that in my own Being.

[quote author=RflctnOfU]Regarding bolded, thank you! Text is one dimensional, and this has frustrated me quite a bit over the years. And no worries. FWIW, I wasn't nitpicking :). [/quote]

It's amazing we can communicate at all as it is! It's infinitely more preferable to do this kind of work in person, though.

[quote author=RflctnOfU]And, specifically, that isn't what I was talking about, though a possible connection between your thoughts and mine wouldn't surprise me.

Unfortunately, I don't have a scanner, and I have a stupid phone.

But, perhaps I can elucidate in part what I meant regarding 'three-fold/layered'. 0/9-3-6 each are a 'Do', and each has it's own "1-4-2-8-5-7" pattern, i.e. 3 functions as [0/9] , and it's "1-4-2-8-5-7" follows 4-7-5-2-8-1, with 6 as [0/9], the 7 pattern follows the 7-1-8-5-2-4 route. These 'circuits', as I visualize it, flow simultaneously. The symmetry between the 'circuits' paths is aesthetically pleasing, as well as suggestive regarding the process of DOing ;)

Kris
[/quote]

I'm not so sure I see it -- will wait for pics. You are only on a phone or have a computer but no scanner? Maybe a simple paint program would help?

 

[Martfotai]

Okay, Kris, I think I know what you are talking about now (I needed my morning coffee -- still human after all ;) ).

Yes! That is certainly what's happening. Gurdjieff's digestion octaves illustrate this pretty clearly, I think (3 octaves interconnected, points 3 and 6 each serving as their own DO).

I personally find it interesting that this places the harnel-aoot (disharmonized interval between the 4th and 5th step) between 1 and 2 and 7 and 8 as well (though in higher or lower octaves respectively -- does that make sense?).

 

[RflctnOfU]

Okay, Kris, I think I know what you are talking about now (I needed my morning coffee -- still human after all ;) ).

Yes! That is certainly what's happening. Gurdjieff's digestion octaves illustrate this pretty clearly, I think (3 octaves interconnected, points 3 and 6 each serving as their own DO).

I personally find it interesting that this places the harnel-aoot (disharmonized interval between the 4th and 5th step) between 1 and 2 and 7 and 8 as well (though in higher or lower octaves respectively -- does that make sense?).

Absolutely! And (theoretically speaking) those 'other Harnel-Aoots' will affect the development of any particular octave under consideration. The trick is observing that in a practical sense

Also, another way I look at/see the flow of the octave is directly along the 7 circuit. With the central intersection (directly below 0/9) in the figure as Do, then 1-Re, 4-Mi, 2-Fa, 8-Sol, 5-La, 7-Si, then DO. My intuition tells me there is something to this, though I haven't been able to elucidate for myself that something as yet - and I could be way off base here as well.

BTW, what were your impressions of Marko as a human?

Kris

 

[Martfotai]

Interesting perspective. Here's another thing about the cross-points in the inner hexad; find the value in MOD9 (also known as digital compression or what Gurdjieff called 'theosophical addition') for each of the lines that create the cross-point. The value for the line 1 to 4 is 5 and 2 to 8 is 10; the point at which they cross we can give the sum 15, or 6. Then we take the value for the line 8 to 5 as 13 or 4, and the value of 7 to 1 as 8. Together these give the cross-point a value of 12, or 3. 7 to 1 gives 8, while 8 to 2 gives 10; together we get 18, or twice (octave) 9.

My impressions of Marko is that he was an incredibly hospitable and kind man, with strong moral values, who has a mind going warp speed and a body that can't necessarily keep up. He sees something of a higher reality which he struggles to communicate into a form of this level, and has all the inner frustration that comes with being the trailblazer for a certain area of 'fringe' yet genuine science.

 

[MusicMan]

Going back to your Enneagram posting of Dec 28th.
It would appear that you have discovered a way of creating, or solving, Sudoku puzzles.
FWIW.

 

[Martfotai]

Talk about using a spiritual dagger to hang a cooking pot! Can it be done? Yes. Should it be done ... ?

These mathematics are also being used to create over-unity 'free energy' devices. Some may say that is a high and noble goal, but not I -- I think it's missing the point. Once we have 'limitless energy' (which for those creating these devices means limitless electricity, the extraction of which from the omnipresent active element is a whole other can of worms), there will be no stopping those power-possessing 'hasnamussnian' psychopaths from implementing their agendas. In reality, the cosmos itself is already a harmonically balanced perpetual motion machine. We don't need 'limitless' energy to hook up our insane technologies to, what we need is to disconnect those technologies and return to a harmonious state with the energies and processes around us

 

[RflctnOfU]

Talk about using a spiritual dagger to hang a cooking pot! Can it be done? Yes. Should it be done ... ?

These mathematics are also being used to create over-unity 'free energy' devices. Some may say that is a high and noble goal, but not I -- I think it's missing the point. Once we have 'limitless energy' (which for those creating these devices means limitless electricity, the extraction of which from the omnipresent active element is a whole other can of worms), there will be no stopping those power-possessing 'hasnamussnian' psychopaths from implementing their agendas. In reality, the cosmos itself is already a harmonically balanced perpetual motion machine. We don't need 'limitless' energy to hook up our insane technologies to, what we need is to disconnect those technologies and return to a harmonious state with the energies and processes around us

I am, for the most part, in agreement with you.

With the caveat that 'perpetual motion' ought to be realized internally - ie Triamazikamno, and Heptaparaparshinokh function Ilnosoparnian, generating Sacred-Askokin in the process.

Kris