Podcast Series 2, Episode 23 “The Harmonic Nature of the Universe Part 3 – The Third Scale of Inner Octaves”
In this episode, we continue to explore the Harmonic Nature of the Universe, the third of a multi-part discussion that began by discovering Dualities and Oscillations, creating a third scale of inner octaves, and finally by revealing an exquisite model of the Transfer RNA Molecule – mathematically verifiable as originating from musical vibrations. This episode examines the three inner scales of an octave. The episode will discuss specific models, and thus requires access to several diagrams which can be found here.
Published July 16th, 2020
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This is a series of talks about objective consciousness, an objective universe, and an objective way to awaken.
It is primarily based on the works of George I. Gurdjieff and Russell A. Smith, and aims to cut through the swathes of subjectivity that cloud our evolution and journey through life.
Each episode in this series focuses upon a particular element of their teachings and aims to bring simple understanding to what was frequently hidden in plain sight within the various subject areas of the Fourth Way.
In our last talk, we completed part 2 of a four part discussion concerning The Harmonic Nature of the Universe. In part 1, we found the Duality. In part 2, we discovered Oscillations.
The third scale of inner octaves.
Today, in part 3, we will explore the third scale of inner octaves.
In this discussion, as in the last, diagrams will be necessary. They can be found on our website thedogteachings.com, by clicking on the link shown in the description of the podcast. So, pause, find the diagrams, print them off if you would like, and let’s begin.
It all started in episode 21, when three octaves of radiations came into existence between four fundamental points, DO, SO, MI, and RE. That is, between 1, ½, ¼, and ⅛.
The first scale, the progenitor scale, we called Scale-0. It contained one octave, an All to Nothing octave.
The All to Nothing octave had a length of 192, 192 to 0. That length allowed us to calculate the three octaves of Scale-1 at whole numbers.
We labeled the second scale, the scale created within the All to Nothing octave, Scale-1.
It contained three Musical octaves, that is, they doubled and halved.
OK. Now let’s do the third scale.
If we continue the logic – that every octave contains three octaves. Then, the three octaves in Scale-1 will create nine octaves in Scale-2.
In order to calculate Scale-2 at whole numbers, we needed to make the All to Nothing octave the octave of 1536, 1536 to 0.
So we did, and produced the diagram called, “According To Scale.”
Here is how we did it. It was actually pretty easy. We already knew how to calculate Scale-0 and Scale-1, so that was a breeze. But, Scale-2 took some thinking. To calculate Scale-2, we started with the vibrations 1536 and 1152. Those two vibrations were the top two fundamental points in Scale-1, DO and SO; and, as such, became DO’s in Scale-2, between which there was an octave.
We found the length of that octave by subtracting 1152 from 1536, which was 384. Second, we divided the length of that octave by eight, which was 48. Third, we added 48 to the value of the bottom DO of that octave, which was 1152. When we did, it gave us the value of the RE of that octave, which was 1200. That is, 1536 minus 1152 is 384, 384 divided by 8 is 48, and 48 plus 1152 is 1200. Simple.
How to calculate octaves
In Episode 6, we explained how to calculate octaves based on their length.
Here, we will share that information with you, just in case you forgot.
Any whole phenomenon can be calculated as an octave, as a “something” that runs from its allness to its nothingness, or vice versa, dividing the totality “diatonically” by the ratios: 1/8, 1/4, 1/3, 1/2, 2/3, and 7/8.
Step 1 – subtract the bottom DO from the top DO to discover the LENGTH of the octave, the totality.
Step 2 – to find Re (1/8) divide the length by 8 and add that quotient to the value of the bottom DO.
Step 3 – to find Mi (1/4) divide the length by 4 and add that quotient to the value of the bottom DO.
Step 4 – to find Fa (1/3) divide the length by 3 and add that quotient to the value of the bottom DO.
Step 5 – to find So (1/2) divide the length by 2 and add that quotient to the value of the bottom DO.
Step 6 – to find La (2/3) divide the length by 3 and multiply that quotient by 2. Then, add that product to the value of the bottom DO.
Step 7 – to find Ti (7/8) divide the length by 8 and multiply that quotient by 7. Then, add that product to the value of the bottom DO.
Note: You cannot calculate octaves using the diatonic ratios of 9/8, 5/4, 4/3, 3/2, 5/3, and 15/8 unless the octaves are musical. That is, octaves that double or half.
Since Scale-2 does not contain octaves that double or half, each octave has to be calculated as a totality, that is, as an octave whose length was segmented into ⅛, ¼, ⅓, ½, ⅔, and ⅞, and then added to the value of its bottom DO.
OK. Back to the diagram. If you are able to print it out, do so. That way, you will be able to scribble on it. Otherwise, listen attentively.
First, we want you to count the vibrations in each scale.
Let’s see, in Scale-0 there is one octave with 8 vibrations: DO 0, RE 192, MI 384, FA 512, SO 768, LA 1024, TI 1344, and DO 1536.
So, put the number 8 below Scale-0, or etch it into your mind.
Now, let’s do Scale-1.
In Scale-1 there are three octaves. So, it is logical for us to think that there are 24 vibrations, 3 times 8, right?
But, that would be wrong. Why? Because the three octaves in Scale-1 are continuous, not separate. And, as such, the two middle DO’s are shared by two octaves. Therefore, they are only counted once. Thus, Scale-1 has 22 vibrations..
OK, below Scale-1, or mentally, write 22.
Now, let’s do Scale-2.
There are nine octaves in Scale-2, three groups of three octaves. And, based on what we just learned, that would be 66 vibrations: Three groups, each with 22 vibrations. But, just to be sure, let’s count them. Yep, I got 66. How about you? Great.
So, put 66 below Scale-2.
OK. Let’s look at the fate of the notes, like we did in episode 21, when we looked at what happened to the vibrations in Scale-0. To see if the same Axioms we discovered hold true.
First, we learned – that a descending DO stays a descending DO.
Does 1536, the descending DO of Scale-1 (the first fundamental point), stay a descending DO in Scale-2?
Yee-haw, the axiom held true, check.
1440, a TI in Scale-1, does not appear in Scale-2, so we do not yet know its fate (just as we did not know the fate of the TI in Scale-0, which did not appear in Scale-1).
1280, a LA in Scale-1, becomes a FA in Scale-2, check.
1152, a SO in Scale-1 (the second fundamental point), becomes an oscillating DO in Scale-2, check.
1024, a FA in Scale-1, becomes a FA in Scale-2, check.
960, a MI in Scale-1 (the third fundamental point), also becomes an oscillating DO in Scale-2, check.
864, a Re in Scale-1 (the fourth fundamental point), becomes an ascending DO in Scale-2, check.
Now, we will see something that is very interesting.
768, the SO from Scale-0 that became an oscillating DO in Scale-1 could both ascend and descend, which was why it was called an oscillating DO. However, in Scale-2, it is not an oscillating DO. That is, in Scale-2, it no longer ascends and descends; it only descends.
Well, we previously learned that descending DO’s go on forever and ascending DO’s disappear. Therefore, DO 768, which is both a descending DO and an ascending DO, has its descending aspect go on forever and its ascending aspect disappear. Thus, it only becomes a descending DO in Scale-2.
Eureka, both axioms held true, double check.
By the way, you should note: this phenomena creates what Mr. Smith calls a pause to occur in Scale-2. A pause between the descending DO at 768 and the ascending DO at 864. A pause, which separates the 22 vibrations of the three upper octaves from the 22 vibrations of the three middle octaves, and it’s quite a big pause.
OK. Continuing with Scale-1.
720, a TI in Scale-1, does not appear in Scale-2, so it, too, we do not yet know about.
640, a LA in Scale-1, becomes a FA in Scale-2, check.
576, a SO in Scale-1, becomes an oscillating DO in Scale-2, check.
512, a FA in Scale-1, stays a FA in Scale-2, check.
480, a MI in Scale-1, becomes an oscillating DO in Scale 2, check.
432, a RE in Scale-1, becomes an ascending DO in Scale-2, check.
And, 384, an oscillating DO in Scale-1, has its descending aspect go on forever and its ascending aspect disappear; and, likewise, creates a pause between the descending DO at 384 and the ascending DO at 432. Thus, separating the 22 vibrations of the three middle octaves from the 22 vibrations of the three bottom octaves.
In the bottom octave, 384 to 192, the same things hold true (I will spare you all the checks): TI we do not yet know about. LA becomes a FA. SO becomes an oscillating DO. FA stays a FA. MI becomes an oscillating DO. RE becomes an ascending DO. And, the bottom DO disappears.
We now have three packets of 22 vibrations.
The bottom octave has a set of three inner octaves with 22 vibrations, followed by a pause; the middle octave has a set of three inner octaves with 22 vibrations also followed by a pause; and, the top octave has its own set of 22 vibrations.
Again, three sets of 22 vibrations – equal a total of 66 vibrations.
OK. Now that we know how to create the diagram, “According To Scale,” which was pretty easy once we learned how to calculate a totality, let’s study it.
We will begin by counting the total number of different vibrations in the diagram. When we do, we find there are 71 vibrations.
Even though there were 96 vibrations in all three scales (8+22+66), there are only 71 different vibrations in the diagram (8+16+47), which is easier to visualize if we start with Scale-2 and work backwards (66+4+1). That is, there are only 4 vibrations in Scale-1 that are not in Scale-2 (the three TI’s and the bottom DO), and only 1 vibration in Scale-0 that is also not in Scale-2 (the bottom DO).
In fact, the vibration of all bottom DO’s are the only vibrations that will never appear in any other octave, or any other scale. Remember the Axiom, “Bottom DO’s disappear?” Well, there you go.
OK. I guess I will tell you another Axiom, Axiom #8. It has to do with the fate of the vibrations at TI.
We previously learned that 1344, the TI in Scale-0, did not appear in Scale-1. However, we can now see that it reappeared as a SO in Scale-2. That is, the vibration at TI, skips a scale then reappears at the note SO.
Axiom #8, “TI skips a scale and becomes a SO.”
After which, the vibration at SO becomes an oscillating DO.
Let’s talk a bit more about what that means.
Put DO 1344 to the right of SO 1344, as that is what SO 1344 will become in Scale-3. You should also put the label Scale-3 at the top of the diagram.
OK. As we said, descending DO’s, or top DO’s, go on forever, so the top DO will always be at the vibration of 1536: Scale-0 has its top DO at 1536, Scale-1 has its top DO at 1536, and Scale-2 has it top DO at 1536. Therefore, Scale-3 will also have its top DO at 1536. Thus, you can put DO 1536 at the top of Scale-3.
We have now identified two DO’s in Scale-3, top DO 1536 and DO 1344.
Between those two DO’s, that is between 1536 and 1344, there is going to be an octave.
Now, if an octave appears between 1536 and 1344 in Scale-3, it is also going to appear between 1536 and 1344 in Scale-0; and, anywhere else we find both 1536 and 1344.
Wow, that means, there is going to be an octave between the notes DO and TI in Scale-0.
We previously learned that our Endlessness shortened the last stopinder (TI-DO), and now we know why He did. He shortened the last stopinder in order to create an octave between TI and DO. Axiom #9, “There is always an octave between TI and DO.”
What does it do?
OK. Find DO 768 in Scale-1.
Below the DO 768 in Scale-1, find TI 720, also in Scale-1.
Since we know that there is always an octave between TI and DO, there is going to be an octave between TI 720 and DO 768 as well.
That octave has a length of 48, 768 minus 720.
Now notice: that the interval between DO 768 and the RE 864 above, has a length of 96, 864 minus 768.
See where we are going?
Do you remember in our talks about the octave of Middle C, which had a length of 256 vibrations (DO 256 to DO 512), how, when Middle C doubled, it created the octave of 512, High C, (DO 512 to DO 1024)? If you do, it will make this much easier.
If the octave of Middle C, 256, is naturally followed by the octave of High C, 512, what do you think is going to naturally follow the octave of 48?
The octave of 96.
And, since the TI-DO octave is followed by an octave that is twice as big, which is precisely the size of the interval between DO and RE, that twice as big octave is going to span the interval between DO and RE. Double eureka!
I repeat. The doubling of the octave between TI and DO, creates an octave between DO and RE.
We previously identified the interval between DO 768 and RE 864 as a pause, which occurred between two sets of 22 vibrations. Now, we see that the pause is going to be spanned by an octave.
Mr. Smith called the pause, the no man’s land, because there was no structure within it.
And, without a structure, there is no way of traversing it.
Fortunately, the TI-DO interval becomes an octave, doubles, and creates one…. Thus, giving structure to the pause.
The same thing happened at the lower pause.
Thus, a continuous flow of ascension is established within the three scales.
OK. Back to our investigations. So far, we have three scales, thirteen octaves, 71 vibrations, and 96 notes.
However, if we further investigate the 71 vibrations, we will see that, actually, there are only 80 notes.
Do you see that? No.
OK, I will explain. I will start with the top vibration, 1536.
There are three DO’s at 1536: the descending DO of Scale-0, the descending DO of Scale-1, and the descending DO of Scale-2. And, if we calculate Scale-3, its descending DO will be there as well.
And, if we calculated a million scales, we then would have a million descending DO’s there.
Question: Would we really have a million descending DO’s there, or would we have just one descending DO there, repeated a million times?
If you are not sure, here is a hint.
How many Gods are there?
OK. If God was 1536, and if we had a million scales, how many Gods would we have?
I got it, just one.
Correct! So, if we now asked, “How many DO’s are at 1536?” You would have to answer, “Just one.”
The best way to figure out how many notes are at a specific vibration is to count every note except the DO’s. You do not count the DO’s.
Well, the DO’s came from a previous scale. Count them back there, when they were notes in that previous scale, not when they become a DO.
In fact, when we counted the initial DO, we were not counting it as the DO of Scale-0. We were actually counting it as a note, which came from a previous scale, which became the DO of Scale-0.
We will explore the previous scale in a future podcast. But for now, back to the present.
So, only count notes, not DO’s. That is, count all notes that were calculated, but do not count the DO’s that came from a previous scale.
Based on this knowledge it should be easy for us to tell if a vibration contains more than one note.
DO’s, SO’s, MI’s, and RE’s, by virtue of being fundamental points, become DO’s in the next scale, and when they become DO’s they are not counted. Whereas, LA’s and FA’s, continue to be calculated as FA’s in the next scale, and thus, are counted.
This means that basically all vibrations contain only one note, except for 1280 which has two notes (LA and FA), 1024 which has three notes (LA, FA, and FA), 640 which has two notes (LA and FA), 512 which has three notes (FA, FA, and FA), 320 which has two notes (LA and FA), and 256 which has two notes (FA and FA).
In addition, we learned that 1344, a TI in scale-0, became a SO in Scale-2, after which, it becomes a DO in Scale-3. Thus, the vibration 1344, also contains two notes (TI and SO)… as will all TI’s, which will skip a scale and become SO’s.
Note: Since LA’s become FA’s and FA’s go on forever, as we add new scales, we will have additional FA’s being added to our count. However, since TI’s become SO’s, then SO’s become DO, and DO’s continue to be DO’s forever, the notes on that vibration will only be counted when they are TI’s and SO’s.
OK, with eight additional FA’s, and the one additional SO, we now have nine additional notes on our 71 vibrations, bringing the count to 80 notes.
Which changes our previous statement of three scales, thirteen octaves, 71 vibrations, and 96 notes, to three scales, thirteen octaves, 71 vibrations, and 80 notes
Or, as Mr. Smith often says, the vibrations and notes in the three scales of an octave are like having 71 bicycles in a race that contains 80 riders, because there are 5 bicycles built for two, and 2 bicycles built for three.
How to define what a “thing” is
We discovered previously that in order to define something, we needed to know what came before it and what came after it. Like in our study of Middle C. Before Middle C was Low C, and after Middle C was High C.
We will add one more thing to that: To define something, we need to know what came before it and what came after it, and we also need to know what its parts are and what it is a part of.
For example: To define any genus of a plant or animal, botanists and zoologists need to know what it evolved from and what it evolved into, which is how they classify things. Additionally, they also classify them by looking at several smaller scales, like claws, talons, etc., and then at the larger scales, of family, order, class, phylum, or the kingdom to which the thing belongs.
Does that make sense?
Let’s make a model that uses this idea. Print the diagram that has the octave of 384 on it, 768 to 384.
Over to the left of that octave, from the top down, write the word A-U-T-O. Take up the whole area from 768 to 384 to show that the octave of the A-U-T-O spans the entire octave of 384.
Now, imagine that some alien visited our planet, and we were trying to explain to him what an automobile was. To do that effectively, we would need to explain what came before the automobile, and what came after it.
Let’s see. Let’s say the bicycle came before the automobile and the airplane came after it.
We will now place those three octaves on the diagram that is below the octave of 384.
The octave of 192 will be the bicycle, the octave of 384 will be the automobile, and the octave of 768 will be the airplane.
Label the octave of 384 (A-U-T-O), label the octave of 192 (B-I-K-E), and label the octave of 768 (P-L-A-N-E).
By explaining what came before the automobile and what came after it, we have a better chance of helping the alien understand what an automobile is.
Now, in the diagram that has the labels, Larger, Original, and Smaller, we will go further still. Again, put the labels P-L-A-N-E, A-U-T-O, and B-I-K-E between the four black arrows in that diagram, to identify The Octave Beyond, The Octave, and The Octave Before. Make sure the labels are large enough to span the entire area between the arrows.
To further explain what a bicycle, an automobile, and an airplane is, we will also need to explain what their parts are.
In the three inner octaves of the bike, we will be explaining bolts and chains and seats and steering handles and wheels and pedals, etc. All the parts of the bike.
Do you see that?
Then, in the three inner octaves of the auto, we would pretty much be explaining the same parts that we found on a bike, since the parts of the auto evolved from the parts of the bike. That is, the auto would also have bolts and chains and seats and steering things and wheels and pedals, etc.
However, the auto would have something the bike does not have. It would have a motor. Note: If something on our automobile broke, we might be able to take a part off our bike and fix our automobile, because the evolution of the parts of the bike, became the parts of the automobile… except for the motor.
Next, we would need to explain the parts of a plane, which would pretty much be like the parts of the auto, because a plane has bolts and chains and seats and steering things and wheels and pedals and a motor, too. And, it has something that the automobile does not have. It has wings.
Again, if something on our plane broke, we might be able to take a part off our auto and fix our plane. In fact, in World War II, the field mechanics often cannibalized jeeps in order to keep the planes flying.
OK. We can now see the evolution of the parts of the bike, the parts of auto, and the parts of the plane. Fun note: The Wright Brothers, who made, and flew, the first airplane, owned a bicycle shop. Go figure.
Does this make sense so far?
OK. After answering what came before the auto and what came after it, as well as, answering what their parts are, we can now ask a bigger question. “What are the bike, the auto, and the plane all a part of? That is, what is the LARGER scale?”
That’s easy, the LARGER scale is the transportation system.
Write that on the left-hand side of the diagram, in great big letters, all the way down the page, T-R-A-N-S-P-O-R-T-A-T-I-O-N S-Y-S-T-E-M.
You and I understand that the bike, the auto, and the plane are a part of a much bigger structure called, “The Transportation System,” but our alien friend may not. And, if we did not explain to him what the transportation system was, he might think that the bike, the auto, and the plane were just some sort of fancy chairs. But. they are not. They are a part of something much bigger than fancy chairs… called, “The Transportation System.”
And, with that added knowledge, our alien might be able to actually understand what an automobile is.
Additionally, we should point out that you cannot ride the transportation system.
That is, if you want to go somewhere, you have to ride a bicycle, an automobile, or an airplane. So, although we have a LARGER scale called the transportation system, you cannot ride it anywhere.
Another good model would be man. We can define what a man is, and then ask, “What is he a part of?” Answer: Humanity. However, humanity does not build things… women and men do.
OK, back to the diagram. Initially, we do not know the mathematics of the LARGER scale, but we have enough knowledge of octaves to figure it out.
For instance, we know that the four fundamental points, DO, SO, MI, and RE, always become DO’s in the next scale. So, perhaps, that will work in reverse as well.
Since there are four DO’s in the ORIGINAL scale, a DO at 1536, a DO at 768, a DO at 384, and a DO at 192, perhaps those DO’s will trace back to the notes DO, SO, MI, and RE of that LARGER scale, which they do, so we placed DO, SO, MI and RE on the diagram.
Also, since we know that LA’s become FA’s… and that FA’s stay FA’s, we should be able to trace them back as well. One FA will trace back to the LA of that LARGER scale, and another FA back to the FA of that LARGER scale, which they also do, so we placed LA and FA on the diagram, and a SO in the Smaller scale also traced back to the TI of that LARGER scale.
By doing this, we are able to see the mathematics of that LARGER scale beginning to emerge.
The only mathematics we could not trace back is to the bottom DO, but with our knowledge of octaves that should be easy to figure out.
We know that the first two intervals in an octave are always the same size, like in the octave of 24 (3–3-2-4-4-5-3), both 3’s. We can, therefore, subtract RE 192 from MI 384 to discover the size of the second interval, which will also be the size of the first interval, and then subtract that amount from RE 192 to reveal the value of the bottom DO.
The bottom DO of that LARGER scale is zero.
Wow, that is convenient.
The transportation system goes from some ultimate movement down to no movement at all… to nothing… to zero.
We just found the All to Nothing octave.
OK. Now that we have peddled, driven, and flown… it’s time for the break.
In our next talk, we will take the harmonic oscillation that we discovered in our last talk, and place it in the 71 vibrations that we uncovered today.
When we do, we will find a remarkable mathematical structure that explains the first molecule of life, the Transfer RNA molecule.
Heck, we may even throw in DNA.
Thank you for listening.
If you would like to know more about the subjects and exercises we’ve been covering in these talks, including the book and guide that underpins it all, which is available for PDF download, and also gives you access to an ultimate exercise that is able to objectively wake people up, you can find us at the website thedogteachings.com.
That’s T H E D O G teachings DOT COM.
There, you can also obtain Mr. Smith’s diagrams of the structure, listen to other talks, as well as learn all the mathematics that supports them, and much much more.
And, you will have real time access to the materials we discuss.
Goodbye until next time.