Podcast Series 2, Episode 29: There is an Octave in Every Interval

Piano - There is an octave in every interval

There is an Octave in Every Interval

In this episode, we show how an octave exists between every note in every octave, and discuss the aspects and ramifications of seven notes within every interval, by looking at the evolutionary existence of plants, insects and fish. This podcast is supported by diagrams, which can be found here on our website thedogteachings.com.

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Associated Diagrams


Octaves that Share Vibrations with the 6p Octave

The Major Oscillations of Life

The Major Oscillations of Life


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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 simplify and explain what Gurdjieff actually meant within the various subject areas of the Fourth Way. All material discussed is drawn from Russell Smith’s book, Gurdjieff: Cosmic Secrets, The Teaching Guide.

In this discussion, diagrams will be necessary, and these can be viewed or downloaded on our website thedogteachings.com, by clicking on the link shown in the description of this podcast. So, pause, find the diagrams, and let’s begin.

Today, we will be discovering that “There is an Octave in Every Interval.”

In our last talk, when we discovered the Three Major Oscillations of Life, we saw that the lower Major oscillation connects the Duplicating Principal to the Moving Center through the Instinctive Center. 

Then, there was a gap. 

The middle Major oscillation connects the Emotional Center to the Higher Emotional Center through the Intellectual Center (wow, that is convenient; the middle oscillation connects lower emotion to higher emotion). 

And, the upper Major oscillation connects the Intellectual Center to the Higher Mental Center (wow, that is also convenient; the upper oscillation connects lower intelligence to higher intelligence). 

I guess we could call them: the Duplicating oscillation, the Emotional oscillation, and the Intellectual oscillation.

In addition, we saw how the three Major oscillations created two gaps; and, a Harnel-Aoot, a time of tension in the fabric of life.

The time of tension begins when a man awakens and acquires Steward. 

Why Steward? 

Well, Steward represents the Higher Emotional Center; and, the Higher Emotional Center is made up of lower centers. Therein lies the tension. 

The lower centers’ functions compete with the Higher Center’s function. That is, the lower centers are still lower centers. And, as such, they want to do what lower centers do. 

The tension occurs, because if the lower centers attain the function of the Higher Emotional Center, that is, the function of conscience, they will still be inclined to function contrary to conscience.

So, when a person acquires Steward, they must avoid serving their lower centers; or as Gurdjieff put it, “Avoid soiling the purity of their brain.”

However, most people will never wake up; so, they need not worry too much about the tension. That is, most people will spend their entire lives in their lower story, in the lower oscillation, and will never get past the gap. 

They are trapped in the lower oscillation, the Duplicating oscillation, as such, they are just automatons; animated by instinctive pleasures, and by the joys of movement. And, as Gurdjieff said, “Will die like dogs.” 

However, we do not want to be like most men. So, we need to find a way to get out of the lower story and get past the gap. 

Fortunately, with the knowledge of the laws of World-creation and World-maintenance and with the April Fools exercise, which can be found on our website thedogteachings.com, one can be taken past the gap and reach the upper story. 

When they do, their lower centers will move into a higher place, and they will awaken.

That is the aim, to put their lower centers into a higher place and awaken.

To create a double arrow of attention. One attention that sees what they are doing; and, another attention that sees themselves doing it. That is, they are writing their name, and watching themselves write their name. 

Their inner world is silent; and, their random thoughts stop. 

Wow, what an incredible moment. They will be empty. They will be at peace. They will be at ease. They will be present. They will be a witness of themselves. They will be here. They will not be tomorrow. They will not be yesterday. They will not be riddled by thoughts of this or that. Instead, they will be here and now. 

And, as such, They will be able to legitimately move towards the Higher Mental Center, and become Human Beings… real Human Beings. 

But, first, they must awaken; they must have a “virgin birth;” they must acquire the Higher Emotional Center… and become good householders. 

Then, they will be able to acquire the Higher Mental Center, and the functions of reason and impartiality.

But, for now, let’s get back to the crux of this talk: That there is an octave between every note.

Gurdjieff once said that at every note of an octave there was a whole octave. That is, out of one, came seven, came forty-nine.

Remember the diagram on page 136 of In Search of the Miraculous by P. D. Ouspensky? If not, it can be found by clicking on the diagrams relating to this podcast.

When Mr. Smith read what Gurdjieff said, and then saw Ouspensky’s diagram, his response was, “Well, Gurdjieff’s instructions were, ‘Do not believe anything.’ Thus, I am not going to believe either Gurdjieff or Ouspensky, unless I, myself, can find and verify there is an octave at every note.” 

So he tried. 

In the last podcast we saw how he found seven notes from different octaves at every vibration. However, the problem was justifying how there could be seven notes from the same octave at every vibration; and, then, seven more after that, ad infinitum, etc. That made no sense. To have an octave, within an octave, that has seven notes, you need to have a span, not a point.

So, Mr. Smith decided that Gurdjieff must have meant that there was an octave in every interval; and, then, an octave in every interval of those octaves, etc., which does make sense.

Furthermore, in episode 5, we learned that things existed in the spaces, like 8th grade, high school, or being a teenager, and that the notes were only there to designate a change of space, like the day we became a teenager, which also made sense.

So, Mr. Smith began looking for octaves in the spaces between the notes, to see if he could find an octave in every interval.

Here is what he discovered.

He began with the RE-MI interval. Let’s see if we can follow his reasoning. 

Remember in episode 11, how the four fundamental points, DO, SO, MI, and RE, occurred at natural positions of halving, and thereby created three octaves of radiations? If you do, then you will understand, since MI and RE are two of those fundamental points, that a natural octave occurs between them. Eureka, Mr. Smith found one. He was able to verify that between MI and RE there is indeed an octave… no questions asked.

Then, he tackled the TI-DO interval. 

Do you remember, in episode 23, how we discovered that the TI-DO interval became an octave, that is, how TI skipped a scale, became a SO, then a DO, and how between that DO and the DO above, an octave was created? If you do, then, you can check a second interval off the list. 

That’s two down, five to go.

OK. So far, we found an octave in two of the intervals. One between RE and MI, and the other between TI and DO. 

Those octaves were fairly easy to discover; but, how the heck are we going to discover octaves in the other intervals?

To answer that question, we will once again return to the diagram of the Octaves that Share Vibrations with the 6p Octave, which was introduced in episode 28. 

The diagram showed us all of the octaves in the Universe that contained one or more of the same vibrations as the 6p octave. And, as such, allowed us to discover that two of those octaves also shared their Major oscillation with the 6p octave as well. 

Now we will use the diagram to see if any of the intervals of those octaves also align with the intervals of the 6p octave. If they do, and if those intervals contain an octave, then, that octave will also be experienced by the 6p octave. 

Previously we placed the math of the octave of 24 on the left side of the diagram. So, let’s place it here as well: 24, 27, 30, 32, 36, 40, 45, and 48. 

Up to this point, we found two intervals, RE-MI and TI-DO, that definitely contain an octave. 

Since that is true, what about the RE-MI interval of the 8p octave?

Does the RE-MI interval of the 8p octave also contain an octave? Yes, of course it does, all RE-MI intervals contain an octave.

OK, if there is an octave between the RE and MI interval of the 8p octave, between thirty-six and forty vibrations, what do you think is going to occur between SO and LA of the 6p octave which is also at thirty-six and forty vibrations?

There is going to be an octave there as well.


The octave created between the RE and MI of the 8p octave, also exists between the SO and LA of the 6p octave! 

It is an amazing thing. 

If an octave is created between thirty-six and forty vibrations, then every octave that has thirty-six and forty vibrations is going to have that octave. 

Another way to understand this is: If you were on a journey and came to a gorge, and in order to get across that gorge, you built a bridge; and, if someone else was on a journey, and came to the same gorge, at the same spot, they could use the bridge that you built to also get across that gorge. 

Awesome, we can now check a third interval off our list. 

Three down, four to go.

OK. We also discovered there was an octave in the TI-DO interval; and, therefore, in all TI-DO intervals. 

What about the TI-DO interval of the 8p octave?

Would the TI-DO interval of the 8p octave also contain an octave? Yes, of course it would, all TI-DO intervals contain an octave.

Thus, if there is an octave in the TI-DO interval of the 8p octave, there must also be an octave in the MI-FA interval of the 6p octave. Again, if an octave is created between thirty and thirty-two vibrations in the 8p octave, every octave that has thirty and thirty-two vibrations is going to have that octave. 

Yay, another bridge! 

We can now check a fourth interval off our list. 

Four down, three to go.

OK. So far, we have found an octave in four of the intervals. The only ones left are the DO-RE interval, the FA-SO interval , and the LA-TI interval. However, since those intervals do not align with someone else’s RE-MI or TI-DO, how are we going to find octaves in those intervals?

Well, do you remember Mr. Gurdjieff’s explanation of why the last stopinder was shortened, which we discussed in episode 10? It was shortened, “for the purpose of facilitating the commencement of a new cycle of its completing process.” 

If we couple that idea, with the knowledge that when the TI-DO interval became an octave it earned the right to double, like all octaves do; and, when it did, it created an octave in the DO-RE interval that followed, thus, sparking the commencement of a new cycle of its completing process. That is, the octave created in the TI-DO interval, between 45 and 48 vibrations, an octave with a length of 3, when it doubles, creates an octave with a length of 6, between 48 and 54 vibrations, which is precisely the span of the DO-RE interval above. 

Thus, there is definitely an octave in the DO-RE interval as well.


Five down, two to go.

OK. If there is definitely an octave in the DO-RE interval of the 6p octave, then, there is definitely an octave in the DO-RE interval of every octave. Which means, since the 8p octave has an octave in its DO-RE interval, between thirty-two and thirty-six vibrations, that the 6p octave also has an octave in its FA-SO interval, which is likewise at thirty-two and thirty-six vibrations.

Double eureka!

Oh my God!

That is six intervals that all contain octaves! 

We just need one more!

Well, look at that… the 7p octave’s DO-RE interval coincides with the 6p octave’s LA-TI interval; and, since the 7p octave’s DO-RE interval contains an octave, so does the 6p octave’s LA-TI interval. 

We have done it! 

We have proved that there is an octave in every interval.

We did not just believe there was an octave in every interval, because someone told us that there was. We looked for them; and, we found them. 

We found them, in the law-conformable mathematics of the octave, in the intervals of RE-MI, TI-DO, and DO-RE. And, since they were there, they were also in the corresponding intervals MI-FA, FA-SO, SO-LA, and LA-TI of other octaves.

Axiom #12, “There is an octave in every interval.” 

I repeat… “There is an octave in every interval!”


That is of tremendous importance. Why? Because, with this knowledge, we will be able to understand the octave of organic life… and, the inner octaves of organic life.

To begin, let’s start with this assertion, “Every note has unique characteristics.” 

Mr. Smith calls the characteristics, “The aspects of the note.” 

Since every note has unique aspects, we can use those aspects to define the octaves that occur in every interval. 

OK. First we need to ask, “What are the aspects of the notes?” 

What are they? 

RE has the aspects of a plant. Things at RE, usually stay in one place. 

MI has the aspects of movement. Things at MI are like creeping vines, crickets, or traveling salesmen. 

FA has emotional aspects. Things at FA are like mothers, who take care of their young, raise them, and protect them. 

SO has intellectual aspects. Things at SO, can remember things; and, will practice smart sex. 

LA has social aspects. Things at LA, group; live in packs, or herds, and take care of each other. 

Finally, TI has the aspects of reason. Things at TI, comprehend, infer, or think in an orderly or rational way; and, thus, are able to calculate, deduce, and figure things out.

OK, those are the basic aspects of the notes. 

Every note, in every octave, will reflect those aspects.

Now, let’s apply this knowledge to the notes of the octaves that we found in every interval. 

We will start with the interval between DO and RE. The DO-RE interval ends at the note RE; and, as such, represents the octave of plants. 

The first note in the octave of plants is the note RE. Do you know of any plants that have the aspects of RE, that is, act like plants, and stay in one place?

Yeah, OK, that was an easy one. Plants that look like plants, check.

What about the next note? The next note is MI. Are there any plants that have the aspects of MI, plants that move? We already mentioned creeping vines; are there any others?

Actually, there is. My favorite is a unique plant in Arizona that literally moves. If you stumble upon it, you find a big ring… a plant growing around the circumference of a fifty-foot wide circle. 

Really? Why? 

Well, two thousand years ago it started out growing in one spot. 

Then, the plant sent out roots, in every direction, and new growth sprang up in a circle around the original plant. The central part of the plant got old and faded away. 

Fortunately, the new growth, which was growing in a circle around the original plant, continued sending out roots, and the circle got bigger; and, after two-thousand years… as the old growth faded away and new growth kept working its way out to new ground, a giant circle was formed. 

It was the same plant that started two-thousand years ago; but, it had moved. OK, it was slow movement, but it was movement, nonetheless.

Thus, we do have plants that move. However, most plants do not… they just release seeds. But, we found some that do. 

OK. So far, we have plants with the aspects of RE and the aspects of MI.

Are there any plants that have the aspects of FA; plants that are like mothers; plants that raise their children?

Did you ever hear of a spider plant or a Chlorophytum comosum?                                       

People usually have them in hanging baskets. They grow little baby plants at the end of long stems: “I am not going to cast my seeds into the wind. I am going to give live birth to my children. I am going to nurture them, feed them, and raise them.” 

It is like an emotional animal, caring for its young.

Each long stem has a baby plant growing on its end; and, as the baby plants grow and get bigger and bigger, they get heavier and heavier. The increasing weight of the growing baby plants causes the long stems to eventually bend over and gently place the baby plants on the ground, away from the parent plant. Then, the baby plants put their roots in the soil, the stems decay, and the baby plants start to grow on their own.

Oh my God! It is like a mother!

OK, we can find plants that have the aspects of FA…. Plants, which birth, feed, and raise their children.

What’s next? 

Are there any intelligent plants, plants that have the aspects of SO?

Well, they say that bean plants can be trained to grow towards a blue light and a signal, and when there is no blue light, just the signal, the trained bean plants will grow towards the signal. 

We can see intelligence there. 

And, of course, plants track the sun across the sky… looks pretty intelligent to me. Or, some plants only release their spores during a full moon, thus, they have smart sex. 

So, some plants do have the aspects of SO.

What about plants with the aspects of LA, plants with social qualities? 

Thickets, briars, and blackberries come to mind. They grow in groups. They are social plants. Together, they protect each other. By being in a cluster, they keep the plant eaters at bay… not to mention their thorns, “Hey, we just wanted to ‘stick’ around and socialize.” 

There are many other plants that have the social aspects of LA, these are just a few.

Finally, are there any plants with the aspects of TI, plants that look like they have reason? 

What would they be? 

How about Venus Flytraps? They actually catch bugs. They do not just sit there and all of a sudden close… hoping there may be a bug on them. They wait until there is a bug on them. They sense it, trap it, and eat it, yum; or, Pitcher plants, which makes gummy goo around their tops with a slippery slope inside, so bugs will slide down the slope and get trapped. 

The Venus Flytrap and the Pitcher plant are different from a blade of grass or spider plant. The Venus Flytrap and the Pitcher plant actually interact with the world around them; and, when bugs and flies are within their grasp, they catch them. 

That is like having reason, making a trap.

Additionally, a Mimosa Pudica, or Sensitive plant, has stems off its trunk, with, what looks like, spread-apart fingers on the end; and, on each finger, there are dozens of little, surf-board-shaped leaflets. 

If you touch one leaflet, the leaflet folds up towards the end of the stem. If you disturb one finger, all the leaflets on that finger fold up. If you disturb the stem, all the fingers come together. Disturb it even more and the stem drops down alongside the trunk. Disturb the entire plant and everything folds and drops. In this way, the Sensitive plant protects itself from danger. And, after the disturbance has ceased, the stems slowly come up, the fingers slowly spread apart, and the leaflets slowly unfold… that is, until the next raindrop hits!

OK. We found plants with the aspects of every note, which, when you think of it, is kind of amazing.

Next, we will do the RE-MI interval. 

The RE-MI interval ends at the note MI; and, as such, represents one-brained-beings, like insects. 

There must be an octave for them as well.

Let’s try spiders first. 

OK, some spiders look like plants. That is, they make a web and spend their entire lives in that web. 

While other spiders crawl all over the place looking for something to jump on and eat. 

Next, are the spiders with emotional aspects; for instance, the Wolf spider. The Wolf spider attaches its eggs to its back. There are eggs all over its back, and when the eggs hatch, you see little baby spiders crawling all over their mother. Most spiders do not do this. Most spiders just lay their eggs in egg sacs and then die; the next season the young are born. However, a Wolf spider puts her eggs on her back. She says, “I am a mother. These are my babies. I am going to stay around until they are born, and help them get started in life.”

Oh my Goodness!

Another great example is a desert spider called the Stegodyphus Lineatus. The female spider lays her eggs close to her web, and then watches over them. When they hatch, she begins releasing some kind of liquid from a gland in her body, and all the little baby spiders run over and feed on the droplets, she is like a mother nursing her children. The baby spiders stay with her in the web, feeding on the droplets. But, as they grow, there comes a moment when they need to learn how to become predators. That is, they need to become hunter-killers and survive on more than just drinking the juice from their mom. So, their mother shakes the web… and when she does, they all run over to her, thinking they are going to get fed; and, she shakes the web again… and more come running. When she has gathered them all up, and they are clustered underneath her, waiting to be fed… she pushes her body down on them and attempts to crush them. Being crushed by the weight of their mother, their only recourse is to fight back. So, they attack her, kill her, and eat her. Their mother’s last act in life is to teach her children how to become predators; and, as such, she sacrifices her own existence to that end.

Oh my God! Oh my God! In the world of spiders!

Yeah, in the world of spiders. 

So, some spiders do have the emotional aspects of FA.

All right. Continuing. Any spiders with the intellectual aspects of SO? Well, some spiders spin beautiful architectural webs; or, send out long strands of silk into the wind, which span across rivers, allowing them to affix their webs to both sides of the river; or, use their silk strands to fly, thus, carrying them to unknown lands. 

They sound like some pretty smart spiders, to me.

OK. Are there any spiders with the social aspects of LA? 

One season, we saw a bunch of spiders working as a team. They were all spinning the same web. A whole bunch of them, spinning the same web, like a social group. I do not know if they had joined the union; or, if it was typical behavior; but, it was amazing to watch. “We are all going to pitch in and spin this web together.” 


Spiders with the social aspects of LA. Check.

Any spiders with the aspects of TI? 

Yep. Some make trapdoors. Some make web-like nets and throw them over bugs. Some make funnels, bury themselves at the bottom, and when ants walk near the funnel, the spiders dig away the sand at the bottom of the funnel and the ants cascade down into the spiders’ reach.


Thus, we can find the aspects of every note in the octave of spiders.

OK. Let’s pick a higher one-brained-being. 

We will try fish next. 

Are there any fish that look like plants? 

Tubeworms come to mind. They grow on the bottom of the ocean. They do not move. They just pop out of the tube and get nutrients. Then, pull back into the tube when there is danger. 

So, yes, some fish do have the aspects of RE.

Are there any fish with the aspects of MI, the aspects of movement? 

Yes, of course, most fish move. Sharks, for example, are constantly on the move… hunting the rest of the fish. In fact, marine biologists say, in order to get oxygen into their gills, sharks never stop moving.

OK. Are there any fish with the aspects of FA, the emotional aspect… fish that care for their young? 

My favorite is in Africa; a mouth brooding fish called the Hardhead. The male fish keeps its babies in its mouth. It opens its mouth and a hundred little minnows come swimming out. A little danger, “Come to daddy,” and they all swim back in. “I am watching the kids. I am not going to eat them. They would be a nice snack, but I care for my children. I am going to raise them until they get too big for my mouth.” There are many other species of mouthbrooding fish, cichlids, cardinalfish, arowanas, etc., who all have the emotional aspects of FA.

Oh my God! Fish with the aspects of emotion!

Are there any fish with the aspects of So, fish that are intelligent?

Remember how intelligence was first driven by duplication, which said, “Find the same place to mate?” Most fish do not do that. In fact, most female fish disperse their eggs on the bottom of an ocean, lake, or river… and then males come along and fertilize them. However, that is not the case with Salmon. They say, “I am a smart fish. I obey the aspects of SO. I am going to swim upstream to where I was born. Since it worked for me, it may work for my children. I am going to have smart sex. I am going to lay my eggs in the same stream in which I was born.” 

Thus, some fish do indeed have the aspects of SO.

And, of course, some fish have the social aspects of LA; they school. A lot of fish school. By being in a group, they have a better chance of surviving. Why? Because they can feed together; and, by schooling, it makes it harder for predators to isolate and attack one fish. In addition, some fish interact socially with other fish. For example, Remora fish. Remora fish have social relationships with sharks. The sharks let Remora fish swim into their mouths and clean their teeth. 

So, some fish do have the aspects of LA.

OK. What about fish that have the higher mental aspects of TI… fish with reason. Do you know of any fish that appear to have reason? 

I do. A good model would be the Archerfish.

Do you know about the Archerfish?

The Archerfish sees a bug in a tree and targets it. In order to target a bug in a tree, the Archerfish must know the law of falling bodies. It must calculate the parabola of a projectile, and also calculate the distortion caused when looking through fluid, versus, looking through air. It moves its side fins and carefully targets… ready, aim, fire! 

It then spits an arcing stream of water eight feet into the air and hits the bug, knocking it out of the tree into the water, then quickly swims over and eats it. The Archerfish does not just come to the surface and randomly spit… hoping that it might hit something. The Archerfish actually targets! 

Is that a property of reason or what? 

Even though they do not have reason, it sure looks like they do. 

So, some fish do demonstrate the aspects of TI.

After finding all the aspects in the world of fish, we can better understand why some fish even keep their babies in their mouths.

And, if we look, we will find these aspects in the octaves of emotional animals, intellectual animals, social animals, and even in people.

But, I shall leave those discoveries to you.

However, I will give you one clue, when you start looking for men who have the aspects of a plant, they are called couch potatoes!

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 will be able to obtain Mr. Smith’s other diagrams, listen to other talks, as well as learn all the mathematics that supports them, and much much more.

But, most importantly, you will have real time access to the materials we are discussing.

That’s thedogteachings.com

Goodbye until next time.

Teachings based upon the works of R. A. Smith and G. I. Gurdjieff.

All material © 2020 THEDOG Publishing

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