Ascending and Descending Octaves
The Ray of Creation
Hierarchy of Octaves
The Cosmic Octave
Go to:Supplementary "Lectures"
See also:Consciousness, Laws, and Influences
The Ray of Creation
Man's Place in the World
Cosmic "Chemistry" and Relativity
Moreover, some laws are more easily observed in the world, others are more easily observed in man. Therefore in certain cases it is better to begin with the world and then pass on to man, and in other cases it is better to begin with man and then pass on to the world.
This parallel study of the world and man shows the student the fundamental unity of everything and helps him to find analogies in phenomena of different orders.
The number of fundamental laws which govern all processes both in the world and in man is very small. Different numerical combinations of a few elementary forces create all the seeming variety of phenomena. [My emphasis. Ed.]
In order to understand the mechanics of the Universe it is necessary to resolve complex phenomena into these elementary forces.
The first fundamental law of the Universe is the law of three forces, or three principles, or, as it is often called, the Law of Three. According to this law, every action, every phenomenon, in all worlds without exception, is the result of a simultaneous action of three forces the positive, the negative, and the neutralising. Of this we have already spoken [see Consciousness, Laws, and Influences Ed.], and in future we shall return to this law with every new line of study.
The next fundamental law of the Universe is the Law of Seven or the Law of Octaves.
The Principle of the Discontinuity of Vibrations means the definite and necessary characteristic of all vibrations in nature, whether ascending or descending in frequency, to develop not uniformly but with periodical accelerations and retardations. This principle can be formulated still more precisely if we say that the force of the original impulse in vibrations does not act uniformly but, as it were, becomes alternately stronger and weaker. The force of the impulse acts without changing its nature; but vibrations develop in a regular way only for a certain time which is determined by various factors such as the nature of the impulse, the medium of transmission, and the conditions affecting the medium.
At a certain moment, a kind of change takes place in the impulse itself and the vibrations, so to speak, cease to obey it. For a short time the vibrations slow down and to some extent change their nature or direction. For example, ascending vibrations at a certain moment begin to ascend more slowly, and descending vibrations begin to descend more slowly. After this temporary retardation, both in ascending and descending, the vibrations again enter the former channel and for a certain time ascend or descend uniformly up to a certain moment when a check in their development again takes place.
In this connection it is significant that the periods of uniform action or momentum are not equal and that the moments of retardation of the vibrations are not symmetrical. One period is shorter, the other longer.
In order to determine these moments of retardation or rather the checks in the ascent and descent of vibrations the lines of development of vibrations are divided into periods corresponding to the doubling or the halving of vibrations in a given space of time.
It has been found and established that in this interval of vibrations, between a given number and a number twice as large, there are two places where a retardation in the rate of increase takes place. One is near the beginning and the other almost at the end:
The laws which govern the retardation or the deflection of vibrations from their primary direction were known to ancient science. These laws were duly incorporated into a particular formula or diagram which has been preserved up to our times. In this formula, the range within which vibrations are doubled was divided into seven unequal steps as exemplified in music by the octave (composed of eight) where the notes marking the first and last notes of the octave are separated by six notes at intervals corresponding to the steps. [Because the whole musical gamut comprises several octaves, the individual notes may be likened to fence-posts and the intervals to the spaces between adjacent fence-posts. Every eighth post represents a note whose frequency is double that of first note of an octave, and it also marks the beginning of the next octave. The spaces between the fence-posts represent the intervals between successive notes in the octave. The tonic sol-fa system employs a "movable do", which means that regardless of the note on which the octave begins, the notes comprising the octave are called, in order, do, re, mi, fa, sol, la, si, do. Ed.]
The principle of dividing the period in which the vibrations are doubled into eight unequal parts is based upon the observation of the non-uniform increase of vibrations in the entire octave: 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 and 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. At the same time, however, if we study the manifestations of the law of octaves in vibrations of other kinds, we shall see that the laws are everywhere the same: that light, heat, chemical, magnetic, and other vibrations are subject to the same laws as sound vibrations. For instance, the light scale is known to physics; in chemistry, the periodic system of the elements is without doubt closely connected with the principle of octaves although this connection is still not fully clear to science.
A study of the structure of the seven-tone musical scale gives a very good foundation for understanding the cosmic law of octaves.
Let us again take the ascending octave, that is the octave in which the frequency of vibrations increases. Let us suppose that this octave begins with 1000 vibrations a second. Let us designate these thousand vibrations by the note do. Vibrations are growing, that is, their frequency is increasing. At the point where they reach two thousand vibrations a second, there will be a second do, that is, the do of the next octave.
The period between one do and the next that is, an octave is divided into seven unequal parts because the frequency of vibrations does not increase uniformly.
The ratio of the pitch of the notes, or of the frequency of vibrations will be as follows:
If we take do as 1 then re will be 9/8, mi 5/4, fa 4/3, sol 3/2, la 5/3, si 15/8, and the next do 2.
The differences in the acceleration or increase in the notes or the difference in tone will be as follows:
|Between do and re||9/8:1||= 9/8|
|Between re and mi||5/4:9/8||= 10/9|
|Between mi and fa||4/3:5/4||= 16/15 increase retarded|
|Between fa and sol||3/2:4/3||= 9/8|
|Between sol and la||5/3:3/2||= 10/9|
|Between la and si||15/8:5/3||= 9/8|
|Between si and do||2:15/8||=16/15 increase again retarded|
The differences in the notes are called intervals. We see that there are three kinds of intervals in the octave: 9/8, 10/9, and 16/15, which in whole numbers correspond to 405, 400, and 384. The smallest interval 16/15, occurs between mi and fa and between si and do. These are precisely the places of retardation in the octave.
In relation to the musical (seven-tone) scale it is generally considered (theoretically) that there are two semitones between each two notes, with the exception of the intervals mi-fa and si-do, which have only one semitone and in which one semitone is regarded as being left out.
In this manner twenty notes are obtained, eight of which are fundamental: do, re. mi, fa. sol, la, si, do; and twelve intermediate, two between each of the following notes: do-re, re-mi, fa-sol, sol-la, la-si, and one between each of the following notes: mi-fa, si-do.
But in practice, that is, in music, instead of twelve intermediate semitones only five are taken, that is, one semitone between: do-re, re-mi, fa-sol, sol-la, la-si.
Between mi and fa and between si and do, the semitone is not taken at all.
In this way the structure of the musical seven-tone scale gives a scheme of the cosmic law of 'hiccups', or absent semitones. In this respect when octaves are spoken of in a 'cosmic' or a 'mechanical' sense, only those intervals between mi-fa and si-do are called intervals.
What precisely does happen at the moment of the retardation of vibrations? A deviation from the original direction takes place. The octave begins in the direction shown by the arrow:
But a deviation takes place between mi and fa; the line begun at do changes its direction:
and through fa, sol, la, and si it proceeds at an angle to its original direction shown by the first three notes.
Between si and do the second 'hiccup' occurs, causing a fresh deviation, a further change of direction.
The next octave gives an even more marked deviation and the one following that a deviation that is more marked still, so that the line of octaves may at last turn completely round and proceed in a direction opposite to the original direction.
In developing further, the line of octaves or the line of development of vibrations may return to the original direction, in other words, make a complete circle.
This law shows why straight lines never occur in our activities; why, having begun to do one thing, we in fact constantly do something entirely different, often the opposite of the first, although we do not notice this and continue to think that we are doing the same thing that we began to do.
All this and many other things can be explained only with the help of the law of octaves together with an understanding of the role and significance of the 'hiccups' which cause the line of development of force continually to change, to go in a broken line, to become its 'own opposite', and so on.
Such a course of things, that is, a change of direction, we can observe in everything. After a certain period of energetic activity or strong emotion or a right understanding, a reaction comes: work becomes tedious and tiring; moments of fatigue and indifference enter into feeling; instead of right thinking, a search for compromises begins and results in suppression or evasion of difficult problems.
But the line continues to develop though now not in the same direction as at the beginning. Work becomes mechanical; feeling becomes weaker and descends to the level of the common events of the day; thought becomes dogmatic, literal. Everything proceeds in this way for a certain time; then again there is a reaction, again a stop, again a deviation. The development of the force may continue but the work which was begun with great zeal and enthusiasm has become an obligatory and useless formality. A number of entirely foreign elements have entered into feeling considering, vexation, irritation, hostility. Thought goes round in a circle, repeating what was known before, and the way out which had been found becomes more and more lost.
The same thing happens in all spheres of human activity. In literature, science, art, philosophy, religion; in individual and, above all, in social and political life, we can observe how the line of the development of forces deviates from its original direction and goes, after a certain time, in a diametrically opposite direction, still preserving its former name. A study of history from this point of view shows the most astonishing facts which mechanical humanity is far from desiring to notice.
Perhaps the most interesting examples of such change of direction in the line of development of forces can be found in the history of religion, particularly in the history of Christianity if it is studied dispassionately. Think how many turns the line of development of forces must have taken to come from the Gospel preaching of love to the Inquisition; or to go from the ascetics of the early centuries studying esoteric Christianity to the scholastics who calculated how many angels could be placed on the point of a needle.
First is the principle of deviation of forces.
Second is the fact that nothing in the world stays in the same place, or remains what it was: everything moves, everything is going somewhere, is changing, and inevitably either develops or goes down, weakens or degenerates, that is to say, it moves along either an ascending or a descending line of octaves.
Third, in the actual development of both ascending and descending octaves, fluctuations, rises, and falls are constantly taking place.
We have spoken so far chiefly about the discontinuity of vibrations and about the deviation of forces. We must now clearly grasp two other principles: the inevitability of either ascent or descent in every line of development of forces, and also the periodic fluctuations, that is, rises and falls, in every line whether ascending or descending.
Nothing can develop by staying on one level. Ascent or descent is the inevitable cosmic condition of any action. We neither understand nor see what is going on around and within us, either because we do not allow for the inevitability of descent where there is no ascent, or because we take descent to be ascent. These are two of the fundamental causes of our self-deception. We do not see the first one because we continually think that things can remain the same for a long time at the same level; and we do not see the second because ascents where we see them are in fact impossible as impossible as it is to increase consciousness by mechanical means.
Having learned to distinguish between ascending and descending octaves in life, we must learn to distinguish between ascent and descent within the octaves themselves. Whatever sphere of life we take, we can see that nothing can ever remain level and constant; everywhere and in everything the waves rise and fall. Our energy in one or another direction suddenly increases and afterwards just as suddenly weakens; our moods become 'better' or 'worse' without any visible reason; our feelings, our desires, our intentions, our decisions all from time to time pass through periods of ascent or descent, become stronger or weaker.
There are perhaps a hundred pendulums swinging here and there in man. These ascents and descents, these wave-like fluctuations of moods, thought, feelings, energy, determination, are periods of the development of forces between 'hiccups' in the octaves as well as in the intervals themselves.
Upon the law of octaves in its three principal manifestations depend many phenomena of a psychic nature as well as those immediately connected with our circumstances of life. Upon the law of octaves depends the imperfection and the incompleteness of our knowledge in all spheres chiefly because we always begin in one direction and afterwards without noticing it proceed in another.
As has been said already, the law of octaves in all its manifestations was known to ancient knowledge.
Even our division of time, that is, the days of the week into work days and Sundays, is connected with the same properties and inner conditions of our activity which depend upon the general law. The biblical myth of the creation of the world in six days and of the seventh day in which God rested from his labours is also an expression of the law of octaves or an indication of it, though an incomplete one.
Observations based on an understanding of the law of octaves show that 'vibrations' may develop in different ways. In interrupted octaves they merely begin and fall, are drowned or swallowed up by other, stronger, vibrations which intersect them or go in an opposite direction. In octaves which deviate from the original direction, the vibrations change their nature and give results opposite to those which might have been expected at the beginning.
It is only in octaves of a cosmic order, both descending and ascending, that vibrations develop in a consecutive and orderly way, following the same direction in which they started.
Further observations show that a right and consistent development of octaves, although rare, can be observed in all the conditions of life, in the activity of Nature, and even in human activity.
The right development of these octaves is based on what looks like an accident. It sometimes happens that octaves going nearly parallel to the given octave, intersecting or meeting it, in some way or another fill up its 'hiccups' and make it possible for the vibrations to develop in freedom and without checks. Observation of such rightly developing octaves establishes the fact that if at the necessary moment, that is, at the moment when the given octave passes through a 'hiccup', there enters into it an 'additional shock' which corresponds in force and character, it will develop further without hindrance along the original direction, neither losing anything nor changing its nature.
In such cases there is an essential difference between ascending and descending octaves.
In an ascending octave the first 'interval' comes between mi and fa. If corresponding additional energy enters at this point the octave will develop without hindrance to si, but between si and do it needs a much stronger additional shock for its right development than between mi and fa, because the vibrations of the octave at this point are of a considerably higher pitch, and so to overcome a check in the development of the octave a greater intensity is needed.
In a descending octave, on the other hand, the greatest 'interval' occurs at the very beginning of the octave, immediately after the first do, and the material for filling it is very often found either in do itself or in the lateral vibrations evoked by do. For this reason a descending octave develops much more easily than an ascending octave, and in passing beyond si it reaches fa without hindrance. Here an 'additional shock' is necessary, though considerably less strong than the first 'shock' between do and si.
Here, between the planetary world as a whole and our Earth, occurs a 'hiccup'. This means that the planetary radiations carrying various influences to the Earth are not able to reach it or, to speak more correctly, they are not received: the Earth reflects them. In order to overcome the 'hiccup' at this point of the ray of creation, a special apparatus is created for receiving and transmitting the influences coming from the planets. This apparatus is organic life on Earth. Organic life transmits to the Earth all the influences intended for it and makes possible the further development and growth of the Earth, mi of the cosmic octave, and then of the Moon, or re. After this follows another do Nothing. Between All and Nothing passes the ray of creation.
You know the prayer "Holy God, Holy the Firm, Holy the Immortal'? This prayer comes from ancient knowledge. "Holy God" means the Absolute or All. "Holy the Firm" also means the Absolute or Nothing. "Holy the Immortal" signifies that which is between them, that is, the six notes of the ray of creation. All three taken together make one. This is the coexistent and indivisible Trinity.
Attaining an aim which one has set before oneself in life or in any particular sphere of human activity is just the same kind of accident. The only difference is that in regard to roulette, a man at least knows for certain whether he has lost or won on each separate occasion, that is, on each separate stake. But in the activities of his life, particularly with activities of the kind that many people are concerned in, and when years pass between the beginning of something and its result, a man can very easily deceive himself and take the result 'obtained' as the result desired that is, believe that he has won when on the whole he has lost.
The greatest insult for a 'man-machine' is to tell him that he can "do" nothing, can attain nothing, can never move towards any aim whatever, and that in striving towards one he will inevitably create another. Actually, of course, it cannot be otherwise. The 'man-machine' is in the power of accident. His activities may fall by accident into some sort of channel which has been created by cosmic or mechanical forces and they may by accident move along this channel for a certain time, giving the illusion that aims of some kind are being attained. Such accidental correspondence of results with the aims we have set before us, or the attainment of aims in small things which can have no consequences, creates in mechanical man the conviction that he is able to attain any aim, is 'able to conquer nature', is able to 'arrange the whole of his life', and so on.
As a matter of fact he is unable to do anything of the kind. Not only has he no control over things outside himself; he has no control over things within himself. This last must be very clearly understood and assimilated. At the same time it must be understood that control over things begins with control over things in ourselves, with control over ourselves. A man who cannot control himself, or the course of things within himself, can control nothing.
The technical part of this is explained by the Law of the Octave. Octaves can develop consecutively and continuously in the desired direction if 'additional shocks' enter them at the moments necessary that is, at the moments when vibrations slow down. If 'additional shocks' do not enter them at the necessary moments, octaves change their direction. To entertain hopes of accidental 'shocks' coming from somewhere by themselves at the moments necessary is of course out of the question. There remains for a man the choice either of finding a direction for his activities which corresponds to the mechanical line of events of a given moment in other words of 'going where the wind blows' or 'swimming with the stream', even if this contradicts his inner inclinations, convictions, and sympathies; or of reconciling himself to the failure of everything he starts out to do; or he can recognise the moments of the 'intervals' in all lines of his activity and learn to create the 'additional shocks' in other words, learn to apply to his own activities the method which cosmic forces make use of in creating 'additional shocks' at the moments necessary.
The possibility of artificial, that is, specially created, 'additional shocks' gives a practical meaning to the study of the law of octaves and makes this study obligatory and necessary if a man desires to step out of the rτle of passive spectator of that which is happening to him and around him.
The 'man-machine' can do nothing. To him and around him everything just happens. In order to "do", it is necessary to know the law of octaves, to know the moments of the 'intervals', and be able to create necessary 'additional shocks'.
It is possible to learn this only in a school that is to say, in a rightly organised school which follows all esoteric traditions. Without the help of a school a man by himself can never understand the law of octaves, the points of the 'intervals', and the order of creating 'shocks'. He cannot understand because certain conditions are necessary for this purpose, and these conditions can be created only in a school which is itself created upon these principles.
How a school is created on the principles of the law of octaves will be explained in due course. This in turn will explain to you one aspect of the union of the law of seven with the law of three. In the meantime it can be said only that in school teaching, a man is given examples of both descending (creative) and ascending (evolutionary) cosmic octaves. Western thought, knowing neither about octaves nor about the law of three, confuses the ascending and the descending lines and does not understand that the line of evolution is opposed to the line of creation, that is to say, it goes against it as though against the stream.
The fundamental octaves are connected with the secondary or subordinate octaves in a certain definite way. Out of the subordinate octaves of the first order come the subordinate octaves of the second order, and so on. The construction of octaves can be compared with the construction of a tree. From the straight basic trunk there come out boughs on all sides. These divide in their turn and pass into branches, which become smaller and smaller, and finally are covered with leaves. The same process goes on in the construction of the leaves, in the formation of the veins, and so on.
Like everything in Nature, the human body bears both within and without the same correlations representing a certain whole. According to the number of the notes in the octave and its 'hiccups', the human body has nine basic measurements expressed by the numbers of a definite measure. These numbers of course differ widely between individuals, but within certain definite limits. These nine basic measurements, giving a full octave of the first order, by combining in a certain way, pass into measurements of subordinate octaves which in their turn give rise to other subordinate octaves, and so on. In this way it is possible to obtain the measurements of any member or any part of the human body as they are all in a definite relationship one to another.
You must understand and feel this law in yourselves. Only then will you see it outside yourselves. [My emphasis. Ed.]
Each tone of any octave can be regarded as an octave on another plane.
Each interval of these inner octaves contains a whole octave and so on, for some considerable way, but not ad infinitum, because there is a definite limit to the development of inner octaves.
These inner vibrations proceed simultaneously in 'media' of different density, interpenetrating one another. They are reflected in one another, give rise to one another; stop, impel, or change one another.
Let us imagine vibrations in a substance or a medium of a certain definite density. Let us suppose this substance or medium to consist of the comparatively coarse atoms of world 48, each of which is, so to speak, an agglomeration of forty-eight primordial atoms. The vibrations which proceed in this medium are divisible into octaves and the octaves are divisible into intervals. Let us imagine that we have taken one octave of these vibrations for the purpose of some kind of investigation. We must realise that within the limits of this octave proceed the vibrations of a still finer substance. The substance of world 48 is saturated with substance of world 24; the vibrations in the substance of world 24 stand in a definite relation to the vibrations of the substance of world 48 namely, each interval of the vibrations in the substance of world 48 contains a whole octave of the vibrations in the substance of world 24. These are the inner octaves.
The substance of world 24 is, in its turn, permeated with the substance of world 12. In this substance also there are vibrations, and each interval of the vibrations of world 24 contains a whole octave of the vibrations of world 12. The substance of world 12 is permeated with the substance of world 6. The substance of world 6 is permeated with the substance of world 3. World 3 is permeated with the substance of world 1. Corresponding vibrations exist in each of these worlds and the order remains always the same: each interval of the vibrations of a coarser substance contains a whole octave of the vibrations of a finer substance.
If we begin with vibrations of world 48, we can say that one interval of the vibrations in this world contains an octave (or seven intervals) of the vibrations of the planetary world. Each interval of the vibrations of the planetary world contains seven intervals of the vibrations of the world of the Sun. Each interval of the vibrations of the world of the Sun will contain seven intervals of the vibrations of the starry world, and so on.
The study of inner octaves, of their relation to outer octaves, and of the possible influence of the former upon the latter constitute a very important part of the study of the world and of Man.
The Absolute or All (world 1) will be do; all worlds (world 3) si; all suns (world 6) la; our Sun (world 12) sol; all planets (world 24) fa; the Earth (world 48) mi; the Moon (world 96) re. The ray of creation begins with the Absolute. The Absolute is All. It is do.
The ray of creation ends in the Moon. Beyond the Moon there is nothing. This also is the Absolute do.
In examining the ray of creation or cosmic octave, we see that 'hiccups' should come in the development of this octave. The first 'hiccup' should come between do and si, that is between world 1 and world 3, between the Absolute and all worlds; the second between fa and mi, that is, between world 24 and world 48, between 'all planets' and the Earth.
The first 'hiccup' is overcome by the Will of the Absolute. One of the manifestations of the Will of the Absolute consists precisely in overcoming this 'hiccup' by means of a conscious manifestation of neutralising force which reconciles the 'dispute' between the active and passive forces. With the second 'hiccup', the situation is more complicated. Something is missing between the planets and the Earth. Planetary influences cannot pass to the Earth consecutively and fully. An 'additional shock' is required to create new conditions that will ensure a proper passage of forces.
These conditions are created by introducing a special mechanical contrivance between the planets and the Earth. This contrivance for the onward transmission of planetary forces is organic life on Earth. It was created to overcome the 'hiccup' in communication between the planets and the Earth.
Organic life represents, so to speak, the Earth's organ of perception. Organic life forms something like a sensitive film which covers the whole of the Earth's globe and takes in those influences coming from the planetary sphere which would otherwise not be able to reach the Earth. In this respect, the vegetable, animal, and human kingdoms are equally important for the Earth. A field covered with grass takes in planetary influences of a definite kind and transmits them to the Earth. The same field with a crowd of people on it will take in and transmit other influences. The population of Europe takes in one kind of planetary influences and transmits them to the Earth. The population of Africa takes in planetary influences of another kind, and so on.
All great events in the life of the human masses are caused by planetary influences. They are the result of taking in planetary influences. Human society is a highly sensitive mass for the reception of planetary influences, and any accidental small tension in planetary spheres can be reflected for years in an increased animation in one or another sphere of human activity. Something accidental and very transient takes place in planetary space. This is immediately received by the human masses, and people begin to hate and to kill one another, justifying their actions by some theory of brotherhood or equality or love or justice.
Organic life is the organ of perception of the Earth, and it is at the same time an organ of radiation. With the help of organic life, each portion of the Earth's surface occupying a given area sends every moment certain kinds of rays in the direction of the Sun, the planets, and the Moon. In connection with this, the Sun needs one kind of radiations, the planets another kind, and the Moon yet another. Everything that happens on Earth creates radiations of this kind. And many things often happen just because certain kinds of radiation are required from a certain place on the Earth's surface.
This additional or lateral octave in the ray of creation begins in the Sun.
The Sun, sol of the cosmic octave, begins at a certain moments to sound as do, sol-do.
It is necessary to realise that every note of any octave, in the present instance every note of the cosmic octave, may represent the do of some other lateral octave issuing from it. It would be still more correct to say that any note of any octave may at the same time be any note of any other octave passing through it.
In the present instance sol begins to sound as do. Descending to the level of the planets, this new octave passes into si; descending still lower it produces three notes la, sol, fa, which create and constitute organic life on Earth in the form that we know it. Mi of this octave blends with mi of the cosmic octave, that is, with the Earth, and re with re of the cosmic octave, that is, with the Moon.