“In right knowledge the study of man must proceed on parallel lines with the study
of the world, and the study of the world must run parallel with the study of man. Laws
are everywhere the same, in the world as well as in man. Having mastered the
principles of any one law we must look for its manifestation in the world and in man
simultaneously. 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 to pass on to man, and in other cases it is better to begin with man
and then to pass on to the world.
“This parallel study of the world and of 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.
“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 neutralizing. Of this we have
already spoken, and in future we will 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.
“In order to understand the meaning of this law it is necessary to regard the universe
as consisting of vibrations. These vibrations proceed in all kinds, aspects, and
densities of the matter which constitutes the universe, from the finest to the coarsest;
they issue from various sources and proceed in various directions, crossing one
another, colliding, strengthening, weakening, arresting one another, and so on.
“In this connection according to the usual views accepted in the West, vibrations are
continuous. This means that vibrations are usually regarded as proceeding
uninterruptedly, ascending or descending so long as there continues to act the force of
the original impulse which caused the vibration and which overcomes the resistance of
the medium in which the vibrations proceed. When the force of the impulse becomes
exhausted and the resistance of the medium gains the upper hand the vibrations
naturally die down and stop. But until this moment is reached, that is, until the
beginning of the natural weakening, the vibrations develop uniformly and gradually,
and, in the absence of resistance, can even be endless. So that one of the fundamental
propositions of our physics is the continuity of vibrations, although this has never been
precisely formulated because it has never been opposed. In certain of the newest
theories this proposition is beginning to be shaken. Nevertheless physics is still very
far from a correct view on the nature of vibrations, or what corresponds to our
conception of vibrations, in the real world.
“In this instance the view of ancient knowledge is opposed to that of contemporary
science because at the base of the understanding of vibrations ancient knowledge
places the principle of the discontinuity of vibrations.
“The principle of the discontinuity of vibration means the definite and necessary
characteristic of all vibrations in nature, whether ascending or descending, 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 and vibrations
develop in a regular way only for a certain time which is determined by the nature of
the impulse, the medium, the conditions, and so forth. But at a certain moment a kind
of change takes place in it and the vibrations, so to speak, cease to obey it and for a
short time they slow down and to a certain 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 of the momentum are not equal and that the moments of retardation
of the vibrations are not symmetrical. One period is shorter, the other is 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 the
number of vibrations in a given space of time.
“Let us imagine a line of increasing vibrations. Let us take them at the moment
when they are vibrating at the rate of one thousand a second. After a certain time the
number of vibrations is doubled, that is, reaches two thousand.
1000 2000
|—————————————————————|
FIG. 7
“It has been found and established that in this interval of vibrations, between the
given number of vibrations and a number twice as large, there are two places where a
retardation in the increase of vibrations takes place. One is near the beginning but not
at the beginning itself. The other occurs almost at the end.
“Approximately:
FIG. 8 1000|————————|———————————|——|2000
“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 period in which vibrations are doubled was divided into eight unequal
steps corresponding to the rate of increase in the vibrations. The eighth step repeats
the first step with double the number of vibrations. This period of the doubling of the
vibrations, or the line of the development of vibrations, between a given number of
vibrations and double that number, is called an octave, that is to say, composed of
eight.
“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. At the same time, how-
ever, 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, and 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 one thousand
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.
do ———————————————————————— do
FIG. 9
“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.
, do, re, mi, fa, sol, la, si , do, FIG. 10
“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 3/2, si 15/8, and
do 2.
1 9/8 5/4 4/3 3/2 5/3 15/8 2

do re mi fa sol la si do FIG. 11
“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 or the differences in the pitch of 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 two notes:
do-re
re-mi
fa-sol
sol-la
la-si
and one between each of the following two 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 ‘intervals,’ 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’
“If we grasp its full meaning the law of octaves gives us an entirely new
explanation of the whole of life, of the progress and development of phenomena on all planes
of the universe observed by us. This law explains why there are
no straight lines in nature and also why we can neither think nor do, why everything
with us is thought, why everything happens with us and happens usually in a way
opposed to what we want or expect. All this is the clear and direct effect of the
‘intervals,’ or retardations in the development of vibrations.
“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:

“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 only be explained with the help of the law of
octaves together with an understanding of the role and significance of ‘intervals’
which cause the line of the development of force constantly to change, to go in a
broken line, to turn round, 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; suppression, 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 weaker, 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 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 the 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.
“The law of octaves explains many phenomena in our lives which are
incomprehensible.
“First is the principle of the 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.
“And third, that in the actual development itself 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
when 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 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 ascending and descending octaves in life we must
learn to distinguish ascent and descent within the octaves themselves. Whatever
sphere of our life we take we can see that nothing can ever remain level and constant;
everywhere and in everything proceeds the swinging of the pendulum, everywhere
and in everything the waves rise and fall. Our energy in one or another direction
which suddenly increases and afterwards just as suddenly weakens; our moods which
‘become better’ or ‘become 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.
“And there are perhaps a hundred pendulums moving 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 ‘intervals’ in
the octaves as well as the ‘intervals’ themselves.
“Upon the law of octaves in its three principal manifestations depend many
phenomena both of a psychic nature as well as those immediately connected with our
life. Upon the law of octaves depends the imperfection and the incompleteness of our
knowledge in all spheres without exception, 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 labors 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 which 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.
“And 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 occasions of life and in the activity of nature
and even in human activity.
“The right development of these octaves is based on what looks an accident. It
sometimes happens that octaves going parallel to the given octave, intersecting or
meeting it, in some way or another fill up its ‘intervals’ and make it possible for the
vibrations of the given octave 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 an ‘interval,’ 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 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
neces-
sary, though considerably less strong than the first ‘shock’ between do and si.
“In the big cosmic octave, which reaches us in the form of the ray of creation, we
can see the first complete example of the law of octaves. The ray of creation begins
with the Absolute. The Absolute is the All. The All, possessing full unity, full will,
and full consciousness, creates worlds within itself, in this way beginning the
descending world octave. The Absolute is the do of this octave. The worlds which the
Absolute creates in itself are si. The ‘interval’ between do and si in this case is filled
by the will of the Absolute. The process of creation is developed further by the force
of the original impulse and an ‘additional shock.’ Si passes into la which for us is our
star world, the Milky Way. La passes into sol—our sun, the solar system. Sol passes
into fa—the planetary world. And here between the planetary world as a whole and
our earth occurs an ‘interval.’ 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 fill the ‘interval’ 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 which 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, with organic life. All three
taken together make one. This is the coexistent and indivisible Trinity.”

“We must now dwell on the idea of the ‘additional shocks’ which make it possible
for the lines of forces to reach a projected aim. As I said before, shocks may occur
accidentally. Accident is of course a very uncertain thing. But those lines of
development of forces which are straightened out by accident, and which man can
sometimes see, or suppose, or expect, create in him more than anything else the
illusion of straight lines. That is to say, he thinks that straight lines are the rule and
broken and interrupted lines the exception. This in its turn creates in him the illusion
that it is possible to do; possible to attain a projected aim. In reality a man can do
nothing. If by accident his activity gives a result, even though it resembles only in
appearance or in name the original aim, a man assures himself and others that he has
attained the aim which he set before him-
self and that anyone else would also be able to attain his aim, and others believe him.
In reality this is illusion. A man can win at roulette. But this would be accident.
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, that he 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’ as it is called, is able to ‘arrange the
whole of his life,’ and so on.
“As a matter of fact he is of course unable to do anything of the kind because not
only has he no control over things outside himself but he has no control even 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.
“In what way can control be attained?
“The technical part of this is explained by the law of octaves. 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 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 learn to recognize 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 role 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 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 only possible to learn this in a school, that is to say, in a rightly organized
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 only be created 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. And this in its 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 (or
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.
“In the study of the law of octaves it must be remembered that octaves in their
relation to each other are divided into fundamental and subordinate. The fundamental
octave can be likened to the trunk of a tree giving off branches of lateral octaves. The
seven fundamental notes of the octave and the two ‘intervals,’ the bearers of new
directions, give altogether nine links of a chain, three groups of three links each.
“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 which divide in their turn and pass into branches- becoming
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, the serrations, and so on.
“Like everything in nature the human body which represents a certain whole bears
both within and without the same correlations. According to the number of the notes
of the octave and its ‘intervals,’ the human body has nine basic measurements
expressed by the numbers of a definite measure. In individuals these numbers of
course differ widely but within certain definite limits. These nine basic measurements,
giving a full octave of the first order, by combining in a certain definite way pass into
measurements of subordinate octaves, which give rise in their turn 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.”
The law of octaves naturally gave rise to a great many talks in our group and to
much perplexity. G. warned us all the time against too much theorizing.
“You must understand and feel this law in yourselves,” he said. “Only then will you
see it outside yourselves.”
This of course is true. But the difficulty was not only in this. Merely a “technical”
understanding of the law of octaves requires a lot of time. And we returned to it
continually, sometimes making unexpected discoveries, sometimes again losing what
had seemed to us already established.
It is now difficult to convey how at different periods now one and now another idea
became the center of gravity in our work, attracted the greatest attention, gave rise to
most talks. The idea of the law of octaves became in its way a permanent center of
gravity. We returned to it on every occasion; we spoke of it and discussed its various
aspects at every meeting until we began gradually to think of everything from the
point of view of this idea.”
excerpts from ISOM P.D. Ouspensky