"It is quite clear that, for proper study, for an exact exchange of thoughts,
an exact language is necessary, which would make it possible to establish
what a man actually means, would include an indication of the point of view
from which a given concept is taken and determine the center of gravity..."
According to Blavatsky, the Upanishads “contain the beginning and the end of all human knowledge, but they have now ceased to reveal it, since the day of Buddha”. The true Secret Doctrine has become a dead letter to all except a certain select sect of Brahmins, who preserve it in great secrecy. Recorded on a few pages, hidden far beyond the eyes of the profane, kept zealously guarded “by that desperately exclusive caste of Brahmins”, revealed only by geometrical signs and glyphs, that supreme knowledge which gives the key to the very kernel of matter is retained in all its pristine purity.
The name, Upanishads, is usually translated “esoteric doctrine”. These treatises form part of the Sruti or revealed knowledge, Revelation, in short, and are generally attached to the Brahmana portion of the Vedas, as their third division.
The commonly accepted origin of the word sruti is the Bengali word shru, meaning “to hear”, or "that which is heard”. [The spelling, shruti or sruti, is irrelevant. In my books I have used both spellings. The important thing is that they are said to be concerned with the realm of sound.] However, we find in the writing of the Theosophist H. P. Blavatsky a more hidden definition:
Almost a decade ago, in chapter nine of my book Nearly All and Almost Everything, I had penned the following words:
"It is interesting that in The Harvard Dictionary of Music Willi Apel, one of the celebrated music historians of our time, laments the fact that research into the Indian classical music tradition “has been greatly hampered by Brahmin secrecy”. Some disgruntled scholars have concluded that such secrecy is most probably a result of ignorance on the part of those Brahmin castes who have either unwittingly lost the key to the puzzle of man’s origins and purpose - or who never had it in the first place. Certainly the concept of sruti is nearly unknown in the western world where it remains ill-defined and grossly underestimated. With the rarest of exceptions, few care to make the effort required for even a cursory knowledge of srutis. Those who do recognize that inherent within srutis is a number theory which merits study are, nevertheless, unwilling to accept the extent to which the ancient musical tradition hides mathematical constructs so sophisticated that they dare to challenge our own conceptual capabilities. Perhaps the very attempts by present-day scholars to oversimplify the srutis shows clearly that our culture is not a “medium” in which to grow profound truth. It appears not at all unlikely that there has indeed been a deliberate withholding of a knowledge so extraordinary that extreme measures have been taken over millennia to prevent its eventual dissipation and dissolution by those few high initiates who know its truths."
A perfect example of the dumbing-down of the srutis can be observed in earlier research into Indian music by European theorists such as Grosset in the late nineteenth century who took the srutis to be equally-tempered intervals. While this is an idea now generally out-of-favor, unfortunately present-day musicologists have done no better. Taking the most simplistic of approaches, they are quite satisfied to regard the sruti as being of “indefinable pitch”.
Although one could cite numerous writers who espouse such a claim, we here restrict ourselves to the words of two music historians of the latter half of the twentieth century, Ernest McClain and Willi Apel. According to McClain, the octave is divided into twenty-two srutis which (as he wrongly states) “are not defined mathematically”. Willi Apel, in the definitive second edition of the Harvard Dictionary of Music, writes that srutis are “theoretically slightly unequal but for all practical purposes equal microtonal intervals, each roughly equal to a quarter tone”.
Granted, as far as the “practical” western mentality is concerned, what we have here is a non-issue. What difference does it really make if, in an already obscure musical system, srutis are for all practical purposes considered as equally-tempered intervals; or if they are only rough approximations and undifferentiated tones? Who, except those pedants of Indian music residing in some tiny obscure corner of academia, would even deign to give the subject a second glance?
The answer is: Those who wish to bring back into focus the mysterial dimension without which the world is only a flat meaningless series of “one damn thing after another”.
The srutis are the musical key to the ancient sacred science which is said to be lost. It is the srutis themselves which “contain the beginning and the end of all human knowledge, but they have now ceased to reveal it, since the day of Buddha”.
From the sruti ratios comes about the measurement system known throughout the ancient world as the sacred canon of proportion. From knowledge of the canon, the entire physical universe - the earth, the solar system, and the stars, as well as man himself - can be measured. How ironic that the very source of measures, the srutis, are now encumbered with the stigma that they are simply indeterminate and unmeasurable pitch quanta!
In our dark state of ignorance we have divested ourselves of their fundamental and inviolate meaning and purpose; and as a result, it is we who are immeasurably poorer as a result.
It soon becomes clear that the srutis concern that “exact language” spoken about in In Search of the Miraculous
It is quite clear that, for proper study, for an exact exchange of thoughts, an exact language is necessary, which would make it possible to establish what a man actually means, would include an indication of the point of view from which a given concept is taken and determine the center of gravity of this concept. . . For exact understanding exact language is necessary. . .
When a man has mastered this language, then, with its help, there can be transmitted and communicated to him a great deal of knowledge and information which cannot be transmitted in ordinary language even by using all possible scientific and philosophical terms. The fundamental property of the new language is that all ideas in it are concentrated round one idea, that is, they are taken in their mutual relationship from the point of view of one idea. This idea is the idea of evolution. Of course, not evolution in the sense of mechanical evolution, because such an evolution does not exist, but in the sense of a conscious and volitional evolution, which alone is possible.
That most precise and exacting of all languages - the musical language of the srutis themselves - is light-years away from the sentimentality usually associated with the idea of “music the universal language”. Rather, the srutis are the revealers of that perfect system known and in use in ancient days, at the time when, in Biblical terms, “the world was of one language and one lip”.
To speak the language of the srutis is no simple matter. Like the study of any language, it requires patience and diligence. The profundity of the ideas is not easily plumbed, and requires musical and mathematical constructs by way of explanation. Many charts and tables and drawings are included to facilitate comprehension of the sometimes difficult concepts. But mental constructs, while very important, are only a part of the picture.
The language of sruti is no ordinary language. The understanding of srutis requires that one comprehend harmony. Harmony touches the world of the feelings. Harmony is the reconciling force. Harmony is a combination of the reason of science and the faith of religion. Harmony is the third force to which men are blind, which hides in the secret place of the heart.
Practicing musicians well know there are precious few who have an innate sense of harmony. Even for those who do, much musical study is still required. Harmony is a complex subject whose understanding comes as a product of school work.
Harmony requires a great deal more musical knowledge, more training - in short, more school work - than melody. While a great many people can “carry a tune”, fewer can harmonize a melody. Far fewer still are able to understand on a deeper level the form and sequence of harmonic structure. Only the understanding of harmony enables true musicianship to flower and bloom. Until that happens, it is just “one damn note after another”.
For the billions of unfortunates living on the brink, existing on that long thin slice of melody line called circumference, the calm harmonizing spaces of the inner world lying just within the circle of time can never be apprehended, for the path to the inner world is not by the circuitous way around the circumference, no matter how close or far one moves upon it. Rather, that inner direction can only be found by means of the radii - the srutis - which go directly to the center. The srutis help us to rediscover ‘I”.
Harmony comes from the vertical dimension - from I - and has the requirement of space. It is by means of I, vertical harmony, that one gets out of the exoteric circle of linear time and into the Higher world inside the shell. Harmony is to melody what melody is to rhythm. Harmony is three-dimensional, while melody is two-dimensional, and rhythm may be said to have only one dimension. The study of harmony - harmonia - is the very school work one must study if one is to become Higher Man. Only then can there be further evolution towards the vertical dimension, I.
The myths and legends of yore, the celebrations and rites of ancient peoples, the chapter-and-verse of religions come alive as feeling, when, by the exploration of srutis there are revealed more and more connecting lines of force. These rays, these lines of radii coming from the inner sun-world of the heart, shine the light of meaning onto the dry dead world of the surface. What formerly were separate points on a line now join by arcs and angles into geometrical forms as the insubstantial takes on flesh to dwell among us.
If one must have knowledge of harmony before one can understand sruti, can it be said that those civilizations which lost the knowledge of sruti perhaps first lost their soul? It is surely the knowledge of sruti which will help us to regain our soul, and find that harmony which we so sorely lack.
As the fairy tales would tell the story, the srutis in their purity have slept for millennia, undisturbed and uninterpreted by the ignorant, preserving their secrets until such a time that their pristine beauty will be awakened by a kiss from a culture whose only love is for the understanding of truth. Only then, when the musical language of the srutis once more becomes the spoken language of the planet, can those initiatic elements identical within all real religious and philosophical traditions, radiate upon the whole of civilization and enlighten it. The srutis are the Alphabet which communicates itself to men, the Word which speaks itself to men, the Language which informs them of the will and law of God. It will surely be the sign of the end of the age of darkness, the Kali yuga, when men no longer see it as heretical that the Word is both God and Number.
The words from The Source of Measures come flooding back:
The ancient knowledge will again abound, and overflow, as water, upon the earth. The remains of this knowledge are everywhere about us, in every-day use, and perfect. Its revival will point to the restoration of the period prior to the confusions of lip. The prophet saw a valley filled with a confusion of dry bones; but the bones were perfect and all there: so with us are the vestiges of this knowledge. At the word, bone came to its bone: the perfect framework of the man.
“And he said, son of man, can these bones live? . . . . and behold a shaking, and the bones came together bone to his bone: . . . then, thus saith the Lord God, come from the four winds, O breath, and breathe upon these slain, that they may live”.
This is coming to pass. Then shall the people know.
The time of sruti has come. Like the Work brought by Gurdjieff, the srutis have a mission to perform: the mission of breathing life into the slain harmonia. Bringing together bone to bone, the srutis reconcile the science of knowledge and the science of being. Gradually, almost without our knowing it, they teach us that what is below - the living water - is indeed intimately connected with what is above; and what is above cannot live without what is below. There is no such thing as disparate and lifeless events. The world once again becomes verdant, filled with purpose. Everything is at once beautiful, in agreement, reconciled, harmonious. There is, after all, only the Whole.
Behold! The day of the Lord cometh, And it shall come to pass in that day That the Light shall not be clear nor dark, But it shall be One day, And the Lord shall be king over all the earth: In that day there shall be One Jehovah, And his name shall be One.
In ancient teachings the undifferentiated ovoid is the most ancient symbol of primordial chaos. The very shape signifies no number, the zero, 0. Hidden within the space of the void is the centermost infinitesimal point, the Origin. From this point, called the Central Sun, radiations go out to determine order in space. In geometry - a word which, by definition, means “the measure of solids” - these radiations are aptly called radii. The radii divide and solidify the undifferentiated space within the void by cutting it into segments of angles and arcs. In biblical language these segments, called angels and archangels, are helpers of the Most High God. They are the Creator Gods. In musical terms the sruti radii are the Arch-measurers of the cosmos.
In the poetic language of religion Brahma, the unmanifest, transforms Himself into vibration (nada) to become the manifested worlds. Nada Brahma: World Sound. From the scientific viewpoint, the original sound generating a series of partials must refer to none other than the harmonic series. At least here, religion and science happily come together to proclaim that the One, resonating from the beginning, vibrates the structure of the universe into being. Everything vibrates, therefore everything comes under the definition of this numerical law of overtones. As the Pythagoreans claimed, everything is number. The first sixteen harmonics, the original genera, are shown below:
In the ancient Vedic tradition, the physical body is said to be composed of sixteen elements. What remains unknown is the fact that these sixteen elements are, in fact, the first sixteen harmonics which, according to a sacred canon of proportions, vibrate into being the physical body of the cosmos. The actual allocation of the twenty-two srutis is based upon these sixteen harmonics. Their exacting derivation can be demonstrated on the 16 x 16 grid below. Measuring from 1/1, the fundamental string, and without repeating any fraction, we proceed through the series, as follows:
Inverting the fractions results in the twenty-two intervals:
Eliminating those that extend outside the range of one octave, the remaining fractions result in a continuum of intervals whose ranking, read from left to right, move from the consonant perfect intervals to the dissonant minor sevenths and seconds.
It is this natural organic hierarchical ranking of pitches which affords to each interval its specific place, its function, in the energy system called “life”. In relation to the non-living world, there is a complexity and order here which is at a higher level than the sixteen harmonics themselves. In other words, the intervals are a step above the genera and deserve a category of their own. The idea corresponds precisely with those of the ancient Greek musical theorist, Aristoxenus, who, in his treatise El Harmonica, ascribes to his first two categories the terms “genera” and “intervals”. The reader will find further elaboration of this topic in my book, Aristoxenus’s Ghost.
The hierarchical structure gains additional properties of organization when the “generic” intervals are ascribed specific degrees. In my books I have generally assumed the fundamental measure to be 360, for the simple reason that it is the measure of one complete circle of 360 degrees. When taken as a cyclic unit, 360 is a frequency well within the range which can be heard by man.
Once the ramrod of the establishment has been named, this “Director” (360) assumes the executive responsibility of selecting his “Staff”. It is an orderly operation, naturally simple and straightforward, without need for “politics”.
Each “staff member” can then find its allotted place in the numerical hierarchy, between the octave 360 and 720, and can assume its individual responsibility according to its assigned position in the numerical scheme.
Look! It becomes immediately apparent, once the differences between each of the ascending frequencies are calculated, that there are three recurring ratios: the just diatonic semitone (jds) 16/15; the just chromatic semitone (jcs) 25/24, and the just enharmonic semitone (jcs) 81/80.
Pay particular attention to these three intervals. Remember, they originate from the sixteen “elements” of the harmonic series. However, it is their “higher” organization into these three ratios that especially interests us. The word “ratio” has to do with “ratiocination”, that is, with thought processes. No one today comprehends how thought is aroused. No one knows what thought is, or where it comes from. How we “think thoughts” is a great mystery.
I propose that these three ratios are the factors underlying the mechanism of human mentation. Indeed, these “thought processors” are contained in all things, they penetrate all and everything, and without them nothing can appear to exist, not even for an instant. While they may be said to form the automatic world of ordinary experience, there is a certain intelligence which manifests in their behavior. Taken as the “controls central” for the “three brains” - the intellectual, the emotional, and the moving - they make manifest, in clear and objective mathematical language, what Gurdjieff meant by the “three centers”.
On the question of functions and centers, Ouspensky relates that Gurdjieff’s exposition of the centers began with three centers - the intellectual, the emotional, and the moving.
On the first occasion he spoke of three centers, the intellectual, the emotional, and the moving, and tried to make us distinguish these functions, find examples, and so on. Afterwards the instinctive center was added, as an independent and self-supporting machine. Afterwards the sex center. (Fragments p. 55)
From the further coalescing of the ratios (jds, jcs, and jes), two more intervals come about which, presumably, are the modus operandi for these next two centers called “instinctive” and “sex”.
Just Diatonic Semitone (16/15) x Just-Chromatic-Semitone (25/24) = 10/9
Just Diatonic Semitone (16/15) x Just-Chromatic-Semitone (25/24) x Comma (81/80) = 9/8
Thus ordinary man’s five centers may be enumerated as 81/80 (intellectual), 25/24 (emotional), 16/15 (moving), 10/9 (instinctive), and 9/8 (sex).
Ouspensky speaks about the suppressions which Gurdjieff himself fostered by his method of presentation, which were the cause of later confusion and misunderstandings in later groups.
Gurdjieff gave the ideas little by little, as though defending or protecting them from us. When touching on new themes for the first time he gave only general principles, often holding back the most essential. Sometimes he himself pointed out apparent discrepancies in the theories given, which were, in fact, precisely due to these reservations and suppressions. . . (Fragments, p. 54)
Having long experience as a teacher of music theory, I could fully appreciate Gurdjieff’s method of exposition. Explaining even the most basic fundamentals of music theory to others is no easy task. Probably his so-called “suppressions” were really attempts to keep possible confusions and wrong conclusions at a minimum. In any case, given my theoretical background, I could well understand why he would continue his lessons by stating “If all the lower story is taken as one whole, then sex can be regarded as the neutralizing part of the moving center”. When taken in this way, there are not five, but three centers: moving, instinctive, and sex; and they make up the whole “lower story”.
Lest anyone has lingering doubts that, in regards to the three centers, Gurdjieff is making specific reference to the musical ratios, one should think on the fact that the three numbers following 360 are precisely the ones mentioned in Fragments (p. 126) as “the three kinds of intervals in the octave, 9/8, 10/9, and 16/15, which in whole numbers correspond to 405, 400, and 384”. Through regular repeating sequences the musical ratios link together, forming “chains of events” on the circumference of recurring Time - that is, on the circle of 360 degrees.
384/360 = 16/15 moving center
400/360 = 10/9 instinctive center
405/360 = 9/8 sex center
The sex center, 9/8, has to do with the creation of a permanent center of gravity, and with equilibrium.
According to its energy, that is to say, if it uses its own energy, the sex center stands on a level with the higher emotional center. And all the other centers are subordinate to it. Therefore it would be a great thing if it worked with its own energy. This alone would indicate a comparatively very high level of being.
Equilibrium has to do with balance. On the musical example, the two sides are held in perfect balance, equilibrated as it were, by the pivotal central tone, 9/8. The smaller ratios naturally separate into two equal divisions at this mid-point, the “left-hand” region between 360 and 480, and the “right-hand” region from 540 to 720. The two parts are “mirror images” of one another. Multiplying together the six smaller ratios on each side produces the perfect fifth, 4/3. In ancient thought, this perfect fourth interval is called the “tetrachord”. The two equal tetrachords are separated by the major whole tone, 9/8. In other words, the line is divided according to the proportion 6:8:9:12.
Look! If the ratios on the left-hand side (whose movement is from left to right) are multiplied by the corresponding opposing ratios on the right-hand side (whose movement is from right to left), each “result” produces the number known as the Platonic Great Year, 259200.
360 x 720 = 259200
384 x 675 = 259200
400 x 648 = 259200
405 x 640 = 259200
432 x 600 = 259200
450 x 576 = 259200
480 x 540 = 259200
One familiar with ancient Greek writings may recall the words of the esteemed Greek mathematician and philosopher, Nicomachus of Gerasa, who wrote about the multiplication of opposites.
Harmonia comes to be in all respects out of opposites: for harmonia is a unification of things multiply mixed, and an agreement of things that disagree. Arithm. ii.19
Eureka! What we have here, confronting us, is indeed the ancient “harmonia”, exactly as it is described in the ancient treatises! It is the same message that was brought and made famous by Aristotle.
Harmonia is heavenly, and its nature is divine, beautiful and marvelous. It is fourfold in its natural capacities, and thus has two means, the arithmetic and the harmonic, and its parts and magnitudes and excesses exhibit themselves in conformity with number and with equal measure, for melodies are rhythmized in two tetrachords.
The two “means, ” coming in between the “extremes” of the two end points 360/720, are 540 and 480.
Arithmetic mean: a + c / 2
360 x 720 / 2 = 540
Harmonic mean: 2ac / a + c
2(360)(720) / 1080 = 480
Plato, for one, considered mean and extremes the “essential knowledge” from which the mind could be made aware of deep cosmic truths.
Apart from the three lower centers (moving, emotional, thinking), and those connected with them (instinctive and sex), there are two more centers, fully developed and properly functioning, but not connected with the three centers we are aware of ourselves.
There are two higher centers in man, fully developed and properly functioning, but they are not connected with our usual life. The existence of these higher centers in us is a greater riddle than the hidden treasure which men who believe in the existence of the mysterious and the miraculous have sought since the remotest times. All mystical and occult systems recognize the existence of higher forces and capacities in man .
So far, we have discovered the five “lower” centers, whose origins are from the harmonic genera, and whose identity relies solely upon intervallic status. Remember that the Greek music theorist, Aristoxenus, in his treatise El Harmonica, applies to his first two musical categories the terms “genera” and “intervals”. His third category, after “intervals”, is “notes”. A note, by definition, must have a pitch. Anyone who knows about music analysis recognizes that a note with pitch is “higher” in the chain-of-command than a note without pitch.
The question then becomes: Which pitch?
The search for an objective standard pitch, an “absolute do”, has been going on for thousands of years. As far back as 1500 B.C. the Chinese were at pains to count the exact number of peas or beans (pulses) needed to fill a pipe of a certain size, the pitch pipe known as the lu setting the standard of measure. By general consensus, the fundamental tone is taken as F#, which is arrived at by powers of 3 (perfect fifths).
On the other side of the world, in Western culture, builders of organs were using the practice of doubling by powers of 2 (the producers of perfect octaves, the C’s), and chose to identify the open diapason as the measuring unit. The perfect octaves and perfect fifths were as incommensurate as the proverbial “apples and oranges”. East was East, and West was West; and the twain, by law, were fated never to meet.
The F# traditionally is the tritone, the diabolus in musica. On a circle of 360 degrees, it generally appears at the apex. According to logarithmic calculations, the five “lower centers” make their appearance on the circle.
In my madcap brain I can easily conjure up the diabolus in musica as the “black cat” that lords it over the “con-cat-enations” going on automatically, incessantly, in the three-brained apparatus in between the ears.
One familiar with Gurdjieff’s piece for Movements titled “Black Magic” will be interested to see how this composition utilizes only the six whole tones (G A B C# D# E#) that are derived solely from ratios of the three “lower centers”: 9/8, 10/9, and 16/15.
Treating 360 as F#, we can place alphabetical names on all the tones.
It is a simple matter to see that there is a “missing principle”. The C is absent. If the interval ratios pertain to our particular type of “ratiocination,” would it not be logical to assume that this missing C has to do with the missing corpus callosum (“hard body”), that thick bridge of neural tissue in the middle of the brain whose role is to convey information from one side to the other, enabling each part to contribute its part to achieve integration of the whole? The corpus callosum, neuroscientists say, maintains a balance between “the arousal of thought” and “attention”. Those persons in which the corpus callosum is thin or non-existent (the technical term for partial or total absence is “agenesis of the corpus callosum”) are plagued with brain disfunctions such as attention-deficit-disorder and autism. Attention requires the center pole, C.
As I wrote in The Meaning of the Musical Tree (p. 122), the popular film, “The Rain Man”, has familiarized the general public with the effects of a missing corpus callosom. This film is a true story about the idiot-savant, Kim Peek, whose phenomenal memory abilities have made him almost a celebrity. Despite his monumental feats of data retention (which are not unlike the memory system of a computer and, at least in Peek’s case, seem to be one of the positive outcomes of agenesis corpus callosum), the fact is, he is retarded and cannot dress himself, brush his teeth, comb his hair - in short, he cannot take care of himself. Peek cannot conceptualize, make analogies. For him, “get a grip on yourself” means to grab yourself with both hands. A literal understanding is all he knows. As Gurdjieff implies, one of the important characteristics of human thinking is that of analogy (“a nail is like a requiem”). For Peek, making analogies is beyond his capabilities. Analogies require the “bridge”. Otherwise, man’s conceptual abilities remain stunted.
A musician familiar with the notes of the grand staff recognizes that middle C is the “bridge” located in between the treble and bass staves, where it is given its own “ledger line”. Its importance is reflected on the piano keyboard, where the location “middle C” occurs directly in front of the pianist’s navel. As piano teachers are well aware, beginning piano students generally start with the “middle C position”.
The middle C is truly the center of the tonal universe, dividing left and right hands, male and female pitch ranges, as well as connoting the two hemispheres of the brain, the “male” left side, and the “female” right side. Generally treated, the left is the mathematical reasoning side and the right the artistic intuitive side. The bass clef and treble clef signs themselves indicate a reverse spiraling motion. In common parlance, the left hand side of the brain is “Mars”, the right hand side “Venus”. It was in the early chapters of Beelzebub’s Tales that Gurdjieff mentions these two planets, their “peculiarities”.
The pitch frequency of C256, as it happens, divides down by 2s until it reaches all the way down to 1. Thus one might say that C is the only note capable of resonating “unity consciousness”, C1. As the picture reveals, there are three octaves of scales, presumably reflecting the idea of man’s three brains, which operate in three different “registers”.
Over the past centuries, the grand staff of eleven lines has evolved to become as we know it today: five lines in the bass clef, five lines in the treble clef, the two clefs separated by the ledger line C in the middle. In between the lines are the spaces, four in each clef, plus the two spaces on either side of ledger line middle C. There are 10 notes below middle C and ten notes above middle C, making a total of 21 notes - or 22, if the top space G is counted.