It is a truism that nature does not proceed in straight lines. But though the processes of nature may be complex and unpredictable, we are find
ing out that there are nearly always patterns in the chaos. Whatever we try to achieve must take these patterns into account, and our success may depend upon the degree to which we can see them at work. Gurd- jieff’s idea of the octave is a metaphor for achievement. This metaphor
is built into the enneagram.
In Music and Painting
In t e l l i g e n c e m a k e s a difference. One of the important differences that it makes is in probabilities. What is unlikely to happen when things are left to themselves can be made to happen with almost certainty by intelligence. We have become used to this in the practical arts, or technics, where we are dealing with mechanical, or at least material, systems. When we, as intelligences, try to deal with each other or with ourselves, the results are not so predictable.
Broadly speaking, then, an intelligence can deal with a certain degree of uncertainty and complexity coming from the environment of its opera
tions; but dealing with itself is another matter. This is important because intelligence begins and ends its path with an aim or purpose. Dealing with the world “outside,” to keep to our aim, is one critical factor on the path. Dealing with the world “vnthin,” to improve on the aim, is quite another. This is now of urgent concern in the running of business organi
zations, which are mostly unable to catch up voth the effects they them
selves create.
A complete intelligent action has various stages or levels in it. It is constructed in steps. In Gurdjieff’s system, the line between start and
44
finish has seven steps in it. These appear around the circle of the ennea- gram. The idea of a sevenfold division of scale or level is a very old one.
Gurdjieff himself referred to its primitive expression in Genesis, where the
“day of rest” refers to the last, completing transition. Of course, we come across the idea of sevenfoldness in such things as the spectrum of colors, where there are no actual transitions of state, leading from one condition to another, but the splitting of a whole (white light) into various comple
mentarities and degrees. According to Gurdjieff, this kind of structure is ubiquitous, but when it comes to bringing about change in some mate
rial, more is involved. There is no straightforward pathway between the start and the finish of a process. The initial impetus would fail part way through if there was only its own momentum. Without adjustments, the process would deflect and never reach its intended end point.
To convey this idea, Gurdjieff made use of the analogy of the musical scale. Numerous scales have developed over the centuries. All involve some compromise. The most natural interval to the ear is that of the octave itself, where the rate of vibration is doubled. The next harmonious interval is based on the ratio 3/2 (the dominant or fifth); the next on 4/3 (the fourth); and the next on 5/4 (major third). This means that we want to use these intervals to determine notes within the octave. The next simi
lar ratio, 6/5, is that of the minor third. The ratios 7/6 and 8/7 do not give results in harmony with the other ratios, but the next again, 9/8, gives the interval we accept as a tone or approximately one-sixth of an octave. If we keep the notes called the fifth, fourth, and major third, and also the tone as determined by 9/8, we find that the interval between the fifth and the fourth turns out conveniently to be 9/8. But the interval between the fourth and the third turns out to be 16/15 (or 1.066), which is close to, but not exactly, the square root of 9/8—that is, a half-tone. Similarly, the interval between the major third and the tone becomes 10/9, which is close enough to 9/8 to be accepted as a tone, but it is also not exact.
Dividing the remaining interval between sol and do (using the measure of a tone in its two approximations 10/9 and 9/8), we get la, which is 10/
9 more than sol, and si, which is 9/8 more again. However, between si and do there is only room for a half-tone (16/15). It is fairly easy to understand, then, that this particular scale, which is called the major dia
tonic scale, is a compromise and that there can be many other alternative solutions; including the “even-tempered” scale, actually used in most
Western music. This also does not give exact intervals, though it allows for identical octaves starting on any note. (See fig. 3.1.)
We are free to divide the octave in other ways. One of the most simple and interesting of these is the whole-tone scale of six notes, which was used a great deal by Debussy. The six points of the enneagram excluding the triangular figure—1, 2, 4, 5, 7, and 8—represent this simple scale.
In all variants of the diatonic scales, there are five “whole-tone” and two “semitone” intervals. In subjective terms, we could call the diatonic scales “dramatic” in contrast with the whole-tone scale of Debussy, which is called “impressionistic.” The dramatic scale has tensions and uncer
tainties in it that the impressionistic scale lacks. The two semitones can be seen as necessary adjustments which have to be made to preserve the steady sequence of tones in the rest of the octave. Many people hear the two semitone intervals (mi-fa and si-do) as tense. There is the sense of a
“retardation” in going from mi to fa and a sense of “being urged on”
from si to do. These subjective evaluations are, of course, no evidence for a physical theory. But they convey an experiential sense of what the two critical intervals mean. Gurdjieff’s use of the musical octave combines art with science.
While science concerns what actually is, art concerns what we intend.
Science uncovers laws, while art proceeds by arranging things “not ac
cording to law” or “otherwise.” They go hand in hand, because it is only on the basis of knowledge of laws that we can construct the deviations
4t> The Frame of Transformation
Note Ratio
do 2/1
si 15/8
la 5/3
sol 3/2
fa 4/3
mi 5/4
re 9/8
do 1
3,1. The musical scale.
which impart a message. Hence, the significance of the musical analogy is to represent the fact that study of phenomena can uncover the traces of an adjustment in the laws which signify the work of intelligence. In this sense, the universe cannot be understood entirely as an object of scientific study. It is also a work of art.
The two semitone intervals represent something that deviates from the other sequences of notes. The symbology is fairly obvious; here are changes in functioning which are needed for the harmony of the whole.
Through them, phenomena can communicate with and influence each other. In Gurdjieff’s model, the half-tone intervals represent the hazards to be found on the way where something new or an act of adjustment has to be made. When the octave is put into the enneagram symbol, we see that the second hazard or interval does not appear where it should (fig. 3.2). This “error” is important because it enables a very important type of information to be conveyed.
Gurdjieff was not alone in his symbolic use of the musical scale. In medieval times, a mnemonic for the musical scale had a celestial symbol
ogy which prefigures a Gurdjieffian cosmology (fig. 3.3).* As this is not the place to make a historical survey of the subject of ancient and classical symbologies based on the octave, I shall only mention, by way of illustra
tion, one example from Renaissance times. In 1499 Botticelli painted his masterpiece, the Primavera (Spring). In this painting, there are eight fig
ures (or nine, counting the cherub). We can correlate diem with a musical octave (fig. 3.4).
3.2. The octave in the enneagram.
48 The Frame of Transformation
DO DOminus The Lord, God
SI SIdera [All] Stars
LA via LActea Milky Way
SOL SOL The Sun
FA FAta Planets
MI MIcrocosmos Microcosm [Earth]
RE REgina Caelum Queen of Heaven [Moon]
DO DOminus
3.3 A celestial octave.
The Lord, God
Mercury Voluptuous Contemplative Active Venus Floris Chloris Zephyr
do si la sol fa mi re do
opposite opposite
3.4 Botticelli’s octave.
Drawing based on Botticelli’s painting Primavera.
Looking from right to left there is: Zephyr, who impregnates the next figure Chloris with his breath; Chloris, who turns toward him while flowers come out of her mouth; these flowers are those which adorn the next figure, Floris (one of the most beautiftil female figures of Renaissance art); next, standing slightly back from the rest, with the cherub above her, is Venus, whose depiction intentionally evokes that of the Madonna; next are the three Graces, to be understood in this case as first active, then contemplative, and finally voluptuous love; voluptuous love turns and is gazing at the contemplative love; finally, there is Mercury, who raises his staff to pierce the very heavens beyond the trees. The sequence of figures follows the notes of one of the musical scales. In this case, the unusual or
“discordant” intervals appear between re and mi and between si and do.
They are clearly shown, because Chloris (re) and the voluptuous Grace
( 5/ ) are turned the other way.^
As is now widely appreciated, the paintings of this period were in
tended to convey ideas and could be read as books. In Primavera even the particular flowers shown at the feet of the figures have significance.
Nothing is put in for effect alone. Painting served as an mnemonic of ideas, compressing classical learning (and, sometimes, contemporary his
tory) into its most attractive and elegant form, in which it could be ap
preciated by the feelings as well as by the mind. We mention this, because time and again Gurdjieff insisted that truly “objective” art should be read like a book, and he obviously wanted his own sacred dances to be taken in this vein. It was also his serious wish that “artists and poets in the future” would make use of his own writings in Beelzebub’s Tales. If we look at Primavera, we can perhaps feel something of what this might have meant.
Another thing to realize is that painting such as that of Botticelli flour
ished in connection with a certain school. Under the patronage of Cosimo de Medici, and the guidance of Marsilio Ficino, one of the rare Greek scholars of his time, a Neoplatonic school was established which sought to emulate Plato’s own Academy. Many followers of Gurdjieff’s ideas have delved into Ficino and the Neoplatonic school of Florence. Cer
tainly, it was a remarkable flowering and of great importance for making a bridge between the classical heritage of the Hellenic world and Chris
tianity. To this day, we still have little knowledge of what went into the making of the modern world and the role that might have been played
by such small creative groups.’ An important role must have been played by the Arabs—particularly by the Sufi orders—and Gurdjieff’s connec
tion with such groups in more recent times is undoubtedly important.
However, our concern is with the way in which Gurdjieff presented his ideas. We have seen that the use of the musical octave (in one or another of its possible diatonic versions) was an established tradition. But Gurd
jieff was at pains to point out that his understanding of it went far beyond that of “the Greeks,” whose ideas he often contrasted with those of “the Chinese.” In this way, incidentally, he also reinforced his underlying mes
sage of retrieving real understanding from cultures on a global scale.
According to Gurdjieff’s model of the octave, any given process needs assistance in two particular places in order to complete itself Here Gurd
jieff ranges far beyond the scope of musical analogy, which can only show us the adjustments needed to establish a harmony. When it comes to making an actual transition of state from a beginning to an end, we have to take account of a buildup in substance. The two critical steps then signify important transitions: in the first, the substance comes “alive,”
while in the second, it acquires a “will” of its own. These ontological steps (having to do with being) cannot be described within the framework of the musical octave. All we can know is that there need to be at least two critical adjustments; we can have no preconception of their content.
Change and Order
To approach Gurdjieff’s understanding of the octave, it might be useful to consider a few basic principles. We start right away with the distinction between causal and intentional change. Causal change depends on what has already happened. Intentional change depends on what will happen.
Causal change is inevitable while intentional change is conditional.
Causal change goes on by itself, but intentional change has to be sus
tained.
Following Gurdjieff’s indications, there is this distinction only in the relative world, the world commensurate with human experience. In the Absolute this distinction does not hold, a notion that comes up in theol
ogy. Hence, the “law of change” differs in the relative world from how it is in the Absolute. In the causal or mechanical sequence, to speak more scientifically, the entropy of the system increases; whereas in the
purpose-50 The Frame of Transformation
fill or intentional sequence, the entropy of the system decreases (because it is expelled elsewhere). We all have the sense that when we want to achieve something deliberately, we have to go uphill against the stream of events. The causal sequences militate against the intentional ones. Going
“against the stream” is intentional, while going “with the stream” is me
chanical (and the notions of intentionally going downstream or uninten
tionally going upstream are both sheer delusion!). Gurdjieff made a strong distinction between these two sequences, “upstream” and “down
stream,” calling the first evolution and the second involution. On the per
sonal level, he focused on the way in which our intentions fail to be realized and turn into their very opposites,"* While involution goes “like a Pianola,” evolution is hazardous.
On the cosmic level, the creation of the universe is involutionary, a successive series of steps which takes “what is” from some primal and pure condition toward a state of cold and meaningless inertia. Because of the mechanical associations of the term creation, we tend to feel that it marks an addition to reality whereas, more logically, it is a privation. In involution possibilities decrease. In this sense, a gallon of gasoline has more possibilities than its combustion products: it can be used to clean stains, produce a weapon, or fiiel a car. In evolution possibilities increase.
Evolution is only feasible for relatively individualized states of existence, which are localized and of specific form. The state with more possibilities is said to be on a higher level than the one with less. The critical question for any process is whether it increases or decreases possibilities, whether it is going up or going down in level. The “going down” and the “going up” are measured in terms of possibilities, not in terms of space and time.
Entropy is a measure of the disorder of a system. All causal (down
ward) sequences result in an increase of disorder. It is, therefore, possible to take entropy as a negative indicator of level. This was not possible for Gurdjieff, since the correlation of entropy with loss of information is a concept that first emerged in the 1940s. He was constrained to present these ideas through traditional and semireligious forms and used a con
cept akin to that of “relative conditioning” to represent what we now call entropy.
He considered that all states of existence are under a certain number of laws. The greater the number of laws, the greater the conditioning and the lower the level. If we picture a given state of existence as partitioned
or divided up according to the various laws, then we can see that the lower levels are more divided. They are not divided in space but accord
ing to their possible states. The more laws, the more states. This makes the character of the lower levels more muddled than that of the higher levels. Muddledness is similar to entropy.
Gurdjiefif considered that the muddle produced by relatively large numbers of laws diminished consciousness and will. This is the equivalent of saying that the lower levels are less intelligent. Conversely, the higher the level, the greater the degree of intelligence. An evolutionary (up) se
quence results in a gain of intelligence. Involutionary (down) sequences result in a loss of intelligence. In Gurdjieff’s cosmic scheme galaxies, stars, and planets are on various levels of intelligence. There are relatively few people who think of the galaxy as having a higher intelligence than the sun, or of the sun as having a higher intelligence than the planets. It will seem strange to most—and something of a relic from earlier periods of divine cosmic geography—to equate intelligence with scale in the uni
verse. But this point of view has always been there, in different guises, throughout the modern era and has counted some of the major scientists among its adherents.^ It is simply that, with our contemporary condition
ing, it is very difficult for us to think in such terms. It requires something coming from the hidden side, the inner side, to help our minds.
Furthermore, if we think of change we might remember that it is multi
faceted. There is change within a given world, and there is change as between different worlds, higher and lower. The two comingle. Intelli
gence is mixed with mechanicality. two representations in our understanding. Gurdjieff’s primary cosmic octave, stretching from the Absolute to Nothing is only an initial sketch of a dynamic and dramatic universe. Each of its levels is like a world in which everything it contains conforms to a certain logic or set of laws. If
52 The Frame of Transformation
we are in one world, our consciousness cannot reach a higher world. The question is: How can these different levels or worlds be connected? and:
What kind of connection is possible?
One of Gurdjieff’s crucial questions was how higher influences could reach into lower worlds. The worlds are separated in a hierarchical order.
What other kind of order is there that brings them into mutual commu
nication?
Notes
1. I am indebted to William Sullivan for pointing this out to me. The topic is taken up again in chapter 14, where I discuss Gurdjieff’s ray of creation.
2. My description is adapted from that of David Foster and Pamela Tudor-Craig in
2. My description is adapted from that of David Foster and Pamela Tudor-Craig in