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Home Enneagram General Enneagram Articles Some Properties of the Enneagram

Some Properties of the Enneagram

The question as to the ultimate origins of the enneagram may be with us for a long time. Beyond the question of origins, or of the origins of a given application of this symbol, such as for personality or ego fixation typing, the question stands: what is the enneagram, and why is it just so? It has clearly been found to resonate strongly as a practical, empirical tool: but what underlies its construction? Is it simply a given, or can we try and find a better foundation for applications based upon it by discovering the how and why of its unique construction. This brief outline attempts to survey what is already known about its construction, and to introduce a new viewpoint that can expand our appreciation of this symbol.

The enneagram figure or symbol first came into general view in the 20th century through the teachings of G. I . Gurdjieff. Gurdjieff's presentation and focus was in many ways different than that found in Ichazo's teaching or in studies derived from it. In general, the enneagram type system is presented primarily a system of three groups of three subtypes. As such, it can be grasped intuitively fairly readily. However, the interior six-pointed figure of the enneagram, suggesting a nonlinear relationship between certain points, is less easy to explain, although it is a key aspect of what makes the enneagram such a compelling visual symbol. Even if we are certain that these relationships exist empirically, we are at a loss as to why just these relationships apply, and not others. It is regarding this inner figure, connecting the points 1-4-2-8-5-7, that this article attempts some fresh insights.


Gurdjieff's presentation of the enneagram did not apply directly to personality or character types, although one of his second generation followers, Rodney Collin, did develop it into a system of 'planetary' 'essence' types. (It is interesting to note that Collin spent his last years in Latin America, the same part of the world from which Ichazo's formulation would arise).

What instead was characteristic of Gurdjieff's presentation of the enneagram was that he described it as a symbol relating the law of the triad (law of three) to the law of the octave (law of seven). Thereby he brought the enneagram into relation with the form of the musical scale. The points along the outer circumference of the enneagram represented corresponding notes on the musical scale:


The Enneagram

The sequence normally considered is that around the circumference, note to note, as in figure 2 (the 'shock points' are disregarded for this discussion).


The Enneagram Outer Circuit

As with the C major musical scale, there are points of 'missing semitones' (that is, the sharps and flats, the "black notes" of the piano). In the representation of the enneagram, the first of these 'gaps' is suggested by the apex of the internal triangle (representative of the 'law of the triad') at point 3.

To Gurdjieff, the motion around the enneagram represented the ascent (clockwise) of an impulse or process from start to finish, to completion, or musically, from 'do' to 'do' on the next higher octave.

The missing semitones' (between mi and fa and si and do on the C major scale) suggest points where the process can go wrong, where a new, corrective influence from outside must be brought to bear in order that the intended impulse reach completion. The second crisis occurs on the musical scale at the interval between si and do - that is, just prior to completion. However, as the enneagram indicates, the second point on the triad (which is intended to show these 'shock' points), occurs at point 6. This is to allow the same impulse (that is, the third octave begun at point 6) to serve as both the first corrective 'shock' for the second octave begun at point 3 as well as provide the impetus to get the original impulse over the si-do impasse.

This description is incomplete and sketchy; to appreciate the necessity for this mechanism involves calculation of the ratios of each of the different 'notes' of the scale. In the diatonic (sevenfold) musical scale, the note 're' is 1/8 (of the length of the octave) above 'do', mi is 1/4, 'fa' is 1/3, 'la' is 1/2, 'so' is 2/3, and 'si' is 7/8. These proportions underlie the structure of the enneagram, although the even spacing of the points of the circle disguises this fact. The best references for exploring this aspect of the construction of the enneagram would be Russell Smith's Gurdjieff: Cosmic Secrets and A. G. E. Blake's The Intelligent Enneagram..

Returning to the interior figure, as explained in P. D. Ouspensky's In Search of the Miraculous , that it is constructed by forming a decimal fraction out of 1/7 (or 2/7, 3/7, etc.): 1//7 = .142857... , that is, it is an infinitely repeating decimal.

Thus this intriguing figure is formed by tracing a line between the points in this sequence.. It is interesting to note that decimal system, being based on the number ten, incorporates the number seven and three by their addition. One may further note that the interior figure suggests a relationship of seven elements that are equally proportioned, whereas when the 'law of seven' interacts with the 'law of three,' the relationships between the elements (now considered as 'notes') assumes the diatonic proportions described above.

All this, however, is merely suggestive and a rather slim basis to impute a special significance to the relationships between points suggested thereby.

Tony Blake, after J. G. Bennet, a pupil of Gurdjieff, has developed a concept of the interior figure as part of a 'self-correcting feedback process' and simply an aspect of one instance of a broad class of 'N-grams' (16-grams, 25-grams etc.) displaying certain similar characteristics. However, fruitful as these insights are, the properties of 'N-grams' do not exhaust the properties of the enneagram, which additionally incorporates the idea of progression across a musically-proportioned scale.

What are the laws underlying the creation of the musical scale? Without going into the details of musical temperament or tuning, the sevenfold (or twelve-fold, if you count the semitones') scale is produced by generating a 'chain of fifths' (or their inversion, fourths). Just as when we strike a tone and then sound the tone with half or double as many vibrations, we hear a unity (the octave), when we relate two tones in the proportion 2:3, we also hear a special consonance -- this is the interval of the fifth. On the piano keyboard, one can travel by fifths: F - C - G - D - A - E - B. Thus all seven notes (and the semitones as well) can be formed from the same basic consonance, the fifth. However, when they are projected in the range of a single octave, they sort themselves into the familiar order of the C major scale, and reveal the distinctive ratios that provide for, among other things, the need for the special 'shocks' that are such a distinctive part of Gurdjieff's teaching.

The assumption that underlies all of this is that there is a correspondence between the expression of musical and acoustic law and the fundamental nature of reality, both in ourselves and the cosmos. Gurdjieff however was not alone in suggesting this; the idea goes back as far as Pythagoras and beyond into ancient India. There thus exists a large body of work - sometimes called 'speculative music' -- concerning these relations.

What then of the interior figure? As we can see, each point corresponds to a note (excepting 'do' or C, which is the 'fundamental' tone). Points 3 and 6 correspond to the 'shocks' or 'place of the missing semitone'.

Whenever the interior figure is discussed, it is usually in terms similar to how the motion along the circumference is described - the motion of a point, or process, from stage to stage. However, if rather than moving from point to point along the path of the interior figure, we instead move the points themselves - considered as notes, not simply as points - simultaneously along the paths of the figure, we obtain a new disposition of notes around the circle (to better correlate the points with the musical intervals, the notes of the scale are given the corresponding notes of the C major scale, thus do = C, re = D, mi = E, etc.). In other words, 'D' at 1 moves to 4; 'E' at 2 moves to 8; 'F' at 4 moves to 2, and so on.



As can be seen in the figure, the order around the circumference (clockwise) is now C - A - F - D - B - G - E - C.

Some qualities of this figure soon become apparent. First, if lines are drawn connecting the 'notes' in their original order C-D-E-F-G-A-B-C -- a regular seven-point star is traced (dashed line in figure). (The two 'shock' points are disregarded). And whereas previously the notes on the circumference progressed clockwise by ascending seconds, considering a form of 'inversion' has occurred, they now progress counterclockwise on the circumference by ascending thirds. (Or descending sixths clockwise). Although the sevenfold star figure seems distorted projected against the ninefold circumference, they are in fact 'evenly-distanced' where 'distance' is understood, not metrically, or even in proportion of 'vibrations', but in proportion of intervals.



The notes can be progressed a second time. A moves from 1 to 4; F from 2 to 8; and so on, yielding the sequence C-G-D-A-E-B-F-C around the circle. This time, the notes are in the relationship of ascending fifths (clockwise, inverting again) to each other, that is, they have assumed the form of the 'generating' chain of fifths. And now a second type of star-figure is formed if one reconnects the points in their original order.

Progressing further, the relationships recur, only this time as 'mirror images' of each other; ascending intervals becoming descending, (or are inverted). The continued progression through the six points of the enneagram thus appears as a kind of 'breathing'.

What might be the significance of this? First, remembering that the enneagram is based on the proportions of the octave, it is striking that by exchanging positions in the way described preserves an ordered musical relationship between the notes. Geometrically speaking, the interior figure is a member of a set of 'Pascal Hexagrams', of which their are twelve possible types - that is, twelve possible figures connecting six points with six lines. However, it is only this particular figure which yields an intelligibly ordered result when the note-values are 'circulated' along the path.

It is also striking, and perhaps suggestive, to see that the path around the circumference is transformed into regular, star-like patterns. It is also suggestive to compare these to the nine-pointed stars of Ichazo's 'enneagram of integration' and 'dynamic enneagram', which display similar (nine-fold instead of sevenfold) star patterns. (There is another geometrical figure that will generate the nine-fold star patterns.)

Both of these orderings suggest that there is more that underlies the construction of the enneagram, and particularly the interior figure, than simply the decimal expression of the fraction one-seventh.

The significance of various constellations of notes or tones is a matter for future study, about which only suggestions are offered here. Within the body of speculative or cosmic music, the most intriguing suggestions are found in the idea that different intervals are related to different types of consciousness. Indeed, in humanity's historical development, there have been a number of different musical systems, each taking a different interval as the cornerstone of its musical system. It is not a great leap to assume that these different musical systems expresses something of their unique inner natures, that is, how they experience the world.

An excellent survey of this idea is found in the work of Hans Erhard Lauer, who developed ideas of Rudolf Steiner's regarding the changing experience of the various musical interval's during mankind's development. In his Evolution of Music Through Changes in Tone-Systems, (translated by Joscelyn Godwin in his Cosmic Music) Lauer gives a comprehensive and very suggestive survey of the development of musical forms throughout history and correlates this with different ways humanity experienced itself in relationship to the cosmos and to itself. Most relevant in this context is the general idea that the experience of the twelvefold progression of fifths (expressed in outward form by the early development of the pentatonic scale) related man to the whole cosmos (that is, to the 'zodiacal' periphery, or specifically, the passage of the earth through the cycle of seasons) whereas the experience of (or expressions of) the chromatic scale of later times was an indication of mankind's progression to a more earthbound consciousness, in which the 'I' could develop fully. Lauer's exposition (based on Steiner) is a very worthy study in itself; it is referred to here because it expresses the idea of different "states of consciousness" being somehow correlated with different experiences of musical scales. This idea is a key to the possible significance of the thoughts presented here.

The original disposition of the notes around the circumference of the enneagram is in the linear sequence that our everyday consciousness is used to processing everything, it is a world of (apparently) ordered cause and effect, yet, as Gurdjieff pointed out, this 'diatonic' law of seven creates a world of hazard, a world where things can go wrong, if the proper corrective steps are not taken.

What might a world of thirds tell us? Musically, the third is where the idea of the major and minor modes is expressed. That is, the 'tension' that is the soul-experience of modern man is expressed now as confident self assurance, now as melancholia. As Rudolf Steiner describes in a lecture of November 12, 1906: "When the minor third is played, one feels pain in the soul, the predominance of the sentient body, but when the major third resounds, it announces the victory of the soul." Thus the progression of the constellation of the enneagram may point to a threshold of enhanced self-awareness, wherein the soul is challenged to overcome the tug of matter (minor mode) and express the spirit (major mode).

Progressing to the circle of fourths and fifths, these intervals are 'perfect', they have no major or minor form. In the fourth and the fifth, we have perhaps returned to the creative source (remember, the scale is generated via chains of fifths, or its inverse, the fourth). From this more cosmic perspective, perhaps this suggests that it is only from our 'earthly' viewpoint that events seem to be out of joint and in disharmony.

From the point of view of a linear process, however - going do, re, mi, fa, so - the approach to the fifth (so) at point 5 represents the point of 'maximum tension' of 'farthest distance from the source', the point of greatest hazard. But from the cosmic, peripheral perspective, everything is related to everything else by the interval of the fifth, which, despite representing (or causing) the 'maximum tension' is also the primal creative consonance (as opposed to the unitive consonance of the octave). By showing this underlying relationship to the production of the diatonic scale by means of the fifth, the enneagram is also brought into direct relationship with the zodiacal symbolism of the number twelve; it can be seen that the 'shocks' in a sense represent the influence of the 'hidden' 'unmanifest' five notes of the complete twelvefold chromatic (zodiacal, peripheral) scale.

Indeed, there is a rich store of literature on 'speculative music' and musical symbolism that can be fruitfully brought into relationship with this figure of the enneagram once the power of metamorphosis of the inner figure is understood. What is intended here is simply to indicate this basis of relationship. By means of these indications, it can be seen that the interior figure is a function for transforming the relationships of the elements of the octave themselves, revealing other modes of relationship beside the 'given' of the 'natural' diatonic sequence. With each progression, a new threshold is experienced.

The inner figure is now seen as a kind of 'cipher ring' or 'metamorphosing function' that transforms the given interval relationships of the enneagram. This transformation shows the inter-relatedness that is part of the deep structure of the enneagram, a symbol that can be interpreted from many directions. The inner figure progresses through different constellations of tone-relationships; these indicate a different relationship among the points than that given in the linear sequence around the circumference. What these constellations ultimately signify, and what is the dynamic underlying this progression, is a study for the future.

When the enneagram is used as a symbol against which to cast the system of personality or ego types, clearly the ideal is the self that is fluid in all points of the enneagram, one that is able to move freely to all points. As seen by the interior figure, 'motion' need not strictly be a linear concept, but rather can be provoked by a re-contextualization of the entire environment. Insight into the construction of the interior figure, and a further study of the symbolism of speculative music, may serve then as a guide to intuition.

The ancient idea of a creative 'divine monochord,' creating the various realms of spiritual and bodily existence, is reflected in the physical world in the concrete example of the so-called Chladni figures that form themselves in vibrating sand or powder in response to a musical tone. If indeed there is a world-creative power in tone, then it will express itself in the structures underlying consciousness and personal expression as as well.

Thanksgiving week, 1997

Copyright 1997, 1998 by David Eyes