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<P><i>This is one of three articles on this site about the enneagram. The others 
  are: <a href="/properties/tree/">The Enneagram and the Tree of Life</a> and 
  <a href="/properties/threeandseven/">An Outline of My Thoughts on the Enneagram: 
  the law of seven and the law of three</a></i> 
<P><font color="#000000">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.</font> 
      <P><font color="#000000">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.</font> 
      <P><font color="#000000">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).</font> 
      <P><font color="#000000">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:</font> 
      <P> 
        <CENTER>
          <font color="#000000"><IMG SRC="/common/graphics/fig1.gif" WIDTH=310
         HEIGHT=310 ALIGN=bottom></font> 
        </CENTER>
      <P><font color="#000000">The sequence normally considered is that around 
        the circumference, note to note, as in figure 2 (the 'shock points' are 
        disregarded for this discussion).</font> 
      <P> 
        <CENTER>
          <font color="#000000"><IMG SRC="/common/graphics/fig2.gif" WIDTH=310
         HEIGHT=330 ALIGN=bottom></font> 
        </CENTER>
      <P><font color="#000000">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.</font> 
      <P><font color="#000000">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.</font> 
      <P><font color="#000000">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.</font> 
      <P><font color="#000000">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: <I>Cosmic Secrets</I> and 
        A. G. E. Blake's <I>The Intelligent Enneagram</I>..</font> 
      <P><font color="#000000">Returning to the interior figure, as explained 
        in P. D. Ouspensky's<I> In Search of the Miraculous</I> , 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.</font> 
      <P><font color="#000000">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.</font> 
      <P><font color="#000000">All this, however, is merely suggestive and a rather 
        slim basis to impute a special significance to the relationships between 
        points suggested thereby.</font> 
      <P><font color="#000000">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.</font> 
      <P><font color="#000000">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.</font> 
      <P><font color="#000000">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.</font> 
      <P><font color="#000000">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'.</font> 
      <P><font color="#000000">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.</font> 
      <P> 
        <CENTER>
          <font color="#000000"><IMG SRC="/common/graphics/fig3.gif" WIDTH=310
         HEIGHT=310 ALIGN=bottom></font> 
        </CENTER>
      <P><font color="#000000">As can be seen in the figure, the order around 
        the circumference (clockwise) is now C - A - F - D - B - G - E - C.</font> 
      <P><font color="#000000">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.</font> 
      <P> 
        <CENTER>
          <font color="#000000"><IMG SRC="/common/graphics/fig4.gif" WIDTH=310
         HEIGHT=310 ALIGN=bottom></font> 
        </CENTER>
      <P><font color="#000000">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.</font> 
      <P><font color="#000000">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'.</font> 
      <P><font color="#000000">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.</font> 
      <P><font color="#000000">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.)</font> 
      <P><font color="#000000">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.</font> 
      <P><font color="#000000">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.</font> 
      <P><font color="#000000">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 <I>Evolution of Music Through Changes in Tone-Systems</I>, 
        (translated by Joscelyn Godwin in his <i>Cosmic Music</i>) 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.</font> 
      <P><font color="#000000">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.</font> 
      <P><font color="#000000">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).</font> 
      <P><font color="#000000">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.</font> 
      <P><font color="#000000">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.</font> 
      <P><font color="#000000">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.</font> 
      <P><font color="#000000">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.</font> 
      <P><font color="#000000">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.</font> 
      <P><font color="#000000">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.</font> 
      
<P>Thanksgiving week, 1997 </p>
<P><font color="#000000">Copyright 1997, 1998 by <a href="javascript: mymail();">David 
  Eyes</a></font> </p>
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