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This is one of three articles on this site about the enneagram. The others
are: The Enneagram and the Tree of Life and
An Outline of My Thoughts on the Enneagram:
the law of seven and the law of three
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 sequence normally considered is that around
the circumference, note to note, as in figure 2 (the 'shock points' are
disregarded for this discussion).
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
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