Aspects: under the three crosses

Incorporating aspects into esoteric astrology

Although it might be argued that aspects—like the houses—are specific to the personal or exoteric horoscope, not the esoteric chart; the three crosses (Cardinal, Fixed, Mutable), seven rays and a more universal application of esoteric astrology’s triangles can be applied to aspects. As with the houses, there are hints towards this throughout Esoteric Astrology.

The great problem… is the need for a much more sound and comprehensive understanding of number symbolism than is usually provided by the general run of books on numerology. —Addey, John M., Harmonics in Astrology, p127.

The images below link directly to separate aspect group pages, and illustrate the geometrical basis of all aspects up to 12 (t)he ‘dodeciles’ that include the 150° quincunx):

Developing individuals are held to be influenced by esoteric rulers and their relationships by ray and sign, as well as—or rather than—the orthodox planets and the aspects between them, although there are several passages with aspect-like metaphors, for instance (from A Treatise on Cosmic Fire):

The Law of Sacrifice “is Vulcan and Neptune in opposition”. (BaileyTCF, p.597)

Note that this is not a direct reference to the astrological aspect of opposition—such snippets only hint at esoteric aspect interpretation.

History and geometrical basis

Dividing the 360° of a circle by the numbers one to twelve, and joining the points, creates the polygons and star polygons—from the triangle to the 12-sided dodecahedron. These form the angles of astrological aspects from the trine (3) to quincunx and semisextile (12). Polygons and stars obviously have more than one point, so—starting with the Quintile and Biquintile of the 5-sided pentagon and pentagram/star—each polygon forms its own aspect groups (as in the diagrams).

However, contemporary astrology tends to use only some of the 24 possible aspect angles. These 24 also include the lesser-used Septiles of the 7-sided polygon and its stars, as well as the “undeciles” or more strictly “hendeciles” (see the origins of the words) from the rarely-used 11-sided polygon with its four stars or hendecagrams.

I see that “undecagon” and “duodecagon” have been rearing their ugly heads again. The full set is: (…) pentagon, hexagon, heptagon, octagon, enneagon, decagon, hendecagon, dodecagon… —the late John Conway, mathematician, discussing polygon names in The Geometry Forum, Swarthmore College, Pennsylvania, 1994

So for aspects from the 11-sided hendecagon, “Hendecile” is more correct than “Undecile”, although it would be clumsy to replace the well-established “Novile” with “Enneile”!

It soon becomes obvious that the naming and traditional meaning of aspects does not always follow their polygonal and numerical origins. For example, the Semisextile and Quincunx are both formed by the 12-sided polygon, so both are duodeciles; while the more obviously-named quintile and biquintile are from the 5-sided polygon. Their groupings only become apparent by looking at the geometry, and it helps to use the polygon’s name.

Instead of focussing on the meanings of each individual aspect, some astrologers acknowledge that aspect groups belong to their originating polygons:

the circle can be divided by any number or its multiples and still offer relevant meaning. (…) The focal aspect plus its multiples are all members of one “family” or “series”. The multiples draw their primary meaning from the main division number that produced them, and thus all share a common theme. (…) Such aspect groupings may provide astrologers with many missing links in aspect analysis.
—Tierney, Bil, Dynamics of aspect analysis, CRCS Publications, California, 1983

Grouping aspect ‘families’ under the 3 crosses

These 12 geometrical families can be resolved even further into 3 core groups that match the Cardinal, Fixed or Mutable crosses at the root of esoteric astrology. Using the numerical primacy of the first three integers 1, 2, 3 to the crosses, these three fundamental groups contain every possible aspect, with the Conjuction, Opposition and Trine at the root of each:

Cardinal Fixed Mutable
life, synthesis, initiation consciousness, intensification, crisis form, change, experience
Conjunction 1 Opposition 2 Trine 3
Quintiles 5 Square 4 Sextiles 6
Septiles 7 Octiles 8 Noviles 9
Deciles 10 (1) Hendeciles 11 (2) Dodeciles 12=3

The digital root of every number higher than nine is found by by adding multiple digits until only one remains e.g. 28=2+8=10, 1+0=1. The numbers one, two or three act as a digital foundation, so the groups under each share patterns and qualities:

The complete aspect range from one to twelve can therefore be divided—like the zodiac—into three ‘meta-families’, each containing four aspect groups under one of the three crosses, with higher-numbered aspects—if present in sufficient quantity or in significant patterns—enhancing the esoteric interpretation, all within the framework of the three crosses and the three rays of aspect (Will, Love-wisdom, Intelligent activity). To summarise:

Cardinal cross
represents the principle of will,
stimulating synthesis and mental polarisation in each of the fields of experience from the intuitive self to material life.
odd numbered aspects from polygons of 1, 5, 7 sides
plus 10 (digital root 1: 1+0)
Fixed cross
represents the principle of love-wisdom
the emotional intensification often accompanied by inner conflict, experienced after the first flush of self-awareness has waned.
aspects from polygons of 2, 4, 8 sides (divisible by 2 but not 3)
plus 11 (digital root 2: 1+1)
Mutable cross
represents the principle of active intelligence
what we learn from lived experience and real-life circumstances, often repeated until the message is driven home.
aspects from polygons of 3, 6, 9 sides (divisible by 3)
plus 12 (digital root 3: 1+2)

Rays 1–3 are held to be rays of attribute because they have fundamental qualities that are simply repeated with variations in the higher numbered rays of aspect 4-7. Geometrically, point (1), line (2) and plane/triangle (3) form the entire basis of simple planar geometry.

From the table above, for further refinement, each aspect family could also be related to the numerically corresponding ray. Under the three rays of aspect and the four rays of attribute the numbers 8-12 also fall into place:

Ray 1 will, synthesis, Conjunction (1)
Ray 5 mental refinement, Quintiles (5)
Ray 7 order, Septiles (7)
Deciles (2x5, 1+0 = 1)
Ray 2 love-wisdom, Opposition (2)
Ray 4 harmony through conflict, Squares (4)
Octiles (8 = 4x2)
Hendeciles (1+1 = 2)
Ray 3 intelligent activity, Trine (3)
Ray 6 idealism, devotion, Sextiles (6 = 2x3)
Noviles (9 = 3x3)
Duodeciles (1+2 = 3)

Because of the divisibility of 12 by both 3 and 4, it might be tempting to match the 4 aspect families under each cross with the 4 elements or other groups of 4, but in practice, this only highlights how correspondences that might appear tidy don’t always hold!

Esoteric aspects in practice

As a visual aid to analysis, each of the three aspect groups under each cross can be drawn up on three separate chart layers and/or in three colours in your Astrology software, following the three primary ray colours:

with (say) lighter shades for the higher numbers.

The relation between the three crosses and three primary rays of aspect (rays 1, 2 and 3) and principles of synthesis, intensification and experience is the crucial point. It underpins the esoteric connection between the various aspect families and their 3 overarching meta-families under each cross, and isolates the possible predominance of aspects under any particular group—e.g. a horoscope with a preponderance of Oppositions, Squares, Octiles and (if calculated) Hendeciles indicates a strong fixed-cross/love-wisdom/emotional-intensification theme to a life. Visualising the distribution of aspects under each cross: Cardinal, Fixed or Mutable may show an emphasis of one cross, or there may be balance between two, or even all three. This weighting of the aspect families as a whole needs to be seen in the light of the overall and more primal weighting of the crosses by planetary position and ray emphasis.

In this way, interpretation of a previously-overwhelming forest of astrological aspects is simplified under the overall esoteric framework, and the essential theme of a life can be revealed.

Weighting and aspect orbs: caution!

Note: it is hard (and possibly misguided) to adhere to a strict weighting of individual aspects in the greater light of the whole chart. Allowances for intuitive flexibility (“this just feels important in the chart I’m working on”) can be too fluid for universal rules regarding orbs for planets, let alone aspects. What makes this even harder is aspect probability, for example: even with narrow orbs, any point within the zodiac can form six possible Septile or Novile family angles, but only two Trine or Square angles (counting the mirrored angles to both the left and right—or to use the loaded terms, sinister and dexter).

The classical attitude towards aspects and orbs was evidently more relaxed than that of contemporary astrology. The simple rule was that where two signs are in aspect, any planets within those signs are in aspect too, regardless of the specific degrees (…) Aspects judged according to the relationship of the signs are called platick, from a term which meant ‘plate’ or ‘broad area’. In later astrology the term partile generally referred to aspects which were exact or near perfection, whereas platick referred to those which were ‘loose’, or within the limits of their recognised orbs. —Houlding, Deborah, 2004, The Classical Origin & Traditional Use of Aspects

For esoteric charts, therefore—especially concerning the rays—it can be more revealing of the deeper purpose to give primacy to the signs involved and their rays, reversing the familiar adage to become “sign trumps aspect”. Orbs are for the individual astrologer to decide, case-by-case. So it’s best to use the three Cardinal/Fixed/Mutable aspect meta-families, while bearing in mind that the fact that the polygons of some higher-numbered aspect families will generate more of their type, statistically.

Subtler aspects need patterns

It’s important to note that the higher-numbered aspects are practically meaningless if only between two points. However, by using narrow or generous orbs (according to your approach) to identify closed or symmetrical aspect patterns between 3 or more points, aspects that would be insignificant alone can offer esoteric indicators when taken in aggregate. Closed patterns (triangles, rectangles) that combine different aspects from the same family are already familiar in orthodox astrology; e.g. the mutable family finger of fate (60° sextile and two 150° quincunx aspects) can span 3 crosses while the fixed family finger of the world (90° square and two 145° sesquiquadrate aspects) usually covers two of the crosses. Depending on the signs involved, the Grand Cross, Mystic Rectangle, T-square, Kite, etc. will enhance one or a combination of crosses.

Where multiple aspects from a specific polygon show a symmetrical pattern i.e. a regular or irregular polygon with three or more points (like a finger of fate or mystic rectangle but with Quintiles/Deciles, septiles, noviles etc.) it’s worth comparing the aspect’s ray sympathies with the rays of the signs and planets involved, as well as the specific aspect meta-family: Cardinal, Fixed or Mutable and the crosses where the points of the polygon fall.

Where aspects with a mixed interpretation (e.g. semisextile, quincunx) appear to strengthen other factors in a chart, or are between planets already significant in a horoscope, it may also be worth examining whether they are applying (moving towards each other) or separating (moving apart). Two astrological classics: The Lunation Cycle (Dane Rudhar, 1985, Aurora Press, Santa Fe) and Cycles of Becoming (Alexander Ruperti, 1978, CRCS Publications) cover how planetary cycles determine whether pairs of planets are applying or separating, and more besides. For a good explanation online, see Understanding planetary cycles from Time Nomad.