John Townley's AstroCocktail

It may be that where aspects and orbs are concerned, the meek may inherit the sky.

All astrologers are familiar with the traditional Ptolomaic aspects (conjunction, sextile, square, trine, opposition) and usually the more recently-used semi-sextile and quincunx. These are all based on dividing the circle into multiples of two and three, to a total of twelve. Multiples of two are hard aspects, multiples of three, easy ones. They are probably the most popular because they are the easiest to spot using the common 1-30 degree per sign labeling system. But there are also aspects which come from dividing the circle into 5ths, 7ths, 9ths, 11ths, and 13ths, often called “harmonic” aspects because of John Addey’s pioneering work on harmonic charts during the 1970’s which brought these aspects into greater usage. Exactly what they mean and how important they are is still a matter to be decided even among those who use them regularly, so here is a personal approach, based on the theory and structure of the number combinations involved, and sustained by observation in practice (anecdotal evidence, as some might call experience).

This is an aspect with some age and tradition behind it, having been used for quite a while. It is generally associated with natural “talent,” though of what kind is not always made clear. In fact, it has to do with the ability to spot and untilize proportion in either time or space or both. Frequent in the charts of musicians, artists, architects, orators, and others who depend on a good sense of timing or proportion for success. This can be for good or ill, as for instance the chart of Hitler is riddled with 5ths and their halves, 10ths -- certainly he was the most talented and compelling orator of the 20th century, and the timing of his decisions was impeccable, despite the way he used it. This quality is likely derived from mathematical applications of the number five itself, from which the Golden Section (phi), is derived. Its formula is:

and it is the universal proportion of growth within the biological kingdom. It’s the proportion of your elbow to your overall arm, your naval to your whole frame, seashell and pinecone spiral length and count from level to level, leaf positioning in vines, and so on. It is much used in all forms of art in architecture, since those are at least in part imitations of life.

This aspect is not so much in use, though it has had some popularity. It appears to represent a kind of large-scale, universal outlook on the applications of the planets so attached. It is an ability (indeed, an insistence), to see the Big Picture instead of getting hung up in the details or in only one part of the story. This has a lot of mythological background, as in most Western and much Eastern scripture and secular beliefs, the number seven is associated with completion: the seven days of creation (and thus, the days of the week), the seven heavens, seven archangels, seven pillars of wisdom, seven colors of the rainbow, seven visible planets, seven chakras, seven deadly sins, etc. Even the maximum number of ideas that can be simultaneously held in the brain. It does indeed seem to lend a broad scope of vision in the planetary areas involved in any given horoscope.

The 9th part of the circle (nonile): 40°, 80°, 160° (120° coincides with trine). This aspect is fundamental in Hindu astrology, but peripheral in the West. It is, in my experience, the ultimate “nice person” aspect, of which the quintessential bleeding heart liberal must be entirely constructed. It indicates sympathy, generosity, humanitarianism, and general good will, although it is does not always translate this into assertive action. You want friends? Get some of these...

The 11th part of the circle: 32°44’, 65°27’, 98°11’, 130°55’, 163°38’. This is a really rough aspect, and wholly unused among traditional astrologers. There is a lot of Biblical symbolism concerning the number 11 itself, and all of it is has to do with insufficiency, frustration, and incompletion, a situation that just falls short of the more whole and complete number 12. It also seems to be a somewhat revolutionary number, as it expresses dissatisfaction with the status quo and fuels a need to overthrow it. Oddly, in numerology it is called the number of the World Savior, but that may also have overtones of overthrow. Remember what Christ did to the money-changers and you may get a hint. Also His statement, “Think not that I came to send peace on earth: I came not to send peace but a sword. For I am come to set a man at variance with his father, and the daughter against her mother, and the daughter-in-law against her mother-in-law.” (Matthew 10:34-35). Troublesome stuff – that’s OK if you’re the Son of God, but hard to handle as a mere mortal. The Ayatollah Khomeini’s chart was loaded with it...

The 13th part of the circle: 27°42’. 55°23’, 83°05’, 110°46’, 138°28’, 166°09’.

This is one step beyond the natural twelve, and folks with a lot of this tend to be one step beyond, indeed. It is an aspect of the eccentric, the adventurer, the person who decides to travel the road less taken or forge out into the woods when the road ends. Sexually, it can be rather kinky (until, of course, kinks become mainstream, and thus boring), and it may lead to great adventure or simply to a useless backwater or cul-de-sac. Some paths are less-traveled for good reason...but there is always interest and amusement here, if nothing else, though those traveling in pastures beyond the pale should take appropriate cautions concerning both the perils of the unknown and those who don’t feel comfortable with the unusual.

Although these are the main extra fractions of the circle I use for aspects, it would seem logical to use more, for structural reasons. Although many of the higher, finer aspects are mutual multiples of larger ones (deciles, for instance, being half of quintiles), there are still some prime numbers to be reckoned with, such as 17, 19, 23, 29, 31, and so on. I have found 17 and 19 to be sort of “upper octaves” of 11 and 13, or at least similar in some ways. For the rest, seek out Addey’s work for clues.

Orbs. The question of orbs for these aspects arises, part of an enduring subject of debate about all aspects among all astrologers, which opens another structural problem, but one which is actually easily solved. If, for instance, we use all fractions of the circle up to the 36th (ten degrees), and we make the orb for any two adjacent aspects inversely proportional to their denominators, we come up with virtually the normal set of orbs for the traditional aspects most astrologers use -- a little under ten degrees max for an important conjunction, , five or six degrees for an opposition, three or four degrees for a trine or square. But, using the same formula, some of the finer aspects get wider orbs than usually in use. A quintile gets 2°, more than a quincunx is entitled to (about 3/4°), a septile gets a full 1 1/4°, and so on. Even the unknown 11th is entitled to more space than a semi-sextile or quincunx. It would appear that perhaps these somewhat neglected aspects are more important than they have been given credit for, as we make the attempt to base our practical usage of astrology on a more mathematically consistent substrate.

The table above lists all the fractions of the circle (2-36), with orb limits assigned according to the size of their denominators (inversely, the smaller the fraction, the smaller the space it takes up compared with its neighbor), and it’s interesting to see the patterns they form around the major aspects. Even though we only go up to the 36th harmonic here, it’s clear that around the conjunction, opposition, square, and trine there is a space of infinitely reducing fractional aspects until the perfect aspect is formed, almost a gravitational or mathematical swath around the aspects, according to their size. The little entries really do bow down to the big ones, so it’s no wonder we favor the traditional aspects. But perhaps we should pay more attention to the real relative mathematics of nature and take a closer look at what we have chosen to ignore through the visual inconvenience of our common 1-30° method of chart layout.

Lagrange Points. Indeed, that image and model may have more to be said for it, as these same major divisions of the circle in any planet’s orbit describe its Lagrange points, the attractively stable areas where other, smaller objects tend to cluster and be ushered along, like many of the “Trojan” asteroids with Jupiter, many of the Centaurs with Neptune. Perhaps the very nature of aspects itself is gravitational, as we are inclined to believe. The bigger the object and the longer the time it’s been there, the more perfectly aligned everything else becomes to it, part of the phenomenon of entrainment. How far that goes down the decreasing scale of existence, right to our own actions here on earth, is one of the most important astrological questions to be addressed.

Lagrange points: Gravitationally, aspects based on three are stable, others not...is that where astrology gets it from?... to play with where these points occur throughout the solar system, plus more nice illustrations, and simple math, go here...

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