LESSON TWO (BEGINNERS/INTERMEDIATE): ASPECTS

CONTENTS:

* Aspects: Traditional and Harmonic

- Traditional Aspects

- Harmonic Aspects

* Orbs

* Time Course of Aspect

* Aspect Patterns

* The Natures of the Aspects

In delineating a chart, one looks not only at the sign and house positions

of the planets and luminaries (Sun and Moon), but at the *relations* among

them. In my opinion, this is where most of the action lies. The relations

give you the dynamics of the chart.

In astrology, the angular relation of a pair of planets is called an

ASPECT. Why "aspect"? This comes from the early anthropomorphism in

astrology. The planets were viewed as animate beings; they were the

"rulers" or "lords" of signs and of the "houses," "domiciles" or "mansions"

in which they resided. Their relations were the ways they looked at or regarded

one another. "To aspect" used to mean "to look at"; in modern English,

the word usually means the appearance of something, or how it looks,

especially how it looks from a particular direction, or else the visible

side itself; so the sense has changed. There is a bit of a chicken and egg

problem here, though; the Oxford dictionary states that the astrological

meaning of the word was the earliest; perhaps the projection of animacy

onto the planets led to the word's taking on the meaning of "looking at."

In discussing aspects, I will first consider aspects between the members

of a planetary pair. I will then deal with aspect patterns involving more

than two (and often several) planets. (The word "planets" is used in

astrology as a shorthand for "planets and luminaries.")

ASPECTS: TRADITIONAL AND HARMONIC

An aspect is an angular distance in the zodiac between two planets that is

considered meaningful in astrology. I will consider two sets of aspects. The

first is the set of "traditional" aspects that has been used for centuries

in the West. The second is the set of "harmonic" aspects, most of which

are relatively new in use, and their use is part of a revolution taking

place in astrology that stems from a critical re-examination of traditional

principles.

TRADITIONAL ASPECTS

The traditional aspects are those associated with Kepler and Ptolemy.

They are:

NAME ANGULAR SEPARATION

Conjunction 0 degrees

Opposition 180 degrees

Trine 120 degrees

Square 90 degrees

Sextile 60 degrees

We might also include the so-called "minor" aspects:

Semi-square 45 degrees

Sesquiquadrate 135 degrees

Semi-sextile 30 degrees

Quincunx 150 degrees

Johannes Kepler was the first to make this distinction between "major" (the

first list) and "minor" aspects. He also included among the "minor" aspects

three aspects that have only recently come into widespread use:

Quintile 72 degrees

Biquintile 144 degrees

Decile 36 degrees

Ptolemy recognised only the "major" aspects, but did not consider the

conjunction an aspect. Why? Two planets in the same position cannot

really be said to be "looking at" (aspecting) one another; so the

conjunction was thought of as a position. Ptolemy dismissed the quincunx

and the semi-sextile as "inconjuncts"; this became a common name for

the quincunx (but not the semi-sextile). Jean-Baptiste Morin claims to

have discovered the semi-sextile and quincunx.

You may have noticed that all of these aspects represent divisions of

the zodiacal circle by integers:

Conjunction Division by 1

Opposition Division by 2

Trine Division by 3

Square Division by 4

Quintile Division by 5

Sextile Division by 6

Semi-Square/

Sesquiquadrate Division by 8

Decile Division by 10

Semi-sextile/

Quincunx Division by 12

Now why isn't there an aspect for division by 7? or 9? or 11? or for

higher integers? And why was division by 5 and 10 traditionally ignored?

And why is the division by 8 considered "minor"?

The answer is one that reveals much about the limitations of the human

mind and little about astrology itself.

The zodiacal circle is traditionally divided into 12 sectors (signs).

All of the commonly-used traditional aspects (the conjunction, opposition,

trine, square, and sextile) can be readily observed, without calculation,

in a circle with twelve divisions. Planets in conjunction are in the same

sign. Planets in opposition are in opposite signs (6 signs apart). Planets

in trine are 4 signs apart; planets in square are 3 signs apart; and planets

in sextile are 2 signs apart. By contrast, planets 1/8 of the circle

apart are 1.5 signs apart, and planets 3/8 of the circle apart

and 4.5 signs apart. Planets in quintile are 2.4 signs apart, and planets

in biquintile are 4.8 signs apart. Planets 1/7 of the circle apart are

1.714 signs apart and are not even a whole number of degrees apart!

Planets separated by 1/9 of the circle are 1.333 signs apart. So the

aspects that have been in common use are ones that are easy to observe

within a wheel divided into 12 sectors of 30 degrees each. In other words,

the popularity of the traditional aspects is an artifact of the traditional

system of division for the zodiac! If we were to divide the zodiac into

5 sectors, the quintile and the biquintile would become the "obvious"

aspects.

Recently, astrologers have begun to abandon the traditional aspect set

in favour of the full set of "harmonic" aspects, a topic to which we

now turn.

HARMONIC ASPECTS

If we adopt the hypothesis that any integer division of the circle is

meaningful, then the set of aspects we consider expands considerably.

We will now allow division by 7, and 9, and 11, and by any higher

integer (although in practice we usually stick to relatively low

integers).

The full set of harmonic aspects includes every angular distance that

is associated with a division of the zodiac by any integer. When we

divide the circle by 5, we get the quintile (72 degrees) and the

biquintile (144 degrees). There is no "triquintile" (216 degrees)

because we measure the angular distance between planets in either

direction; if two planets are 216 degrees apart moving counter-clockwise,

then they are 144 degrees apart moving clockwise (144 + 216 = 360).

Likewise, we have no need of a "quadraquintile" (288 degrees), because

this distance is equivalent to 72 degrees (the quintile) in the other

direction (288 + 72 = 360).

So the full set for divisions of the circle up to 12 is:

NAME ANGULAR DISTANCE DIVISION BY

Conjunction 0 degrees 1

Opposition 180 degrees 2

Trine 120 degrees 3

Square 90 degrees 4

Quintile 72 degrees 5

Biquintile 144 degrees 5

Sextile 60 degrees 6

Septile 51.43 degrees 7

Biseptile 102.86 degrees 7

Triseptile 154.29 degrees 7

Octile (Semi-

Square) 45 degrees 8

Trioctile (Sesqui-

quadrate) 135 degrees 8

Nonile (Novile) 40 degrees 9

Binonile 80 degrees 9

Quadranonile 160 degrees 9

Decile 36 degrees 10

Tridecile 108 degrees 10

Undecile 32.7 degrees 11

Biundecile 65.5 degrees 11

Triundecile 98.2 degrees 11

Quadraundecile 130.9 degrees 11

Quintundecile 163.6 degrees 11

Dodecile (semi-

sextile) 30 degrees 12

Quincunx (Quint-

dodecile?) 150 degrees 12

In practice, I have never seen the 11 series used, but I suspect this is

because it requires messy (non-integer) numbers of degrees. Why use the

division by 10 and 12 but not the division by 11?

Now one can go further; a division by 14 would begin with an aspect we

might call a "semi-septile"; by 16, a "semi-octile"; and so on. But then

we would miss the 13th and 15th harmonics! We must not let zodiacal

divisions or naming conventions blind us to potential divisions of the

circle.

To increase our ability to observe the messy divisions of the zodiac, there

are three things we can do. The first is to draw (or have a computer draw,

if you have the right software) a chart in which the planets are situated

in their actual positions in the zodiac. This requires a chart with the

zodiac drawn on it, and the divisions for the degrees marked. Each planet

is marked at the degree where it fell at birth. So if the Sun was at

10 degrees 30 minutes Aquarius, then the Sun is drawn on the chart at

a position one-third of the way through Aquarius plus one-half of a degree.

The next step is to make up paper discs for each harmonic series (or for

the ones that are difficult to observe). For the 5th harmonic, take a disc

that will fit nicely on top of the chart but won't cover up the zodiac or

planets (i.e., one that covers just the centre of the chart); draw lines

on the disc that divide it into 5 equal sectors. This is like cutting a

pie into five equal pieces. Do this accurately, using a protractor to

measure the angles (72 degrees) from a point in the centre of the disc.

Now to determine if Saturn, for instance, is making a fifth-harmonic

aspect to any planets in the chart, place the disc on top of the chart

so that one of the lines is lined up with Saturn's position in the

zodiac. If any other planets (or points) are very near any other line

marked on the disc, then such an aspect exists. You can do this for

any of the harmonics (e.g., 7 and 9).

If you have the computing power, you can accomplish the same task in one

of two ways. The first is to customise the programme so that it automatically

computes all of the harmonic aspects. (This set of aspects is rarely the

default. With the current version of Astrolog, you can only get aspects

up to the 9th harmonic, plus one 10th harmonic aspect and the 12th

harmonic aspects; to do so, you must use the -A option; you type

astrolog -A 18.) If this is not possible, you can often produce harmonic

charts. (Astrolog includes this feature with the -x option; astrolog -x 10

gives you the 10th harmonic chart.) What is a harmonic chart? Imagine

that we have divided up the zodiac like a pie into 5 pieces. Some

planets may fall in each of these 5 sectors. Now imagine that we

re-draw the zodiac, the *full* zodiac, within each of the 5 sectors.

So each of the 5 sectors begins with 0 degrees Aries and ends with

30 degrees Pisces. Now each planet has a new position in the zodiac.

We now re-draw the chart with the new zodiacal positions for the planets.

Another way to think of it is that we cut up the zodiac into 5 pieces and

then superimpose them upon one another. We then "expand" the length

of the arc along the edge of the pieces so that it becomes a whole circle

(72 degrees becomes 360 degrees). If we now look for conjunctions in this

5th harmonic chart, we will have found planets in 5th harmonic aspects

in the natal chart. The quintile and biquintile both appear as conjunctions

in this chart. Tenth harmonic aspects appear as oppositions, and 15th

harmonic aspects appear as trines. 20th harmonic aspects appear as

squares. We can do this for any of the harmonics.

One caution: When we look for aspects in a harmonic chart, we must

use wider orbs than we would in a natal chart. I have not yet introduced

the concept of an orb, so I will return to this later. But at the risk

of confusing you now, I will say that if we consider two planets separated

by 72 + 1 degrees in the natal chart to be in a quintile aspect, then we must

consider planets separated by 5 degrees in the 5th harmonic chart to be

in quintile aspect. In other words, the "orb" we allow for an aspect must

be multiplied by the harmonic number to get the "orb" we allow in the

harmonic chart.

A second caution: In natal charts, when we talk about the square (4th

harmonic), we do not include the conjunction and opposition as squares,

even though these aspects are part of the 4th harmonic. In the harmonic

chart, however, all aspects in a harmonic appear as the same aspect. All

5th harmonic aspects appear as conjunctions in the 5th harmonic chart; this

includes the conjunction, the quintile, and the biquintile. All 10th

harmonic aspects that are not also 5th harmonic aspects appear as

oppositions in the 5th harmonic chart; this includes the decile, the

tridecile, and the opposition (but not the conjunction, quintile, or

biquintile, even though they are part of the 10th harmonic).

Why do we call the divisions of the circle "harmonics"? This term comes

from the study of sounds or other vibrations. Suppose we take a vibration,

perhaps a vibration (oscillation) of air waves that produces a sound at

the ear. This vibration has a *frequency* of oscillation. Let us take,

as an example, a tone with an oscillatory frequency of 200 cycles per

second (Hertz; Hz for short). Call this the "fundamental frequency"

because this will be the lowest frequency in a harmonic series. Now let

us produce other tones, each having a frequency that is an integer

multiple of the fundamental frequency (200 Hz). The series we get is:

200 Hz, 400 Hz, 600 Hz, 800 Hz, 1000 Hz, 1200 Hz, and so on. (We can

stop at any point we like.)

This is a "harmonic series." It is called "harmonic" because the combination

of all these tones (in phase) sounds harmonious to the ear (or rather in

the brain, which is processing signals from the ear). If we combined tones

that were not all harmonics (integer multiples) of a fundamental frequency,

the combination would sound discordant/dissonant. The word harmonic also

captures the reinforcing property of such waveforms; higher harmonics

augment the amplitude of lower harmonics so that the combined waveform

has the same period (and number of peaks) as the fundamental. Probably for

this reason, the perceived *pitch* of a harmonic series is roughly equivalent

to the perceived pitch of the fundamental frequency, although it is also

influenced to some degree by the 2nd and 3rd harmonics so that it is slightly

higher than the pitch of the fundamental by itself. In influencing pitch,

the fundamental has more "power," but only because it is *reinforced* by

higher harmonics (through increases in amplitude associated with wave

summation).

So what does this have to do with planetary aspects? What sort of "waves"

are we dealing with when planets interact in harmonic relations? Answer:

we don't know. Perhaps the "waves" are just the roughly circular motions

of the planets themselves (which follow the sinusoidal path we associate with

waves). But harmonic theory seems to be relevant because *observation*

of the effects of planetary interactions suggests that integer divisions

of the circle have a power that arbitrary angular distances do not.

Stranger still, different integer divisions seem to have a *qualitatively*

different effect. I will describe some of the observed properties of the

different aspects at the end of the lesson.

ORBS

An orb is an imaginary sphere around a planet, a kind of "sphere of

influence." When we compare the positions of two planets, we do not

require that they be *exactly* 120 degrees apart for them to be considered

in trine aspect to one another. We allow a little leeway. The amount of

leeway we allow (the "orb") depends on the nature of the aspect, the

planets involved, and even the houses in which they reside in the chart.

No comprehensive empirical study has been conducted to determine the

appropriate orbs, so astrologers use whichever orbs seem to work best

in their own experience.

Experience shows that a much wider orb can be used for the lower harmonics

(e.g., conjunction, opposition) than for higher harmonics (e.g., semi-

sextile). The orb for a conjunction can be up to 15 degrees (at least

according to the Church of Light) if a luminary is involved and at least

one planet is in an angular house (1, 4, 7 or 10). A more usual orb for

the conjunction would be 9 or 10 degrees. In contrast, for a semi-sextile

or quincunx (12th harmonic aspect), 1 degree is about the maximum orb

we would want to use for planets in cadent houses (2, 3, 5 or 6), and

the absolute maximum orb we would ever use is around 4 degrees, which

we might consider using if the Sun or Moon was involved and one planet was

in an angular house. An average orb for these aspects might be 2 degrees.

(Unfortunately, current computer software does not allow the size of the

orb to vary with the planets and their houses, although it usually allows

the orb to vary with the nature of the aspect. Perhaps Walter or one of

his programming elves will add this feature to Astrolog?)

Aspects closer to exactitude are more powerful, so not much is to be

gained by using wide orbs. In practice, you might use 10 degrees for

a conjunction, 9 degrees for an opposition, 8 degrees for a trine,

7 degrees for a square, 6 degrees for a quintile, 5 degrees for a sextile,

4 degrees for a septile, 3 degrees for an octile, 2 degrees for a novile,

and 1 degree for slightly higher harmonics. Some astrologers use much tighter

orbs (e.g., 2 degrees even for the lower harmonics); others ignore

orbs altogether and count signs, so that any planets four signs

apart are in trine! (This method only works for aspects that are a

multiple of 30 degrees.) I do not recommend the sign-to-sign approach,

although it is common in Hindu astrology.

With harmonic charts (as described earlier), you must increase the orb.

In particular, you must multiply by the harmonic number the orb you would

use in a natal chart for the harmonic aspect. So if you are using a

7th harmonic chart, and you use an orb of 4 degrees in the natal chart

for a septile, then you must use an orb of 28 degrees for the conjunction

in the 7th harmonic chart.

The reason we can use larger orbs for the lower harmonics is that these

aspects are more "powerful." This may be because their "amplitude" is

boosted by higher harmonics. You may have noticed that when I described

the harmonic aspects earlier, some were missing for certain harmonics. For

example, with the 8th harmonic, I only listed 2 of the 8 aspects. This

is partly because of symmetry; we measure aspects in either direction

(clockwise and counter-clockwise). But the rest of the explanation lies

in overlap with lower harmonics. 2/8 of the circle is equal to 1/4 (the

square); 4/8 is equal to 1/2 (the opposition). So two planets in opposition

are simultaneously part of the 2nd harmonic, the 4th harmonic, the 6th

harmonic, the 8th harmonic, the 10th harmonic, and so on to infinity.

The idea is expressed below in a figure showing the locations of "peaks"

for the first 9 harmonics:

9

8

7

6

5

4 8

3 9 6 9

2 8 6 4 6 8

1 9 87 65 9 4 7 3 8 579 2 975 8 3 7 4 5 6 789

__________________________________________________________________

___________

0 90 180 270

The vertical axis shows frequency of a peak in a waveform, that is, of

the presence of an aspect. The horizontal axis shows degrees of angular

separation. The symbols represent the harmonics; 1 is the first harmonic,

2 is the second, and so on. At 0 degrees, every harmonic is represented.

At 180 degrees, the even-numbered harmonics are present. At 120 degrees,

the harmonics that are multiples of 3 are present. At 90 degrees, the

multiples of 4 are present. If we assume (with Robert Hand) that the

"amplitude" of the waveform increases by one "unit" for each harmonic

present at a given degree, then if we consider just the first 9 harmonics,

the amplitude is 9 at 0 degrees, 4 at 180 degrees, 3 at 120 degrees, 2 at 90

degrees, and 1 or 0 elsewhere. If we included an infinite number of harmonics,

then the amplitude at 0 degrees would be infinite! We might make a more

reasonable assumption that the same amount of "energy" is spread throughout

each whole waveform so that each "peak" in the 2nd harmonic has half

the amplitude of the single peak in the 1st harmonic, the peaks in the 3rd

harmonic have 1/3 the amplitude, and so on. Then the amplitude at 0 degrees

would be 1 + 1/2 + 1/3 + 1/4 + 1/5 + . . .; the amplitude at 180 degrees would

be 1/2 + 1/4 + 1/6 + 1/8 + 1/10 + . . .; the amplitude at 120 degrees

would be 1/3 + 1/6 + 1/9 + 1/12 + 1/15 + . . .; and the amplitude at

90 degrees would be 1/4 + 1/8 + 1/12 + 1/16 + . . . All of these series

diverge to infinity, so even this assumption fails. We can avoid this

problem if we limit ourselves to a finite number of harmonics, say the

first 12. By doing so, we get the following values for amplitude:

Harmonic: Amplitude:

1 3.103

2 1.225

3 0.694

4 0.458

5 0.300

6 0.250

7 0.143

8 0.125

9 0.111

10 0.100

11 0.091

12 0.083

There is yet another approach we could take, which is a variation

of the first one. We can just count the number of harmonics at each

degree, stopping at some arbitrary number. For example, let us

restrict ourselves to the first 180 harmonics. At 0 degrees, 180

harmonics will reach a peak. At 180 degrees, 90 will do so. At 120

degrees, 60 will peak. At 90 degrees, 45 peak. At 72 degrees, 36 peak.

And so on.

If we plot the amplitudes based on the first assumption (i.e., that the

amplitude increases by one unit for each harmonic at a given point), the

decrease in "power" (amplitude) across successively higher harmonics

follows a curve of the following shape (for the first 12 harmonics):

(Like the figure above, i.e., 1 is the first harmonic, 2 is the 2nd;

# is the 10th; + is the 11th; * is the 12th.)

*

+

#

9

8

7

6 *

5 #

4 8 *

3 6 9 *

2 4 6 8 *

1 2 3 4 5 6 7 8 9

This appears log-linear. A possible function for this curve is:

y = C * 1/(log x) (base 10 for log; C is a constant)

If we adopt the second assumption (that amplitude varies inversely with

harmonic number), the curve has the same shape, but the decline in power

is more gradual:

|

3|'

|

|

|

2|

|

|

| .

1|

| .

| .

| ' -

0| ' ' ' ' ' '

|__________________________________

1 2 3 4 5 6 7 8 9 10 11 12

(Harmonic Series)

(The vertical axis shows amplitude in arbitrary units.)

If we adopt the third assumption and look at the first 180 harmonics,

the frequency plot looks like this:

180|*

|

|

|

135|

|

|

|

90| *

|

| *

|

45| *

| *

| *

| * * * * * * * * *

0|

|______________________________________________________________

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21

Harmonic

(The vertical axis shows the number of harmonics that peak at the same

points as the harmonics on the horizontal axis.) This curve also appears

log-linear (naturally, since it is a variation of the first one).

The point of this exercise has been to show that the lower harmonics

may be more "powerful" due to some sort of summation of harmonics

such that the "amplitude" of the lower harmonics is pumped up relative

to the others. This increased power may explain the observation that

the lower harmonics are felt for a wider range of positions (i.e., within

a wider orb). They stand out more clearly against a background of noise.

The wider orb may also be related to the shape of the curve; a wave

with a lower frequency is broader, and the area where it is near its

maximum amplitude is wider.

I only know of one astrologer who has stuck his neck out and tried to

explain why the relative positions of the planets have effects reminiscent

of harmonics in various kinds of wave theory. I am not sure the theory

works, but it is an interesting idea. The theoretician is Robert Hand,

and he presents the theory in the chapter entitled "The Wave Theory

of Astrology" in his book "Essays on Astrology" (Rockport, MA: Para Research,

1982, pp. 19-32). Here is an excert (with my clarifications in square

brackets):

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==================

If you pluck a guitar string, you primarily get the fundamental pitch, but

if you listen carefully you can hear other notes going, too: those are the

harmonics. If you put your finger half way down the guitar string, and

touch it lightly exactly half way and pluck it, you get the octave of that

tone [i.e., the second harmonic] without any of the fundamental at all.

This is because by putting your finger in the middle you remove the

fundamental and leave only the harmonics. [Actually, you leave the even-

numbered harmonics.] That is an example of a harmonic standing wave.

My basic proposition is simply this: the planets are like the fingers. The

zodiac is in a continual state of ringing, but it is full of many different

basic waves, making absolutely no sense or order whatsoever -- what we would

call in physics white noise -- a mixture of all frequencies with no

particular bias toward any frequency. What the planets do as they go around

the zodiac is form angles, which represent even whole-number subdivisions

of a circle. They stop out all those vibrations that will not fit in

between them. So, when two planets are 120 degrees apart they will remove

from this white-noise configuration all vibrations that will not divide

evenly into 120 degrees. This includes the conjunction and the opposition.

As you will see shortly, it does not include, oddly enough, the square.

[Actually, the square *is* eliminated; he arrives at the erroneous

conclusion that it is not because of some dubious assumptions he makes

in his later discussion and in constructing curves showing wave summation;

in the 3rd harmonic curve, he finds a peak at 90 degrees which is an

artifact of his assumptions and the way he constructed the curve.]

As this goes on, you will not only have a wave of 120 degrees, but you

also get wave lengths of 60 degrees, 30 degrees, 15 degrees, 7.5 degrees,

and so forth, because these all divide evenly into 120 degrees. [You will

also get wavelengths of 40 and 20 degrees, etc., which divide into 120.]

These all have a curious quality. If the 120-degree wave were a musical tone,

the 60-degree wave would be an octave above it, the 30-degree wave would be

an octave above that, the 15 would be another octave, and the 7.5 would be

another octave -- in other words, 7.5, 15, 30, 60 and 120 are all the same

tone. We know that the trine and the sextile are very similar in nature.

The basic difference seems to be that the sextile is not quite as strong

as the trine. . . . Basically, this suggests that the sextile is nothing but

the octave of the trine, and therefore that they would be fundamentally

similar in nature. [Other astrologers would dispute this claim; see later.]

. . . Similarly, if we take the fundamental, which is the conjunction,

its octave will be the opposition, the double octave will be the square,

the triple octave will be the 45 and the 135, and fourth octave will be

the 22.25. . . . So again, these aspects, which traditionally have been

considered to be rather similar, turn out to be, in terms of this theory,

octaves of each other. . . . If you take a wave and superimpose its various

octaves on it, you create the effect of sharpening the peak tremendously.

The peak increases in amplitude: that is to say, instead of remaining

quite low, it goes much higher, and instead of being wide and graceful,

it becomes almost a point, like a peak. What this suggests is that the

aspect is the sum total of the fundamental and all of its octaves put

together. How many octaves we don't really know, but probably quite a few.

===========================================================

================

I won't summarise the rest of his argument, because I think his reasoning

becomes dubious. For one thing, he confuses the fundamental (first

harmonic) series with the octaves of the fundamental; the fundamental series

includes all multiples of its frequency, not just those that are octaves.

He also makes some remarks about the brain being a receiver for the

mysterious waveforms, which does not provide any explanation for mundane

astrology, synastry, and so on. Furthermore, he uses a cosine function

in summing waveforms (i.e., he assumes that the harmonics coincide at

peaks and troughs, not at points of zero amplitude), but the sine function

(i.e., the assumption of coincidence at the zero points or "nodes") is

the appropriate one because standing waves between two bodies end at

nodes (zero-points), not at peaks or troughs. If we use a sine function

in wave summation, we get a saw-tooth curve, with a high, sudden peak at the

degrees for the aspects (e.g., 0, 120 and 240 for the 3rd harmonic) and

gradual change in amplitude between aspects in the series (which predicts,

incidentally, that the strength of an aspect rises gradually as it is applying

and falls off dramatically after the aspect reaches exactitude or a point

just before it). With the cosine function Hand uses, the rises on either

side of the aspect are symmetrical and sharp.

I would replace his explanation in terms of octaves with one in terms of

harmonics. The difference is that an octave of a tone is always twice

its frequency, whereas harmonics are simply integer multiples of the

fundamental. So the harmonics of the conjunction include all aspects,

but the octaves of the conjunction include only successive doublings

of harmonic number: 2, 4, 8, 16, 32, 64, etc. (the opposition, square,

octile, etc.). The harmonics of the trine include the sextile, nonile,

semi-sextile (dodecile), and so on; the octaves of the trine include

the sextile and the dodecile, but not the nonile. So the two theories

make different predictions. Hand's theory predicts that the conjunction

is difficult like the opposition and square; the harmonic theory predicts

that it is neutral (containing all harmonics). Hand claims the conjunction

is difficult, but I do not find it so. It is traditionally considered

neutral. Also, his theory of planets blocking certain frequencies (harmonics)

does not predict that non-octave waveforms will be knocked out, but that

non-harmonic ones will. The nonile is not blocked because planets are

1/3 of the circle apart. All vibrations with frequencies that are

multiples of three can persist in 1/3 of the zodiac.

Back to astrology proper. (Ahem.)

We have seen that orbs differ according to (1) the particular aspect,

(2) the particular planets involved, and (3) the houses in which the

planets reside (angular, succedent, or cadent). There is one other factor

that may affect the orbs, and the power of the aspect in general.

TIME COURSE OF ASPECT

Imagine two planets, one slow-moving and one quicker, the quicker one

being 65 degrees behind the slower one in the zodiac (e.g., the slow one

in Gemini, the fast one in Aries). With a 5 degree orb, the two planets

are in sextile (60 degrees). As the planets continue to move, the aspect

will become progressively closer to 60 degrees (an exact sextile), and it

will then become smaller than 60 degrees. Before the aspect becomes exact,

the aspect is said to be "applying" (or "entering"). After the aspect

has become exact and the planets begin to separate from a sextile, the

aspect is said to be "separating" (or "leaving"). In looking at transits

of planets in the sky to planets in a natal chart, the applying aspect

is what counts. Events almost always culminate as the aspect is applying.

During the separation phase, we experience the aftermath, as it were.

In natal charts, an applying aspect is often considered to be more

powerful than a separating aspect. Some astrologers use different orbs

for the two types of aspect for this reason.

How can you tell if an aspect is applying or separating? You first have

to determine the relative speed of the two planets. If one planet is the

Moon and one is Pluto, you know immediately that the Moon is faster.

For Mercury and Venus (for example), you might have to check an ephemeris

and see if the date they reached the exact aspect was before or after

the date of birth. You must also take into account retrograde motion.

If a planet is in retrograde apparent motion, it can be moving towards

a sextile (i.e., applying to a sextile) with a planet that is 65 degrees

behind it in the zodiac. You must also check that a retrograde planet

actually makes the exact aspect. If it does its station and turns direct

before it forms the aspect, then the effect is greatly weakened. Finally,

you must take into account whether the aspect is "dexter" or "sinister."

The Moon can sextile Pluto in two ways: it can be behind Pluto in the

zodiac and moving towards it, or it can be ahead of Pluto in the zodiac

and moving away from it. In the first case (which is called the "sinister"

sextile), the aspect is applying when the Moon is (say) between 65 and

60 degrees from Pluto. In the second case, when the Moon has already

made the conjunction with Pluto (which is called the "dexter" sextile),

the aspect is applying when the Moon is between 55 and 60 degrees from

Pluto. Most astrological software tells you automatically whether an

aspect is applying or separating. This does not seem to be a feature

of the current version of Astrolog.

ASPECT PATTERNS

After you compare the positions of all possible pairs of planets in a

chart to determine if any of them are in aspect, you should look for

global patterns of aspects in the chart. One pattern (or lack of pattern)

is a planet without any aspects. This planet becomes very powerful because

it is "left to its own devices," unfettered by influences from other planets.

It has a mind of its own.

Another pattern is the Stellium. This consists of a group of planets in

conjunction with one another. We do not refer to the conjunction

as a Stellium unless at least three planets are involved. The Stellium

creates great emphasis in the sign(s) and house(s) where it falls. How

it manifests depends largely on aspects to the Stellium from other

parts of the chart. A difficult transit to the Stellium (e.g., a square

from Saturn in the sky) is experienced as a period of severe crisis

because so many pieces of the personality are affected all at once.

Another pattern is the T-square. This pattern is formed by an opposition

combined with squares from the planets in opposition to another planet:

o

|

|

o_______|_______o

This pattern produces great tension and difficulty in the areas ruled by

the planets and their houses. But the problems generated by the opposition

can be resolved through the planet in square to the planets in opposition.

Like all patterns involving squares, there is potential for personal growth

inherent in this pattern, where the growth is usually a response to the

difficulties associated with the pattern. The energy exists in the pattern

to address those difficulties and rise above them.

An even more difficult (and rarer) pattern is the Grand Cross; this consists

of two oppositions that are orthogonal to one another:

o

|

|

o_______|_______o

|

|

|

o

This is a very dynamic pattern which generates lots of energy, but there

may be almost continual instability unless there are softer aspects in the

chart (trines or sextiles, for example).

A pattern called a Yod is formed by two planets in quincunx (150 degrees)

to a third planet, with one dexter quincunx and one sinister quincunx:

o \

/ |

/ |

o_______/ | 60 degrees (the angle is smaller than shown here)

\ |

\ |

\ /

o

This pattern is also called the finger of God, or finger of fate.

The yod pattern tends to produce vacillation between two modus operandi

with respect to the matters ruled by the focal planet and its house.

Another pattern is the Grand Trine. This consists of three trines that

form a triangular pattern:

o

/ \

/ \

/ \

/ \

o___________________o

People with a Grand Trine (and no difficult patterns in the chart) tend

to have things fall into their lap with minimal effort. They are "lucky."

This good fortune often generates complacency, and the person may come

to rely on luck and fail to exert themselves. Unless there are some tense

aspects in the chart (e.g., oppositions and squares), the person may be a

"good for nothing," wasting their tremendous potential through a lack

of effort.

A much rarer and much more powerful pattern is the Kite. This consists of

a Grand Trine with an opposition from one of the vertices, and sextiles

from the opposed planet to the other two vertices of the Grand Trine:

o

. | .

. | .

. | .

. | .

. | .

o____________|____________o

. | .

. | .

o

The opposition provides the energy needed for the great potential of the

Grand Trine to be realised. The kite will manifest itself primarily

through the planet in opposition to one vertex and in sextile to the

two others (the bottom one in the picture) and will have its greatest

effect in the house of that planet.

A pattern called the Mystic Rectangle or Harmonic Rectangle is formed by two

oppositions separated by sextiles and trines:

o o \

. . |

. . |

. | 60 degrees

. . |

. . |

o o /

This configuration tends to bring the opposing planets into harmony with

one another through the energies of the planets in sextile and trine to

them. This pattern can facilitate spiritual development. Its proportions

match the proportions of many initiation chambers, temples, and altars

used in older civilisations.

These patterns have been recognised for a long time. But in the light of

the new harmonic approach to aspects, we can see that each of these is

really just a partial or complete harmonic configuration. The Stellium is

a first harmonic (or "fundamental") configuration. The Grand Trine

is a division of the chart into three sectors. The Grand Cross is a

division of the chart into four sectors. The T-Square is an incomplete

Grand Cross, a partial 4th harmonic configuration. And a Kite is a partial

6th harmonic configuration; it has two sextiles and two trines; the full

configuration would have 6 sextiles and would look like a hexagram (or Star

of David/Seal of Solomon; two interleaved Grand Trines) or hexagon. The Mystic

Rectangle is another partial 6th harmonic configuration. The Yod is a partial

12th harmonic configuration (albeit with a dynamic uniquely its own).

By applying harmonic theory, we can invent new global patterns to look

for. These don't yet have names, but we can use names of geometrical

figures or follow naming conventions. One possible pattern is an opposition

of two stellia, a second harmonic configuration. Another possible pattern

is a pentagram or pentagon (or Grand Quintile): 5 planets all in 5th harmonic

aspect to one another. A "septagon" or Grand Septile would have 7 planets

in 7th harmonic aspect to one another. We could also have an octagon or

octagram or Grand Octile (two interleaved Grand Crosses). Or a Grand

Nonile (9 sided figure). Or a Grand Decile (10 sides). If we include

points other than the 10 planets, such as the Ascendant and Midheaven,

then we could even have an 11-sided or 12-sided figure. In practice,

any complete harmonic configuration (except perhaps for the Grand Trine)

will be rare. But an incomplete pattern is still powerful, and the closer

to completion it is, the more powerful it is. Each incomplete version

of a harmonic configuration will have a dynamic of its own.

THE NATURES OF THE ASPECTS

Astrologers differ as to the qualitative effect of the various aspects.

In general, the square and opposition are felt to be difficult, the

sextile and trine are felt to be easy or facilitative, and the conjunction

and quincunx are considered neutral and dependent on the nature of the

planets involved. Some consider the semi-sextile (dodecile) to be easy

because it is 1/2 the sextile, but others consider it to be either

difficult or neutral.

The difficult/easy/neutral (or bad/good/indifferent) trichotomy is not very

useful. This simplistic approach to aspects has given way in recent years to

attempts to understand the unique nature of each harmonic.

I am experimenting with an approach which assigns traits to aspects according

to the nature of the planet associated with their harmonic number in

quabbalistic numerology. The planets rule signs, and the signs have

a polarity, element, and mode, so I can infer the nature of the aspect from

what I know about the planet associated with it and the sign ruled by that

planet. The correspondence is as follows:

HARMONIC

ASPECT NUMBER PLANET SIGN POLARITY ELEMENT

MODE

Conjunction 1 Sun Leo Positive Fire Fixed

Opposition 2 Moon Cancer Negative Water Cardinal

Trine 3 Jupiter Sagittarius Positive Fire Mutable

Square 4 Uranus Aquarius Positive Air Fixed

Quintile series 5 Mercury Gemini Positive Air Mutable

Sextile 6 Venus Libra Positive Air Cardinal

Septile series 7 Neptune Pisces Negative Water Mutable

Octile series 8 Saturn Capricorn Negative Earth Cardinal

Nonile series 9 Mars Aries Positive Fire Cardinal

Decile series 10 (Pluto) (Scorpio) (Negative) (Water) (Fixed)

Undecile series 11 (Virgo) (Negative) (Earth) (Mutable)

Dodecile series 12 (Pan) (Taurus) (Negative) (Earth) (Fixed)

(The last three are the most experimental because in the current tradition

there is no explicit numerological support.)

Interpretations of the harmonics can be derived from these correspondences.

Brief descriptions of the meaning I assign aspects in each of the

harmonics appear below. In these descriptions, planet A refers to the planet

in the pair that is in or rules a Cardinal and/or Positive (Fire, Air)

sign, or that is in an angular house (1, 4, 7 or 10); if both planets fit

this description, then the relation between planets A and B goes both ways.

Following my descriptions are excerts from various authors which sometimes

confirm and sometimes contradict my own interpretations. I also sometimes

include examples of aspects in charts of public figures.

1st harmonic (conjunction): Planet A gives prominence to planet B. The

area ruled by the sign and house takes on the nature of both A and B.

A and B unite in action. A and B lose their individual identities and

merge into one. A and B lose sight of one another, as lovers do in a

tight embrace.

Of the conjunction, Robert Hand says, "It is often difficult for the person

whose chart has this aspect to be clear about its effects. Usually the

conjunction colors the personality so completely that it is hard for the

native to get perspective on this aspect. Though the effects of a

conjunction may not be apparent to the native, they are obvious to

others. The conjunction has a dynamic quality. It tends to signify

patterns of action rather than passive states of being: that is, its

effects usually consist of events or changes in a person's life. These

are not necessarily events in the physical world; they may be

psychological."

Sue Tompkins says, "Planets in conjunction are always united. Their

energies are merged, blended and always act together. . . . When [the

conjunction is] exact, it's rather like having two bells struck

simultaneously: it's difficult to differentiate the sound of either one.

In the same way, planets in conjunction tend to have problems in `seeing'

each other. In fact, if the conjunction is an exact one the two planets

often don't appear to the individual to have separate identities. The

differentiation may be seen by others but to the person concerned the

two energies may appear as if they were one, almost as if a new planet

had been formed. Thus planets in conjunction can have difficulties in

separating and objectifying each other. . . . It is interesting to

remember that at New Moon when the Sun and Moon are in conjunction

one cannot actually see the Moon and this gives us a clue to this

`blind spot' quality of the conjunction. People whose charts are

dominated by conjunctions . . . tend to be very self-driven and self-

motivated individuals. They don't tend to look outside of themselves

for self-definition or validation and therefore are less prone to

self-doubt. Again, it's as if they look at themselves without the aid

of a mirror. Clearly, this is a difficult task as we tend to define

the self through meeting and interacting with others. Imagine an artist

trying to paint a self-portrait having never seen their face in a mirror

or photograph. I suspect the picture would differ greatly from the usual

artist/sitter portraits and probably would not describe a very good

likeness. At any rate, it would be a very subjective likeness, for the

mirror, sitter or photograph allows the possibility of greater objectivity."

2nd harmonic (opposition): Planet B reflects planet A. A and B complement

one another. Planet A causes planet B to vacillate between expressing its

own nature and reflecting the nature of A. Planet B increases planet A's

consciousness of itself.

Of this aspect, Hand says, "The symbolism of the opposition aspect is very

much what one would expect: polarity, strife, conflict, and so on, but

also partnership and cooperation, as well as consciousness itself.

... Whatever energies are linked by the opposition, they are combined

in such a way that they produce instability and change through conflict.

If one examines the conflict, it is seen to arise between an aspect of

oneself that has been projected outward and an aspect of oneself that

is experienced inwardly. Put more concretely, the opposition signifies

a conflict between an external factor and an internal one, and the

external factor is the result of an inward energy that one does not

as yet understand to be within the self. . . . It should be clear,

especially in the case of the individual who finds others disruptive,

that the disruptive person, entity, or situation is being used by the

individual's subconscious as a mirror to confront an aspect of himself

which he then tries to make conscious. Thus the opposition aspect has,

through such confrontation, the potential to increase the level of

consciousness. . . . The goal is a state of perfect equilibrium between

the two energies involved in the opposition: it represents the aspect's

partnership and cooperation side."

Tompkins says, "As children we all learn that Jack Sprat could eat no fat

and his wife could eat no lean. Like Jack Sprat and his wife, oppositions

in the chart want opposite but related things. We often experience the

opposition aspect as if we have both Jack and his wife inside of us, each

wanting seemingly opposite things. Or perhaps a better image is that it

is as if we are standing in the middle of our house and hear the front

door and back door bell ring at exactly the same time. Which one do

we answer? We can't be in two places at once. As part of the secret of

dealing with an opposition is to become aware of and use both sides of it,

the important point is that although we cannot attend to the front door

and back door at the same time, we can answer both of them, if we just

take it in turns. Otherwise we are leaving a stranger standing outside

an unopened door and missing a valuable encounter. Even if the stranger

is a foe as opposed to a friend, ignoring the enemy will not make it go

away but is more likely to reinforce its determination to get in somehow.

Invariably, we become aware of and `own' one half of an opposition some

time before we become conscious of the other half. For some time one side

of the opposition does remain like a stranger outside an unopened door.

Usually the planet we accept is the one which is more in keeping with our

image of ourselves. The stranger, the rejected planet is usually the

`heavier' one and, in our view, the less socially acceptable planet.

. . . Reject an energy we may, but the psyche insists upon wholeness

and thus insists that the energy of the rejected planet will intrude

upon our lives in some way, and will intrude to the extent that we have

disowned it. And so we meet this seemingly alien energy outside of

ourselves in another person, group or object and thus become a `victim'

of it. This is of course what is meant by the term `projection'. We are

offered the opportunity of becoming more conscious and `owning' our

rejected planet every time we meet it outside of ourselves in another

person or group. Meet it we will, time and time again, until awareness

dawns. This is not unjust or `bad,' for until we live out all sides of

our nature we cannot become whole. In living out just one side of an

opposition we are only using half the energy at our disposal."

3rd harmonic (trine): A expands B by adding its traits to B's expression.

A facilitates B's actions. A and B together bring abundance.

(Example: Saturn trine Mercury adds discipline, patience, and seriousness

to the thinking and communication, expanding the capacity for effective

thought, speech, and writing, but also expanding the capacity for undue

mental caution, pessimism and melancholy.)

Here is Hand on the 3rd harmonic: "The trine indicates that the energies

linked do not resist or conflict with each other in any way. They are in a

state of equilibrium with respect to one another. Whenever one chooses

to act according to the nature of the energies combined by a trine, there

is ease of action and lack of difficulty -- so long as one chooses to act

within the framework of a status quo into [sic] one's life. . . . When trines

do signify events, they are events in which one is passive. Things seem

to fall into one's lap and work out of their own accord. . . . The principal

flaw of trines is their passivity. Whenever the individual is challenged

by the environment to make a change or adjustment, the energy is lacking.

The old patterns indicated by the trine persist, and even if they are

temporarily deflected, they soon return."

Of the trine, Rael and Rudhyar say, "As the self is able constructively

to respond to this incarnation of purpose and meaning, one not only

displays the faculty of vision and understanding (often-used keywords

for the trine), but also *experiences ideas*. On this basis, the self

actually begins to transform the outer world and all the relationships

in which it has accepted to participate. . . . However, as the self

seeks to meet the outer world (or its companion) in terms of ideas and

mental vision, the inertia of the whole universe resists the transforming

thoughts."

Isabel Hickey says, "Like Jupiter, trines throw a protective influence.

Benefits that come without effort and without any activity on the part

of the individual concerned. They are the results of constructive service,

and harmonious actions in other lifetimes. We earn everything that happens,

good or ill. What we send forth returns home again. Everything returns

to its source. Trine aspects are the good we have given out returning

to us."

4th harmonic (square): A disrupts B's expression. A confronts B. A unsettles

B, sometimes bringing sudden change. A is at odds with B. The square is

not Saturnian as is sometimes thought, but Uranian. The most Uranian person

I know of, Nikola Tesla, had the full 4th harmonic configuration in his

chart: a Grand Cross involving 6 planets and the Midheaven. There is not

a single planet in Aquarius in his chart. He did have Uranus 20 degrees

into his first house, but then I have it 14 degrees into mine, and I'm

certainly not as Uranian as he was. (His birth time was accurately

recorded.) For those of you not familiar with the man, he was Uranus

personified. Tall, popular but often reclusive, quirky, a perennial bachelor,

and a "mad" inventor who is responsible for alternating current (AC) and radio

(according to a Supreme Court decision showing that one of Tesla's patents

anticipated Marconi's apparatus) but also for many weird and wonderful

inventions and "quack" theories that are only popular among his many

followers. He used to pass high-voltage current (up to two *million*

volts) across the surface of his body in public demonstrations so that

sparks and "lightning" shot from the ends of his fingers, toes, nose,

and chin. (I have seen this demonstrated by a member of the Tesla Society.)

He created a machine to send huge electrical currents into the atmosphere

(to test his theory that the air around Earth can be used as an

electrical conductor for standing waves of electricity, which could

conceivably be tapped via antennae anywhere on Earth); the machine,

when put into operation, created a lightning storm over his laboratory

and then blacked out the entire city! (Colorado Springs.) Further, his

life was full of incredible ups and downs, from glory to obscurity.

Such sudden and stark changes are characteristic of the energy of

Uranus. Now not everyone with a Grand Cross is this Uranian! Tesla's

Grand Cross involved all of his personal planets except Mercury. In

contrast, the Grand Cross in the chart of Charles Manson involves only

two personal planets (Moon and Mercury) and two of the outermost

("impersonal") planets (Uranus and Pluto).

Of the square, Rael and Rudhyar say, "It [when dexter] represents the need to

clear the ground of all obsolete structures before the building operation of

an integrated, harmonious way of life can begin in earnest. . . .

[or, when it is sinister] it represents the stage at which concretization

of the ideal or idea envisioned at the trine is necessary and possible."

5th harmonic (quintile series): A communicates with B. A informs B.

If A and B are in signs or rule signs of opposite polarity, then the

two polarities are integrated in an alchemical marriage and issue in

creative activity (usually of an intellectual nature).

Example: In the chart of Carl Jung, there is a quintile between Mercury

and Neptune; insights and inspiration from the world beyond everyday

reality informed Jung's thought and writing, and his intellectual probing

informed, or focused, his inspirational experience; Saturn is in quintile

to Neptune as well, the 3 planets marking 3 vertices of an incomplete

5th harmonic configuration; the structures (Saturn) in myth, literature,

religion and art, informed Jung's Neptunian insights and his thinking

(Mercury). A partial 5th harmonic configuration is often present in

intellectually productive people. Albert Einstein had planets (Moon,

Jupiter, and Neptune) in three consecutive vertices of a pentagon, with

his Mercury-Saturn conjunction at the mid-point of Jupiter and Neptune.

He also had a biquintile between Mars and Uranus. (Einstein also had

a T-square, providing some Uranian energy; Uranus is often associated

with genius. Of course he also had Uranus in the third and Jupiter in

the ninth.)

Of the 5th harmonic, Charles Harvey says, "The apple seems intertwined

with the meaning of the number 5 and the development of conscious

knowledge, and as such can serve as a useful image for the 5th harmonic

and its interpretation. In the ancient world, and still today, Pythagoreans

identified themselves to each other by cutting an apple across its diameter

and exposing the two halves. If you do this you will find that you are

looking at two perfect pentagons, for the seed pods in the apple are

always arranged in a fivefold symmetry. In Greek mythology the Golden

Apple, like the sun, is used as a symbol of the conscious mind through

which we can rise above, or, if we are not careful, through which we

can cut ourselves off from, the animal innocence and ignorance of the

body. 5 is said to be the `Number of Man' as a self-conscious being who

takes command of his own destiny. In this it will be recalled that the

most famous apple in history was given by Eve to Adam. It was the fruit

of the tree of the knowledge of Good and of Evil. In other words it was

the fruit of the tree of choice, of free will, which is both the reward

and the penalty of possessing self-consciousness. This idea of conscious,

personal choice -- and the power which comes from such choice -- is the

nub of what fiveness is about. It is knowledge that gives us the powers

to shape and create our world."

Rael and Rudhyar say, "Vibration Five, Mind, can operate in one of two

ways: in terms of purely material, intellectual or selfish desires

(regression), or by expressing one's creative genius (progression or

forward evolutionary motion)."

Seymour-Smith says,"The 5H chart indicates . . . facility. People who

tend to explode into the world in a fluent or cacophonous manner are

likely to have charts loaded with quintiles."

Tompkins says, "The relationship between *mind* and the quintile series

has long been made, which . . . sounds very Mercurial. More precisely,

John Addey links this aspect with the idea of *imposing one's mind on

the world*. If quintiles describe style, perhaps we can go one step

further and say that a quintile aspect will describe how we might

communicate or give form to our mental processes either orally, through

the written word or through the use of our hands. Hamblin also points

out that the quintile series is strongly emphasised in the charts of

people who are preoccupied with making, forming, linking and

arranging things."

6th harmonic (sextile): A refines B. A and B maintain a state of harmony.

A cooperates with B. A and B act as partners.

People with charts dominated by 6th harmonic aspects are often the epitome

of beauty and grace. Catherine Deneuve has two not-quite overlapping

incomplete 6th harmonic configurations in her chart, each with three

vertices occupied by planets, and they involve 9 of her planets; the

remaining planet, Venus, is sextile to the midheaven. Grace Kelly had

a partial 6th harmonic configuration with 4 vertices filled that involved

5 planets and the midheaven. (She also had a sextile between the Sun and

Pluto.)

Tompkins says, "The number six is often associated with Venus and there

is a Venusian feeling to this aspect. The sextile is an aspect of enjoyment,

pleasure and, I believe, valuation -- particularly *intellectual valuation*.

Sextiles have also been linked to rhythm and repetition and thus with

dancers and musicians, which also sounds rather Venusian. Certainly the

sextile is an aspect of harmony and planets linked by this kind of contact

tend to co-operate with each other. That's not quite the same as the

`hand-holding,' non-questioning flavour of planets linked by trine

aspect. Co-operation does involve some degree of effort."

7th harmonic (septile series): A brings B into contact with the unknown.

This link is the key to inspirational experience. A confuses B and

dissipates its energy. A and B together show the nature of the ideals.

Michael Harding says of the 7th harmonic, "When someone is profoundly

moved, inspired, turned-on, excited, absorbed, captivated or besotted

with some image or ideal then the mechanism of...inner fantasy is

probably at work and projections are actively engaged. This is the circle

of the 7th harmonic, where the base and the numinous can merge; where

the noble cause, the highest ideal and the darkest longing are a

septile apart. As astrologers we must approach this chart with respect

and caution, and be prepared to acknowledge all the riches it contains;

for here we are truly walking with dreams of others."

Hand says, "The seven-series aspects are difficult to formulate in

rigorous and clear terms. Part of the reason is that they have a

Uranus-Neptune flavor, which suggests that they have to do with energy

linkings that are not entirely of this world. For example, these aspects

are prominent in the chart of Madame Blavatsky, the founder of the

Theosophical movement. They are also prominent in the charts of poets.

If the five-series gives the ability to turn creative inspiration

into concrete end-products, the seven-series gives the creative

inspiration itself. It is as if these aspects enable one to peer

outside the everyday universe into one of expanded possibilities

and truths. There are dangers here also. I have seen the seven-series

indicate mental and emotional difficulties as well as creative inspiration.

An excess of these aspects appears to give one a lack of connection

with the physical universe as most of us know it. This is the dangerous

or at least difficult side of creative inspiration."

8th harmonic (octile series): A restricts B. A and B combined show the

nature of karmic obligations in this life. The combination of A and B

describes the tests to which one will be subjected. A and B together

are the passage to patient wisdom or the road to hell, depending on

the will. A and B create structures from which it is difficult to

break free. For those who take the higher path, the link between A and

B provides a source of self-discipline, patience, and perseverance.

Of the 8th harmonic, Charles Harvey says, "those ideas which we can

purposefully and productively pursue; fruitful efforts; built-in skills

and behaviour patterns. The `goods' delivered; the manifest destiny."

Tompkins says, "According to Charles Harvey, semi-squares and sesqui-

quadrates `can be remarkably productive of solid concrete results.'

Personally I suspect that this is because these aspects do not have

the uncertainty and hesitant quality of the square aspect. Because they

are so purposeful, it is as if nothing can stand in the way of the

concrete release of these aspects. They manifest and become actualised

in a very obvious exterior way in the world. In other words, these

aspects *precipitate events*. Squares do this too of course but

whereas the energy of a square often gets blocked for a time because

of the difficulty and uncertainty of integrating two energies that are

at variance, [aspects in the octile series] tend to *force* some kind

of release." (Notice that in my scheme the 8th harmonic aspects are

Cardinal, whereas the 4th harmonic aspects are Fixed.)

A dominance of 8th harmonic aspects often brings hardship and difficulty

into the life, although in struggling against the hardship, much may be

accomplished. Elizabeth Taylor has planets at 5 vertices of a Grand Octile,

7 planets in all (4 of them personal). While her life may appear glamourous

to some, her passage has been difficult (including the early loss of her

first husband and subsequent futile attempts to replace him).

A large number of 8th harmonic aspects also tend to make the nature serious.

Ed Sullivan had a partial 8th harmonic configuration with 5 vertices

occupied by planets. (This was a man who sometimes failed to "get" a

joke after it had been explained to him several times.) Stalin had 4

planets at vertices of a partial 8th harmonic configuration (plus a

Sun in Capricorn, whose square to Saturn is part of the 8 H configuration).

He was not only serious, but oppressive.

9th harmonic (nonile series): A potentiates B. A activates B. A excites

B to action. A and B combine to create a unique mission towards which

energy is directed. The combination of A and B provide the key to

self-realisation. A and B act in response to considerations of the self

alone, a selfishness necessary in finding one's own highest or most

fulfilling path.

Of the 9th harmonic, Rael and Rudhyar say, "At the level of the Nine,

the individualized person discovers and envisions the meaning and purpose

of what he or she *is*. . . . the novile (when at all operative in an

individual's life) leads to personal rebirth -- or `Initiation' -- to a

basic identification of the self with the purpose this self is seen to

have within the harmony of the universal Whole. The novile thus represents

the level at which complete fulfillment of individual being is possible --

either as an end in itself (negative approach) or as the condition for

positive emergence into an altogether new and higher realm of being."

Seymour-Smith says, "[the 9th harmonic shows] the nature of anything that

the native achieves."

The relation of the nonile to one's unique mission can be seen in Sigmund

Freud's exact nonile of the Moon and Pluto. Freud was able to show the

relationship between the emotions and the adequacy of the mother's

nurturance (Moon) and subconscious drives and impulses (Pluto).

Carl Jung had a partial 9th harmonic configuration with 4 vertices

occupied by the Sun, the Moon, Jupiter, and Saturn. His pioneering

work focused on the relation of the masculine and feminine principles

(Sun and Moon; animus and anima) and the universal (Jupiter) structures

(Saturn) in the mind and its creations (myth, dreams, literature, art,

religion). Hitler's Mercury-Pluto nonile is associated with his unique

mission to use (or abuse) ideas (Mercury) about enemies (7th house)

to control and exterminate them (Pluto). Richard Nixon's mission was

to be an all-powerful and controlling leader, which is reflected in

his quadranonile of the Sun and Pluto. Robert Browning, the romantic

poet, had an almost exact (2 minutes of arc) nonile between Mercury and

Venus, and both planets were in quadranonile to Neptune. His unique

path consisted in writing (Mercury) dreamily beautiful love poetry

(Venus) about an idealised love and lover (Neptune).

10th harmonic (decile series): A empowers B. A compells B. A transforms B.

A and B act together unconsciously but ubiquitously. A and B provide the

path to regeneration.

Power is often an issue with people whose charts contain many 10th harmonic

aspects. One example is Hitler; if we include Chiron and the ascendant,

he had 7 vertices of a 10th harmonic configuration occupied by planets (or

points), with 9 points involved. Stalin had 5 vertices occupied in a partial

10th harmonic configuration. One might expect that people with many such

aspects would sometimes have great healing power and a great capacity to

transform themselves or the not-self. They might also have a hypnotic

effect on others, with a great capacity to sway the masses.

Seymour-Smith says, "[the decile is] indicative of the interpersonal

difficulties which arise from the exercise of any kind of power or

talent, whether for good or evil."

11th harmonic (undecile series): I do not yet have a clear interpretation

of these aspects. One hypothesis is that with 11th harmonic aspects,

A resists integration with B. The combination of A and B may represent

areas where dualities or multiplicities exist, and the natures of the

planets involved may indicate how one deals with them.

Seymour-Smith says, "11H aspects manifest in a very definite way and they

indicate excess. They also, according to Williamsen, describe a `person's

ability to integrate diversities and dualisms.' These interpretations

are reconcilable: the tension of `double-bind' situations, which can be

external -- where you are trapped by feelings of obligation or duty, but

cannot entirely please one or more people -- or internal -- the tug

between scepticism and faith -- is likely to lead to a type of stress

which in its turn will lead to excess in one form or another.

Here are examples of 11th harmonic aspects, expressed as planetary pairs;

if anyone can see what is common in these, please let me know: Hitler,

Saturn-Uranus; Christopher Columbus, Mercury-Mars; Tesla, Mars-Pluto,

Moon-Saturn; Bette Midler, Mars-Neptune; Stalin, Mars-Jupiter, Moon-

Pluto (exact); Ed Sullivan, Mercury-Pluto; Nixon, Mars-Uranus, Mercury-

Uranus; Liz Taylor, Mercury-Pluto; Charles Manson, Sun-Mars, Sun-Neptune;

J.P. Morgan, Moon-Mars; Thomas Edison, Venus-Mars, Mercury-Pluto; Benjamin

Franklin, Venus-Pluto; Grace Kelly, Jupiter-Uranus; Catherine Deneuve,

Sun-Jupiter, Moon-Mercury; Robert Browning, Sun-Mercury, Venus-Jupiter;

Elizabeth Kubler-Ross, Jupiter-Uranus, Venus-Pluto; Janis Joplin, Uranus-

Pluto, Moon-Saturn; Edgar Cayce, Jupiter-Uranus; Franz Mesmer (inventor

of hypnotism), Mercury-Neptune, Saturn-Uranus; Harry Houdini, Uranus-

Neptune, Saturn-Pluto; Howard Hughes, Saturn-Neptune, Neptune-Mars;

Luciano Pavarotti, Sun-Uranus (exact), Sun-Neptune, Uranus-Neptune; Jean

-Paul Sartre, Mars-Jupiter; Elvis Presley, Jupiter-Saturn; Emily Bronte,

Sun-Pluto.

12th harmonic (dodecile series): A damps B. A steadies B. A retards B.

A and B act at the material level to produce concrete effects. A and B

act in a patient, persistent manner to achieve material ends.

The relevance of the dodecile to the material world can be seen by looking

at the people whose charts contain partial 12th harmonic configurations.

Examples are J. P. Morgan (with 6 of 12 vertices marked by planets, and

with 8 planets involved) and Richard Millhouse Nixon (with planets at

6 vertices, 8 planets being involved in the configuration). Both of these

men had strong ambitions on the material plane.

Of the 12th harmonic aspects, Hand says, "In the past, observers merely

noted that [the semi-sextile and quincunx] were both based on one-half

of a sextile, and they therefore drew the conclusion that both were

essentially weak sextiles. This has not turned out to be the case. In

fact, the weight of opinion on these aspects has changed from a judgment

of weakly benefic to decidedly difficult. . . . They represent tensions

and difficulties that are annoying, but usually too trivial and too

thoroughly bound up in the fabric of everyday life to be worth changing.

The exception to this is that there does seem, according to many

investigators, to be a connection between quincunxes and illnesses and

death." [This is because they fall in the 6th or 8th house from the

position of the aspected planet.]

Seymour-Smith says, "The semisextile aspect was once called, with

exquisite vagueness, `slightly beneficial.' It is not. It denotes

strain, and at close orbs very severe strain, between the two bodies

or points involved. . . . The quincunx has more to do with health,

mental and physical, than the semisextile, and is a little like the

opposition inasmuch as it concerns interpersonal rather than wholly

`internal' matters. It shows what a person will, or will not, do for

others, and how much this costs him; it indicates what a person believes

are his obligations, and his feelings about carrying them out. People

can get ill if they starve themselves of the input gained from others

or if they refuse, or cannot find a way, to reciprocate the affections

of others."

Tompkins says, "The main problem with the quincunx, as many astrologers

have noted, is that it is too passive an aspect to deal, without

considerable conscious effort anyway, with the conflict. In fact, it

is not so much conflict as *friction*."

SPECIFIC ASPECTS

For delineations of specific aspects in a chart, see:

Tompkins, Sue, "Aspects in Astrology: A Comprehensive Guide to

Interpretation," Longmead: Element Books, 1989.

Pelletier, Robert, "Planets in Aspect: Understanding Your Inner

Dynamics," West Chester, PA: Para Research, 1974.

Sakoian, Frances, & Acker, Louis S., "The Astrologer's Handbook,"

New York: Harper & Row, 1973.