1. 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.")

2. 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

3. 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,

4. 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).

5. 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

6. 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

7. 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,

8. 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

9. 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

10. 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

11. 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

12. 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):

13. (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#
48*
369*
2468 *
123456789
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|

14. | .
| .
| ' -
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

15. 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):
===========================================================
==================
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

16. 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

17. 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,

18. 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

19. 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

20. 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

21. 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

22. 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 /

23. 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.

24. 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

25. 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

26. 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.

27. 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

28. `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."

29. 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,

30. 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,

31. 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

32. 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."

33. 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

34. 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.

35. 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

36. 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

37. 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

38. 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.

39. Sakoian, Frances, & Acker, Louis S., "The Astrologer's Handbook,"
New York: Harper & Row, 1973.