LESSON TWO (BEGINNERS/INTERMEDIATE): ASPECTSCONTENTS:* Aspects: Traditional and Harmonic - Traditional Aspects - Harmonic Aspects* Orbs* Time Course of Aspect* Aspect Patterns* The Natures of the AspectsIn delineating a chart, one looks not only at the sign and house positionsof the planets and luminaries (Sun and Moon), but at the *relations* amongthem. In my opinion, this is where most of the action lies. The relationsgive you the dynamics of the chart.In astrology, the angular relation of a pair of planets is called anASPECT. Why "aspect"? This comes from the early anthropomorphism inastrology. 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 regardedone 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 visibleside itself; so the sense has changed. There is a bit of a chicken and eggproblem here, though; the Oxford dictionary states that the astrologicalmeaning of the word was the earliest; perhaps the projection of animacyonto the planets led to the words taking on the meaning of "looking at."In discussing aspects, I will first consider aspects between the membersof a planetary pair. I will then deal with aspect patterns involving morethan two (and often several) planets. (The word "planets" is used inastrology as a shorthand for "planets and luminaries.")
ASPECTS: TRADITIONAL AND HARMONICAn aspect is an angular distance in the zodiac between two planets that isconsidered meaningful in astrology. I will consider two sets of aspects. Thefirst is the set of "traditional" aspects that has been used for centuriesin the West. The second is the set of "harmonic" aspects, most of whichare relatively new in use, and their use is part of a revolution takingplace in astrology that stems from a critical re-examination of traditionalprinciples.TRADITIONAL ASPECTSThe traditional aspects are those associated with Kepler and Ptolemy.They are:NAME ANGULAR SEPARATIONConjunction 0 degreesOpposition 180 degreesTrine 120 degreesSquare 90 degreesSextile 60 degreesWe might also include the so-called "minor" aspects:Semi-square 45 degreesSesquiquadrate 135 degreesSemi-sextile 30 degreesQuincunx 150 degreesJohannes Kepler was the first to make this distinction between "major" (thefirst list) and "minor" aspects. He also included among the "minor" aspectsthree aspects that have only recently come into widespread use:Quintile 72 degreesBiquintile 144 degrees
Decile 36 degreesPtolemy recognised only the "major" aspects, but did not consider theconjunction an aspect. Why? Two planets in the same position cannotreally be said to be "looking at" (aspecting) one another; so theconjunction was thought of as a position. Ptolemy dismissed the quincunxand the semi-sextile as "inconjuncts"; this became a common name forthe quincunx (but not the semi-sextile). Jean-Baptiste Morin claims tohave discovered the semi-sextile and quincunx.You may have noticed that all of these aspects represent divisions ofthe zodiacal circle by integers:Conjunction Division by 1Opposition Division by 2Trine Division by 3Square Division by 4Quintile Division by 5Sextile Division by 6Semi-Square/Sesquiquadrate Division by 8Decile Division by 10Semi-sextile/Quincunx Division by 12Now why isnt there an aspect for division by 7? or 9? or 11? or forhigher 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 humanmind 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 samesign. Planets in opposition are in opposite signs (6 signs apart). Planetsin trine are 4 signs apart; planets in square are 3 signs apart; and planetsin sextile are 2 signs apart. By contrast, planets 1/8 of the circleapart are 1.5 signs apart, and planets 3/8 of the circle apartand 4.5 signs apart. Planets in quintile are 2.4 signs apart, and planetsin biquintile are 4.8 signs apart. Planets 1/7 of the circle apart are1.714 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 theaspects that have been in common use are ones that are easy to observewithin a wheel divided into 12 sectors of 30 degrees each. In other words,the popularity of the traditional aspects is an artifact of the traditionalsystem of division for the zodiac! If we were to divide the zodiac into5 sectors, the quintile and the biquintile would become the "obvious"aspects.Recently, astrologers have begun to abandon the traditional aspect setin favour of the full set of "harmonic" aspects, a topic to which wenow turn.HARMONIC ASPECTSIf we adopt the hypothesis that any integer division of the circle ismeaningful, then the set of aspects we consider expands considerably.We will now allow division by 7, and 9, and 11, and by any higherinteger (although in practice we usually stick to relatively lowintegers).The full set of harmonic aspects includes every angular distance thatis associated with a division of the zodiac by any integer. When wedivide the circle by 5, we get the quintile (72 degrees) and thebiquintile (144 degrees). There is no "triquintile" (216 degrees)because we measure the angular distance between planets in eitherdirection; 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), becausethis distance is equivalent to 72 degrees (the quintile) in the otherdirection (288 + 72 = 360).So the full set for divisions of the circle up to 12 is:NAME ANGULAR DISTANCE DIVISION BYConjunction 0 degrees 1Opposition 180 degrees 2Trine 120 degrees 3Square 90 degrees 4Quintile 72 degrees 5Biquintile 144 degrees 5Sextile 60 degrees 6Septile 51.43 degrees 7Biseptile 102.86 degrees 7Triseptile 154.29 degrees 7Octile (Semi-Square) 45 degrees 8Trioctile (Sesqui-quadrate) 135 degrees 8Nonile (Novile) 40 degrees 9Binonile 80 degrees 9Quadranonile 160 degrees 9Decile 36 degrees 10Tridecile 108 degrees 10Undecile 32.7 degrees 11Biundecile 65.5 degrees 11Triundecile 98.2 degrees 11Quadraundecile 130.9 degrees 11Quintundecile 163.6 degrees 11Dodecile (semi-sextile) 30 degrees 12Quincunx (Quint-dodecile?) 150 degrees 12
In practice, I have never seen the 11 series used, but I suspect this isbecause it requires messy (non-integer) numbers of degrees. Why use thedivision by 10 and 12 but not the division by 11?Now one can go further; a division by 14 would begin with an aspect wemight call a "semi-septile"; by 16, a "semi-octile"; and so on. But thenwe would miss the 13th and 15th harmonics! We must not let zodiacaldivisions or naming conventions blind us to potential divisions of thecircle.To increase our ability to observe the messy divisions of the zodiac, thereare 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 situatedin their actual positions in the zodiac. This requires a chart with thezodiac drawn on it, and the divisions for the degrees marked. Each planetis marked at the degree where it fell at birth. So if the Sun was at10 degrees 30 minutes Aquarius, then the Sun is drawn on the chart ata 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 forthe ones that are difficult to observe). For the 5th harmonic, take a discthat will fit nicely on top of the chart but wont cover up the zodiac orplanets (i.e., one that covers just the centre of the chart); draw lineson the disc that divide it into 5 equal sectors. This is like cutting apie into five equal pieces. Do this accurately, using a protractor tomeasure the angles (72 degrees) from a point in the centre of the disc.Now to determine if Saturn, for instance, is making a fifth-harmonicaspect to any planets in the chart, place the disc on top of the chartso that one of the lines is lined up with Saturns position in thezodiac. If any other planets (or points) are very near any other linemarked on the disc, then such an aspect exists. You can do this forany of the harmonics (e.g., 7 and 9).If you have the computing power, you can accomplish the same task in oneof 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 thedefault. With the current version of Astrolog, you can only get aspectsup to the 9th harmonic, plus one 10th harmonic aspect and the 12thharmonic aspects; to do so, you must use the -A option; you typeastrolog -A 18.) If this is not possible, you can often produce harmoniccharts. (Astrolog includes this feature with the -x option; astrolog -x 10gives you the 10th harmonic chart.) What is a harmonic chart? Imaginethat we have divided up the zodiac like a pie into 5 pieces. Someplanets may fall in each of these 5 sectors. Now imagine that were-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 with30 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 andthen superimpose them upon one another. We then "expand" the lengthof 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 this5th harmonic chart, we will have found planets in 5th harmonic aspectsin the natal chart. The quintile and biquintile both appear as conjunctionsin this chart. Tenth harmonic aspects appear as oppositions, and 15thharmonic aspects appear as trines. 20th harmonic aspects appear assquares. We can do this for any of the harmonics.One caution: When we look for aspects in a harmonic chart, we mustuse wider orbs than we would in a natal chart. I have not yet introducedthe concept of an orb, so I will return to this later. But at the riskof confusing you now, I will say that if we consider two planets separatedby 72 + 1 degrees in the natal chart to be in a quintile aspect, then we mustconsider planets separated by 5 degrees in the 5th harmonic chart to bein quintile aspect. In other words, the "orb" we allow for an aspect mustbe multiplied by the harmonic number to get the "orb" we allow in theharmonic chart.A second caution: In natal charts, when we talk about the square (4thharmonic), we do not include the conjunction and opposition as squares,
even though these aspects are part of the 4th harmonic. In the harmonicchart, however, all aspects in a harmonic appear as the same aspect. All5th harmonic aspects appear as conjunctions in the 5th harmonic chart; thisincludes the conjunction, the quintile, and the biquintile. All 10thharmonic aspects that are not also 5th harmonic aspects appear asoppositions in the 5th harmonic chart; this includes the decile, thetridecile, and the opposition (but not the conjunction, quintile, orbiquintile, even though they are part of the 10th harmonic).Why do we call the divisions of the circle "harmonics"? This term comesfrom the study of sounds or other vibrations. Suppose we take a vibration,perhaps a vibration (oscillation) of air waves that produces a sound atthe ear. This vibration has a *frequency* of oscillation. Let us take,as an example, a tone with an oscillatory frequency of 200 cycles persecond (Hertz; Hz for short). Call this the "fundamental frequency"because this will be the lowest frequency in a harmonic series. Now letus produce other tones, each having a frequency that is an integermultiple 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 canstop at any point we like.)This is a "harmonic series." It is called "harmonic" because the combinationof all these tones (in phase) sounds harmonious to the ear (or rather inthe brain, which is processing signals from the ear). If we combined tonesthat were not all harmonics (integer multiples) of a fundamental frequency,the combination would sound discordant/dissonant. The word harmonic alsocaptures the reinforcing property of such waveforms; higher harmonicsaugment the amplitude of lower harmonics so that the combined waveformhas the same period (and number of peaks) as the fundamental. Probably forthis reason, the perceived *pitch* of a harmonic series is roughly equivalentto the perceived pitch of the fundamental frequency, although it is alsoinfluenced to some degree by the 2nd and 3rd harmonics so that it is slightlyhigher 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 wavesummation).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 dont know. Perhaps the "waves" are just the roughly circular motionsof the planets themselves (which follow the sinusoidal path we associate withwaves). But harmonic theory seems to be relevant because *observation*of the effects of planetary interactions suggests that integer divisionsof 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 thedifferent aspects at the end of the lesson.ORBSAn orb is an imaginary sphere around a planet, a kind of "sphere ofinfluence." When we compare the positions of two planets, we do notrequire that they be *exactly* 120 degrees apart for them to be consideredin trine aspect to one another. We allow a little leeway. The amount ofleeway we allow (the "orb") depends on the nature of the aspect, theplanets involved, and even the houses in which they reside in the chart.No comprehensive empirical study has been conducted to determine theappropriate orbs, so astrologers use whichever orbs seem to work bestin 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 leastaccording to the Church of Light) if a luminary is involved and at leastone planet is in an angular house (1, 4, 7 or 10). A more usual orb forthe conjunction would be 9 or 10 degrees. In contrast, for a semi-sextileor quincunx (12th harmonic aspect), 1 degree is about the maximum orbwe would want to use for planets in cadent houses (2, 3, 5 or 6), andthe 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 wasin an angular house. An average orb for these aspects might be 2 degrees.(Unfortunately, current computer software does not allow the size of theorb to vary with the planets and their houses, although it usually allowsthe orb to vary with the nature of the aspect. Perhaps Walter or one ofhis programming elves will add this feature to Astrolog?)Aspects closer to exactitude are more powerful, so not much is to begained by using wide orbs. In practice, you might use 10 degrees fora 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 tighterorbs (e.g., 2 degrees even for the lower harmonics); others ignoreorbs altogether and count signs, so that any planets four signsapart are in trine! (This method only works for aspects that are amultiple 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 woulduse in a natal chart for the harmonic aspect. So if you are using a7th harmonic chart, and you use an orb of 4 degrees in the natal chartfor a septile, then you must use an orb of 28 degrees for the conjunctionin the 7th harmonic chart.The reason we can use larger orbs for the lower harmonics is that theseaspects are more "powerful." This may be because their "amplitude" isboosted by higher harmonics. You may have noticed that when I describedthe harmonic aspects earlier, some were missing for certain harmonics. Forexample, with the 8th harmonic, I only listed 2 of the 8 aspects. Thisis partly because of symmetry; we measure aspects in either direction(clockwise and counter-clockwise). But the rest of the explanation liesin overlap with lower harmonics. 2/8 of the circle is equal to 1/4 (thesquare); 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 6thharmonic, 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:987654 83 9 6 92 8 6 4 6 81 9 87 65 9 4 7 3 8 579 2 975 8 3 7 4 5 6 789_____________________________________________________________________________0 90 180 270The vertical axis shows frequency of a peak in a waveform, that is, ofthe presence of an aspect. The horizontal axis shows degrees of angularseparation. 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, themultiples of 4 are present. If we assume (with Robert Hand) that the"amplitude" of the waveform increases by one "unit" for each harmonicpresent 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 90degrees, 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 morereasonable assumption that the same amount of "energy" is spread throughouteach whole waveform so that each "peak" in the 2nd harmonic has halfthe amplitude of the single peak in the 1st harmonic, the peaks in the 3rdharmonic have 1/3 the amplitude, and so on. Then the amplitude at 0 degreeswould 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 degreeswould be 1/3 + 1/6 + 1/9 + 1/12 + 1/15 + . . .; and the amplitude at90 degrees would be 1/4 + 1/8 + 1/12 + 1/16 + . . . All of these seriesdiverge to infinity, so even this assumption fails. We can avoid thisproblem if we limit ourselves to a finite number of harmonics, say thefirst 12. By doing so, we get the following values for amplitude:Harmonic: Amplitude:1 3.1032 1.2253 0.6944 0.4585 0.3006 0.2507 0.1438 0.1259 0.11110 0.10011 0.09112 0.083There is yet another approach we could take, which is a variationof the first one. We can just count the number of harmonics at eachdegree, stopping at some arbitrary number. For example, let usrestrict ourselves to the first 180 harmonics. At 0 degrees, 180harmonics will reach a peak. At 180 degrees, 90 will do so. At 120degrees, 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 theamplitude increases by one unit for each harmonic at a given point), thedecrease in "power" (amplitude) across successively higher harmonicsfollows 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.)*+#9876*5#48*369*2468 *123456789This 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 withharmonic number), the curve has the same shape, but the decline in poweris 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 appearslog-linear (naturally, since it is a variation of the first one).The point of this exercise has been to show that the lower harmonicsmay be more "powerful" due to some sort of summation of harmonicssuch that the "amplitude" of the lower harmonics is pumped up relativeto the others. This increased power may explain the observation thatthe lower harmonics are felt for a wider range of positions (i.e., withina 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 wavewith a lower frequency is broader, and the area where it is near itsmaximum amplitude is wider.I only know of one astrologer who has stuck his neck out and tried toexplain why the relative positions of the planets have effects reminiscentof harmonics in various kinds of wave theory. I am not sure the theoryworks, but it is an interesting idea. The theoretician is Robert Hand,and he presents the theory in the chapter entitled "The Wave Theoryof Astrology" in his book "Essays on Astrology" (Rockport, MA: Para Research,1982, pp. 19-32). Here is an excert (with my clarifications in squarebrackets):=============================================================================If you pluck a guitar string, you primarily get the fundamental pitch, butif you listen carefully you can hear other notes going, too: those are theharmonics. If you put your finger half way down the guitar string, andtouch it lightly exactly half way and pluck it, you get the octave of thattone [i.e., the second harmonic] without any of the fundamental at all.This is because by putting your finger in the middle you remove thefundamental 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. Thezodiac 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 wouldcall in physics white noise -- a mixture of all frequencies with noparticular bias toward any frequency. What the planets do as they go aroundthe zodiac is form angles, which represent even whole-number subdivisionsof a circle. They stop out all those vibrations that will not fit inbetween them. So, when two planets are 120 degrees apart they will removefrom this white-noise configuration all vibrations that will not divideevenly 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 erroneousconclusion that it is not because of some dubious assumptions he makesin his later discussion and in constructing curves showing wave summation;in the 3rd harmonic curve, he finds a peak at 90 degrees which is anartifact 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 youalso 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 willalso 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 bean octave above that, the 15 would be another octave, and the 7.5 would beanother octave -- in other words, 7.5, 15, 30, 60 and 120 are all the sametone. 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 strongas the trine. . . . Basically, this suggests that the sextile is nothing butthe octave of the trine, and therefore that they would be fundamentallysimilar 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 bethe 22.25. . . . So again, these aspects, which traditionally have beenconsidered 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 variousoctaves 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 theaspect is the sum total of the fundamental and all of its octaves puttogether. How many octaves we dont really know, but probably quite a few.===========================================================================I wont summarise the rest of his argument, because I think his reasoningbecomes dubious. For one thing, he confuses the fundamental (firstharmonic) series with the octaves of the fundamental; the fundamental seriesincludes all multiples of its frequency, not just those that are octaves.He also makes some remarks about the brain being a receiver for themysterious waveforms, which does not provide any explanation for mundaneastrology, synastry, and so on. Furthermore, he uses a cosine functionin summing waveforms (i.e., he assumes that the harmonics coincide atpeaks and troughs, not at points of zero amplitude), but the sine function(i.e., the assumption of coincidence at the zero points or "nodes") isthe appropriate one because standing waves between two bodies end atnodes (zero-points), not at peaks or troughs. If we use a sine functionin wave summation, we get a saw-tooth curve, with a high, sudden peak at thedegrees for the aspects (e.g., 0, 120 and 240 for the 3rd harmonic) andgradual change in amplitude between aspects in the series (which predicts,incidentally, that the strength of an aspect rises gradually as it is applyingand falls off dramatically after the aspect reaches exactitude or a pointjust before it). With the cosine function Hand uses, the rises on eitherside of the aspect are symmetrical and sharp.I would replace his explanation in terms of octaves with one in terms ofharmonics. The difference is that an octave of a tone is always twiceits frequency, whereas harmonics are simply integer multiples of thefundamental. So the harmonics of the conjunction include all aspects,but the octaves of the conjunction include only successive doublingsof 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 includethe sextile and the dodecile, but not the nonile. So the two theoriesmake different predictions. Hands theory predicts that the conjunctionis difficult like the opposition and square; the harmonic theory predictsthat it is neutral (containing all harmonics). Hand claims the conjunctionis difficult, but I do not find it so. It is traditionally consideredneutral. Also, his theory of planets blocking certain frequencies (harmonics)does not predict that non-octave waveforms will be knocked out, but thatnon-harmonic ones will. The nonile is not blocked because planets are1/3 of the circle apart. All vibrations with frequencies that aremultiples 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 theplanets reside (angular, succedent, or cadent). There is one other factorthat may affect the orbs, and the power of the aspect in general.TIME COURSE OF ASPECTImagine two planets, one slow-moving and one quicker, the quicker onebeing 65 degrees behind the slower one in the zodiac (e.g., the slow onein Gemini, the fast one in Aries). With a 5 degree orb, the two planetsare in sextile (60 degrees). As the planets continue to move, the aspectwill become progressively closer to 60 degrees (an exact sextile), and itwill then become smaller than 60 degrees. Before the aspect becomes exact,the aspect is said to be "applying" (or "entering"). After the aspecthas become exact and the planets begin to separate from a sextile, theaspect is said to be "separating" (or "leaving"). In looking at transitsof planets in the sky to planets in a natal chart, the applying aspectis 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 morepowerful 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 haveto determine the relative speed of the two planets. If one planet is theMoon and one is Pluto, you know immediately that the Moon is faster.For Mercury and Venus (for example), you might have to check an ephemerisand see if the date they reached the exact aspect was before or afterthe date of birth. You must also take into account retrograde motion.If a planet is in retrograde apparent motion, it can be moving towardsa sextile (i.e., applying to a sextile) with a planet that is 65 degreesbehind it in the zodiac. You must also check that a retrograde planetactually makes the exact aspect. If it does its station and turns directbefore 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 thezodiac and moving towards it, or it can be ahead of Pluto in the zodiacand 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 and60 degrees from Pluto. In the second case, when the Moon has alreadymade the conjunction with Pluto (which is called the "dexter" sextile),the aspect is applying when the Moon is between 55 and 60 degrees fromPluto. Most astrological software tells you automatically whether anaspect is applying or separating. This does not seem to be a featureof the current version of Astrolog.ASPECT PATTERNSAfter you compare the positions of all possible pairs of planets in achart to determine if any of them are in aspect, you should look forglobal patterns of aspects in the chart. One pattern (or lack of pattern)is a planet without any aspects. This planet becomes very powerful becauseit 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 conjunctionas a Stellium unless at least three planets are involved. The Stelliumcreates great emphasis in the sign(s) and house(s) where it falls. Howit manifests depends largely on aspects to the Stellium from otherparts of the chart. A difficult transit to the Stellium (e.g., a squarefrom Saturn in the sky) is experienced as a period of severe crisisbecause so many pieces of the personality are affected all at once.Another pattern is the T-square. This pattern is formed by an oppositioncombined with squares from the planets in opposition to another planet: o | |o_______|_______oThis pattern produces great tension and difficulty in the areas ruled bythe planets and their houses. But the problems generated by the oppositioncan be resolved through the planet in square to the planets in opposition.Like all patterns involving squares, there is potential for personal growthinherent in this pattern, where the growth is usually a response to thedifficulties associated with the pattern. The energy exists in the patternto address those difficulties and rise above them.An even more difficult (and rarer) pattern is the Grand Cross; this consistsof two oppositions that are orthogonal to one another: o | |o_______|_______o | | | o
This is a very dynamic pattern which generates lots of energy, but theremay be almost continual instability unless there are softer aspects in thechart (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) | | / oThis pattern is also called the finger of God, or finger of fate.The yod pattern tends to produce vacillation between two modus operandiwith respect to the matters ruled by the focal planet and its house.Another pattern is the Grand Trine. This consists of three trines thatform a triangular pattern: o / / / / o___________________oPeople with a Grand Trine (and no difficult patterns in the chart) tendto have things fall into their lap with minimal effort. They are "lucky."This good fortune often generates complacency, and the person may cometo 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 lackof effort.A much rarer and much more powerful pattern is the Kite. This consists ofa Grand Trine with an opposition from one of the vertices, and sextilesfrom the opposed planet to the other two vertices of the Grand Trine: o . | . . | . . | . . | . . | .o____________|____________o . | . . | . oThe opposition provides the energy needed for the great potential of theGrand Trine to be realised. The kite will manifest itself primarilythrough the planet in opposition to one vertex and in sextile to thetwo others (the bottom one in the picture) and will have its greatesteffect in the house of that planet.A pattern called the Mystic Rectangle or Harmonic Rectangle is formed by twooppositions separated by sextiles and trines:o o . . | . . | . | 60 degrees . . | . . |o o /
This configuration tends to bring the opposing planets into harmony withone another through the energies of the planets in sextile and trine tothem. This pattern can facilitate spiritual development. Its proportionsmatch the proportions of many initiation chambers, temples, and altarsused in older civilisations.These patterns have been recognised for a long time. But in the light ofthe new harmonic approach to aspects, we can see that each of these isreally just a partial or complete harmonic configuration. The Stellium isa first harmonic (or "fundamental") configuration. The Grand Trineis a division of the chart into three sectors. The Grand Cross is adivision of the chart into four sectors. The T-Square is an incompleteGrand Cross, a partial 4th harmonic configuration. And a Kite is a partial6th harmonic configuration; it has two sextiles and two trines; the fullconfiguration would have 6 sextiles and would look like a hexagram (or Starof David/Seal of Solomon; two interleaved Grand Trines) or hexagon. The MysticRectangle is another partial 6th harmonic configuration. The Yod is a partial12th harmonic configuration (albeit with a dynamic uniquely its own).By applying harmonic theory, we can invent new global patterns to lookfor. These dont yet have names, but we can use names of geometricalfigures or follow naming conventions. One possible pattern is an oppositionof two stellia, a second harmonic configuration. Another possible patternis a pentagram or pentagon (or Grand Quintile): 5 planets all in 5th harmonicaspect to one another. A "septagon" or Grand Septile would have 7 planetsin 7th harmonic aspect to one another. We could also have an octagon oroctagram or Grand Octile (two interleaved Grand Crosses). Or a GrandNonile (9 sided figure). Or a Grand Decile (10 sides). If we includepoints 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 closerto completion it is, the more powerful it is. Each incomplete versionof a harmonic configuration will have a dynamic of its own.
THE NATURES OF THE ASPECTSAstrologers differ as to the qualitative effect of the various aspects.In general, the square and opposition are felt to be difficult, thesextile and trine are felt to be easy or facilitative, and the conjunctionand quincunx are considered neutral and dependent on the nature of theplanets involved. Some consider the semi-sextile (dodecile) to be easybecause it is 1/2 the sextile, but others consider it to be eitherdifficult or neutral.The difficult/easy/neutral (or bad/good/indifferent) trichotomy is not veryuseful. This simplistic approach to aspects has given way in recent years toattempts to understand the unique nature of each harmonic.I am experimenting with an approach which assigns traits to aspects accordingto the nature of the planet associated with their harmonic number inquabbalistic numerology. The planets rule signs, and the signs havea polarity, element, and mode, so I can infer the nature of the aspect fromwhat I know about the planet associated with it and the sign ruled by thatplanet. The correspondence is as follows: HARMONICASPECT NUMBER PLANET SIGN POLARITY ELEMENTMODEConjunction 1 Sun Leo Positive Fire FixedOpposition 2 Moon Cancer Negative Water CardinalTrine 3 Jupiter Sagittarius Positive Fire MutableSquare 4 Uranus Aquarius Positive Air FixedQuintile series 5 Mercury Gemini Positive Air MutableSextile 6 Venus Libra Positive Air CardinalSeptile series 7 Neptune Pisces Negative Water MutableOctile series 8 Saturn Capricorn Negative Earth CardinalNonile 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 traditionthere 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 theharmonics appear below. In these descriptions, planet A refers to the planetin 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 fitthis description, then the relation between planets A and B goes both ways.Following my descriptions are excerts from various authors which sometimesconfirm and sometimes contradict my own interpretations. I also sometimesinclude examples of aspects in charts of public figures.1st harmonic (conjunction): Planet A gives prominence to planet B. Thearea 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 andmerge into one. A and B lose sight of one another, as lovers do in atight embrace.Of the conjunction, Robert Hand says, "It is often difficult for the personwhose chart has this aspect to be clear about its effects. Usually theconjunction colors the personality so completely that it is hard for thenative to get perspective on this aspect. Though the effects of aconjunction may not be apparent to the native, they are obvious toothers. The conjunction has a dynamic quality. It tends to signifypatterns of action rather than passive states of being: that is, itseffects usually consist of events or changes in a persons life. Theseare not necessarily events in the physical world; they may bepsychological."Sue Tompkins says, "Planets in conjunction are always united. Their
energies are merged, blended and always act together. . . . When [theconjunction is] exact, its rather like having two bells strucksimultaneously: its difficult to differentiate the sound of either one.In the same way, planets in conjunction tend to have problems in `seeingeach other. In fact, if the conjunction is an exact one the two planetsoften dont appear to the individual to have separate identities. Thedifferentiation may be seen by others but to the person concerned thetwo energies may appear as if they were one, almost as if a new planethad been formed. Thus planets in conjunction can have difficulties inseparating and objectifying each other. . . . It is interesting toremember that at New Moon when the Sun and Moon are in conjunctionone cannot actually see the Moon and this gives us a clue to this`blind spot quality of the conjunction. People whose charts aredominated by conjunctions . . . tend to be very self-driven and self-motivated individuals. They dont tend to look outside of themselvesfor self-definition or validation and therefore are less prone toself-doubt. Again, its as if they look at themselves without the aidof a mirror. Clearly, this is a difficult task as we tend to definethe self through meeting and interacting with others. Imagine an artisttrying to paint a self-portrait having never seen their face in a mirroror photograph. I suspect the picture would differ greatly from the usualartist/sitter portraits and probably would not describe a very goodlikeness. At any rate, it would be a very subjective likeness, for themirror, sitter or photograph allows the possibility of greater objectivity."2nd harmonic (opposition): Planet B reflects planet A. A and B complementone another. Planet A causes planet B to vacillate between expressing itsown nature and reflecting the nature of A. Planet B increases planet Asconsciousness of itself.Of this aspect, Hand says, "The symbolism of the opposition aspect is verymuch what one would expect: polarity, strife, conflict, and so on, butalso partnership and cooperation, as well as consciousness itself.... Whatever energies are linked by the opposition, they are combinedin such a way that they produce instability and change through conflict.
If one examines the conflict, it is seen to arise between an aspect ofoneself that has been projected outward and an aspect of oneself thatis experienced inwardly. Put more concretely, the opposition signifiesa conflict between an external factor and an internal one, and theexternal factor is the result of an inward energy that one does notas 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 theindividuals subconscious as a mirror to confront an aspect of himselfwhich he then tries to make conscious. Thus the opposition aspect has,through such confrontation, the potential to increase the level ofconsciousness. . . . The goal is a state of perfect equilibrium betweenthe two energies involved in the opposition: it represents the aspectspartnership and cooperation side."Tompkins says, "As children we all learn that Jack Sprat could eat no fatand his wife could eat no lean. Like Jack Sprat and his wife, oppositionsin the chart want opposite but related things. We often experience theopposition aspect as if we have both Jack and his wife inside of us, eachwanting seemingly opposite things. Or perhaps a better image is that itis as if we are standing in the middle of our house and hear the frontdoor and back door bell ring at exactly the same time. Which one dowe answer? We cant be in two places at once. As part of the secret ofdealing 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 doorand back door at the same time, we can answer both of them, if we justtake it in turns. Otherwise we are leaving a stranger standing outsidean unopened door and missing a valuable encounter. Even if the strangeris a foe as opposed to a friend, ignoring the enemy will not make it goaway but is more likely to reinforce its determination to get in somehow.Invariably, we become aware of and `own one half of an opposition sometime before we become conscious of the other half. For some time one sideof 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 ourimage 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 wholenessand thus insists that the energy of the rejected planet will intrudeupon our lives in some way, and will intrude to the extent that we havedisowned it. And so we meet this seemingly alien energy outside ofourselves in another person, group or object and thus become a `victimof it. This is of course what is meant by the term `projection. We areoffered the opportunity of becoming more conscious and `owning ourrejected planet every time we meet it outside of ourselves in anotherperson or group. Meet it we will, time and time again, until awarenessdawns. This is not unjust or `bad, for until we live out all sides ofour nature we cannot become whole. In living out just one side of anopposition we are only using half the energy at our disposal."3rd harmonic (trine): A expands B by adding its traits to Bs expression.A facilitates Bs actions. A and B together bring abundance.(Example: Saturn trine Mercury adds discipline, patience, and seriousnessto the thinking and communication, expanding the capacity for effectivethought, speech, and writing, but also expanding the capacity for unduemental caution, pessimism and melancholy.)Here is Hand on the 3rd harmonic: "The trine indicates that the energieslinked do not resist or conflict with each other in any way. They are in astate of equilibrium with respect to one another. Whenever one choosesto act according to the nature of the energies combined by a trine, thereis ease of action and lack of difficulty -- so long as one chooses to actwithin the framework of a status quo into [sic] ones life. . . . When trinesdo signify events, they are events in which one is passive. Things seemto fall into ones lap and work out of their own accord. . . . The principalflaw of trines is their passivity. Whenever the individual is challengedby the environment to make a change or adjustment, the energy is lacking.The old patterns indicated by the trine persist, and even if they aretemporarily deflected, they soon return."
Of the trine, Rael and Rudhyar say, "As the self is able constructivelyto respond to this incarnation of purpose and meaning, one not onlydisplays the faculty of vision and understanding (often-used keywordsfor the trine), but also *experiences ideas*. On this basis, the selfactually begins to transform the outer world and all the relationshipsin which it has accepted to participate. . . . However, as the selfseeks to meet the outer world (or its companion) in terms of ideas andmental vision, the inertia of the whole universe resists the transformingthoughts."Isabel Hickey says, "Like Jupiter, trines throw a protective influence.Benefits that come without effort and without any activity on the partof 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 returnsto its source. Trine aspects are the good we have given out returningto us."4th harmonic (square): A disrupts Bs expression. A confronts B. A unsettlesB, sometimes bringing sudden change. A is at odds with B. The square isnot Saturnian as is sometimes thought, but Uranian. The most Uranian personI know of, Nikola Tesla, had the full 4th harmonic configuration in hischart: a Grand Cross involving 6 planets and the Midheaven. There is nota single planet in Aquarius in his chart. He did have Uranus 20 degreesinto his first house, but then I have it 14 degrees into mine, and Imcertainly not as Uranian as he was. (His birth time was accuratelyrecorded.) For those of you not familiar with the man, he was Uranuspersonified. 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 Teslas patentsanticipated Marconis apparatus) but also for many weird and wonderfulinventions and "quack" theories that are only popular among his manyfollowers. He used to pass high-voltage current (up to two *million*volts) across the surface of his body in public demonstrations so thatsparks 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 anelectrical conductor for standing waves of electricity, which couldconceivably be tapped via antennae anywhere on Earth); the machine,when put into operation, created a lightning storm over his laboratoryand then blacked out the entire city! (Colorado Springs.) Further, hislife was full of incredible ups and downs, from glory to obscurity.Such sudden and stark changes are characteristic of the energy ofUranus. Now not everyone with a Grand Cross is this Uranian! TeslasGrand Cross involved all of his personal planets except Mercury. Incontrast, the Grand Cross in the chart of Charles Manson involves onlytwo 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 toclear the ground of all obsolete structures before the building operation ofan integrated, harmonious way of life can begin in earnest. . . .[or, when it is sinister] it represents the stage at which concretizationof 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 thetwo polarities are integrated in an alchemical marriage and issue increative activity (usually of an intellectual nature).Example: In the chart of Carl Jung, there is a quintile between Mercuryand Neptune; insights and inspiration from the world beyond everydayreality informed Jungs thought and writing, and his intellectual probinginformed, or focused, his inspirational experience; Saturn is in quintileto Neptune as well, the 3 planets marking 3 vertices of an incomplete5th harmonic configuration; the structures (Saturn) in myth, literature,religion and art, informed Jungs Neptunian insights and his thinking(Mercury). A partial 5th harmonic configuration is often present inintellectually productive people. Albert Einstein had planets (Moon,
Jupiter, and Neptune) in three consecutive vertices of a pentagon, withhis Mercury-Saturn conjunction at the mid-point of Jupiter and Neptune.He also had a biquintile between Mars and Uranus. (Einstein also hada T-square, providing some Uranian energy; Uranus is often associatedwith genius. Of course he also had Uranus in the third and Jupiter inthe ninth.)Of the 5th harmonic, Charles Harvey says, "The apple seems intertwinedwith the meaning of the number 5 and the development of consciousknowledge, and as such can serve as a useful image for the 5th harmonicand its interpretation. In the ancient world, and still today, Pythagoreansidentified themselves to each other by cutting an apple across its diameterand exposing the two halves. If you do this you will find that you arelooking at two perfect pentagons, for the seed pods in the apple arealways arranged in a fivefold symmetry. In Greek mythology the GoldenApple, like the sun, is used as a symbol of the conscious mind throughwhich we can rise above, or, if we are not careful, through which wecan cut ourselves off from, the animal innocence and ignorance of thebody. 5 is said to be the `Number of Man as a self-conscious being whotakes command of his own destiny. In this it will be recalled that themost famous apple in history was given by Eve to Adam. It was the fruitof the tree of the knowledge of Good and of Evil. In other words it wasthe fruit of the tree of choice, of free will, which is both the rewardand the penalty of possessing self-consciousness. This idea of conscious,personal choice -- and the power which comes from such choice -- is thenub of what fiveness is about. It is knowledge that gives us the powersto shape and create our world."Rael and Rudhyar say, "Vibration Five, Mind, can operate in one of twoways: in terms of purely material, intellectual or selfish desires(regression), or by expressing ones creative genius (progression orforward evolutionary motion)."Seymour-Smith says,"The 5H chart indicates . . . facility. People whotend 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 serieshas long been made, which . . . sounds very Mercurial. More precisely,John Addey links this aspect with the idea of *imposing ones mind onthe world*. If quintiles describe style, perhaps we can go one stepfurther and say that a quintile aspect will describe how we mightcommunicate or give form to our mental processes either orally, throughthe written word or through the use of our hands. Hamblin also pointsout that the quintile series is strongly emphasised in the charts ofpeople who are preoccupied with making, forming, linking andarranging 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 epitomeof beauty and grace. Catherine Deneuve has two not-quite overlappingincomplete 6th harmonic configurations in her chart, each with threevertices occupied by planets, and they involve 9 of her planets; theremaining planet, Venus, is sextile to the midheaven. Grace Kelly hada partial 6th harmonic configuration with 4 vertices filled that involved5 planets and the midheaven. (She also had a sextile between the Sun andPluto.)Tompkins says, "The number six is often associated with Venus and thereis 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 withdancers and musicians, which also sounds rather Venusian. Certainly thesextile is an aspect of harmony and planets linked by this kind of contacttend to co-operate with each other. Thats not quite the same as the`hand-holding, non-questioning flavour of planets linked by trineaspect. 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 anddissipates its energy. A and B together show the nature of the ideals.Michael Harding says of the 7th harmonic, "When someone is profoundlymoved, inspired, turned-on, excited, absorbed, captivated or besottedwith some image or ideal then the mechanism of...inner fantasy isprobably at work and projections are actively engaged. This is the circleof the 7th harmonic, where the base and the numinous can merge; wherethe noble cause, the highest ideal and the darkest longing are aseptile apart. As astrologers we must approach this chart with respectand 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 inrigorous and clear terms. Part of the reason is that they have aUranus-Neptune flavor, which suggests that they have to do with energylinkings that are not entirely of this world. For example, these aspectsare prominent in the chart of Madame Blavatsky, the founder of theTheosophical movement. They are also prominent in the charts of poets.If the five-series gives the ability to turn creative inspirationinto concrete end-products, the seven-series gives the creativeinspiration itself. It is as if these aspects enable one to peeroutside the everyday universe into one of expanded possibilitiesand truths. There are dangers here also. I have seen the seven-seriesindicate mental and emotional difficulties as well as creative inspiration.An excess of these aspects appears to give one a lack of connectionwith the physical universe as most of us know it. This is the dangerousor at least difficult side of creative inspiration."8th harmonic (octile series): A restricts B. A and B combined show thenature of karmic obligations in this life. The combination of A and Bdescribes the tests to which one will be subjected. A and B togetherare the passage to patient wisdom or the road to hell, depending onthe 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 andB provides a source of self-discipline, patience, and perseverance.Of the 8th harmonic, Charles Harvey says, "those ideas which we canpurposefully and productively pursue; fruitful efforts; built-in skillsand 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 havethe uncertainty and hesitant quality of the square aspect. Because theyare so purposeful, it is as if nothing can stand in the way of theconcrete release of these aspects. They manifest and become actualisedin a very obvious exterior way in the world. In other words, theseaspects *precipitate events*. Squares do this too of course butwhereas the energy of a square often gets blocked for a time becauseof the difficulty and uncertainty of integrating two energies that areat variance, [aspects in the octile series] tend to *force* some kindof release." (Notice that in my scheme the 8th harmonic aspects areCardinal, whereas the 4th harmonic aspects are Fixed.)A dominance of 8th harmonic aspects often brings hardship and difficultyinto the life, although in struggling against the hardship, much may beaccomplished. Elizabeth Taylor has planets at 5 vertices of a Grand Octile,7 planets in all (4 of them personal). While her life may appear glamourousto some, her passage has been difficult (including the early loss of herfirst 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 verticesoccupied by planets. (This was a man who sometimes failed to "get" ajoke after it had been explained to him several times.) Stalin had 4planets at vertices of a partial 8th harmonic configuration (plus aSun 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 excitesB to action. A and B combine to create a unique mission towards whichenergy is directed. The combination of A and B provide the key toself-realisation. A and B act in response to considerations of the selfalone, a selfishness necessary in finding ones own highest or mostfulfilling path.Of the 9th harmonic, Rael and Rudhyar say, "At the level of the Nine,the individualized person discovers and envisions the meaning and purposeof what he or she *is*. . . . the novile (when at all operative in anindividuals life) leads to personal rebirth -- or `Initiation -- to abasic identification of the self with the purpose this self is seen tohave within the harmony of the universal Whole. The novile thus representsthe level at which complete fulfillment of individual being is possible --either as an end in itself (negative approach) or as the condition forpositive emergence into an altogether new and higher realm of being."Seymour-Smith says, "[the 9th harmonic shows] the nature of anything thatthe native achieves."The relation of the nonile to ones unique mission can be seen in SigmundFreuds exact nonile of the Moon and Pluto. Freud was able to show therelationship between the emotions and the adequacy of the mothersnurturance (Moon) and subconscious drives and impulses (Pluto).Carl Jung had a partial 9th harmonic configuration with 4 verticesoccupied by the Sun, the Moon, Jupiter, and Saturn. His pioneeringwork 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). Hitlers Mercury-Pluto nonile is associated with his uniquemission to use (or abuse) ideas (Mercury) about enemies (7th house)to control and exterminate them (Pluto). Richard Nixons mission wasto be an all-powerful and controlling leader, which is reflected inhis quadranonile of the Sun and Pluto. Robert Browning, the romantic
poet, had an almost exact (2 minutes of arc) nonile between Mercury andVenus, and both planets were in quadranonile to Neptune. His uniquepath 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 thepath to regeneration.Power is often an issue with people whose charts contain many 10th harmonicaspects. One example is Hitler; if we include Chiron and the ascendant,he had 7 vertices of a 10th harmonic configuration occupied by planets (orpoints), with 9 points involved. Stalin had 5 vertices occupied in a partial10th harmonic configuration. One might expect that people with many suchaspects would sometimes have great healing power and a great capacity totransform themselves or the not-self. They might also have a hypnoticeffect on others, with a great capacity to sway the masses.Seymour-Smith says, "[the decile is] indicative of the interpersonaldifficulties which arise from the exercise of any kind of power ortalent, whether for good or evil."11th harmonic (undecile series): I do not yet have a clear interpretationof these aspects. One hypothesis is that with 11th harmonic aspects,A resists integration with B. The combination of A and B may representareas where dualities or multiplicities exist, and the natures of theplanets involved may indicate how one deals with them.Seymour-Smith says, "11H aspects manifest in a very definite way and theyindicate excess. They also, according to Williamsen, describe a `personsability to integrate diversities and dualisms. These interpretationsare reconcilable: the tension of `double-bind situations, which can beexternal -- where you are trapped by feelings of obligation or duty, butcannot entirely please one or more people -- or internal -- the tugbetween 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; BenjaminFranklin, 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 (inventorof 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 Bact in a patient, persistent manner to achieve material ends.The relevance of the dodecile to the material world can be seen by lookingat the people whose charts contain partial 12th harmonic configurations.Examples are J. P. Morgan (with 6 of 12 vertices marked by planets, andwith 8 planets involved) and Richard Millhouse Nixon (with planets at6 vertices, 8 planets being involved in the configuration). Both of thesemen had strong ambitions on the material plane.Of the 12th harmonic aspects, Hand says, "In the past, observers merelynoted that [the semi-sextile and quincunx] were both based on one-halfof a sextile, and they therefore drew the conclusion that both wereessentially weak sextiles. This has not turned out to be the case. Infact, the weight of opinion on these aspects has changed from a judgment
of weakly benefic to decidedly difficult. . . . They represent tensionsand difficulties that are annoying, but usually too trivial and toothoroughly bound up in the fabric of everyday life to be worth changing.The exception to this is that there does seem, according to manyinvestigators, to be a connection between quincunxes and illnesses anddeath." [This is because they fall in the 6th or 8th house from theposition of the aspected planet.]Seymour-Smith says, "The semisextile aspect was once called, withexquisite vagueness, `slightly beneficial. It is not. It denotesstrain, and at close orbs very severe strain, between the two bodiesor points involved. . . . The quincunx has more to do with health,mental and physical, than the semisextile, and is a little like theopposition inasmuch as it concerns interpersonal rather than wholly`internal matters. It shows what a person will, or will not, do forothers, and how much this costs him; it indicates what a person believesare his obligations, and his feelings about carrying them out. Peoplecan get ill if they starve themselves of the input gained from othersor if they refuse, or cannot find a way, to reciprocate the affectionsof others."Tompkins says, "The main problem with the quincunx, as many astrologershave noted, is that it is too passive an aspect to deal, withoutconsiderable conscious effort anyway, with the conflict. In fact, itis not so much conflict as *friction*."SPECIFIC ASPECTSFor delineations of specific aspects in a chart, see:Tompkins, Sue, "Aspects in Astrology: A Comprehensive Guide toInterpretation," Longmead: Element Books, 1989.Pelletier, Robert, "Planets in Aspect: Understanding Your InnerDynamics," West Chester, PA: Para Research, 1974.
Sakoian, Frances, & Acker, Louis S., "The Astrologers Handbook,"New York: Harper & Row, 1973.