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By computer, of course. Please, PLEASE do not try to do the calculations by hand. If you do, you might see numbers in front of your face for a week. You would first have to assign numbers to all of the degrees of the zodiac, starting with the first degree of Aries as number one and ending with the last degree of Pisces as number 360. Then, you will have to give each planet a number, depending on the degree it happens to be in. It gets more complicated. You have to put in the minutes and seconds of arc as well.

HARMONICS IN ASTROLOGY An Introductory Textbook to the New Understanding of an Old Science By John M. Re-edited by Chistabo, A.D. The Astrology of Harmonics were developed by the late John Addey. There is an out-of-print book by David Hamblin called Harmonic Charts. A brilliant book. If you ever have a chance to pick it up, do so. It is one of the top ten in books written on astrology in the.

Or you can let a computer do it at the click of a mouse. The choice is yours. However, if you choose the first method, be sure to check your medical insurance first to see if it covers mental breakdowns.

There are as many harmonics as there are numbers. Fortunately, only a few are needed to give us insight into the horoscope. Most of them are covered in David Hamblin's book Harmonic Charts, (The Aquarian Press, Eng.), which is unfortunately out of print. Still, if you can find a used copy somewhere, it is well worth it.
Some VERY IMPORTANT words of caution:
1) DON'T EVER try to do aspects between harmonics of different numbers. They are totally different animals.
2) There are no signs or houses in harmonic charts. Remember that everything has been rearranged, so please don't do sign or house interpretations because they are no longer there. The purpose of harmonics is to get more information about aspects and aspect patterns.
Now, let's take a look at some actual harmonics and how they can add depth to horoscope interpretation.
The Fourth Harmonic: The 4th harmonic shows how we deal with stress, strain, and struggle. When you construct a 4th harmonic chart, all of the conjunction, square, and opposition aspects in the original horoscope appear as conjunctions and this makes them easier to see. Of course, these aspects are pretty easy to see in the original horoscope as well, so what's the point? The point is that the minor aspects, the semi-square (45 degrees) and sequa-square (135 degrees), which are difficult to spot by a quick visual inspection, now appear as oppositions, and can be seen at a glance. Not only that, but other minor stress aspects (22 ½ degrees, 67 ½ degrees, 157 ½ degrees), which can take a very long time to locate, now become squares. In the 4th harmonic, whole patterns of stress aspects can be spotted, and this gives you a big edge for interpretation.
The horoscope of Francisco Assis, the Brazilian serial killer who killed at least nine women, doesn't seem, at first, to be excessively violent. But when you look at Francisco's 4th Harmonic Chart, you see another story. The Sun is opposite Venus, which can give feelings of being unloved. Yes, but lots of people have that and they don't become serial killers. What they don't have is Uranus making square aspects in the 4th harmonic to both the Sun and Venus. Uranus can make one prone to sudden, hysterical outbursts. Still, everyone born that day had the same thing. What else is there here to drive him over the edge? The Ascendant also makes stress aspects. It opposes Uranus and squares both the Sun and Venus. This makes a Grand Cross, a rare and highly stressful pattern. The Ascendant is very sensitive to changes in the time of birth. In the 4th harmonic chart, this Grand Cross could only have formed in a time interval of about 20 minutes!
But there's more to come. Mercury (the mind) Mars (violence) and Saturn (depression) make a T-Cross formation (another stressful configuration) in the 4th harmonic as well. Once again though, everyone born that day had the same thing. Why is this case different? Take another look at the birth chart. There is a close semi-square between Mars and the cusp (beginning) of the 8th house (death). Not only that, but Mars rules the sign of Aries, which happens to be the sign on the cusp of the 12th house (psychological problems) as well. This is the classic 8th house-12th house connection frequently found in the charts of serial killers. Where does the 8th house cusp land in the 4th harmonic chart? Opposite Mars, with square aspects to both Mercury and Saturn. It forms another Grand Cross. And this too, could only have been formed in an interval of about 20 minutes. It could take hours to see this in a birth chart. In the 4th harmonic chart, the conclusion leaps out at you.
What happens though, if you have harmonious aspects (sextiles and trines) in a 4th harmonic chart? The best example of that comes from Hamblin's 'Harmonic Charts.' It is the horoscope of a little known French Marshal from World War I, Franchet d'Esperey. Hamblin claims that sextiles and trines in a 4th harmonic chart show 'effort towards pleasure, or pleasure in effort.' In other words, someone who likes stress, strain, and struggle. Hamblin quotes Gauquelin's description of him:

In d'Esperey's 4th Harmonic Chart, there is a Grand Trine between the Sun, Mars, and Pluto, a perfect aspect pattern for a soldier. A Moon/Venus conjunction sextiles the Sun and Pluto and opposes Mars, making for a Kite formation. Here is someone who had an emotional need (the Moon) for action and violence (Moon/Mars) and got a lot of pleasure from it (Moon/Venus).
Muhammad Ali's 4th Harmonic Chart also has a lot of harmonious aspects, especially to the Mid-Heaven. The Sun makes a sextile and the Moon a conjunction, and both aspects are within one degree of being exact. This means that stress, strain, and struggle are more likely to bring him before the public. The Mid-Heaven also has a trine from Jupiter and a sextile from Uranus. In Ali's Birth Chart, Jupiter rules the 5th house (sports and games) and Uranus rules his 7th house (open enemies), a perfect setup for someone to become famous through competitive sports.
Robert Blake, the actor arrested for his wife's murder, has a 4th Harmonic Chart with a highly stressful T-Cross formation. There is a conjunction of the Moon (feelings, emotions) and Neptune (imagination, film), which helped him in his film career, but it is opposite Pluto (extremes) and all three of these planets make a square to Jupiter (expansion and over optimism). There is hostility towards women here, and when his emotions go, they can really go (Moon, Jupiter, Pluto T-Cross), especially if he happens to be under the influence of alcohol or other intoxicants (Neptune).
The Fifth Harmonic: The 5th harmonic chart indicates talent, if any. In the 5th harmonic chart, all of the quintiles and bi-quintiles come together as conjunctions, making them very easy to spot. The semi-quintiles and sesqua-quintiles become oppositions. Quintiles are one fifth of a circle (72 degrees) and they give talent and power, and show our ability to put things together (pattern recognition). It also has to do with creative play, the joy of making up games of finding patterns (like looking for 'patterns' of cracks in the ceiling, or always stepping on cracks in the sidewalk, or always avoiding the cracks). People with strong 5th harmonics do things like that all the time. Of course, taken to the extreme, this is a mental disorder, but those with a strong 5th harmonic usually manage to keep it under control, and then it becomes the basis for creative talent. You don't need a strong 5th harmonic to succeed as an artist, designer, scientist, or engineer, but it really helps.
Let's start with a negative example, a very negative example: Adolph Hitler's 5th Harmonic. Mercury, planet of communications, is opposite the Moon, Neptune, Saturn, and Jupiter. This gives a talent for communicating and power to his words. Chiron makes a conjunction to Mercury, as well as oppositions to the Moon, Neptune, and Saturn. Remember that Chiron is a 'bridge' between the inner planets (which rule 'normal,' everyday functions) and the outer planets, which rule forces that are out of the ordinary. Chiron also has to do with a feeling of being wounded. Hitler was able to deal with his psychological problems (Mercury rules the 12th house in his birth chart) by communications. Now everyone born that day had similar configurations in their charts. Why was Hitler different? Well for one thing, the Moon was part of the configuration, and the Moon was in place for only a few hours. But his Mid-Heaven closely aspects his Moon, Neptune, and Chiron, and also his Sun providing a link between that powerful communication configuration and his personality. The Mid-Heaven is, of course, the career and the public image, showing that Hitler's whole personality was involved when he communicated in public. The fact that the German public also felt 'wounded' after the defeat in World War I tied right in with Hitler's Mercury/Chiron quintile. Unfortunately, he dealt with these wounds by making more wounds.
A more positive example of a strong 5th harmonic chart is Mozart. In his birth chart, Venus (art) is powerful because it is his only planet in a Cadent House. This means that it is a singleton by house, and can draw all of the horoscope's energy to the 6th house (work). But the only apparent aspect seems to be a trine to Mars, and while this does add activity, it seems to leave poor Venus without connection to the rest of his life. Let's take a look at his 5th Harmonic Chart. Venus now has conjunctions with Pluto (extremes, obsession, intensity) and the Moon (which rules both one's own emotions and the ability to appeal to the public). In fact, there are eight conjunctions in his 5th harmonic, and each one represents a quintile or a bi-quintile in his birth chart. Talent on top of talent. The Sun and Mercury in that 5th harmonic chart make trines to the Mid-Heaven, making it easier for that talent to come before the public. Most of Mozart's first drafts were the same as his final drafts. He would hear the music in his head and write it down with few, if any revisions.
The Seventh Harmonic:
According to Hamblin in his book, 'Harmonic Charts,' the seventh harmonic has to do with
'…man's highest flights of creative imagination, and his lowest depths of destructive illusion. It is a number not of permanence, but of transience; not of unchanging truth, but of sudden flashes of light and darkness; not of objective reality, but of subjective impressions and the emotional experience which man derives from those impressions; not of knowledge, but of fantasy. It is, in short, a romantic number.'(Pg. 65).
In other words, the 7th harmonic has to do with inspiration, with what inspires us and how we can inspire others. This is an important ingredient of creativity.
In the 7th harmonic, the septiles, biseptiles, and tri-septiles appear as conjunctions. A septile is one-seventh of a circle, or 51.42857 degrees. Try finding that aspect by visual inspection of a birth chart!
Woody Allen's 7th Harmonic has Venus (artistic ability) opposite Chiron (our 'wounds' and recurring problems). Since Venus is also our ability to experience happiness, a Venus/Chiron stress aspect can show problems with enjoyment. But Chiron is also a teacher. Woody has taken his neuroses and turned them into entertainment. Of course, there is more than just those two involved. For real creative ability, you need to have several planets linked in an overall complex of aspects. That Venus/Chiron combination has aspects to Jupiter (ability to see the big picture) and Pluto (depth, psychological insight). Jupiter has a conjunction to Pallas (pattern recognition ability). On top of that, Uranus (ability to see things in strange and startling ways) aspects Venus, Pluto, and the Moon. That's six planets making up one pattern. The real key, though, is the Mid-Heaven. Why? Because without that, no one would ever see his creativity. The Mid-Heaven is the career, and, even more importantly, the public image. Aspect patterns involving planets sometimes last for more than a day. Everyone born that day has them. Aspects involving the Ascendant and Mid-Heaven, however, will show up in the harmonic charts for about 20 minutes, and this can make all the difference.
Tennessee William's 7th Harmonic also has a series of aspects linked together in one complex pattern. Mars, Jupiter, Saturn, and Pluto form a Grand Trine in his 7th harmonic. Mars give the energy and desire to do things, Jupiter gives optimism that they can be done, Saturn gives the discipline and determination to do them, and Pluto adds the desire to see hidden secrets. His birth chart does have a Scorpio Mid-Heaven, and his plays are famous for characters that are tragically flawed. Jupiter in conjunction with the Mid-Heaven, however, does add a note of optimism, and many times the plays end with some sort of rebirth (Pluto again) of the main protagonist.

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The Mid-Heaven is also connected to that Grand Trine, since it has a conjunction to Jupiter and a trine to Saturn. Jupiter is the storyteller, but Saturn gives the discipline to work and produce Tennessee William's 7th HarmonicMid-Heaven also makes a sextile to Mercury (writing) and a trine to Neptune (imagination) making it easier for his inspiration and imagination to be communicated to the public.
Andrew Lloyd Webber also has a strongly aspected Mid-Heaven in his 7th Harmonic Chart. There is a sextile to the Moon, and that doesn't hurt if you want your inspiration to be noticed in public. But his 7th harmonic Mid-Heaven also has an opposition to Mercury (communication) and a square to Neptune (imagination). While this does mean that his imaginative communications can come before the public, the stressful nature of the aspects does indicate that this will be a struggle for him. Saturn aspects the 7th harmonic Mid-Heaven as well, giving the determination and discipline to pound his inspiration into a completed and polished work.
The Ninth Harmonic:According to Hamblin, the 9th harmonic chart shows '…a person's capacity for joy and happiness,' and it also '…shows the person's capacity to spread joy and happiness to those around (them).' While the 4th harmonic shows how we can deal with stress, strain, and struggle, the 9th harmonic, by contrast, shows how we can be at peace.
But that means it can also show blockages to being at peace. The 9th Harmonic of David Berkowitz, the infamous 'Son of Sam' serial killer, has a Grand Cross formation involving Pluto (death) opposing a conjunction of 4 planets: Mercury (the mind, and, in this case, his Sun-sign ruler), Saturn (depression), Neptune (dreams and illusions), and Mars (action, aggression, violence). The Sun makes square aspects with all of them. The aspects to Mars are wide, but we can use a wider orb here because Mars is part of an over-all pattern.

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This pattern would occur in the 9th harmonic charts of everyone born that day. What sets David Berkowitz 9th Harmonic chart apart is the presence of the Ascendant in this pattern, and it completes the Grand Cross formation (which can be highly stressful). In David Berkowitz's Natal Chart, Venus is the ruler of both the 8th house (death) and the 12th house (psychological problems), and in his 9th harmonic chart, Venus and Uranus (sudden change) both oppose the Mid-Heaven (the public image) bringing his 'work' before the public. Again, we have to remember that the Ascendant and Mid-Heaven were only part of these configurations for a few minutes for the time and place of his birth.
Mozart's Ninth Harmonic Chart has a T-Cross formation involving the Sun, the Moon, Mercury, Jupiter, Pluto, and the Mid-Heaven. Since the Mid-Heaven is involved, appearing before the public is part of what made him happy. But it could also mean that when he does whatever made him happy, it would help him come before the public. What do those stressful aspects tell us? They show either that it was a struggle for Mozart to experience joy, or that it was the struggle itself that made him happy.
Michelle Pfeiffer's Ninth Harmonic Chart has a Kite formation, and once again the Mid-Heaven is involved. The Sun and Mars make a Grand Trine with Saturn showing happiness with action, but only if it is disciplined and focused action. A triple conjunction of the Moon, Jupiter, and the Mid-Heaven is opposite Saturn and sextiles both the Sun and Mars, and this completes the Kite. With the Mid-Heaven involved, success in career is difficult to avoid. But Saturn is opposite Jupiter and the Mid-Heaven. Jupiter expands. Saturn contracts. Jupiter is optimism. Saturn is pessimism. Jupiter is up. Saturn is down. Jupiter gives her the luck and optimism to succeed. Saturn gives the ambition and discipline. But she will tend to be of two minds about her success, sometimes loving and sometimes hating it. Periodically, she has to get away from it all (Saturn), but then she gets bored (Jupiter) and has to get back into action.
The Eleventh Harmonic:This one shows pure imagination, fantasy. Sometimes this stays inside in our own private little world. Every now and then, we let it out. The results vary. We can get a beautiful dream made real, or a nightmare of horror.
Ian Stuart Brady's 11th Harmonic is an example of the nightmare come to life. Brady, the 'Monster of the Moors,' and his girlfriend, Myra Hyndley, were a serial killer team. In Brady's 11th Harmonic chart, the Moon (emotions) is opposite Mercury (the mind) and Mars (anger) showing an imagination that tended to violence. That configuration was in effect for a few hours on the day Brady was born. As always, it is the placement of the Ascendant and the Mid-Heaven that make the difference. Aspects involving those two only last for about five minutes in an 11th harmonic chart. Brady's 11th Harmonic Mid-Heaven makes a T-Cross formation with Saturn (depression) and Neptune (imagination). The depression can sometimes be displaced into fantasies of controlling and harming others, which is what happened here. The stress aspects to the Mid-Heaven showed that these fantasies would one day come before the public. The 11th harmonic Ascendant makes a square to Pluto (death) that is only one minute of arc from exact. This is the key aspect here, the one that pushed his fantasies to become obsessions, and the obsessions to into reality.
George Gershwin's 11 Harmonic shows the positive side, the beautiful dream come to life. Venus (art) and Jupiter (optimism, 'luck,' expansion) are opposite the 11th harmonic Ascendant, while the Moon opposite the 11th harmonic Mid-Heaven makes it easier for his dreams to come before the public. Uranus (innovation) makes trine aspects to Venus and Jupiter, making it easier for Gershwin to innovate. The strong 11th harmonic adds to the creativity of Gershwin's Birth Chart, which has Neptune (imagination) making a square aspect and Venus (art) making a sextile to the Mid-Heaven.
Dr. Martin Luther King, Jr. has Sagittarius (sign of the archer) on the cusp (beginning) of his 8th house (death). Jupiter, the ruler, is in his 12th house (hidden enemies). He was shot by a sniper who was concealed at a distance. Dr. King was most famous for his 'I have a Dream' speech, so it is only natural to check Dr. King's 11th Harmonic. To see if his dream came before the public, we have to look at the Mid-Heaven. Remember that aspects to the Mid-Heaven are in effect for only a few minutes, so the chances are very small that other people would have them unless they happened to be born at the same place and time. Jupiter and Pluto make sextiles, Saturn and Uranus make conjunctions, and Neptune makes an opposition to his Mid-Heaven. That's five planets, or half of all the planets in the chart! Do you notice something else? They are all Outer Planets, the ones that rule the large-scale events in our lives.

There is more here, much more. Saturn and Neptune are in opposition and both aspect the Mid-Heaven. But didn't Ian Brady have something similar in his 11th harmonic? Yes, however we must remember that there is always a positive and a negative way for things to work out. Similar aspect patterns are common to the horoscopes of murderers and murder victims, an ironic fact that was first noted by Darling and Oliver in their book Astro Psychiatry (CSA Press, 1972).

With Ian Brady, his imagination added to his murderous urges. In the case of Dr. King, it was a setup for martyrdom. Uranus is there as well, making a conjunction to Saturn and an opposition to Neptune. Uranus is the planet of sudden, shocking events. Of course, this makes us think of his assassination, but his whole life was a struggle and involved demonstrations which (at the time) were considered shocking. The trine between Jupiter (ruler of the house of death in his birth chart) and Pluto (the 'natural' ruler of death) is also significant, very significant.

They both aspect his 11th harmonic Mid-Heaven, but, on top of that, the Mid-Heaven sits on their Midpoint! Yes, the connection with his death seems obvious here, but so is the connection with his life. The 8th house rules more than death. It also shows the values of the groups to which we belong, all the groups, including the society that we live in. The effect the group values have on us is an 8th house matter, but so is the impact we can have on the values of the group. With his 11th harmonic Mid-Heaven on the midpoint of Jupiter and Pluto, King's dream had an immense impact on an entire nation, during his life and even in death.
The Thirteenth Harmonic: The 13th harmonic seems to have a similar effect to the sign of Scorpio. They both relate to death and rebirth, transformation, as well as group resources and values.
The birth chart of Dr. Jonas Salk, inventor of the first effective anti-polio vaccine, does not (at first glance) seem too special. The Sun rules them Mid-Heaven (career) and sits in the 12th house in Scorpio. That's a good placement for doing research behind the scenes, and the Leo Mid-Heaven can give the chance of eventual fame. Pluto, the ruler of the Sun-sign, has a conjunction with Saturn (ambition, discipline) and they both make out-of-sign sextile aspects with the Mid-Heaven, as well as square aspects (challenges) to his Sun. But when we look at Jonas Salk's 13th Harmonic Chart, the picture becomes far more clear. Jupiter, Mars, Pluto, and Saturn all make conjunction aspects to his Mid-Heaven, while the Moon and the North Lunar Node make square aspects, and the Sun makes a quincunx (the 150 degree aspect). Six out of ten planets aspect his Mid-Heaven (career and public image) and that configuration only held for a few minutes on that day and location. Salk's vaccine ended a yearly epidemic of polio and (long after Salk's death) is still saving thousands of lives a year.

Harmonic charts can provide greater depth to most horoscope interpretations. Just be sure to remember that they are used for aspect patterns only, and not for sign or house interpretation. You can use them for chart comparison as well, but please don't compare harmonics of different numbers (that's like comparing apples and oranges).

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Harmonic horoscopes are based on principles of resonance, like overtones, which are present in every horoscope. The whole zodiac (360°) is taken as the basic tone, representing the number one (1). By using a higher vibration, we can 'cause' the circle to oscillate more quickly, so to speak, and investigate which planets work together in this particular pattern. For example, the fourth harmonic would involve all those planets which share square aspects (90° - division of the circle by four). In the harmonic chart, these planets form conjunctions. The number corresponding to each 'vibration' influences the interpretation.

At the risk over oversimplifying, one can say that the study of harmonics greatly extends and differentiates the theory of aspects.

Numerical Symbolism and Aspects

The aspects imply favorable, unfavorable or ambivalent relationships between the planets. Although the interpretation depends greatly on the nature of the planets involved, this view largely derives from the traditional symbolism of the numbers 1,2,3 and 4: When the circle is divided by the number one, the result is again 360° or 0° - the distance which defines a conjunction. Division by 2 gives us 180° (Opposition); division by 3 gives us the trine(120°), When we divide by 4 we have a square (90°).

The number one symbolizes the original oneness of all being, and consequently two planets in conjunction become a unified whole. The number two is the division of this one-ness into polarities, for example male and female, upper and lower, yin and yang, etc., leading to a certain tension of opposites. The number three symbolizes a creative striving ' thesis and antithesis leading to a synthesis. Usually, planets in trine are in the same element. Accordingly, they support and complement each other. The number four is matter made manifest, law fulfilled, that which has become. The corresponding square is generally considered difficult, each side obstructing the other, unable to give way.

Minor Aspects and Harmonics

Considering the above, we might well wonder about the division of the circle by other numbers, for example 5, 6, 7, 8, 9 and 10. This is as far as the minor aspects go, giving us the quintile, sextile, septile, octile, novile and decile aspects. However, these aspects and their multiples can only be arrived at by calculation. Also, the interpretation of the minor aspects is by no means as clear as that of the major aspects.

Using the technique of harmonics, one can concentrate on a certain division of the circle, instead of searching for minor aspects. The division of the circle is a matter of choice, e.g. by 5, by 57 or by 228, and one should be aware of the symbolic meaning of the number one chooses. Using the chosen number, for example 36, one can calculate a sort of auxiliary horoscope, which can be used for further analysis.

Applied Harmonics

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Using the 36th harmonic chart, one can immediately see which planets form 10°-angles (360 : 36 = 10), since all of these planets will stand in conjunction. One could for example take the number 36 as indicative of an ability of fine problem solving: 36=(2x2)x(3x3), as a tension between opposites and the striving for solution multiplied many times. In that case, the 36th harmonic would tell us about someone's approach to problem-solving and of the difficulties to be reckoned with. Within the 36th harmonic one can use major aspects, one can compare the harmonic and the natal charts, one can relate transits to the harmonic positions to events, etc. Finally, the 36th harmonic can be related to the 36th year of life - since it is the 36th time one has completed the journey around the sun, the person will be sensitive to this frequency.

When working with harmonics, one of the difficulties one meets with lies in determining the particular significance of each harmonic, in other words, in finding out what the symbolic value of the numerical factor is. In practice, one usually reduces the numbers in question to multiples of those numbers whose interpretation is assured ' as in the above-mentioned example. Another means of arriving at the meaning of the higher values is to resort to cross-sums and other mathematical and numerological practices. In theory, one could calculate an endless number of harmonic horoscopes for each natal chart. One is left with the choice of resorting to a vague numerological mysticism or working toward a systematic evaluation of the subject through comparative study.

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Literature

John M. Addey, Harmonics in Astrology, Fowler & Co. The most comprehensive work on this subject, with detailed instructions regarding the calculation, interpretation and application of harmonics.

Michael Harding u. Charles Harvey, Working with Astrology, Arkana 1990, An introduction to harmonics which is easy to read, with lots of practical examples. A great practical guide.

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David Hamblin, Harmonic Charts, Aquarian Press. John Addey thought it was important too, as he wrote the foreword.