Harmonics as a Search for Aspect Themes
Subscribers who have been with The Mutable Dilemma from the beginning will remember that we had a number of articles on harmonics in early issues of the journal. Rob Hand and two of my sons, Mark and Rique, had developed some mathematical formulas to help me achieve a long-standing desire; a convenient way to spot aspect themes in horoscopes including many more aspects than the ones in common usage. No single formula was adequate, so we experimented with a variety of approaches to my goal. When Austin Levy from Australia visited us a couple of years ago, we added his procedure to our collection. Over the years, I have run the collection of programs rather sporadically; unfortunately, without keeping records of the results.
Two events during the last month renewed my interest in the search for aspect patterns. I received a copy of David Hamblin’s new book Harmonic Charts: A New Dimension in Astrology, and Mark got the original programs translated into MBASIC so they could be run on the Osborne computer. The original NorthStar computer had turned flaky and its printer was even worse, so having the programs readily available and adding the interesting theories proposed in David’s book, generated enough excitement to keep the Osborne working for several days. One of the programs is quite time-consuming, so even with the aid of the computer, a good many hours have only produced a few dozen chart analyses. Still, there are some preliminary suggestions that seem worth communicating.
To refresh the memories of readers who joined us later, the current work on harmonics stems mostly from John Addey of England. Classical astrology in the days of Ptolemy used five aspects; divisions of the circle by 1 (conjunction), by 2 (opposition), by 3 (trine), by 4 (square), and by 6 (sextile). Over the centuries, added aspects included division by 8 (octile or semi-square) along with 3/8ths of the circle, the trioctile or sesquisquare, division by 12 (semisextile) along with 5/12ths (quincunx or inconjunct), and a few astrologers included a division by five (quintile), by seven (septile), by nine (novile), by ten (decile) and by eleven (undecile).
Addey approved of these additions to our array of aspects, and suggested going much farther. In some of his work, he went as far as a division of the circle by 180, giving an aspect of two degrees. He also adapted an idea much practiced in India, the erection of a series of new charts based on these divisions of the circle. The navamsa chart is considered almost as important as the natal chart in Indian astrology. The procedure for calculating a harmonic chart involves a translation of the natal planetary positions into numbers from zero (for zero Aries) to 359 (for 29 degrees of Pisces). Each number is then multiplied by the number of the desired harmonic (by nine for a navamsa chart) and if the result is more than 360, that amount is subtracted from it repeatedly until a final result is less than 360. This figure is then translated back into zodiacal degree, sign, and minute.
A new chart is then produced, using equal houses from either the Ascendant or from the MC. The other angles (those not being used to determine the house cusps) are put in the chart wherever they fall. Addey suggested that these harmonic charts could be read in two ways: the smaller numbers could be interpreted as different facets of the character; the charts might also be a key to current patterns in the life. The second harmonic chart might indicate conditions in the life from age two to three and so on.
David Hamblin has worked extensively with these harmonic charts and concluded that there are serious questions concerning the validity of the charts as a key to different years of the life. I had reached the same conclusion in my own limited work, so was glad to know that David shared my feeling that if the harmonic charts were valuable, the natal chart should apply to the first year only, then the second harmonic chart to age one to two and so on. Since different astrologers made a case for two different charts applying to the same year, one has to question the whole concept. David also had concluded (as I had) that the use of the new signs in the harmonic charts was a questionable technique. He felt that the main value of the new charts was in making aspects highly visible, showing a network of interrelated aspects, and especially in focusing attention on the previously little used aspects such as septile, novile, etc.
In the book, David analyses a large number of interesting charts, including famous people, mundane events, and some personal clients. For one of the latter, David felt that the harmonic charts would have helped him to understand the individual and to be more helpful. Although it is a digression from our focus on harmonics as aspects, I found David’s difficulty in understanding “Susan” sufficiently frustrating to justify a discussion of her chart.
David had mentioned and dismissed the theory that horoscope houses are like “boxes” with similar natures to the signs and planets, and yet Susan’s lack of confidence which he found so baffling is a clear potential with her Jupiter and Saturn (rulers of the Sagittarius and Capricorn in the first house) and her Mars (the natural ruler of the first house) all in the fourth house. As all of our readers know, we feel that the house is more important than the sign. To add more potential for self-doubt and self-blocking, Susan has the Moon in the first house conjunct the East Point in Capricorn, and the south node of the Moon is in the fourth house between Mars and Saturn. Note that repeated theme of identification with letters four and ten, (mixtures of one-four-ten), with Moon-Capricorn in the first house, and the planetary rulers of the first house all in the fourth house. Having two first house rulers conjunct a node (another form of letter four), one ruler being Saturn itself, the most important form of letter ten, is a repetition of the one-four-ten combination. I find the south node much like Saturn, a lesson to learn after which we have something to give involving that part of life. Both Saturn and the south node of the Moon suggest a tendency toward anxiety and doubt at the beginning of life and a conjunction of the two intensifies the issue.
Combinations of four, ten, and twelve are the ones most likely to be expressed as anxiety and depression until the individual gets out of the baby side of letter four by becoming parent and caring for others; gets over the feeling that the world has the power by handling a job successfully, and develops faith in a higher power (where letter twelve is concerned). Susan has Neptune in the ninth house which might indicate she had faith, but it is square her Moon and quincunx south node and Saturn, showing the likelihood of a problem. As long as she stays home, depending on someone else to support her, she is likely to remain anxious and depressed. With Venus and Juno in Pisces, she tends to idealize marriage, which often means putting one’s faith in the marriage partner rather than in God, and with Cancer in the eighth house, she is looking for a mate to play mother for her. She will discover her fire and her Aquarius when she becomes self- supporting and independent. David came to that conclusion with the help of the harmonic charts, but the message is clear enough if we know that the fourth house symbolizes the same part of life as does the Moon, its nodes, and the sign Cancer.
Despite the preceding being a digression from the subject, charts like Susan’s are valuable for testing our theories of astrology as keys to psychological insight. To return to the pursuit of aspects through harmonics, as has been suggested, harmonic charts may be used simply to spot less-used aspects including, as David pointed out in his book, to see variations on those aspects. For example, an opposition in a fourth harmonic chart is an octile or a trioctile in the natal chart. A square in the fourth harmonic chart is a multiple of 22 1/2 degrees other than the classic aspects already listed. Of course all connected conjunctions, oppositions, and squares in the natal chart will be bunched as a conjunction in the fourth harmonic chart. By connected, I mean a network of those aspects linked to each other. If the natal chart has two grand crosses, the fourth harmonic chart will have each set of four planets as a conjunction. The 90 degree dial developed in Germany by the Ebertins reaches the same goal without using new signs or any houses, using the technique to see minor aspects quickly and easily.
Even with a computer, it is still a lot of work to set up and study a variety of harmonic charts, and there is no logical reason to stop at any point in our proliferation of aspects. So I have pursued the programs developed by Rob, Rique, and Mark as a series of approaches to the goal of discovering aspect themes; an emphasis on one or a series of aspects. It is necessary to calculate many hundreds more charts of a variety of individuals and events before we can feel at all sure of the meaning of some of the less-used aspects such as quintile, septile, novile, etc., but I feel that the computer programs now available will eventually help us find answers. None of the programs gives the full picture, hence a series, each offering part of the information.
The program I plan to discuss in this article approaches the goal in three different ways. First, harmonic charts are calculated up to the 60th harmonic (an aspect of 6 degrees, since we are dividing the circle by the number of the harmonic). The computer then counts the number of conjunctions for each harmonic chart. Each harmonic chart will include all harmonic numbers that divide evenly into it. For example, as already indicated, the fourth harmonic chart puts conjunctions (division of the circle by one, so no change from the natal chart), oppositions (division by two) and squares (division by four) together as a conjunction. A ninth harmonic chart would have conjunctions (one divides evenly into all numbers) and trines (three divides evenly into nine) as well as noviles grouped in a conjunction. To be able to count the number of conjunctions in these harmonic charts, we have to decide on an acceptable orb. How close must the aspect be to count it? Since this whole enterprise is exploratory, we started with two orbs to see whether either gave more significant results. The program prints two columns with a conjunction given a 12 degree orb in one and a 24 degree orb in the other. The opposition gets half that orb, the square a fourth of it, and so on. By the time we reach the small aspects such as 6 degree, the orb is very tiny in the natal chart.
A second part of this same program calculates what we call “vector addition”. In this column, a higher figure results when the aspect in the natal chart is part of a network of planets linked by the same aspect. For example, five separate quintiles would receive a smaller figure than would a grand quintile; five planets all quintile each other. Hopefully, this type of discrimination will enable us in time to determine whether several planets connected by the same aspect makes the aspect more important than the same number of that aspect in isolated pairs in the chart. This part of the program has one serious problem; under certain mathematical conditions, some numbers cancel each other. Unfortunately, as yet I don’t know how often that happens or how to prevent it. I think it is a rare occurrence but we still need more work to remedy it.
The third part of the same program uses the formula of Austin Levy of Australia to derive what he calls the degree of “centricity” in each of the harmonic charts; in other words, the degree to which the planets are bunched in one area like a Mark Edmund Jones’ “bundle.” Again, the goal to simply to determine the relative emphasis on that type of aspect, looking at all aspects from a natal conjunction to a six degree aspect. The whole program produces four columns with a figure for each of the 60 aspects. I then underline the high ones, and look to see which are high in several of the columns. I also look for patterns in which a series of related numbers are all high.
Though this work is preliminary, as previously stated, some interesting patterns have occurred. I have run a series of charts of people we might call “normal” or “non-famous;” a series of famous or infamous people (including three murderers or more if we add the politicians who give the orders that result in killing); a small series of mundane events (mostly data from David Hamblin’s book), 21 charts of crib death cases, infants who died before the age of one year, and some family members who could mostly be included with the non- famous people though some may be as well known as some in the famous group. I use a score of 20 or more in the first column, 35 or more in the second column, 7 or more in the third column, and 30 or more in the last column as the lower of two thresholds, and I underline the harmonics (aspects) which reach those levels. Figures of 30 or more are rarely seen in the first column, 45 or more in the second, 10 or more in the third, and 40 or more in the last column. This set of figures can be taken as a higher threshold, marking a very high focus on the aspects with these scores.
To move on to some of my results, first checking for charts above the higher threshold, only my son, Mark, scored above 30 in the first column in the group of 15 non-famous. None of the 29 individuals in the famous group had a score of 30. One of the six mundane charts (the eruption of Mt. St. Helens) scored a 31. Four of 21 cases of crib death scored 30 or more. In the second column, Rique had two scores of 45 and Mark one of 51. The rest of the non- famous individuals had no scores at that level. The 29 famous people had ten scores of 45 or more, with two of them over 50. The 21 crib deaths had four scores of 45 or more. The six mundane charts had four scores at that level.
In the third column, our vector addition, Rique and Mark again topped our ceiling of 10, and only one other person in the non-famous group had a score of 10. The famous group had 17 scores of 10 or more. The crib deaths had 13 scores at that level. The six mundane charts had 5 high scores, including one of almost 14. In the last column, centricity, in the non-famous group, Rique was the only one with a score of 40. Eight of the 29 famous individuals reached that level, one topping 50. There were ten scores that high in the 21 crib deaths, and three in the six mundane charts, two of them topping 50.
After I have increased our sample in all the sub-groups, I will check for statistical significance. If the numbers are similar to those listed here, we should get reasonable significance. Aspects are one of the tools in astrology which have been neglected in research because the problem of determining expected frequency is so formidable. But by matching different groups against each other, they can function as controls for each other. To summarize the preceding results, if we leave Rique and Mark out of the non-famous (I suspect they are both on their way to joining the famous group), we have a total of one high score for 13 people. The already famous 29 produce 35 high scores. The 21 crib death charts produce 34 high scores. The six mundane charts have 13 high scores.
What theories can we offer to fit these results? As I have said often in the past, a large number of close aspects indicates a quality of intensity in the person which can manifest as either major talent and success or serious problems. These computer programs make it possible for us to look for many little-used aspects which may be relevant to such talents or problems. The attempt to deduce the meaning of these “new” aspects, to which much of David Hamblin’s book is devoted, is an additional challenge. I have noted when there are series of related aspects, such as multiples of 5, 7, 9, 11, etc. in analyzing the charts being discussed here. I found David’s theories about the meaning of these aspects interesting but still feel the need for much more work; that is, many more charts need to be run on our computer programs. Oh for a 48 hour day!
David associates the fourth harmonic with struggle, striving, and an intense need to integrate and manifest the planets which are in traditional conflict aspects. Albert Schweitzer, the famous medical missionary to Africa, is one of the strongest 4-dominated charts of the ones I have calculated so far. Shifting now to the lower threshold figures that were listed above, and counting any score of 20 up in the first column, any of 35 up in the second column, of 7 up in the third column, and of 30 up in the last column, high scores for Schweitzer include division of the circle by 4, 16, 36, 44, 48, 52, and 60. Including the nodes of the Moon and the East Point (as an auxiliary Ascendant), he has a strong, cardinal t-square, and bringing in Juno, he has a close grand cross in fixed signs. I consider the cardinal and fixed squares and oppositions to mark a power-struggle capacity in the person. Schweitzer ruled his associates with an iron hand but his power was also used constructively to help many.
David associates the fifth harmonic, the quintile and its relatives, with “arranging, building, constructing, structuring, forming.” p. 48. I am more inclined to associate four with such solid results and to see five as much like Leo, concerned with personal power whether the power is used creatively or destructively. As most know by now, Hitler had a strong five series in his chart. High scores, using the same cut-off points mentioned for Schweitzer, include dividing the circle by 5, 10, 25, 40, 50, 60. Churchill had four of the multiples of five: 25, 35, 45, 55. The Houston, TX. murderer, Dean Corll, had 5, 15, 25, 30, 45, and 55 at high levels. Sai Baba, a spiritual teacher reported to have amazing psychokinetic powers, has 5, 10, 15, and 50. Another murderer whose data is given in David’s book has 20, 30, and 60 high, but two or three in a series is a very common and probably not significant occurrence. John Addey, the initiator of this proliferation of work with harmonics, had 5, 10, 15, 20, and 45 high. The largest number I have found yet in a single series occurred in a progressed chart. Marguerite, the mainstay of ISAR, as of September 1983, has high scores on every multiple of five except 35 and 60, and she only missed them by one number since 36 and 59 are both high. Her natal chart is quite “normal,” with no clear pattern. Another religious guru with many high fives is Muktananda with 15, 25, 30, 45, 50, and 55 all high. He is well-known for his work with the Kundalini. I might mention one more person, the outstanding English psychic, Matthew Manning, who has 5, 10, 20, 30, 40, and 50 all high.
With such a varied group, I am reluctant to be too committed to any theory of meaning until we run more charts. Indira Gandhi also has six of the five series high; 5, 10, 20, 30, 40, and 60. Obviously, we still need to note which planets form these aspects. Two other programs examine that issue, but they will have to wait for another article.
To look briefly at the multiples of seven, of nine, and of eleven, David associates the septiles with imagination and inspiration; the noviles with spiritual seeking and tact but especially with inner joy and peace; and he quotes others who associate the eleven series with excess but also the integration of dualities and diversities. David also mentions people who lack a clear pattern and seem confused or lacking in a strong sense of identity. I have some reservations on several of these ideas, but the problem may be more semantic than substantial. A number of individuals have a strong seven series in my sample. Therese Neumann, the German stigmatist, had high scores on 14, 21, 28, 35, 42, 49. It would seem appropriate to credit her with both intense spiritual devotion and with a strong imagination. It is recognized today that a stigmatist is creating his or her own wounds with the unconscious mind. Historically, all have had wounds in the hands since until recently, it was believed that Jesus was crucified with nails through the hands. But it is now known that the nails were driven through the wrists. The bones of the hands are not strong enough to support the weight of a body.
Jose’ Silva, founder of Mind Control which uses the power of the imagination to enhance psychic ability and to heal, has 7, 14, 21, and 42 all high. Richard Nixon, as David pointed out, also has a seven series; 7, 14, 28, 35, 42, and 56 are all high. His imagination got him into considerable trouble when he decided the world was against him. Bobby Fischer, the paranoid former chess champion, also has a seven series; 14, 21, 28, 42, 49, and 56 are all high. His paranoia, like Nixon’s, suggests an over-active imagination and a lack of faith, so both the spiritual search issue of faith and the active unconscious may be associated with the septiles.
I think my main problem with David’s associations with the novile series is the assumption that it would be positive. In all cases, we can manifest positive or painful results. I do think that the novile may mark a spiritual search but since it dominates the chart of Jim Jones, there is no guarantee that the search will result in joy or inner peace. Jones’ highest figures were in the 9th and 18th harmonics. He just missed our extra- high threshold in the first column with 29 on the 18th harmonic. He had the highest score on any of my 71 charts on the second column; 59 for the 18th harmonic. He topped 10 on the third column on the 18th harmonic, and he had over 40 on the last column on the 9th harmonic. Almost all of his high scores were on division of the circle by multiples of 3.
I should add that David would interpret the 18th harmonic as an opposition in the 9th harmonic, and therefore as a struggle to attain enlightenment. It is clear that multiples of three do not guarantee an easy or pleasant life when we note that two of the three murderers (not counting Jones or Hitler) had an emphasis on the 3 series. It is quite possible to have a chart full of trines and have it indicate a strong sense of “I know what I want. Why can’t I have it?” But then Benjamin Creme, the spiritual guru, also has mostly 3s, 5s, and 9s, so we have to repeat that the chart shows the issues in the life. The person determines the results.
So far, I do not have too many people with an emphasis on the eleven series. Churchill is outstanding. He has high scores on every one possible up to our cut-off point of 60: 11, 22, 33, 44, and 55. He also has a combination like our former Vice President, Walter Mondale, who is now running for President of the U.S. I did not include Mondale’s chart in my current group, but remember the results from earlier work. Mondale has 14, 28, and 42 high. Churchill has 14, 28, and 35 high. Churchill also has 16, 32, and 48 high. One of the tabulations I have not yet done is simply to count the total number of high scores to see who has the most. Churchill is certainly one of the high scorers. I may include a table at the end of the article listing those figures.
Still another possible meaningful emphasis might appear for the individuals who have many prime numbers in place of the series we have been noting. Only counting the primes over 10, Matthew Manning and the famous psychic Edgar Cayce both have five primes among their high scores. Olga Worrel, the spiritual healer and psychic has six primes. I remember from earlier work that our former California governor, Jerry Brown, had a large number of primes. They might indicate people who are unusual or individualistic but I have too few cases to do more than preliminary speculation. One additional approach has already been mentioned; calculating the aspect analyses on progressed charts. I have done very few of these so far, but have gotten interesting results. One of my non-famous individuals is a young man whose natal chart had few high aspects and no particular patterns, but his progressed chart for the time of an accident which left him almost totally paralyzed showed much higher scores. His highest scores were on the 19th and the 38th harmonics, the latter reaching 47 in the second column and over 11 on the third column. But don’t ask me what it means, other than he had a network of tight connections in aspects which would normally be totally ignored in astrology. The other case was Marcia Moore, the well-known astrologer who died mysteriously in the state of Washington. I analyzed her natal and progressed charts in both her birth place and in Washington to see if the patterns changed. The highest scores were present for the progressed chart in Washington. So far, we cannot mix aspects between natal and progressed or between natal and local residences, but even the small amount of work done so far suggests that these aspect analyses may prove useful on a variety of charts.
On averaging the numbers of high scores for my four groups, counting the number of scores above the lower threshold, a wide range is clearly present in each group. The non-famous small group of 13 individuals has an average of 13.77 high scores, combining all four columns. The mundane charts average 20.16 high scores. The famous individuals average 23.79, and the crib deaths average 26.28. But the range is from 6 to 21 on the non-famous; from 10 to 30 on the mundane; from 7 to 40 on the famous; from 9 to 50 on the crib deaths. The low number is David Hamblin’s client, Susan, while the high number of an identified person is Albert Schweitzer. My crib death cases are anonymous. Fischer, the paranoid chess champion has just one less than Schweitzer with 39 high scores. Obviously, we get a different picture if we use the lower threshold levels (to get the numbers just listed) or the higher thresholds which put the mundane charts proportionately ahead of the other three groups. But the order remained the same for the other three groups.
I expect to run many more charts in the future, including the alcoholics and earthquakes which will be examined during the ISAR research week in March, 1984. I am also hoping to run more of the crib deaths, famous people, and non- famous to maintain a control group. We will look at the results on some of the other aspect analysis programs in a later issue of The Mutable Dilemma.
Reference: Hamblin, David; Harmonic Charts, a New Dimension in Astrology; The Aquarian Press, Wellingborough, Great Britain, 1983.