Harmonics—Aspects Gone Wild
The word “harmonics” is being used in a variety of ways and some of the most exciting work in astrology involves related concepts. Readers who have studied music will be familiar with the ideas of octaves and resonance. The timbre of different musical instruments stems from the variations in resonance and overtones produced. In music, the primary note is called the base tone, and its harmonics are multiples of this tone—first, second, etc. In astrology, the equivalent of the “base tone” is called the first harmonic and variations derived by dividing the circle (the natal horoscope or the zodiac) by whole numbers are named for the number used for the division. An opposition is derived by dividing the circle by 2, and it is called the second harmonic. The 90 degree dial used extensively by Cosmobiologists is a fourth harmonic chart with each quarter of the circle of the zodiac super-imposed on the others so that the cardinal signs all fall conjunct each other, and the fixed signs are all conjunct each other, and the mutables are conjunct each other.
As is obvious by now, work with harmonics starts with astrology’s familiar tool, the aspect. The ancient world divided the circle by 2, 3, 4, and 6, thus producing the opposition, trine, square, and sextile in addition to the conjunction when planets were close together. Some astrologers still refer to a planet as without aspect if it lacks one of these five. The void of course moon is a moon which will leave its current sign without forming one of these five aspects to another planet.
Over the centuries, astrologers have continued to add other aspects, including a division of the circle by 12 (the semi-sextile); by 8 (the semi-square) and by fractions of these such as 5/12ths (the quincunx) and 3/8ths (the sesqui-square). Kepler, the great astrologer-astronomer, discovered the quintile of 72 degrees (division of the circle by 5), and the bi-quintile (144 degrees). A few astrologers have suggested dividing the circle by 7 (septile), by 9 (nonagon) and by 11 (undecagon). More modern names have also been suggested: octile for semi-square, tri-octile for sesqui-square, novile for nonagon, undecile for undecagon, to match the septile and attain more consistency. A division by 10 (the decile) is related to the quintile “family.”
A new chapter in astrology began in the early 1950s with the work of radio engineer John Nelson. Hired by Radio Communications of America to search for more effective means of forecasting ionospheric disturbances which might disrupt short-wave radio transmission, Nelson discovered that the angular distances between the planets provided a clue to the state of the ionosphere. As early as 1952, Nelson wrote that angles of 0, 90, and 180 were often present at the onset of solar storms and ionospheric turbulence. When major planets were separated by 60 and 120 degrees, there was relative harmony. Thus, the ancient observations about “good” and “bad” aspects were supported by modern research.
But Nelson did not stop there. He continued to make forecasts, observe results, revise his theories, and repeat the procedure, in the best tradition of scientific method. By the 1970s, he was achieving 90% accuracy in his forecasts, using all divisions of the circle which were multiples of 7-1/2, 11-1/4, and 18 degrees. He also found that if three planets were positioned so that one was in the center between the other two (at their midpoint), the effect was equivalent to a traditional aspect between them. Nelson called his “new” aspects “harmonics,” and wrote that at least one of them must be present in addition to traditional aspects for a major ionospheric disturbance to occur. Nelson also wrote that at least four planets had to be involved in inter-related aspects for a major disturbance.
John Addey took the next leap forward in the exploration of the field. Addey is the founder and first president of the Astrological Association of England, a relatively new organization but one strongly committed to research in astrology and thus influential far beyond its age or size. Addey carried the experimentation to divisions of the circle by all whole numbers, and offered possible meanings for the results in terms of the numerological meanings of the divisors. As with the septile and the undecile, results might produce repeating fractions rather than whole numbers, but all were potentially meaningful. Several major books have now been produced, including a compilation of all the harmonics so that they can be looked up in tables and need not be computed, and including a major textbook by John Addey.
Addey’s unique application of harmonic theory has been the analysis of large numbers of individuals grouped according to a variety of criteria. For example, he has analyzed clergymen, octogenarians (individuals living to very old age), polio victims, several samples of people who had cancer, etc. Smaller studies have examined engineers from several sub-disciplines. The Sun degrees of the subjects are tabulated so that a frequency distribution is obtained, and this is recalculated for all harmonics through 180. If the frequency distribution for any harmonic is relatively random (without consistent high peaks), it is non-significant. If high peaks appear in the distribution of the Sun degrees around the circle for a given harmonic, there is theoretically a relationship between the number of the harmonic and the illness, vocation, or other criteria used to produce the sample. Since untimed birth dates are sufficient to carry out such a harmonic analysis, massive amounts of data are readily available from such volumes as Who’s Who in different fields, from hospital records, census records, etc. The limiting factors are the time and energy of the astrologers carrying out the tedious calculations, or the money to hire computers to do the job.
Addey has also worked with a variation of harmonics theory which can be applied to individual charts and which is an integral part of traditional Indian astrology. Many Hindus consider the Navamsa chart to be as important as the birth chart, and use it to judge the outcome of the individual’s life. The Navamsa chart is simply a 9th harmonic chart, taking each section of 40 degrees (1/9th of the circle) and stretching it over the 360 degree circle, and placing all such circles conjunct each other. Addey suggests producing houses by equal divisions from the navamsa Ascendant, with the navamsa MC placed wherever it falls. Equal houses from the MC can also be tested. Addey has worked most with the 5th harmonic, and he suggests that it is related to perceptual ability, especially in its higher octaves, the 25th and 125th. He also relates the 5th harmonic to family ties, finding that the horoscopes of several generations repeat some of the same degree-sign positions and that these positions often form quintiles to each other.
In addition to the use of harmonic charts to represent general areas of life up to the 9th which is considered a key to the life’s outcome, Addey suggests using the harmonic charts as keys to respective years of life. He seems uncertain whether the number of the harmonic fits the number of the age being completed or the age to be entered. E.g. does the 12th harmonic symbolize age 11 to 12 or the 12th year (age 12 to 13)? In the limited amount of testing I have done, the first method seems more accurate. For many years, the harmonic charts seemed very inconclusive. But for a few really big years of major turning points, they seemed meaningful. Perhaps the big things show in all systems.
Still another suggestion in the massive Astrologer’s Guide to the Harmonics by Dr. and Mrs. James Williamson is an “arc transform”. As an example, Dr. Williamson takes the aspect between Mercury and Uranus as a key to Kepler’s genius and calculates a chart for the nearest whole number used as a harmonic (division of the circle). The resultant chart is supposed to portray Kepler’s exceptional mind. So far, our experiments with such arcs have been unconvincing. Hitler’s Mars square Saturn arc produced a very innocuous chart with a focus on air and mutables. Moreover, very different charts are obtained when one uses the exact arc, giving a fractional harmonic, the closest whole number to the fraction, or the whole number which puts the two planets closest to conjunct. Using the exact fraction of a degree as a harmonic, the two planets are exactly conjunct, of course. For those still struggling with the basic concept of harmonics, remember we are taking the distance between the two planets and stretching it over the whole 360 degree circle so that one planet falls exactly on the other in the harmonic chart.
Our own efforts at CCRS have included considerable testing of Nelson’s “new” aspects, and results support his findings. More recently, we have run two sizable samples through the harmonic frequency analysis: a group of over 800 mentally retarded individuals and over 1200 chronic, hospitalized, male alcoholics. The work is too new to report general conclusions. Only an inter-disciplinary, coordinated effort can hope to make real and lasting progress in astrology research, and the efforts described here certainly qualify. The original theory came from John Addey; the English Astrological Association produced the computer calculations to do the analysis. Rique Pottenger of CCRS revised the program so that only the date of birth was required and the computer did the rest. Dr. Paul Liberty Jr. of Austin, Texas donated the computer time to actually run the data, paying for it himself as a contribution to astrology research. Gyanam in Kansas painstakingly copied the 1200 birth dates of alcoholics from hospital records; not once but twice since the data was lost in between two different runs which attempted different approaches. Hal White and Eric Tarkington did the preliminary analysis in Toronto, Canada. Much additional analysis is needed, but we certainly want to express our deep gratitude to all those listed above who have contributed to the effort. We are also grateful to Ann Demerest for the birth dates of the mentally retarded, and hope that they will also provide meaningful results.
The initial analysis by Hal and Eric suggested an emphasis on the 9th harmonic in the alcoholics with the multiples of 9 by odd numbers (9, 27, 45, 63, etc.) especially high. But Addey pointed out the differing phase angles and felt that several other harmonics were more important. Addey commented that the complexity of alcoholism could involve a number of root causes, hence several harmonics, but he also feels that the diurnal circle is more important than the zodiacal circle. Unfortunately, birth time is required to work with the diurnal circle.
In addition to the varied approaches to harmonics listed above, I have long wanted to try another application of the theory to individual charts. Robert Hand, the well known Cape Cod astrological writer and researcher, provided us with the formulas for carrying out my wish. I have long emphasized the importance of basic “themes” in horoscopes. What is the chart saying repeatedly? A network of inter-related aspects is one such logical theme. Does the chart have an unusual number of one type of aspects (squares, trines, or some of the little noticed ones such as septiles)? Does it matter whether they are connected to each other, whether, for example, there are five separate pairs of planets with quintiles or whether there is a grand quintile like a five-pointed star in the chart?
In the spring of 1977, using the formulas of Rob Hand and the microcomputer being built by Rique Pottenger for CCRS, we finally began exploring this new area. Progress has been slow since I have been on the road most of the time since the computer became operational with the new programs. But some fascinating bits and pieces have appeared, including a suggestion that the number five and the fifth harmonic in general are associated with power, whether the power is used constructively or destructively. This result would fit Nelson’s observations that major solar storms only occurred when the planets formed at least two aspects that were multiples of 18 degrees. Addey has also associated 5 with power.
On a limited number of charts of earthquakes, the variations on the 5th harmonic stood out, including multiples such as 25, 35, and 45. Eventually, of course, we plan to run hundreds of charts on quakes, and to check to see if there are variations between “normal” ones which occur constantly, and those in which there is heavy loss of life. But Hitler’s chart was the most impressive, with the four top harmonics being multiples of five: 5, 10, 20, 25. Of the other famous people tried out on the new programs, Nixon’s chart emphasized the 7th harmonic; Rockefeller emphasized the 8th; Carter had more multiples of 3; Indira Gandhi had a focus on 4; and Mondale on 14.
We are trying out two variations of this approach: one which simply counts the number of each type of aspect using an arbitrary orb, and one which weights for inter-relationship of factors (hence closeness of orb in the harmonic chart) so that a higher figure is produced by the grand quintile than by five separate quintiles. The two programs are called CC (conjunction counting) and VA (vector addition) and future discussion of ongoing research will refer to results with those initials. We hope to run our 200 alcoholics for which birth time is available on these programs, and we have run about 70 airplane crashes, but the results have not yet been analyzed. If results continue to be promising, other collections of data will be run and compared, including a massive group of SIDS (sudden infant death syndrome). Work has hardly started on this latest approach to harmonic theory, and it is much too early for any conclusions. But additional timed birth data is needed, and will be much appreciated—especially on alcoholics and hemophiliacs. We’ll keep you posted as results come in.
Still another variety of harmonic chart being run on our microcomputer currently is the exact solar arc for an important event in a life. The harmonic will be a fraction rather than the whole number of the person’s age. Nancy Madsen of Racine, Wisconsin suggested this refinement, which is similar to shifting from the use of a simple degree-for-a-year as a form of direction to directing (moving) all the planets the exact solar arc. To obtain the solar arc, one calculates the distance the Sun has moved in the number of days since birth that match the age of the individual at the desired period. If the event being considered took place at 10 years and 3 months of age, the Sun’s position on the birth date is subtracted from the Sun’s position 10 days later, 15 minutes are added for the 3 months, and the result is the solar arc or Sun’s motion in that interval. Addey’s method would use the 10th or 11th harmonic for this age. The actual solar arc could vary between 9 and 11, depending on birth date, since the Sun is faster in winter and slower in summer. The resulting charts (fractional vs. whole number) will be very different, and work to date suggests that the harmonic chart for the exact solar arc can be quite fascinating and indicative of the psychological state of the individual at the time.
At this point, our only conclusion points to a need to hang loose and keep our options open. The cosmic order is so pervasive, no matter what we do, we see some of it.