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John Addey (1920-1982) was an English astrologer who wrote Harmonics in Astrology (first edition in 1976), a book which represented his vision in astrology: "All astrological effects can be understood in terms of the harmonics of cosmic periods". Charles Harvey see the book as "the single most important contribution to astrological theory and practice since the emergence of astrology in the ancient world".
Part One - The General Theory
The idea with which the book starts is that we don't have a strong basis in astrology, an obvious fact if we think why we are dealing with problems like: which is the best system (Eastern or Western) in astrology, what is the correct house system, where is the cusp of a house, the delineations in "good" and "bad" aspects or "good" and "bad" signs. The fact that we can't solve those questions shows that we don't have good, reliable principles at the foundation of the astrology we use. The author propose a solution:
"What is needed is a vision of the underlying realities of our science in the light of which astrological concepts can be co-ordinated, simplified and unified. [...] The picture that has so emerged is one of the harmonics, that is, the rhythms and sub-rhytms of cosmic periods, which can be demonstrated to provide the basis of all astrological doctrine both ancient and modern."
Then, in chapters 2 and 3, the author presents the basic elements of the theory of harmonics: a wave is a determined by length, amplitude and phase, which shows where the peak is. In astrology, the period where waves are measured is the Zodiac circle (ecliptic) which has 360 degrees, so this is the maximum length of a wave, or the fundamental wave. The length of other waves is given by the number of the harmonic which divides the basic period, for example a wave of 180 degrees (half of the circle) corresponds to harmonic 2, a wave of 90 degrees to harmonic 4 and so on.
After the theory, the author presents a first application of harmonics 3 and 4 using Michel Gauquelin study about the planet Saturn on the charts of scientists and physicians - see Cosmic Influences in Human Behaviour.
Chapter 5 is about the astrological symbolism which can be better understood with harmonics, as the author explains:
"the limits of the conventional houses do not correspond to the realities of situation" - houses in the traditional system don't fit well on harmonics for many reasons (for example phase positions in harmonics can be at every 45 degrees);
"we are always dealing with a circle of potential relationships; the symbolic significance of the relationship is based on the number by which the circle must by divided to yield a relationship."
"the traditional emphasis on number twelve (twelve signs of the Zodiac, twelve houses of the horoscope, twelve main aspect points) is shown to be one of extreme poverty. Once the harmonic principle is grasped it can be seen that all numbers play their part in the symbolism of astrological relationships"
Why don't divide the Zodiac in 36 or 4 parts, for example? Why 12? Indeed, this observation should be like a red flag for astrologers, because if those divisions of houses or signs in 12 are not the most important, not only that don't help us, but more they put obstacles to a better understanding. It gives to the chart reader additional distorting information which will distract attention from the important points of the chart.
In Chapter 6 the author shows how to calculate a harmonic (4th in his example) and her sub-harmonics (12th in his example). Another very good observation can be found:
"If we divide any circle into a number of sectors of equal length (say four sectors of 90 degrees or nine of 40 degrees) and set down our totals for each sector in order then this will have the effect of revealing more clearly the harmonics which will fit in that sector length, because it also has the effect of eliminating, in the result, all harmonics of the whole circle which will not fit into that sector length."
In Chapters 7 and 8 - "Harmonics in the Ecliptic Circle", the author shows another time that the division of the Zodiac in the well known 12 signs is limited because the signs distinct boundaries from which the influence should change radically and between which the influence should be equally the same don't reflect the reality because every small group of degrees has a different symbolism, a fact emphasized with harmonics.