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The Importance of Harmonics

In 1971, John Addey, the co-founder and second President of the Astrological Association, delivered the Carter Memorial Lecture, Astrology Reborn (now available as a pamphlet1), in which he claimed that astrology would be “reborn” as a result of the introduction of the concept of harmonics. And then in 1976 he published his book Harmonics in Astrology2, in which he wrote:

“What is needed is a vision of the underlying realities of our science in the light of which astrological concepts can be coordinated, simplified and unified. Now at last we appear to be in sight of such a vision … The picture that has so emerged is one of the harmonics, that is, the rhythms and sub-rhythms of cosmic periods, which can be demonstrated to provide the basis of all astrological doctrine, both ancient and modern.”

But this has not happened. Astrology has not been reborn, and the concept of harmonics has been largely forgotten. I have not found a single reference to harmonics in recent issues of the Astrological Journal.

Why should this be? Partly it is because John Addey died in 1982, at the age of only 61, when his work on harmonics was far from complete. Also, I am myself partly responsible for the decline in interest in harmonics. In 1983 I published my book Harmonic Charts3, and for a time in the 1980s I edited the Harmonic Astrology Newsletter in which astrologers shared their experience of working with harmonics. But at the end of the 1980s I turned away from astrology, and was absent from the astrological community for nearly 20 years. During this time (except for the excellent book Working with Astrology by Michael Harding and Charles Harvey4) very little was written about harmonics.

However, there are now signs of a revival of interest in harmonics. Since I came back to astrology I have published two books, The Spirit of Numbers: a New Exploration of Harmonic Astrology5 and Harmonic Astrology in Practice6. And in America David Cochrane has developed his system of Vibrational Astrology, in which harmonics play a central part, and he has published an online book, The First 32 Harmonics, a Qualitative Research Study7, describing his findings about the interpretation of harmonics.

In this article I will try to explain why harmonics are important, and how they can yield fascinating new insights into the interpretation of charts which would not otherwise be available.

First, what is a harmonic?

“Harmonic” is a term that was first used in physics and in music. It has been defined as follows: “A harmonic is a signal or wave whose frequency is an integral (whole-number) multiple of the frequency of some reference signal or wave.” Thus, “for a signal whose fundamental frequency is f, the second harmonic has a frequency of 2f, the third harmonic has a frequency of 3f, and so on … A signal can, in theory, have infinitely many harmonics”8.

In physics and in music, the “reference signal or wave” (the first harmonic) can be of any length. But in astrology we are always talking about the harmonics of a circle. Therefore, in astrology, the first harmonic always has a length of 360 degrees (the whole circle), the second harmonic has a length of 360 ÷ 2 = 180 degrees, and so on. So the second harmonic refers to a signal that occurs (or a wave that peaks) at two points around the circle.

John Addey makes it clear that the concept of harmonics can be applied to all of the circles with which astrologers are concerned: the circle of the Zodiac, the diurnal circle (the circle of the houses), and the aspectual circle (the circle of interplanetary aspects, starting from the conjunction and moving round to the opposition and back to the conjunction again). However, the advances that have been made in the interpretation of harmonics have been almost entirely in relation to the aspectual circle, and so it is with the aspectual circle that this article will be concerned.

If we look at the aspects that are traditionally used in astrology, we can see at once that we are already dealing with harmonics. Thus:

The conjunction is the aspect of the 1st harmonic.
The opposition is the aspect of the 2nd harmonic (i.e., if two planets are opposite to each other, they come together in the 2nd harmonic).
The trine is the aspect of the 3rd harmonic.
The square is the aspect of the 4th harmonic.
The sextile is the aspect of the 6th harmonic.
The semi-square and sesquiquadrate are aspects of the 8th harmonic.
The semi-sextile and quincunx are aspects of the 12th harmonic.

Looking at this list, we can see that certain numbers are missing. What about aspects in the 5th, 7th, 9th, 10th and 11th harmonics? Might not these harmonics also have astrological significance? And what about numbers higher than 12?

Thus, the study of harmonics is essentially about the study of interplanetary aspects that are not used in traditional astrology. In my own work I have studied all the harmonics up to the 32nd, and David Cochrane has also independently chosen to stop at the 32nd harmonic. Thus, there is now a large amount of information about the significance of all of the first 32 harmonics. Of course, far more work needs to be done before we understand them fully. But I believe that we now understand these harmonics well enough to be able to use them in the interpretation of charts, and to obtain valuable new insights from them.

Before we look at some of these insights, I need to set out the three basic principles of harmonic astrology.

The first principle of harmonic astrology is that each prime number introduces a new quality. I call these qualities Twoness, Threeness, and so on. (Twoness is the quality of being Two, just as Oneness is the quality of being One.) As astrologers, we already know about the qualities of Twoness and Threeness. Twoness (the quality of the “hard” aspects) signifies effort and struggle, whereas Threeness (the quality of the “soft” aspects) signifies ease and pleasure. But what are the qualities of the higher prime numbers?

As a result of my investigation into more than a thousand charts, I have reached the following conclusions about the qualities associated with each of the higher prime numbers. (These keywords are of course provisional, and are subject to amendment in the light of further research.)

Fiveness is about building and re-shaping (conscious creativity).
Sevenness is about inspiration and intuition.
Elevenness is about defiance and dogged persistence.
Thirteenness is about adventurousness (testing one’s limits, the search for one’s identity);
Seventeenness is about rebelliousness, subversiveness, campaigning for change.
Nineteenness is about humility, empathy, acceptance of one’s lot.
Twenty-threeness is about inventiveness and story-telling.
Twenty-nineness is is about pride in ones uniqueness.
Thirty-oneness is about openness to unconscious desires.

There are also numbers (4, 8, 16, 32; 9, 27; 25) which are higher powers of prime numbers, and signify the qualities of that prime number but maybe in a more refined form. And finally there are composite numbers, which combine the qualities of more than one prime number. Thus, 15 is a combination of Threeness and Fiveness, and signifies pleasure in creativity, and 22 is a combination of Twoness and Elevenness, and signifies effort towards defiance.

The second principle of harmonic astrology is that, the closer an aspect is to exactitude, the stronger it will be. Astrologers usually allow an orb of 8 degrees for the major aspects, and they may not pay much attention to the closeness of the aspect. But in harmonic astrology we are saying that a signal occurs at the point where the aspect becomes exact, and the strongest aspects are those that are closest to this point.

The third principle of harmonic astrology is that the orb allowed for any harmonic is the orb for the conjunction, divided by the number of the harmonic. Thus, for example, if we allow a maximum orb of 12 degrees (720 minutes) for the conjunction, the maximum orb for the 13th harmonic is 720 ÷ 13 = 55 minutes.

Having set out these principles, we can look at some of the insights that can be gained from studying harmonic aspects.

I will take two examples of famous (or perhaps I should say infamous) people, Adolf Hitler and Donald Trump. Whatever we think of Hitler and Trump, we cannot deny that they are very distinctive characters, and so we would expect that the harmonic aspects would shed some light on the nature of this distinctiveness.

If we look at the harmonic aspects in Hitler’s birth chart, we can see that he has great strength in Twoness, Fiveness and Sevenness. (I have analysed Hitler’s chart in more detail in The Spirit of Numbers, pp.221-6.)

First, Twoness is about effort and struggle. Hitler has a cluster of Twoness aspects connecting Sun, Jupiter, Uranus and Pluto. These aspects are at the higher levels of Twoness (the 8th, 16th and 32nd harmonics), and signify a struggle deep within Hitler’s psyche (as shown in Hitler’s own book, Mein Kampf, “My Struggle”). He is struggling to express himself (Sun) in ways which combine the qualities of Jupiter, Uranus and Pluto. There could scarcely be a clearer indication of Hitler’s desire to achieve personal grandeur in startling and transformative ways.

Secondly, Hitler has an exceptionally strong pattern of Fiveness aspects involving all the planets except Sun and Uranus. Fiveness is about creativity, re-shaping the world, and this pattern shows Hitler as the chief architect of the Nazi regime, which was one of the most tightly-controlled and all-embracing regimes in history, determining the ways in which people were expected to think and behave.

Thirdly, Hitler has two very close Sevenness aspects: Sun linked to Saturn in the 7th harmonic, and Mercury linked to Uranus in the 14th harmonic (14 = 7 x 2). Sevenness is about inspiration (“what turns you on”), and the Sun-Saturn link (with Saturn in the 10th house) shows that Hitler is inspired by the idea of his own destiny as the saviour of his country. The Mercury-Uranus link shows that he is also inspired by the idea of electrifying communication, and this is perhaps the clearest indication of Hitler’s skill as an orator, able to whip up passions in his audience.

But perhaps the most remarkable thing about Hitler’s chart is the almost complete absence of Threeness aspects. I think that I have never seen a chart with such a total lack of Threeness. Threeness is about ease and pleasure, so Hitler was very definitely not an easy-going, happy-go-lucky person.

When we turn to Donald Trump’s birth chart, we see that (as I described in Harmonic Astrology in Practice, page 79) Trump has two very strong clusters of Elevenness. Elevenness is about defiance and dogged persistence, so we can say that these are central features of Trump’s personality. One of these clusters involves Sun, Venus and Jupiter, and seems to be saying “I defy you to love me”. The other cluster involves Moon, Mars, Saturn and Pluto, which shows Trump defiantly responding to people who criticize or attack him.

Trump also has a very close Sevenness link between Sun and Neptune, with Sun in the 10th house. It is interesting to compare Trump’s Sun-7-Neptune with Hitler’s Sun-7-Saturn. Whereas Hitler fancies himself as an imposer of rules and discipline, Trump sees himself as a purveyor of Neptunian ideals and fantasies. Perhaps this is an indication of Trump’s scant regard for the truth. (Sun-7-Neptune could be valuable for a poet, a fiction writer, or an adventurer, but in a politician it can be dangerous.)

I can also mention the case of John Wayne Gacy (born 17 March 1942, 00.29 a.m., Chicago), who sadistically murdered 33 young men. Tim Allen9 sent Gacy’s birth chart anonymously to five prominent astrologers, and asked them to comment on whether this person would be suitable for work in the youth ministry. All of these astrologers returned very positive reports, saying (for instance) that Gacy was “kind, gentle and considerate” and had “a marked capacity to uplift others”. Allen regarded this as evidence that astrology does not work. But harmonic analysis reveals that Gacy had a strong cluster of planets (Sun, Mars, Saturn and Pluto) linked together in the 31st harmonic, which is similar to clusters found in the charts of three other sadistic serial murderers (Marc Dutroux, Robert Black and Jeffrey Dahmer) and also in the chart of the original sadist, the Marquis de Sade.

These are examples of how harmonic analysis can yield insights which would not otherwise be available. We can, of course, obtain much information from the signs and houses in which the planets are placed (and we can continue to do this even if we are also using harmonics). But harmonic analysis provides a far clearer picture of the ways in which the planets interact with one another, and so build up patterns of behaviour.

There is also the issue of aspects between Sun and Venus. Since Sun represents a person’s view of himself or herself, and Venus represents (among other things) attractiveness and lovability, we can say that Sun-Venus aspects show a person’s feelings about his own attractiveness. But, since Venus is never more than 46 degrees from the Sun, most of the traditional aspects between Sun and Venus never occur. For instance, we can never find Sun-Venus trines and sextiles, and so we can never find cases where Sun and Venus are linked by the Threeness principle of ease and pleasure. However, harmonic analysis enables us to find cases of Sun-9-Venus and Sun-27-Venus, and (since 9 and 27 are higher powers of 3) these are aspects of pure Threeness. Among the people with close Sun-9-Venus aspects are the film stars Elizabeth Taylor and Natalie Wood, the footballer David Beckham, the tennis player Chris Evert, the saintly priest Padre Pio, the pianist Liberace, and the comedian Jerry Lewis. All these are people who are (or were) comfortable and at ease with their own attractiveness. Also we can find people with other kinds of Sun-Venus links: thus, for instance, Prince Charles has Sun-10-Venus (10 = 5 x 2), showing that he is seeking to create ways of behaving which will cause people to love and accept him; and Donald Trump has (as we have said) Sun-11-Venus, showing that he is defiantly requiring people to love him. (The same is also true of aspects between Sun and Mercury, and between Mercury and Venus.)

The problem with harmonic aspects, of course, is that (unlike the traditional aspects) they are not easily visible on the chart, and therefore they have to be calculated. In Harmonic Astrology in Practice I propose several methods by which (with the aid of computer software) this calculation can be done. It has to be admitted, however, that there is a certain amount of labour involved (although it becomes quicker and easier with practice), and some astrologers may be unwilling to make this effort. I can only say that, in my opinion, the effort is well worthwhile for the benefits that it brings.

So far we have been talking only about birth charts, but in Harmonic Astrology in Practice I also discuss the use of harmonic analysis in mundane charts, in synastry, and in transits and progressions. Also I propose that we should move away from the “boxes” model of signs and houses, in which (for instance) the Sun at 0º00’ Taurus suddenly moves from pure Aries to pure Taurus, and adopt instead a system of “overlapping signs and houses”, in which (for instance) Aries is gradually transformed into Taurus. This would bring us closer to a harmonics model of waves rising and falling (whereas the “boxes” model is incompatible with harmonic theory).

Finally, I would like to raise a wider point about the whole nature of astrology. Readers of this article may well be aware that Geoffrey Cornelius10 and many other authors on the “Cosmocritic” website11 have argued that astrology is essentially a process of divination. In this view, the planets are valuable only as symbols, and one consults them in the same way that one might consult the cards of the Tarot pack or the hexagrams of the I Ching, in order to obtain an answer to a question.

However, my work with harmonics has helped to convince me that astrology (other than horary astrology) is not essentially divination. The planets are not just symbols, they are real objects occupying positions in the sky, and their positions in the sky really do have an effect on events here on Earth. In a later article I hope to set out my reasons for this belief, and also to delineate a particular theory about the nature of the relationship between heavenly and earthly events.


1 John Addey, Astrology Reborn, Sutton: Faculty of Astrological Studies, 1971.

2 John Addey, Harmonics in Astrology, Romford: L.N. Fowler, 1976.

3 David Hamblin, Harmonic Charts, Wellingborough: Aquarian Press, 1983.

4 Michael Harding and Charles Harvey, Working with Astrology, London: Arcana, 1990.

5 David Hamblin, The Spirit of Numbers, a New Exploration of Harmonic Astrology, Bournemouth: The Wessex Astrologer, 2011.

6 David Hamblin, Harmonic Astrology in Practice, Bournemouth: The Wessex Astrologer, 2019.

7 David Cochrane, The First 32 Harmonics, a Qualitative Research Study,


9 Tim Allen, “Story 2: Astrology versus death row”, in Geoffrey Dean (ed.), Tests of Astrology, Amsterdam: AinO Publications, 2016.

10 Geoffrey Cornelius, The Moment of Astrology, Origins in Divination, 2nd edition, Bournemouth: The Wessex Astrologer, 2003.


- Reprinted from Astrological Journal, Jan/Feb 2020.