Astrology is concerned with the positions of planets at the time of someone’s birth. In an ordinary natal chart, we are concerned not only with the placement of planets in signs and houses, but also with the angles that planets make between each other. These are called “aspects”.

When plotting a natal chart on a wheel, some aspects stand out immediately; conjunctions (where two planets occupy more or less the same spot) are immediately obvious, as are oppositions (where two planets are 180 apart). Most of us with a little effort can spot squares (90 separation) and trines (120 separation) as well. However, these aren’t the only aspects used in astrology, and most of the other aspects such as semi-square (45) and sesquisquare (135) are not easy to spot, and aspects such as the quintile (72) and septile (51.43) are virtually impossible to spot visually.

This problem can be overcome using the technique of harmonics, and this article looks at how this technique is used. However, using harmonics is not simply a technique to find complex aspects – it is more fundamental than that, as harmonics represent the underlying pattern in an astrological chart out of which arise all the aspects, both familiar and complex.

Resonance

Are things starting to sound rather musical? The word harmonics suggests harmony, and the ancient Greeks would have had no problem linking topics as diverse as astrology and music. Such ideas have not been very popular in contemporary scientific thinking, until a couple of years ago. The physicists’ equivalent of the Holy Grail is something called a unified field theory (Einstein spent most of his life working on this problem without ever solving it), and the latest and most promising contender is something called superstring theory. This postulates that all fundamental particles (such as protons, neutrons and electrons out of which atoms are made) are actually made of tiny vibrating, resonating loops called “strings”. The jury is still out as to whether this theory may be valid, but if it is vindicated it has a curious and beautiful conclusion: the Universe is made out of music.

Music differs from noise (except in the minds of some twentieth-century composers) in that music is structured, and when two or more notes are played simultaneously they are designed to blend to produce a pleasing tone. Any sound, whether music or noise, consists of “sound waves”. Sometimes two different sound waves will combine to produce what we hear as a pleasant combination, sometimes they will combine to produce something that sounds raucous or clashing to our ears. It has often been assumed that whether a piece of music sounds good or bad is a cultural thing, but there is some recent evidence to suggest that it’s actually something far more fundamental than this – that certain combinations of sound waves really are perceived universally as “nicer” than others.

Consider a string on a guitar. It is held under tension, and plucking the string will cause it to vibrate rapidly at a particular “resonant frequency”. The higher the frequency, the higher in pitch the note sounds. If we construct a guitar string of the right length and tension, plucking it will cause it to vibrate, say, 440 times a second. This corresponds to the A above middle C. If we halve the length of the string that can vibrate by pressing down half way along the string, it will now vibrate at 880 times a second. This corresponds to the note A, but an octave higher than the original A. If we hear these two notes played together, they sound harmonious. Certain other combinations sound harmonious, too – C and G together for instance.

The reason that some combinations sound “nice” is because they relate to particular “standing waves”. The easiest way to think of a standing wave is to imagine tying a skipping rope to a pole and holding the other end and jiggling the rope up and down. Most of the time, you would notice an irregular pattern as the rope bobs up and down. However, by jiggling the rope at exactly the right frequency, you can make the rope appear to stand still (this is the standing wave) by getting exactly one wave to appear along the rope. If you then jiggle faster, the pattern breaks down but then suddenly, at about twice the speed, you get another standing wave – this time, there appear to be exactly two waves along the length of the rope. The same things happens with three wavelengths, four and so on. These are the frequencies at which the rope “resonates”, and a similar pattern occurs in music, using air molecules in place of the rope.

Resonance in the chart

To get back to astrology – and, coincidentally, superstring theory – imagine our piece of rope with one or more standing waves, but tied in a loop. It’s circular, so it’s the same shape as an astrological chart wheel. If there is one standing wave, there will be one point of resonance on the wheel. If there are two standing waves, there will be two points of resonance, and so on. Each planet has its own “loop” of string like this; if a second planet (say Mars) occupies the resonance point of the first planet (say Jupiter), we say that the two planets are conjunct. Now imagine the case where there are two resonance points for a planet. One of these resonance points is in opposition to the first. When there are three resonance points, these points are trine to each other. When there are four, they are square to each other and so on.

So we can see that each aspect – whether it’s a simple one like a trine, or a complex one like a novile – corresponds to a resonance point. In addition, there are an infinite number of standing waves that we can superimpose on the chart – each of these waves is called a harmonic. In the same way that the final sound of Bach’s Toccata in D minor consists of several harmonious notes, our natal chart can be thought of as the basic chart with an infinite number of harmonic charts superimposed on it; a kind of “grand chord”. As the harmonic number increases, the influence of that harmonic chart reduces, so the 360^th harmonic is not as important as the third harmonic (if it were as important, then every planet would be in aspect to every other planet in some harmonic and each of these aspects would be of equal importance, which we have to assume is not the case in astrology).

Using this model, everything we’ve ever considered as an aspect simply boils down to a conjunction in a particular harmonic. A trine in your natal chart in the first harmonic, for example, shows up as a conjunction if you produce the third harmonic chart.

TECHNIQUE

To calculate a harmonic chart, we must remember that there are a whole number of “wavelengths” in the circle. In the basic natal chart (first harmonic), we are interested in how far around the circle a particular planet is. For subsequent harmonics, we are only interested in how far along a particular wave the planet is.

Let’s say we’re interested in calculating the fifth harmonic. This means there are five identical “waves” around the circle, each occupying 72. So we divide the chart wheel into five segments of 72 starting, by convention, at the zero point of Aries. We then see how far into its particular segment each planet is – so each planet will have a position between 0 and 72. In this scheme, if Mars is at 5 Aries (5) and Jupiter is at 17 Gemini (77), they will both have a position of 5 within the segment. In other words, in the fifth harmonic chart, they will be conjunct. In the basic natal chart, of course, they are actually 72 apart and so are seen to be quintile to each other (although it’s unlikely you would spot this visually).

Trying to cram all the planets into a 72 segment of a circle would make the chart look very crowded, so we actually stretch the segment to occupy 360. We do this by multiplying each final position by 5 before plotting it on the chart. We then end up with a traditional looking chart, but where quintiles and semi-quintiles appear as conjunctions and oppositions.

WORKED EXAMPLE

Alan Turing was born in Paddington on 23 June 1912. His birth time is unknown, but some authorities have come up with a rectified chart using a birth time of 02:15. We’ll just look at three planets for this example: Saturn, Neptune and Chiron.

1. Convert each position to absolute longitude:

2. Now work out where these appear within each 72 degree segment:

3. Finally, multiply these figures by 5 so they map nicely into a 360 circle:

These points can then be plotted onto a chart. It is not a good idea to convert these figures into signs (for instance, to say Saturn is 22 Capricorn 10, as this simply is not relevant; Saturn is not in Capricorn in any real sense in this chart).

WHAT DOES IT MEAN?

Each harmonic chart can be thought of as adding a subtle flavour to the main chart. Research is still taking place into what each harmonic might mean, in particular whether given harmonics relate to certain times of life, such as the 41st harmonic relating to the 41st year of life. However, there are certain generally accepted meanings for many of the harmonics:

Case Study: Alan Turing