Harmonic Chart Calculator

A harmonic chart is made by multiplying the longitude of every point in the birth chart by a chosen number (N) and placing the result back on the 360-degree circle. In the fifth harmonic every longitude is multiplied by five: a Sun at 14° Aries becomes 70°, so it falls at 10° Gemini. As a result, two planets that stand 72° or 144° apart in the natal chart come to the same degree in the fifth harmonic chart. The general rule is this: two points that are conjunct in the Nth harmonic chart form, in the natal chart, one of the aspects that divide the circle by N. In the fourth harmonic the square and opposition appear as conjunctions, in the seventh harmonic the septile family, and in the ninth harmonic the novile family.

This method belongs to modern astrology and is not a classical technique. The English astrologer John Addey studied the distribution of planetary positions in collections of birth data as wave forms and gathered his findings in Harmonics in Astrology, published in 1976. Addey also pointed out that the navamsa division of Indian astrology does the same work as the ninth harmonic. David Hamblin set out the way harmonic charts are read today in Harmonic Charts, published in 1983. Classical astrology works with the conjunction and with the opposition, trine, square and sextile defined by Ptolemy. Aspects such as 72° were proposed by Kepler in the 17th century. Instead of searching for these small aspects one by one, the harmonic chart gathers the whole family of a number on a single wheel. A short definition of the term is in the Harmonic Charts glossary entry.

In the literature of harmonic astrology each number is tied to a theme. In Hamblin's book the fifth harmonic is linked with giving form, building order and creative power. The seventh harmonic is read with inspiration and imagination, the ninth with harmony and inner contentment. The fourth harmonic carries the theme of effort and strain. These meanings rest on the authors' observation, they are not statistically proven results, and writers on harmonic astrology differ in the details. The tool gives no meanings for 11 and higher numbers and offers these harmonics for you to study through your own observation.

The calculation works like this. Planetary positions are calculated geocentrically and tropically with the astronomy-engine ephemeris, and the true node is used for the lunar node. The Ascendant and MC are found with apparent sidereal time and the true obliquity of the ecliptic. Each longitude is multiplied by N and reduced modulo 360. Multiplying the house cusps by N would break their order, so the wheel is drawn with equal houses starting from the harmonic Ascendant, and the harmonic MC is shown with a separate mark inside the wheel. The conjunction orb is measured in the harmonic chart. Its equivalent in the natal chart is the orb divided by N: in the fifth harmonic a 3° orb means a 36-minute orb in the natal chart.

The last column of the conjunction table states which aspect each conjunction corresponds to in the natal chart. One aspect can appear in more than one harmonic. A natal opposition becomes a conjunction in every even harmonic. The table therefore also names the aspect's own number, that is, the first harmonic in which it becomes a conjunction. If a conjunction in the tenth harmonic is 180°, you will see it as the "2nd harmonic family", and if it is 36°, as the "10th harmonic family".

As the harmonic number grows, small errors grow too. A four-minute error in the birth time shifts the Ascendant by about one degree. In the 32nd harmonic that shift becomes 32 degrees. The Moon is exposed to the same effect, because it moves about half a degree per hour. So in the higher harmonics, use the Ascendant, MC and Moon only if your birth time is exact. If your time is uncertain, you can settle it with an event-based rectification consultation. The harmonic scan row counts how many conjunctions form in this chart in each harmonic from 1 to 32. Addey's harmonic analysis rested on the statistics of a large number of charts. A count in a single chart does not replace that, it only helps you choose which harmonic to look at.