Harmonic Chart: A chart derived by multiplying all radical chart positions, expressed in absolute celestial longitude, by the harmonic number under consideration.

The resulting longitudes are the positions in the harmonic chart.

If a resulting longitude is more than 360°, then 360° is subtracted from it enough times to reduce it to less than 360°.

For example, if in a chart the radical Sun is at 10°10′Aries and the radical Moon at 20°10′ Taurus, then their ninth-harmonic chart positions (which are identical to the Hindu na-vamsa chart positions) are calculated as follows:

Sun's absolute longitude = 10°10′x 9＝91°30′＝ 1°30′ Cancer

Moon's absolute longitude＝50°10′x 9＝451°30′- 360°＝91°30′＝1°30′Cancer

After converting all radical positions in this way, the astrologer takes a chart form and either places the new Ascendant position in the normal place on the left and fills in the rest of the chart in equal houses, or places the new Midheaven in its normal po-sition and fills in the rest of the chart in equal houses.

In judging a harmonic chart one must bear in mind the meaning of the harmonic number in question. Particular attention is paid to con-junctions. These reveal either that the factors were already in conjunction in the radical or that they were close to one harmonic wavelength apart or an exact number of wavelength a part.

Aspects within a harmonic chart can be interpreted, but strictly these imply a conjunction on a higher harmonic.

Thus, oppositions in a harmonic chart will become conjunctions if the harmonic number is doubled. In judging a harmonic chart it is also of great importance to see if any of the harmonic chart positions are in conjunction with radical positions.

If they are, this gives great emphasis to the factors involved.

It will be seen that cosmobiologists who use the 90°dial are actually examining the fourth harmonic of the chart, while those who use a 30° dial are working with the twelfth harmonic.

Harmonics: Integral divisions of the circle; the study of such divisions, especially as they relate to astrology; the extension of the traditional concept of aspect to the division of the circle by any whole number.

Thus, in traditional aspect terms, the second harmonic is 360°/2 = 180°, the opposition; the third harmonic is 360°/3 = 120°, the trine; the fourth harmonic is 360° /4 = 90°, the square; and the sixth harmonic is 360°/6 = 60°, the sextile; but the study of harmonics extends this sequence to much smaller divisions of the circle. Table 2 gives the first thirty harmonics:

The technique of harmonics has been in use for centuries in Indian astrology as a predictive device. In the West, the theory of harmonics was anticipated by Pytagoras' ideas about the meaning of numbers and by Kepler's theory of aspects and his introduction of the quintile series, which corresponds to the fifth harmonic.

The concept as it is understood today was probably introduced in the 1930s by the Swiss astrologer Karl Krafft, who used the term harmonics to describe the wave patterns he observed in his statistical studies on longevity, illness, talent, and other effects.

Interestingly enough, the term has been used independently by a number of researchers.

Engineer John Nelson calls the clusters of planetary aspects he has observed in connection with radio interference "simultaneous multiple harmonics"; and Theodor Landscheidt uses the term harmonics to refer to the microaspects between the outer planets, which he has found to coincide with times of increased solar activity.

But the term has come into its own, and the concept has been fully developed, through the work of the English astrologer John Addey.

Addey has extended the idea of harmonics beyond the theory of aspects and expanded it into the beginnings of a fundamental theory of the underlying principles of astrology.

Addey's theory of the harmonic basis of astrology, which rests on the analysis of a vast range of statistical studies, suggests that all astrological effects-apart from the planets themselves-can best be understood in terms of the "harmonics of cosmic periods." By a "cosmic period" Addey means any one of the many cycles studied by astrologers, such as the zodiac, the houses, the aspect cycles, and so on.

According to his theory, an understanding of the meaning of each number, in the Pythagorean sense, and an understanding of the meaning of each particular cycle will ultimately enable astrologers to reconstruct astrology from its first principles. Addey's harmonics have had a profound impact on serious modern astrologers, especially in England. Charles Harvey, president of the Astrological Association, writes that the great achievement of the theory is that it

"(1) provides a unified basis for understanding almost all existing astrological concepts in both Western and Eastern traditions;

(2) provides a methodology for statistical research in all areas of astrology; and

(3) allows the logical extension and articulation of existing astrological principles in a way that has not been possible before~" Geoffrey Dean believes that the study of harmonics, along with a systematic investigation of the symbology of numbers, may at last yield a convincing scientific theory of astrology.

(Larousse Encyclopedia of Astrology)