ハ ー モ ニ ク ス 占 星 術









1 ヨーロッパとインドの伝統的な占星術の概念を融合するベースとなるものです。

2 占星術の分野に統計調査の方法論を導入したこと。

3 占星術の原理について従来不明確とされていた論理的方向性と明確性を与えています。


ハーモニクスは、通常のホロスコープ(第1 ハーモニクス)を特定の数字で分割することで作成されます。









第7ハーモニクス 人生での満足度(特に性的)を表示する。

第9ハーモニクス 人生で達成できる終局を表示する。

The harmonics are subdivisions of the signs. The second harmonic is a division by two, the third harmonic a division by three and so on. The third and thirteenth harmonics were in use in ancient Greece, but the other harmonics have only been recently introduced into the West from India.

In this example the Sun, Moon and Mercury change signs as their positions are converted into the different harmonics. In the fifth harmonic(creativity), the Moon and Mercury make a conjunction, forming a relationship that is not apparent in the birth chart. This suggests skill and sensitivity in communication and creative matters. In plain English this indicates poetic ability. (THE PRACTICAL ASTROLOGER by Ncholas Campion)

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)

The Fifth Harmonic (Figure1)

The Nineth Harmonic (Figure2)

If one asks a Hindu astrologer to interpret one's horoscope he will almost always begin by calculating at least two charts and probably more.
First he will have the radical, Rasi, or sign chart giving the natal positions as ordinarily understood, but in addition he will also calculate the Navamsa or 'ninth division' chart (pronounced Na-vam-sha).

This Navamsa chart is one of
16 sub-charts which he can call upon known as the Shodasavargas or sixteen-divisons (strictly speaking there are 15 sub-charts for the natal chart is counted as the first of the 16) and each of' these has a special application to the life of the native.

The way in which the Navamsa or ninth division chart is calculated is very simple. Each sign of the Zodiac is divided into nine equal sectors of
3°20′each. The first sector, extending from 0° to 3°20′Aries, is then allocated to Aries; the second, from 3°20′~ to 6°40′ Aries, is allocated to Taurus; the third, 6°40′to 10°, is given to Gemini and so on round the circle.

It will be seen that by the time one has reached the end of the sign Aries one has got
nine small (Navamsa) divisions allocated from Aries to Sagittarius inclusive. The first 3°20′of Taurus then goes to Capricorn, the second to Aquarius and the third (taking us to 10° Taurus) goes to Pisces. Thus the first 40° of the Zodiac have been made into a new little Zodiac of twelve miniature signs.

One then starts again with Aries at 10° Taurus and continues round the circle, each 40° yielding another set of twelve signs, so that, since 40°is one-ninth part of 360°, one ends by having nine little Zodiacs extending in due order through the original twelve signs. (See Fig. 2.)
Notice that by dividing each sign into nine equal divisions and then making these into groups of twelve signs one is in fact dividing the whole circle into nine Zodiacs.

So we are back with our idea of circles within circles. Fuller details of methods of calculating the various harmonic charts are given in the next chapter, but we can use Figure 2 to show quite simply how the positions in the radical chart are recalculated so as to give their positions in the Navamsa chart.


Let us suppose that the natal Sun is in 11°06′of Aries.
We can see from
Figure 2 that this will fall in a Cancer division of the Navamsa circle for this extends from 10°to 13°20' Aries.

How far into that little Cancer sign has the Sun moved?
The division starts at 10° Aries and the natal Sun is at 11°06' Aries. so it has travelled 1°06' into the mini-sign. But the new Zodiac has been created by collapsing the original Zodiac into nine smaller Zodiacs, so in order to find the new position of the Sun we must multiply1°06' by nine; thus 9x1°06' gives us 9°54°Cancer as the position of the Sun in the Navamsa chart.

Again, suppose the radical Moon was in 7°50′Taurus. Reference to Figure 53 shows that this falls in a Pisces sub-division in the Navamsa circle. How far has it moved into Pisces? The sub-division starts at 6° 40' Taurus so, at 7° 50' the Moon has moved 1°10′into that sub-division. Thus 9x1°10′= 10°30' Pisces, which will be the Moons Navamsa position; therefore, the Sun at 9°54′ Cancer will be in trine to the Moon in10°30' Pisces.

If the radical Jupiter was at 17°48' of Gemini it would have moved 1°08′into a Pisces sub-division; 9x1°08′= 10°12′of Pisces. Thus in the Navamsa chart we have Moon conjunct Jupiter - which is another way of saying that they are just about 40°apart (7°50' Taurus and17°48' Gemini) in the radix.

We can now see that this old tradition in Hindu astrology of creating sub-cycle charts is really a practical application of the idea of harmonics. Each division of the circle into a subordinate number of cycles or cercle has its own significance, derived from the symbolism of the number by which the  division is made. By dividing up the original circle of the Zodiac into a number of lesser circles one is, in effect, considering the distribution of the natal positions within the sub-circle of a particular harmonic.

It is true perhaps that the Indian astrologer may think of this technique as one in which each sign is divided by a particular number - in this case nine - but in point of fact, what he has done first and foremost is to (divide the whole circle by nine, and then divide each of those nine divisions into a little Zodiac of twelve signs.

It may be that this secondary division into twelve signs has a symbolic validity, for the number twelve relates to the 'mundane' order of things and so the subordinate division by twelve has the effect, so to speak, of ‘earthing' his original division of the circle by nine, for the purposes of interpretation.

However, from another point of view it is arguable that the chief purpose of the secondary division into mini-signs is primarily a system of nomenclature whereby to identify points in the sub-cycles which would not otherwise have a name.

Thus in
Figure 3 we have divided our circle into nine parts and the encircling wave-form shows the resultant cycles of the 9th harmomc.

Let us suppose that in a particular horoscope there are planets at X, Y and Z. They look as though they fall at about the same point in the 9th harmonic wave (so that they would be conjunct in the Navamsa chart) but how can we make an accurate comparison of their positions? Only by having some system of measuring exactly where, in each sector, they fall. The traditional Indian practice is thus to divide each of the nine sectors into twelve signs so that we can recalculate the positions of X, Y and Z in a familiar system of coordinates-namely, the Zodiac-and so identify their positions exactly.

We have said that each of these 'harmonic charts', as we might call them, has its own symbolism as applied to the life of the native, based upon the number by which the whole circle is divided-that is the number of sub-cycles within the complete circle.

Indian astrology has its own traditions regarding the appropriate significance and symbolic application for each of its Shodasavarga charts. For example it is said that one of the primary meanings of the Navarosa chart is that it describes the marriage partner.

This is an interesting allocation and deserves some comment.

Most of the basic Shodasavarga divisions are related to departments of life with which one might expect them to be connected on the basis of Zodiacal symbolism. Thus the Hora or 2nd harmonic chart is said to signify wealth and possessions, the 3td (or Dreshkhana) brothers and sisters, the 4th (or Chaturthamsa) home and property, the 6th health and so on. But it is the 7th (or Saptamsa) chart which is said to indicate children and the 9th or Navamsa which is said to show the marriage partner. let us, then, consider the symbolism of the number nine.

The reason why Pythagoras and other philosophers of antiquity attached so much importance to the first nine fnumbers derives from the teaching that everything unfblds from its innermost idea, which is pure potentiality, to its outermost expression, which is its manifest, actualised perfection, through nine stages.

This complete actualised perfection in which all the parts are finally brought into harmony is called the entelechy of a thing. Of 'entelechy' my dictionary says: 'In Aristotelian and Scholastic philosophy a term used to signify the perfect form attained by anything by reason of which it actually exists and realises its true function; the actual as opposed to its potential cause'