Details of Tibetan Astrology 4: Magic-Squares and Trigrams

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Magic-squares (sme-ba) are also employed, specifically the one in which there is a grid of three by three, with the numbers one through nine arranged, one in each box, such that whether one adds horizontally, vertically or diagonally, the sum of any line is 15. The nine numbers are combined with the 60-year cycle so that every 180 years the same magic-square number will correlate with the same element-animal year. The sequence begins with the number one, and then proceeds in reverse order: nine, eight, seven and so on. Unlike the 60-year cycle of element-animal combinations which begins in the Tibetan system with the year of the fire-hare, the first 60-year cycle of a 180-year magic-square number cycle begins with a wood-rat year, as in the Chinese system.

Each of the nine magic-square numbers is correlated with a color and each of those to one of the five Chinese elements. The numbers are usually referred to in conjunction with their color. 

  • 1-white – iron
  • 2-black – water
  • 3-navy-blue – water
  • 4-green – wood
  • 5-yellow – earth
  • 6-white – iron
  • 7-red – fire
  • 8-white – iron
  • 9-maroon or sometimes 9-red – fire. 

Thus, black is equivalent to blue and maroon to red. When the magic-square is printed, the color of each box is in accordance with this scheme.

The classical Chinese system of the nine magic-square numbers also associates them with the same set of colors, except that jade-green is used instead of navy-blue, and purple for maroon. In some Chinese astrological documents of the 10th century found in Dunhuang, the magic-square numbers are referred to only by their colors, with no mention of the numbers themselves. 

In one Japanese-derived account of the Chinese system used in connection with macrobiotics, each number is correlated with and referred to in conjunction with the element of its corresponding trigram, which is not the same element as is associated with the number itself as appears in the Tibetan system. In this version, the magic-square numbers are given as 

  • 1-water
  • 2-earth
  • 3-wood
  • 4-wood
  • 5-earth
  • 6-metal
  • 7-metal
  • 8-earth 
  • 9-fire. 

The eight trigrams will be discussed in a moment, but this difference in element-assignment very much affects all the interpretations. It is unclear whether this Japanese-derived version reflects a standard classical Chinese assignment of elements to and interpretation of the magic-square numbers, or whether it is yet a further variant. More research needs to be done. 

In the Tibetan system, each year and each date has a magic-square number. The sequence for the numbers for the dates is ascending order: one, two, three and so on, 30 per month and starting each year with the Tibetan 11th month, which is approximately the time of the winter solstice. In the Bon variation of Tibetan astrology, the magic-square numbers for the dates are like this for males, but in reverse sequence for females. 

In the classical Chinese system, magic-square numbers are associated not only with the year and date, but also the month. For the date, for both genders, the numbers are in ascending order from approximately the winter solstice until the summer one and descending from approximately the summer solstice until the winter one. The turning points are the date having number 9 directly before the summer solstice and the one having one directly before the winter solstice. Each is followed by a date with the same number and then the sequence reverses. Thus, the Chinese and Tibetan systems for assigning magic-square numbers to the dates are quite different.

Progressed Magic-Square Numbers

In the Tibetan system, the natal magic-square number is calculated by going backwards from that of the present transiting year. From the natal number, a progressed magic-square number is derived for each year of age. As with the progressed element-animal combination, the calculation is different for males and females. One uses the arrangement of numbers in the magic-square and counts the center box as the first year of age. The box to its immediate left is age two. 

  • Then for males, one counts the ring of boxes from there, going clockwise, as ages three, four, five, etc., until one reaches the box in the lower left corner as age nine. The center box is again age ten and the sequence is repeated until one reaches the box at which the progressed age in question falls. One notes the box position. 
  • For females, age one is the central box and two the box to its immediate left, as with males, but then one counts counterclockwise from there. The upper left box, then, is age nine for females. One also notes the box position in which the age in question falls. 

Next, one constructs a magic-square with the natal square number in the center box and the subsequent sequence of numbers in the magic-square order. This means that the number immediately after the natal one is in the bottom right corner, the next in the box immediately above that one, the next in the bottom left box and so on. Whatever number falls on the previously noted box is the progressed number for that year of age.

Each natal square number has an interpretation, which includes a description of past lives, with their residue propensities in this life, as well as the probable next future life together with religious ceremonies and statues to commission in order to improve it, and what type of rebirth might then be possible. This is the source, then, for information on past and future lives given in Tibetan horoscopes. Chinese horoscopes do not generally include such information. Furthermore, these numbers are sometimes also correlated to positions of moles, birthmarks and “beauty-spots,” for the Tibetan word for magic-square number (sme-ba) is the same as that for these kinds of spots on the body. Certain combinations of natal, progressed and transiting magic-square numbers are also interpreted. Body, life-force, power and horse-of-fortune magic-square numbers can also be calculated and examined, as is done with the elements.

Comparison with the Chinese System of Magic-Squares

By way of contrast, in the classical Chinese system of magic-square numbers, the natal numbers of the year as well as the month of birth are analyzed for information about the basic personality. In the Japanese-derived version of the Chinese system mentioned just a moment ago, the progressed number for each year of age is calculated in a very different manner from that done by the Tibetans. No differentiation is made between males and females. One constructs a magic-square with the transiting magic-square number in the center box and the subsequent numbers in the magic-square sequence. One then locates one’s natal number in that magic-square and notes its box position. Each box position is called a “house,” and is assigned the number of the magic-square number that would occupy it in the standard magic-square with five in the center. This house number is taken as the progressed magic-square number. Each natal number has a particular interpretation in each of the houses, and during that progressed year of age, one will feel a particular attraction to those whose natal number falls in the box on the opposite side of the square from one’s own. 

Since the transiting number for one’s year of birth is the same as one’s natal number, everyone has the 5th house for age one. Thus, it works out that for everyone the sequence is in ascending order, with age two as the 6th house, age three the seventh and so on. Therefore, everyone has the same progressed number when they are the same age. In the Tibetan system, the progressed number for any particular age is different not only for men and women, but for each group of persons with the same natal number.

In the classical Chinese system, the magic-square forms the basis of what is called nine-star astrology. The nine numbers are associated with the Pole Star (Polaris), Vega and the seven stars of the Big Dipper. The square itself is said to have developed from the “Luo River Writings” (Luoshu 洛書, 洛书) arrangement of the eight trigrams, which shall be discussed in a moment. The boxes in the diagram are associated with the directions, with one at the bottom being north and nine at the top south. This forms the basis for the calculations of Chinese geomancy for balanced directional orientation of houses, businesses, gardens, graves and so on. 

Since this arrangement of nine boxes, according to Chinese accounts, arose from the designs on the underside of a tortoise shell, the motif of the magic-square and other Chinese-derived astro symbols appearing on a tortoise-shell belly with the head, hands, feet and tail sticking out, is extremely common in the Tibetan system. Certain calculations, in fact, are performed by assigning different elements to the appendages of such a tortoise.

Magic-squares are also found in Arabian astrology. There, each of the five planets and the sun and moon is associated with a different size magic-square. The square with three numbers on each side that adds to 15 is connected with Saturn, the one with four on a side that adds to 34 with Jupiter and so on, up to the square with nine numbers on each side that is associated with the moon. In Tibetan astrology, as well as Chinese, only the magic-square with three numbers on a side is used. 


The eight trigrams of the I Ching are also employed in Tibetan element or black calculations, though never the 60-four hexagrams and never the classical Chinese system of I Ching astrology based on the heavenly stems and earthly branches. The eight trigrams are arranged in the classical Chinese configuration of nine boxes, called the “Luo River Writings,” with each box correlated to its corresponding magic-square number. Each trigram is referred to by the Tibetan transliteration of its Chinese name together with the physical sign it represents. The signs are similar to the classical Chinese presentation, but with some differences. Each trigram is associated with one of the five Chinese elements. This element correspondence, however, as already noted, is not the same as that of the Tibetan magic-square number to which each trigram is linked.

The correlations are as follows:

  • Connected with magic-square number 1 is the trigram ☵ kam-water, associated with the element water, and corresponding to the Chinese trigram “kan” (坎) the abysmal, correlated with the element water.
  • 2 is ☷ kon-earth, which is earth and the Chinese  “kun” (坤) the receptive, correlated with earth 
  • 3 is ☳ zin-wood, which is wood and “zhen” (震)the arousing, correlated with thunder. 
  • 4 is ☴ zon-wind, which is wood and the Chinese “xun” (巽) the gentle, the penetrating, correlated with wind or wood. 
  • 5 in the center is not fixed to any trigram in the classical Chinese presentation. Tibetan astrology repeats ☷ kon-earth in this place for males and ☶ gin-mountain for females in marriage calculations, which shall be described in a moment. This trigram value for five in the center, differing for males and females, is the same as that found in the classical Chinese system of I Ching astrology. 
  • 6 is ☰ ken-sky, which is iron and  “qian” (乾) the creative, correlated with heaven, the sky.
  • 7 is ☱ dva-iron, which is also iron and “dui” (兌) the joyful, correlated with lake. 
  • 8 is ☶ gin-mountain, which is earth and “gen” (艮) keeping still, correlated with mountain. 
  • 9 is ☲ li-fire, which is fire and the Chinese “li” (離, 离) the clinging, correlated with fire.

This arrangement of the trigrams is what the Chinese call the “later-heaven” (houtian 後天, 后天) sequence of the trigrams, in which the center box is left empty and not counted. From this is derived the progressed trigram for each year of age in the Tibetan system. Every male has li-fire as the progressed trigram for his first year of age. One then counts clockwise from this according to the later-heaven sequence to derive the progressed trigram for each subsequent year of age. For females, age one is kam-water and from there the count is made counterclockwise. Thus, everyone of the same gender has the same progressed trigram for the same age.

Except for in the Bon variation of Tibetan astrology, there are no transiting annual trigrams which would entail each calendar-year in general being assigned one in a particular sequence. The natal trigram, then, for both males and females is not calculated from their year of birth, but rather is taken as their mother’s progressed trigram for her age at the year she gave birth to them. The interpretation of the natal and progressed trigrams gives further information for the predictive horoscope. 

There is a trigram associated with each lunar date, but none with the month. As with the assignment of magic-square numbers with the dates, the sequence begins at the start of the Tibetan eleventh month near the winter solstice. 

In addition, body, life-force, power and valley-of-fortune trigrams can be calculated as well, and these are derived from the four types of magic-square numbers calculated from the natal number. These four trigrams, as well as the body, life-force, power and valley-of-fortune natal pebble-elements of a perspective couple are what are compared in the marriage calculations to determine compatibility.

Comparison with Chinese I Ching Astrology

As was mentioned, Tibetan astrology does not make use of the 60-four hexagrams that are constructed from these eight trigrams. But it is interesting to note the basic principles used in classical Chinese I Ching astrology for deriving the hexagrams from the trigrams, since it entails another application of these magic-square number correlations of the trigrams. It involves the use of the 10 heavenly stems and 12 earthly branches, which are assigned numbers according to a very complex scheme. First of all, each stem and branch is assigned an element in a manner that will be explained a little later. For the 10 heavenly stems, trigrams are correlated with the elements from what is known as the “earlier-heaven” (xiantian 先天) sequence and then numbers assigned in accordance with the magic-square number values of the trigrams just outlined. For the twelve earthly branches, the elements are assigned numbers, one odd and one even, from another scheme known as the “Yellow River Map” (Hetu 河圖, 河图). It is not necessary to give the details.

The odd and even numbers of the stems and branches of a birth year, month, date and hour are added separately. The sum of the odd numbers is converted into what is called a “heavenly” trigram, and the even to an “earthly” one, again in accordance with the magic-square number equivalencies of the trigrams, with slightly complicated rules for the sums divisible by five or ten. For men born in even-numbered years, the heavenly trigram is on top and the earthly on bottom to form the early-life natal hexagram, and in odd-numbered years the reverse. For women born in even-numbered years, the earthly is on top and the heavenly on bottom, and in odd-numbered years the reverse. Through a very complicated scheme of changing lines, hexagrams and ruling lines are derived that govern the years, seasons and individual dates of one’s life, divided into early and later life periods.