The Numerology of Nine Star Fengshui 
Illuminating the Eight Halls 

The technique of residential fengshui known as Bazhai mingjing (Illuminating the eight halls), one of the most popular systems in use since the Qing dynasty, has been called the most obscure and difficult to understand of the different versions of the compass school. This is because there has never been a satisfactory explanation of the cosmological principles employed by this school, including, but not limited to, a justification for its apparently arbitrary assignment of good and bad fortune to the compass directions. This essay will first outline the rudiments of the technique as currently practiced, then suggest a possible derivation of its most baffling methodologies. 
Houtian Trigrams and Directional Correlates 
A unique characteristic of this technique of fengshui is its apparent sole reliance on the bagua, or eight trigrams of the Yijing, and particularly on the sequence of those eight trigrams known as the houtian (postheaven) configuration. In the Shuogua zhuan "Trigram Explanation" commentary of the Yijing, each trigram of the houtian sequence is also correlated with one of the eight directions, as in fig. 1 (click on the link to the left to see the illustration). The 3x3 grid illustrated in this diagram is called the jiugong, or Palace of Nine Halls. A trigram and one of the eight directions represent each of eight of the nine halls (in traditional Chinese cartography, south is placed at the top of the map rather than north). The direction identifies its location in space and the trigram characterizes the qi of that location. The ninth hall is the courtyard of the palace. 
Other correlations were undoubtedly being made at this time. For example, the trigrams of the houtian sequence were also given seasonal associations as well as agricultural connotations (see below). Later on (conceivably as early as the Han dynasty) the houtian configuration of trigrams was correlated with a sequence of numbers known as the luoshu, or "Luo River writing." The luoshu is first mentioned in the Confucian Analects, and the Daoist philosopher Zhuangzi first mentioned the "nine numbers" of the luo. The Xici zhuan or "Great Commentary" of the Yijing, first connected the luoshu with another configuration of numbers known as the hetu, or "River chart," which will be discussed in some detail later in this analysis. At the very latest by the beginning of the Han dynasty the luoshu was understood as the magic square of three, an arrangement of the digits 1 through 9 in a threebythree grid such that rows, columns, and diagonals all add up to 15 (see fig. 2). 
Houtian Trigrams and Luoshu Numbers 
On various divination boards buried in Han era tombs the numbers and the trigrams can be indirectly related. As for the numbers, in an early Han dynasty tomb in Anhui province a zhanpan divination board (dated to 173 BCE) was discovered on the face of which were inscribed nine numbers in the luoshu configuration. The disc of the zhanpan was divided into eight equal segments by four intersecting diameters, the endpoints of which were numbered in the order 4, 9, 2, 7, 6, 1, 8, 3, reading clockwise. As for the trigrams, a shipan "cosmograph" was discovered in another Han dynasty tomb in Korea, the tomb of Wang Xu (d. 69 CE). The square plate of this divining board was also dissected by four intersecting diameters, each of which was labeled with one of the eight trigrams of the houtian sequence. Figure 2 correlates houtian trigrams and luoshu numbers (click on the link to the left to view the illustration). 
The Nine Stars and the Great Roving Year 


The correlation of the luoshu numbers and bagua trigrams is the minimum requirement for conducting bazhai fengshui readings. A formula called the da you nian, "Great Roving Year" is the means by which number and trigram merge. First, the sequence of digits 1 through 9 is repeated 20 times to match three sixtyterm, ganzhi cycles of 180 years called the sanyuan, "Triepoch." Since every year has a ganzhi designation, in the Triepoch everyone's year of birth has a digital correlate from 1 to 9. Each luo number has a unique trigram, derived from its houtian correlation (see fig. 2), so when the Triepoch digit is equated with the luo number, each person has a trigram that corresponds to his/her natal year. This is called the minggua, or the natal trigram, and it identifies the character of cosmic qi present at the person's birth. Finally, the natal trigram is paired with each of the eight directional trigrams in the houtian sequence (called zhaigua or hall trigrams). Each of the eight minggua therefore has a corresponding eight zhaigua, and these eight groups of eight trigrams complete the da you nian. This complement of a natal trigram and its set of hall trigrams represents a metaphysical interaction between the individual's natal qi and the qi of the environment that surrounds that individual. This conjunction is essentially thought of as a transformation of the minggua into the zhaigua and viceversa (called biangua or bianyao), and each transformation is capable of generating good or bad fortune for the individual. The auspice generated by the conjunction is known as jiuxing, or the Nine Stars. 
The provenance of the concept of Nine Stars is unknown, but the scant textual evidence suggests at the very least that it was religious in origin. The unusual nouns (see table 1 below) supposedly name the seven stars of Beidou, the Northern Ladle (Big Dipper), plus two secret "companions" to the penultimate star of the handle. There is a considerable body of legend attached to the stars of Beidou, which were recognized as deities by Daoist priests of the 4^{th} century. By the late Tang dynasty, when fengshui texts such as Hanlong jing were written, the Nine Stars referred to archetypal terrestrial counterparts of the celestial namesakes, mountain shapes that seemingly have nothing to do with the original names. Finally, by the time bazhai fengshui flourished in the Qing dynasty, the Nine Stars were apparently arbitrary names for the eight levels of auspice associated with trigram transformation. 
Let us now return to the Great Roving Year. When the natal trigram is known, it is compared with each of the eight directional trigrams. The divergence of lines across the space of each pair of trigrams determines the star that will govern a particular direction for that particular person. Each star in turn is characterized by a specific auspice. For example, if the natal trigram and the hall trigram differ by only the top line, the Ravenous Wolf star governs the transformation, and the auspice is "great fortune." Table 1 enumerates the four lucky stars and the four unlucky stars, their unique auspices, and the diverging lines that mark the transformation from one trigram to the next (click on the link to the left to view the table). 
To provide an example of da you nian transformation table 2 uses the trigram qian as the natal trigram, and then lists the eight trigrams, their directions, and the accompanying auspices from table 1 (click on the link to the left to view table 2). From these two tables it can be seen that of the eight directional auspices for each minggua of the Nine Star system, four are auspicious and four are inauspicious. 
Eastern and Western Halls 
If the remaining natal trigrams are expanded according to the da you nian transformations as in table 2 above, an interesting phenomenon emerges. Half of the natal trigrams are fortunate matches with the same four hall trigramsspecifically, the directions west, southwest, northeast, and northwest, as in table 2. And the other half of the natal trigrams are fortunate matches with the remaining four hall trigramsspecifically the directions south, east, north, and southeast. These two groups of trigrams are called the dong si zhai, the "four eastern halls," and the xi si zhai, the "four western halls," and form the configuration around the houtian sequence of trigrams as illustrated in figure 3 (click on the link to the left to see the illustration). The logic of this array, which is not externally evident, has never been satisfactorily explained. Later in this analysis it will be shown how this physical arrangement of the palace is the one scientifically valid basis of bazhai fengshui. 
The foregoing discussion has provided the reader with a brief outline of the methodology of the bazhai or jiugong method of residential fengshui. If the birthdate is known, the four lucky halls and the four unlucky halls can be easily derived, and the individual will then know which is the most appropriate direction in which to face the house or orient its rooms. However, the question still remains, what exactly is it that makes a Ravenous Wolf auspicious and Virtue baleful? The auspice of these stars seems to contradict their nature. Logically, should not a "virtuous" star bring good fortune and a "ravenous" star bad fortune? What accounts for the apparently arbitrary assignment of good and bad fortune to the da you nian directions? 
The Fortune of Five and the Hetu Key 

Five Phase Values of Houtian Trigrams 
Obviously these questions have been asked before, because of the popular texts that discuss the bazhai methodology, most rely on wuxing "five phase" correlations to explain the derivation of auspice. The five phase and eight trigram cosmological systems were also correlated early on, even though five and eightterm series are not easily overlaid. Figure 4 gives the houtian sequence of trigrams, the orthodox translation of trigram names, their directions, and their five phase correlations (click on the link to the left to view the illustration). 
The supposition of orthodox fengshui is that when the five phase value of the natal trigram is matched with the five phase value of the directional trigram, good fortune is indicated when the two exhibit a relationship of xiangsheng, or "mutual production," while bad fortune is indicated when the two exhibit a relationship of xiangke, or "mutual conquest." Developed by the late Warring States yinyang theorist Zou Yan, these two sequences are illustrated in table 3 (click on the link to the left to view table 3). 
For example, let us imagine that a person with the natal trigram xun wanted to build a house facing the direction north. From fig. 4 we see that xun has the phase "wood," whereas the direction north is occupied by the trigram kan, which has the phase "water." In the mutual production order of the five phases, water nourishes wood, so this conjunction of xun and kan would indicate good fortune. From fig. 1 we see that the xun and kan trigrams differ by the top line, and table 1 confirms that the Ravenous Wolf, which brings great fortune, governs this transformation. On the other hand, suppose the same person wanted to build a house facing the direction southwest. The direction southwest is occupied by the trigram kun, which has the phase "earth." In the mutual conquest order of the five phases, wood saps earth, so the conjunction of xun and kun would indicate bad fortune. From fig. 1 we see that the xun and kun trigrams differ by the middle and top lines, and table 1 confirms that this transformation is governed by the star Virtue, which brings great misfortune. In similar fashion five phase theory can predict the auspice of the remaining six directions of the natal trigram xun. 
However, let us take as another example a person born under the trigram li who plans to build a house facing in the direction northeast. From fig. 4 we see that li has the phase "fire," whereas the direction northeast is occupied by the trigram gen, which has the phase "earth." In the mutual production order of the five phases, fire builds earth, so the conjunction of li and gen should indicate good fortune. From fig. 1 we see that the li and gen trigrams differ by the bottom line. But, to our surprise, table 1 refutes our five phase projection. The Mandarinate, a baleful star that brings lesser misfortune, governs this transformation. In fact, of the 64 possible trigram conjunctions, fully 15% of da you nian auspices cannot be predicted accurately by five phase correlations. Add to this the fact that five phase theories cannot differentiate between the different levels of good or bad fortune (great, lesser, small), and it is clear that these theories, while passable indicators of good and bad fortune, cannot be considered the origin of da you nian auspice. 
Xiantian and Houtian Trigrams with Luoshu Numbers

Up to now we have seen how the houtian trigrams correlate with the luoshu numbers to provide the characteristics of a person's natal qi. But the resolution of the mystery of auspice determination requires the juxtaposition of five factors, not just two. In order to facilitate the reader's comprehension of the numerology underlying bazhai fengshui, I have prepared a heuristic device in fig. 5, patterned after the early Han dynasty cosmograph (click on the link to the left to view the illustration). This numerical dial juxtaposes the following four factors: the xiantian and houtian sequences of trigrams, the luoshu numbers, and the directions. Around the inner dial are arrayed the xiantian trigram names with their luoshu correlates. On the square grid are arranged the trigrams of the houtian sequence, along with their luoshu numbers from the xiantian dial. On the outer square I have placed the cardinal directions. From just these factors, in other words, without five phase theories and their mutual orders, we can conduct fengshui readings as sophisticated as those outlined above. What makes this possible, however, is the fact that there lies embedded within this number dial one more hidden factor, the hetu system of numbers mentioned briefly above. More importantly, however, this board will reveal a most intriguing phenomenon that may have begun as a wellguarded secret centuries ago but was eventually forgotten. From a numerological standpoint good fortune always and without exception reveals itself as 5 or a multiple of 5. 
The dial works in this fashion. First choose the natal trigram on the inner disc and note its number. Next, match this number with each trigram in turn on the square grid, each of which will correspond to a direction the house might face. Then take the sum or difference of the numbers attached to the juxtaposed trigrams. The result will be eight numbers, four of which are divisible by five (that is, 0, 5, 10, and 15) and four that are not. Once each of the eight natal trigrams is paired with its eight directions and the numbers have been computed, it will become clear that half of the 64 possible conjunctions are multiples of five. For example, suppose a person has the natal trigram xun, or number 2 on the dial. It can be matched with the number 3 of direction south (which equals 5 when added), or the number 8 of the direction east (which equals 10 when added), or the number 7 of the direction north (which equals 5 when subtracted), or the number 2 of the direction southeast (which equals 0 when subtracted). The remaining four directions produce sums or differences all not divisible by 5. 

Now, when each trigram of the disc is matched in turn with all trigrams of the grid, we find that half of the disc trigrams are fortunate matches (their sums or differences are multiples of 5) with the same four trigrams of the gridspecifically, the directions east, southeast, south, and north. The other half of the disc trigrams are fortunate matches with the remaining four trigrams of the gridspecifically, the directions southwest, west, northwest, and northeast. These are none other than the dong si zhai and the xi si zhai, that is, the Eastern and Western Halls of the Palace of Nine Halls. These two groups of four trigrams form an array around the plate that is quite revealing. See figure 6 (click on the link to the left). 
The Hetu Numbers 
When the numbers of these two groups are compared with the numbers appearing on the hetu, we find that the numbers of the eastern group (the dong si zhai) correspond to the eastern and southern arms of the hetu (left and top arms), while the numbers of the western group (the xi si zhai) correspond to the western and northern arms of the hetu (right and bottom arms). Refer to the illustration of the hetu in figure 7 (click on the link to the left). 
If these two pairs of hetu arms are compared, we see that when the numbers of each pair are added, that is, the eastern and southern (left and top) arms on the one hand (3+2, 8+7, 3+7, 8+2), and the western and northern (right and bottom) arms on the other hand (4+1, 9+6, 4+6, 9+ 1), the sums are 5, 10, and 15, all multiples of 5. Subtraction of numbers within each arm always equals five (72, 83, 94, 61). All of these numbers correspond to trigram pairs whose Nine Star auspice is great, lesser, or small fortune. However, when the numbers of the eastern and northern (left and bottom) arms, or the numbers of the western and southern (right and top) arms, or the numbers of the northern and southern (bottom and top) arms, or the numbers of the eastern and western (left and right) arms, are added or subtracted, never is the sum or difference a multiple of five. All of the numbers on these pairs of arms correspond to trigram pairs whose Nine Star auspice is great or lesser misfortune.  
The hetu configuration of numbers can also account for the rank of auspice among the eight directions. As it turns out, relative auspice is a factor of proximity. Each number of the pair of numbers that we add or subtract to determine auspice can come from the same arm of the hetu (closest in proximity) or from different arms. Different arms can be either adjacent (next closest in proximity) or opposite (farthest in proximity). The numbers closest in proximitythose pairs sharing the same arm which equal 5 when subtractedare the most fortunate, so their Nine Star auspice is great good fortune. Next, when adjacent arms of the hetu conform to the Eastern and Western Halls of the Palace of Nine Halls (that is, the east/south and west/north arms), pairs of numbers from these arms always correspond to trigram pairs whose Nine Star auspice is good fortune. When adjacent arms of the hetu do not conform to the Eastern and Western Halls (that is, the east/north and west/south arms), pairs of numbers from these arms always correspond to trigram pairs whose Nine Star auspice is misfortune. Finally, pairs of numbers from opposite arms of the hetu (that is, the north/south and east/west arms) always correspond to trigram pairs whose Nine Star auspice is great misfortune.  
This essay is excerpted from my article of the same name published by The Journal of Chinese Religions, No. 27 (1999) pages 1333. © 2000 Dr. Stephen L. Field , All Rights Reserved 