m fr

Figure 2.7 Zibai diagram for 1985 in a Chinese calendar.

(purple-and-white). In the diagram shown in Smith (1991), the so-called colour-coded diagram in the centre is a representation of the year xinhai in the zibai system, known as a '8 white'.22 The diagram at the bottom right-hand corner on the next page is the zibai representation, i.e. '4 green', for the second lunar month. Figure 2.7 shows a '6 white' year, an yihai year in the Chinese luni-solar calendar for the year 1985, and Figure 2.8 shows another '6 white' year, this time a bingchen year in the Japanese luni-solar calendar for the year 1976. A difference of nine years between fs m a

Figure 2.8 Zibai diagram for 1976 in a calendar from a Japanese shrine.

the two indicates that the same zibai system is used today both among Chinese and Japanese communities.23 Generally speaking, 'white' was the auspicious colour. Chinese astrologers used this system to work out days and time, auspicious or otherwise, but the positions of the Eight Gates (bamen API) are important, as are the combinations of stems and branches.24 Chinese astrologers used this system to work out lucky and unlucky moments for certain events in private and social life, for example having a bath or a haircut, meeting a friend, doing a business transaction, moving house, getting married, and so forth. This system has outwardly been frowned upon, as it has been dismissed as superstitious by some, and has escaped the careful attention of modern scholars until quite recently. For the purpose of understanding the three cosmic boards, more specifically the Qimen Dunjia system, knowing the process of feigong - flying across the palaces in the magic square - is essential.

The calendar

It is common knowledge that the Chinese employed a luni-solar calendar, which is far more complicated than the Gregorian calendar we use. One year in the Chinese calendar consisted of 12 lunar months. In every three or four years there is an additional month known as the intercalary month. A month is either of 29 or 30 days, and is not fixed. Calendar systems also changed from time to time. There were no less than one hundred different systems in use in the course of Chinese history. Moreover, some regions did not always adopt the official calendar. For example, the calendars used in Dunhuang at certain periods were not the contemporary Chinese official calendars. The Chinese used sexagenary cycles to denote the year, the month, the day and the time of the day. These cycles are of immense help in Chinese chronology, and Sinologists have conversion tables to help them convert Chinese dates to Western equivalents. Problems still remain, however, as for example in the case of Dunhuang chronology when the official calendars were not followed.

Now in Chinese astrology, the year, month and day are each denoted by a number and its colour according to the zibai system, thus providing us with a clockwise 9-year cycle, an anticlockwise 9-month cycle and a clockwise 9-day cycle. For example, the year 1997 corresponds to the wuyin Chinese luni-solar year and to the '3 blue-green' year of the astrologer. Then there is also a 12-day jianchu Ml^, lucky-and-unlucky day cycle that restarts on encountering any of the 12 jieqi in the 24 fortnightly periods. There was more than one system on the use of the jianchu cycle and members of the cycle were also known by different names. The most common names seem to be jian >3! (establishment), chu (removal), man (full), ping ^ (level), ding ® (steady), zhi $A (hold), po (broken), wet fsL (lofty), cheng (success), shou ift (receive), kai ¡^ (open) and bi Pfl (shut). These names are still employed in modern traditional Chinese almanacs.

Using the zibai cycle of 9 days, months and year and the jianchu cycle of 12 days in addition to the sexagenary cycles for the year, month and day, Huang Yi-Long has demonstrated that the Dunhuang calendars can be reconstructed and that there are errors in the chronology tables used to convert historical Chinese dates to Western.25

Ancient Chinese calendar-makers employed a Superior Epoch (shangyuan ±7n), the time in ancient past when the Five Planets together with the sun and the moon were supposed to be in conjunction at midnight, and when the year, the lunar month, the day and the time began with the same sexagenary cyclic term jiazi. Liu Xin (50 bc-ad 22) in making the Santongli HiHtJB calendar took one epoch (yuan 7u) to be three sequences (Santong EL$t), from which came the name of the calendar. One sequence (tong M.) was taken as 81 Metonic Cycles of 235 lunations in 19 years {zhang M), giving 4,617 years to an epoch.26 Intercalations and eclipses during the Spring-and-Autumn period, i.e. between the years 722 bc and 475 bc, were studied separately by Shinsei Shinzo liM®?!®?, Wang Tao ZEIS and others.27 It was found that up to the reign of Lu Xuangong lit-lE-^" (reigned 608-591 bc), intercalation varied between six and eight in every 19 years, but as from the year 589 bc it remained constant at seven intercalations in every 19 years, or (19 x 12) + 7 = 235 lunations in 19 years. The Sifenli K:^® (Quarterly Remainder Calendar), using a tropical year of 365'/<» days and 235 lunations in 19 years, came into use in the fifth century bc. Liu Xin then took a period of 138,240 years for the conjunction of the five planets and derived the Superior Epoch (shangyuan) of 23,639,040 years as the least common multiple of the epoch and his period of conjunction. Subsequent calendar-makers for the next 1,200 years all followed him to calculate a Superior Epoch. None of them, however, had left any record of the method they used to work out the period of conjunction for the planets. It was left to the Song mathematician Qin Jiushao MJLbE (c.1202-c.1261) to figure out that the method used was similar to the Remainder Theorem problem given in the Sunzi suanjing. In any case, we do not have records to inform us how the ancient Chinese calendar-makers worked out periods of conjunction of the planets.

In actual practice, any attempt to find a common multiple for the lunar and planetary cycles would be a matter of great complexity. These cycles expressed in units of the earth's rotation about its own axis, or revolution round the sun, would give numbers that are incommensurable. As Joseph Needham puts it, 'The whole history of calendar making (in China) therefore, is that of successive attempts to reconcile the irreconcilable.'28 Modern scholars have expressed doubts on whether the Chinese calendar-makers had ever used the periods of all the planets at all in their calculations to obtain the interval of the Superior Epoch. Recently, Qu Anjing has even shown that, in the calendar systems he investigated, he could find no sign of any planetary period being ever used.29 Nevertheless, Chinese calendar-makers had somehow produced intervals of the Superior Epoch with a wide range of values. Superior Epochs for some of the more prominent calendars are given in Table 2.8.30The cumbersome procedure of finding an ancient Superior Epoch for calendar-making was eventually dispensed with in Guo Shoujing's SP^Ffi (1231-1316) Sbousbili S^M calendar, the most advanced calendar ever produced in traditional China.31 We shall encounter the Superior Epoch in the Taiyi method.

Table 2.8

Name of calendar


Year from

Interval from

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