The Traditional Calendar of the Chinese then and now

 

The Traditional Calendar of the Chinese then and now

On Saturday, January 27, 2024, I posted an article in this blog called:

“Chronometry: The Measurement of Time, Seasons and Year by the Chinese” here:

https://scientificlogic.blogspot.com/2024/01/

I promised I shall post another version about the Chinese calendar just before Chinese New Year of the Dragon in just two days’ time that falls this Friday, 10 February 2024.  

This article is especially written in red to signify prosperity for a New Year for the Chinese. 

According to Isaac Asimov, the Chinese probably began some millennia BC to reckon the passage of time by days and by approximate lunar synodic months. After a time, as 12 such months got out of step with the seasons, they seem, like the inhabitants of early Mesopotamia, to have let in every now and then an embolistic year with a thirteenth or intercalary month. By the thirteenth century BC they appear to have worked out that the year was about 365.25 days and the synodic month about 29.53 days, better values perhaps than those arrived at by any contemporaries in other places. By the early part of the first millennium AD, they had 365.242815 days for the tropical year, 365.255989 days for the sidereal year and 29.530585 days for the synodic month (see Needham, 1959), again values nearer the mark than those used elsewhere at that time.

From at least 104 BC, when Emperor Wei-ti instituted a revised calendar, and possibly for a few centuries before, the Chinese had a luni-solar calendar basically like the Babylonian standardized calendar which was adopted in the early fourth century BC. There were many official variations in the calendar from 104 BC until AD 1912 when the Gregorian calendar was adopted by the new Republic, but the changes were relatively minor. This calendar had months (yüeh) of 29 or 30 days in rough alternation (a system going back no doubt to the second millennium BC); it had ordinary years of 12 months and so of 354 or less commonly 355 days and embolistic years with an intercalary month (jun yüeh) and so of 383, 384 or 385 days. The Chinese embolistic year, as in the Babylonian standardized calendar, occurred seven times in a cycle of 19 years and in about the same positions within the cycle as in Babylonia, namely the third, the fifth or the sixth, the eighth, the eleventh, the thirteenth of fourteenth, the sixteenth or the seventeenth and the nineteenth years.

The cycle of 19 years and 235 lunar months was called chang (the Metonic cycle of the West). In rounded days it totalled 6940 days which was about two-fifths of a day longer than 19 tropical years at that time and 235 lunations which of course did not quite match. Later, perhaps early in the first millennium AD, a longer cycle pu (four chang cycles with 1 day left out of one of them) was introduced. Such a pu cycle was only 0.6 day longer than 76 tropical years. It was the same as the cycle proposed by Kallippos circa 334 BC. These similarities suggest a borrowing by one set of calendar makers from the other, in which case history suggests that the Babylonians and perhaps the Greeks had temporal priority. Careful observes, recorders and analysts could, of course, arrive at all these matters independently and the Chinese may well have done so.

There are some differences between Babylonian and Chinese calendrical systems which should be noted. First, whereas the Babylonians began the year with the new Moon (strictly, in their case, the first visible crescent after sunset) about the time of the Spring Equinox, the Chinese began it with the new Moon mid-way between the Winter Solstice and the Spring Equinox. Second, whereas the Babylonian calendar let in the intercalary month usually after the twelfth month (though occasionally after the sixth), the Chinese let it in after various non-Winter months in accordance with a rule which will be explained later.

There are similarities and differences in the arbitrary divisions of the day by the Babylonians and the Chinese. At one time, as we have seen, the Babylonians divided the day (reckoned from sunset) into twelve equal divisions, each a beru (they later substituted the Egyptian 24 ‘temporal hours’), and the Chinese from the fourth century BC divided the day (ordinarily reckoned from midnight but for this operation from 11 p.m.) into twelve equal shih periods. However, whereas the Babylonians divided the beru into sixtieths and the fraction into further sixtieths, the Chinese divided the shih into eights called kho, equal to 15 minutes of our time. The Chinese also divided the day into hundredths, each also called a kho, but which were 14 minutes 24 seconds of our time.

At a very early date, at least early in the first millennium BC, the Chinese divided the Equator into twenty-four segments, each 15˚ of longitude in extent. The period taken by the Sun to traverse such a segment is called a chhi. It averages 15.23 days but because of the variable apparent velocity of the Sun (least in the northern Summer and the greatest in the northern Winter) the period may be as long as about 15.74 days or as short as about 14.72 days. The Chinese rounded the periods to whole days to produce five or six chhi of 16 days and nineteen or eighteen of 15 days. Those chhi usually spanning the middle of a lunar month were called chung-chhi (chung is ‘middle’) and those usually spanning the ends of neighbouring months were chieh-chhi (chieh is ‘nodal’ or ‘at a junction’). Each chhi had its own name, thus Li-chhun (the beginning of Spring) was the period during which the Sun was between 315˚ and 330˚ of Equatorial longitude, that is, at least approximately, in the second half of the Western sign Aquarius; Yu-shui (the rains) when the Sun was between 330˚ and 345˚, that is, in the first half of Pisces; Ching-chih (awakening of insects) when the Sun was between 345˚ and 360˚, that is, the second half of Pisces; Chung-fen (Spring Equinox) when the Sun was between 360˚(0˚) and 15˚, that is the first half of Aries; and so on. The chhi system was very early in origin, say second millennium BC (Needham, 1959) and so predated the Near Eastern Zodiacal signs by 30˚ extent. Much later, about AD 600, pairs of 15˚ segments were combined to form signs of the Zodiac which had by then been borrowed from Babylonia through India but given distinctive Chinese animal names which had been used for other duodenary cycles.

The new year began with the new Moon nearest to the beginning of Li-chhun which occurred on or about 5 February (Gregorian). As a month is 29 or 30 days, New Year’s Day occurred between about 20 January and 19 February. After an ordinary year of 354 or 355 days, New Year’s Day moved forward by about 11 days in terms of Gregorian dates. When it moved forward to a date between 20 January and 30 January, the year's beginning had to be embolistic (otherwise the following year would begin with the new Moon next but one nearest the beginning of Li-chhun). It is this rule which determines which years in the 19- year cycle is embolistic. Further the intercalary month in the embolistic year is that one which ended before the beginning of a chieh-chhi (information from Professor Ho Peng- yoke). This could be any of the non-winter months as the chhi tend to be shortest in winter, but it would most likely be a summer month when the chhi tend to be longest. This rule for selecting the intercalary month is similar in principle to that used by the Hindus in selecting their intercalary chandra masa; it is likely, however, to have yielded a slightly different result as the Hindus were using Signs 30 ̊ in extent and were anchoring them to a fixed and not a precessing First Point of Aries; the Chinese located the beginning of Chung-fen at the precessing First Point of Aries.

It has been stated above, following various authorities but particularly Needham (1959) and de Saussure (1920) on this occasion, that the Chinese lunar month began with the new Moon. In modern astronomical usage ‘new Moon’ refers to the conjunction, yet one may reasonably imagine watchers for the first visible crescent, such as the Babylonians, the Greeks, the early Romans and the Jews, not to mention some other Semitic peoples, referring to that apparition as the new Moon, as we tend to do. The early Egyptians by contrast used the day (ending at dawn) of the last visible crescent before sunrise as the last day of the lunar calendar month and began the new month on the next day. The term ‘new Moon’ can thus have several meanings: the first visible crescent, the conjunction or even the disappearance of the ‘old Moon’. We have sought to establish, with no great success, what criterion the Chinese used for the beginning of the lunar calendar months. We suspect that there were changes with the passage of time.

The Chinese engaged in a great deal of minor tinkering with their calendar over the two millennia for which we have records. Professor Ho Peng-Yoke kindly extracted for us  some relevant information given in Li-fa t`ung-chih written by Chu Wen-hsin and not yet translated into English. From 104 BC when Emperor Wei-ti reformed the existing lunar or perhaps luni-solar calendar there were until its official replacement in AD 1912 by the Gregorian calendar forty-two further reforms, not to mention many regional variants.

Professor Ho Peng-Yoke says that in the Chinese mind to promulgate a calendar is to exercise the right of a ruler. Chu Wen-hsin in addition to giving the dates of introduction of the forty- two variants of the T`ai-ch`u calendar produced by or for Wei-ti in 104 BC (some lasted only a couple of decades and others a couple of centuries) also states the average duration of the years in each. Quite early the years approximated on average 365.25 days, but the average shrank, in zig-zag fashion, to about 365.2423 days in the mid-seventeenth century. We suspect that the criterion for the first day of the month may also have changed from time to time.

Sivin (1969) cites two early first millennium AD treatises which dealt with the beginning of the month. The first discussing the calendar prior to 104 BC says that ‘the new moon visible on the last day of the calendar month and the old moon visible on the first day are omens of the ruler’s laxity or overstrictness’. Isaac Asimov inclined to interpret this as meaning that the first day of the calendar month should have occurred on a day between those on which the old moon was visible (before sunrise) and the new moon was visible (after sunset), but it may have some other implication. The second treatise quoted by Sivin speaking of the T`ai-ch`u calendar of Wei-ti says the calendar ran slightly behind the phenomena so that the new moon occurred earlier than the calendar predicted. The conjunction would take place on the last day of the month in some cases and the moon would appear on the first day in other cases.

To check what might be happening in the Kuei-mao calendar (AD 1742 to 1911), Issac Asimov took more or less at random a run of 26 months from 2 December 1880 as set out in A Sino- Western Calendar for Two Thousand Years:1-2000 AD by Hsueh Chung-san and Ou-yang (1955). He compared the dates of the first days of these 26 months as given in that work with the times and dates of conjunction (converted to ‘Peking Mean Time’) as set out in the Nautical Almanac for the years 1880, 1881 and 1882. Eleven of these Chinese months began on the day of conjunction, 15 on the day after but none of the day before (the day being reckoned from midnight). On eight of the eleven occasions when the first calendar month day coincided with the day of conjunction, conjunction occurred before midday in ‘Peking Mean Time’; on twelve of the fifteen occasions when the first day of the month occurred on the day after conjunction, conjunction occurred after midday. There is an obvious tendency here, akin to one to be found in Indian calendrical practice. There are, however, some fairly marked departures from the tendency, for example 27 May 1881 was the first day of a calendar month although the conjunction occurred at about 3.50 p.m. on that day and 20 June 1882 was the first day of a calendar month although the conjunction occurred at about 8.05 a.m. on the day before. Further using data from The Nautical Almanac for the relevant year.  Isaac Asimov had no difficulty in generating months of roughly alternating 29 and 30 days with their first days on the day of conjunction. At this time the Chinese would have had data almost as precise as those in The Nautical Almanac, certainly good enough for this purpose. It is almost as though the Chinese at this time in trying to avoid under shooting the day of conjunction quite often over-shot it. There is, however, another possibility. They may have been aiming at the first visible crescent. To check this possibility, Isaac Asimov worked out from a table in Norton’s Star Atlas and Reference Book times of sunset in Peking on the first days of the 26 calendar months, and in qualitative way tried to estimate the probability of a visible crescent after sunset on the first day of these calendar months. Asimov took into account the obliquity of the Ecliptic to the horizon, the latitude of the Moon and the rapidity with which the Moon was separating from the Sun. He concluded that on one occasion there was very probably, perhaps certainly, a first visible crescent after sunset on the first day of the calendar month, that on 2 or 3 other first days visible crescent was possible but that on the remaining 22 or 23 first days of the month a first visible crescent was impossible or highly improbable. On no first day could there have been a last visible crescent before sunrise on the first day of the calendar month.

All the foregoing is better evidence for the day of conjunction if the conjunction is early in the day, or the day after, if the conjunction is late in its day, then it is for the first visible crescent. It is all fairly clear evidence against the day after the last visible crescent as the first day of the calendar month.

Emboldened by the exercise just described, Asimov dipped back much earlier into the data in A Sino-European Calendar for Two Thousand Years. The data for the first century AD have many gaps and hence seemed suspect as well as not readily usable. The data for the late second century seemed more confidently stated (though, of course, this does not mean that they were more accurate). No issues of The Nautical Almanac were available for the epoch, but Bickerman provides appropriate dates and times of conjunction. Bickerman’s data have been obtained by projection back from modern data on rules which have been improved since they were used to generate his data; this may well be a weakness in the next exercise.

Isaac Asimov comparisons were necessarily much rougher than for the period 1880-2. He had no data on the Moon’s position north or south of the Ecliptic nor on the rate at which the Moon was separating from the Sun. Hence, Asimov constructed a nomograph based on Schoch’s values for Babylon but adapted for the latitude of Peking and incorporating in a somewhat qualitative way variations arising from other relevant considerations which entered into the making of this nomograph. It was so rough that he did not believe that the use of space would be justified. More important to mention is the result of its application to the 1880-2 data already investigated. The nomograph gave essentially the same results as his earlier more careful investigation, though slightly more generous in respect of probable and possible first crescents on the first day of the month.

Isacc Asimov took for investigation two runs of 25 months beginning on 16 January AD 150 and on 21 January AD 155. He concluded that there were perhaps fourteen occasions when there was probably a first visible crescent on the first day of the month, sixteen occasions when there was a possible first visible crescent, twenty occasions when a first visible crescent was highly improbable or impossible and no occasion on which there could have been a last visible crescent before sunrise on that day. If these inferences are correct, the Chinese in the second century AD were using either the day of the predicted but not observed first visible crescent and often undershooting it or the day of conjunction and often overshooting it.

Nomograph constructed for estimating the likelihood of a first visible crescent at certain intervals between conjunction and sunset and for various times within the year, at the latitude of Peking. The band of ‘possible’ first visible crescent allows for the occurrence of some unfavourable conditions, for example, the Moon being south of the Ecliptic, whereas the band of ‘probables’ assumes all conditions are favourable.

Sivin’s reports and  two dubious studies suggest to Issac Asimov  and he should not wish to use a stronger word, (i) that the Chinese for at least some two millennia or more were aiming at the day of conjunction, (ii) that at first, they tolerated but with some dismay both last visible and first visible crescents on the first day of the calendar month, later they became intolerant of last visible crescents on that day and (iv) still later they tried to minimize first visible crescents but suffered a few of them in preference to undershooting the day of conjunction. Perhaps in this last suggested phase they used the rule ‘First day of the calendar month if the conjunction is before midday and next day if it is after midday’ but through inadequacies of data or obsessions about alternating months of 29 or 30 days (which is doubtful) or on some other considerations (which have not been able to locate) sometimes broke the rule.

Issac Asimov should then like to turn to some cycles of years other than the chang cycle of 19 years (like the Metonic cycle) and the pu cycle of 76 years (like the cycle proposed by Kallipos). These were based on considerations other than those of adjusting a lunar year to the tropical year by periodic intercalary months.

First, the Chinese had a duodenary cycle of years based, like that in India, on Jupiter’s progress among the fixed stars. As Jupiter’s sidereal period is 11.86 years, the planet moves eastward each tropical year about 30.354˚. This is slightly greater than a Babylonian Sign of the Zodiac. Each of the 12 Jupiter years was given one of the names of the twelve ‘terrestrial branches’ which shall be discussed below, and which were also bestowed on the Signs of the Zodiac when they were adopted very much later.

Second, they had a sexagenary cycle not based on five Jupiter cycles as in India and not confined to the years, indeed it seems to have been employed first, in perhaps the late second millennium BC, for a cycle of days and was not applied to the years until near the end of the first millennium BC. The manner of its generation is peculiar (though the same principle of generating a cycle is to be found in the Meso-American calendars). Successive items in two lists, the ten ‘celestial stems’ (chih) and the twelve ‘terrestrial branches (kan), are paired. Let capital letters stand for the members of the chih list, thus A, B, C, D, …, J, and minuscules for the members of the kan list, thus a, b, c, d, …, l. Then a sixty-item set of pairs may be generated to produce

Aa, Bb, Cc, Dd, Ee, Ff, Gg, Hh, Ii, Jj

Ak, Bl, Ca, Db, Ec, Fd, Ge, Hf, lg, Jh

Ai, Bj, Ck, Dl, Ea, Fb, Gc, Hd, Ie, Jf

And so on.

The sixtieth pair is Jl and the sixty-first Aa thus beginning a new cycle.

According to Needham (1959) the origins of the chih and the kan lists are obscure.

He suggests that the former may have begun as the names of the 10-day period (obtained by dividing the ‘full’ lunar month into thirds). The latter seem to have been associated with the 12 lunar months which almost make up a year, with the twelve shih into which the day is divided and later with the 12 years in the Jupiter cycle. We shall list the twelve kan with the animal names in Chinese and English long associated with them.

Tzu (rat), chhou (ox), yin (tiger), mao (hare), chhen (dragon), ssu (snake),

wu (horse), wei (sheep), shen (monkey), yu (cock), hsii (dog) and hai (pig)

In accordance with this list the Chinese have: (i) the ‘hour’ (strictly double hour or shih) of the rat, of the ox, of the tiger and so on; (ii) the day of the rat, of the ox, of the tiger and so on, qualified by the appropriate chih term in the sexagenary cycle, thus chia-tzu or tzu or ping-tzu, for days which are 12 apart; (iii) the month of the rat, of the ox, and so on, although they are more usually known as the first, the second, the third and so on year of some named Emperor’s reign.

Twelve double hours (shih) make a day. A sexagenary cycle of days comes close to 2 lunar synodic months rounded to 29 or 30 days (say 59 days for the pair). A sexagenary cycle of months comes out to rather less than 5 years, assuming that intercalation is being employed. A sexagenary cycle years (averaging about 365.25 days) comes out a little longer (21914.5 days) than five Jupiter cycles (21662.95 days). Perhaps these near coincidences (the deviations of which would not be so evident at first) were enough to convince the early Chinese calendar-makers that the sexagenary cycles could be applied to the days, the months and the years. Whatever be the case they applied them. It would be roughly analogous were we to say the Sun hour of the Moon day of the Twia-month of the Wooden year or the Januarius hour of Februarius day of the Martius month of the Aprilis year or better still the Aries hour of the Taurus day of the Gemini month of the Cancer year.

Though this very ancient calendar was officially abolished on the establishment of the Republic of China in AD 1912, it lingered on in China and in Chinese communities abroad. Unfortunately, not many Malaysians or Singaporeans are aware of this. They only know about the cycles of Zodiac years of the various years that comes and goes in cycles like this Rabbit Years that has just two days left to give way to the Year of the Dragon on 10 February 2024.

 The Chinese calendar in its basic form has had a slightly longer run than the essentially Roman calendar which we use, though both have had a shorter run than the Egyptian civil calendar especially if we count its continued modified forms among the Copts and Ethiopians, among the Persians and among the Parsees in India. Calendars are hard both to make and to unmake, partly because conventions and traditions are so important in them whatever hard core of adjusted astronomical fact, they have in them. It is difficult to distinguish independent creations and borrowings when comparing practices in the Far East and the Near East. There are clear instances of borrowings, sometimes through India but sometimes along the trade-route north of India. The concept of the Zodiac almost certainly moved from the Near East to the Far East through India.

Gunpowder and silk came from China to the West through the Near East perhaps on the northern route. The seven-day planetary week came temporarily into China from Hellenistic sources possibly through India but perhaps through the northern route from northern Persian regions. Sunday in the short-lived Chinese week was Mit, possibly from Mithra, the Sun god. The 360˚ division of the circle also seems to have drifted from Mesopotamia, though in China it was corrected for a time to 365.25˚, on the assumption that it was based on the average daily rate of the Sun’s progress amongst the fixed stars. There is clear evidence of Chinese innovation. As have claimed the Chinese could easily have discovered the Metonic Cycle without influence from the Near East. It is also important to recognize that while astronomers in the Near East, including the Greeks, and in India adopted an orientation for celestial location based on the Ecliptic, the Chinese from the outset adopted an orientation based on the Celestial Equator and Poles, the reference frame now adopted internationally by astronomers.

On this note, let me wish all the Chinese the world over a very Happy and Prosperous New Year of the Dragon.