The Structure of
the Chinese Calendar
by Peter Meyer
There are two Chinese calendars, a solar calendar and a lunar calendar (the latter is also a 'lunisolar' calendar, since it more or less stays in sync with the solar year). Both calendars depend on the times of certain astronomical events, such as dark moons and winter solstices. For at least several centuries (according to some scholars, since the 5th C. BCE) the times of these events have been ascertained not by observation but rather by calculation, so these calendars can be classified as rule-based.
The Chinese solar calendar consists of a sequence of solar years which are not divided into months but rather into 24 periods which begin at the "solar terms" (see below). The Chinese lunar calendar consists of a sequence of lunar years which are divided into 12 or 13 lunar months. A solar year begins at the (northern) winter solstice, which is on or around December 22 in the Common Era Calendar. A lunar month begins on the day of a dark moon. The beginning of a lunar year (i.e, lunar new year's day) is more difficult to define (but see below); it always begins from about January 20th to about February 20th, i.e., about a month or so after the start of the Chinese solar year.
The Chinese Calendar assumes a prime meridian of 120 degrees East (120°E). This means that a day (or rather, a nychthemeron, a day and a night) is taken to run from midnight Beijing standard time (BST = CCT = GMT+8) to the next midnight BST. This is in contrast to the Common Era Calendar, where a nychthemeron runs from midnight Greenwich Mean Time (GMT) to the next midnight GMT. The time difference between Beijing and London is eight hours, so nychthemerons (or nychthemera) in the Chinese Calendar begin eight hours earlier than nychthemerons in the Common Era Calendar.
Before proceeding further we define some terms:
A dark moon occurs when the Sun and the Moon are astronomically conjunct (or more exactly, when either the Moon's center lies on the line joining the centers of the Earth and the Sun or the plane defined by the Sun, Earth and Moon is perpendicular to the Earth's orbital plane).
The term "new moon" is not used here, since it is ambiguous. It can mean either a dark moon or the phase of the Moon when a crescent is first visible (in which sense a month in the Muslim calendar begins at new moon).
A lunation is a passage of the Moon from one dark moon to the next. A lunation begins at the dark moon (astronomical conjunction of Sun and Moon), and the next dark moon marks the beginning of the next lunation.
An equinox occurs when the angle formed at the Earth's center between its axis of rotation and the line joining the Earth to the Sun is a right angle. At such a point in the Earth's orbit the length of day and night is almost equal (but not exactly equal, due to atmospheric refraction of the Sun's rays near the horizon and the practice of measuring the start and end of the day from the first or last appearance of the Sun). The northern vernal equinox occurs around March 20th of each year, and the northern autumnal equinox occurs around September 21st.
A solstice occurs when this angle reaches a maximum or a minimum. At such a point the duration of the day and the night is either longest or shortest. The northern winter solstice occurs around December 21st of each year, and the northern summer solstice occurs around June 21st.
2. Chinese and Western Years
The Chinese Calendar uses cycles of sixty years. A year within a cycle is designated by a combination of an element name (e.g., "Water") and an animal name (e.g. "Rabbit"):
For the order in which the various element-animal-designated years occur within a cycle of sixty years (Wood-Rat, Wood-Ox, Fire-Tiger, ...) see Interconverting Chinese and Western Years.
Wood Fire Earth Metal Water
Rat Ox Tiger Rabbit Dragon Snake Horse Sheep Monkey Chicken Dog Pig
A Chinese year is uniquely determined by an element name, an animal name and a cycle number, e.g., the Water-Dragon year in the 21st cycle.
Since the years of the Chinese Calendar run concurrently with the years of the Common Era Calendar (although they do not overlap exactly) each year at a certain position in a certain cycle in the Chinese Calendar can be uniquely associated with a year in the Common Era Calendar provided that one such correlation is known. Actually two such correlations are used by different scholars: The first year in the first cycle is correlated either with -2696 CE (i.e., 2697 BC) or with -2636 CE (i.e., 2637 BC). 2004 is a Wood-Monkey year in Cycle 79 (according to the first correlation) or in Cycle 78 (according to the second).
3. The Chinese Solar Calendar
As noted above, a Chinese solar year always begins at the winter solstice. It may be thought of either (i) as running from the exact moment of a winter solstice to the exact moment of the next winter solstice or (ii) as running from midnight (Beijing time) at the start of the day during which the winter solstice occurs to the midnight (Beijing time) of the start of the day during which the next winter solstice occurs. We could call these "astronomical" and "calendrical" solar years.
The astronomical solar year is divided into 24 periods. The times of the start and end of these are called "solar terms". These are denoted by the symbols J1, Z1, J2, Z2, ..., J12, Z12. The two (northern) solstices and the two equinoxes coincide with four of these solar terms, as follows:
vernal equinox (VE) Z2 summer solstice (SS) Z5 autumnal equinox (AE) Z8 winter solstice (WS) Z11
The other eight Z's (the "major solar terms", also known as "zhong qi")) occur at equal (or nearly equal) intervals between these four Z's. The major solar terms thus are like the hour numbers on a clock face, with the vernal equinox at 2 o'clock, etc. (and the minor solar terms, the J's, marking the half-hours).
There are two variations on the Chinese solar calendar. It used to be defined so that the period from each solar term to the next was exactly 1/24th of an astronomical solar year, i.e., approximately 15.22 days. This is called the "Mean Sun" variation.
In the 17th Century Chinese calendricists adopted calculations based on the true motions of the Earth and Sun, and in this variation of the solar calendar each solar term consists of the time required for the Earth to move exactly fifteen (= 360/24) degrees in its orbit (starting from a solstice or an equinox). This is called the "True Sun" variation. Since the Earth moves at slightly different speeds at different places in its orbit (it moves slightly faster when it is closer to the Sun) this implies that in the True Sun variation the period from one solar term to the next is not always the same.
Strictly speaking, solar terms are points in time, namely, the times at which the Sun (as seen from the Earth to be travelling along the ecliptic) reaches 0°, 15°, 45°, ..., measured from a solstice or an equinox. A solar term may also be understood as a period of time, namely, the period between two such solar terms. We can thus say that (in this sense) the solar year is divided into 24 solar terms.
Although there are 12 pairs of adjacent solar terms, a pair of solar terms cannot be regarded as a 'month'. The solar year is divisible into solar terms, but not into months. An attempt to do so (as is done in Wikipedia) flounders on the astronomical facts underlying why the lunar year sometimes has 12 months and sometimes has 13 months.
Just as "solar year" has two meanings, an astronomical and a calendrical, so a "solar term" may be thought of either (i) as running from the exact moment of a solar term as defined above to the exact moment of the next solar term (an "astronomical solar term") or (ii) as running from midnight (Beijing time) at the start of the day during which the solar term (in the first sense occurs) to the midnight (Beijing time) of the start of the day during which the next solar term occurs (a "calendrical solar term").
The day on which a calendrical solar term begins in the Chinese solar calendar is the day in which the astronomical solar term occurs. E.g., if a winter solstice occurs at 23:03 then the calendrical solar term Z2 begins at midnight (Beijing time) at the start of that day.
The 24 calendrical solar terms in a calendrical solar year are numbered 1 - 24 (1 = Z11, 2 = J12, 3 = Z12, 4 = J1, 5 = Z1, and so on). Within a calendrical solar term the days are numbered 1, 2, ... Thus a date in the solar calendar may be represented by a quadruple of the form cycle-position-solarterm-day, where c-p-s-d denotes day d (1-16) of solar term s (1-24) of the year at position p (1-60) in cycle c. Thus a sequence of dates in the Chinese solar calendar looks like this:
1-59-24-14, 1-59-24-15, 1-60-01-01, ..., 1-60-24-16, 2-01-01-01, ...
As noted in the preceding section each position-in-cycle is associated with a unique element-animal combination, so, e.g., "1-59-24-14" can also be expressed as "The 14th day of the last solar term of the Water-Dog year in the 1st cycle."
Dates in the Chinese solar calendar may be marked by CHS, as in "2-01-01-01 CHS".
4. The Chinese Lunar Calendar
The definition of the lunar calendar depends on the definition of the solar calendar, but not vice-versa.
The first day of a lunar month begins at midnight (Beijing time) on the day in which the dark moon occurs. Thus a lunar month always runs from the day of the dark moon up to but not including the day of the next dark moon. It is thus tautologous (and hence true) to say that the dark moon always occurs on the first day of the lunar month.
This series of lunar months is partitioned into lunar years, which consist of either twelve or thirteen lunar months. Months are labelled with a numeral from "1" through "12" or (when a year contains a thirteenth month) with a numeral-plus-asterisk, e.g., "9*".
The way the series of lunar months is partitioned into lunar years is as follows:
A nian is the period of a whole number of lunar months making up a lunar year, beginning with month "1". A nian consists of 12 or 13 months. A related concept is a sui, which is a period of a whole number of lunar months such that the first month of the period contains the winter solstice. A sui also consists either of 12 or 13 lunar months. A sui largely overlaps the solar year, but can begin up to nearly a month before the solar year begins (when the winter solstice occurs close to the end of the first month of the sui).
Consider the series of lunar months partitioned into suis. Consider a particular sui. If it has twelve months then the months are to be numbered "11", "12", "1", "2", ..., "10". The third month will thus be the first month of the nian which largely overlaps this sui.
Suppose, on the other hand, that there are thirteen months in the sui. A sui can contain only twelve major solar terms (the Z's, or zhong qi's, described above), so at least one of the months does not contain a major solar term. The first month which does not contain a major solar term is distinguished as a "leap" month (a.k.a. an "intercalary" month). The first month in the sui cannot be a leap month because it contains the solar term Z11. The twelve non-leap months are numbered "11", "12", "1", ..., "10". The leap month has the same number as its preceding month. Leap months are distinguished by an asterisk or a plus sign, so that, e.g., month "4" may be followed by leap month "4*" (or "+4" or "4+"), which is followed by month "5".
A date in the Chinese lunar calendar may be represented by a quadruple of the form cycle-position-month[*]-day, where c-p-m[*]-d denotes day d (1-30) of month s (1-12) — a leap month if this is s* — of the year at position p (1-60) in cycle c. Thus a sequence of dates in the Chinese lunar calendar looks like this:
1-59-11-29, 1-59-11-30, 1-59-11*-01, ..., 1-59-11*-29, 1-59-12-01, ..., 1-59-12-30, 1-60-01-01, ...
As with solar dates the position-in-cycle number can be replaced by an element-animal combination.
Dates in the Chinese lunar calendar may be marked by CHL, as in "1-60-01-01 CHL".
Overseas Chinese number years sequentially, as in the Gregorian Calendar, with Chinese year 4709 corresponding to Gregorian year 2011. Thus the Overseas Chinese date "4709-07-13 CHL" denotes the same day as the cycle-position date "79-28-07-13 CHL".
5. Comparison with the Gregorian Calendar
New Year's Day in the Chinese Lunar Calendar can occur on any date in the Gregorian Calendar from January 21 to February 21 (though not all dates are equally likely).
New Year's Day in the Gregorian Calendar always occurs about a week after the northern winter solstice, whereas on average New Year's Day in the Chinese Calendar occurs approximately midway between that solstice and the northern vernal equinox.
A year in the Gregorian Calendar always has 12 months, whereas a year in the Chinese Calendar usually has 12 but in about one year in three it has 13 months.
A month in the Gregorian Calendar may have any number of days from 28 through 31. A month in the Chinese Calendar always has either 29 or 30 days.
A month in the Chinese Calendar always begins at the dark moon, and the full moon always occurs in mid-month. In the Gregorian Calendar the dark moon and full moon can occur at any time during a month.
Traditionally associated with (although not formally a part of) the Gregorian Calendar is a cycle of 7 days ("the week"). There is no such cycle in the Chinese Calendar; instead there are cycles of 60 days, 60 months and 60 years.
Each day, month and year in the Chinese Calendar is traditionally associated with one of twelve animals and one of five elements. There is no such association in the Gregorian Calendar, although months are loosely connected with astrological signs of the zodiac (whose periods are offset from the months by about nine days).
The Gregorian Calendar is rule-based (although only a small proportion of people can state its leap year rule correctly), whereas the Chinese Calendar depends on exact calculation of the times of dark moons and solar terms (which must be done by calendrical experts using astronomical methods and data).
Reliable conversion between dates in the Gregorian Calendar and dates in the Chinese Lunar Calendar is thus possible only by means of such calculation, which is performed by computer software such as Chinese Calendrics.
Links to other articles on the web about the Chinese Calendar
Interconverting Chinese and Western Years Messages to CALNDR-L re the Archetypes Calendar
and the Chinese Calendar
Calendar Software Hermetic Systems Home Page