Chinese Calendrics Software 4. The Chinese Calendars Defined
The definition of the lunar calendar depends on the definition of the solar calendar, but not vice-versa.
(a) The Chinese solar calendar
As stated earlier, a 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 (Chinese time) at the start of the day during which the winter solstice occurs to the midnight (Chinese time) of the start of the day during which the next winter solstice occurs. We could call these "astronomical" and "calendrical" solar years. ("Chinese time" is defined in Times.)
The astronomical solar year is divided into 24 equal parts known as "solar terms" (each about half the time of a lunation). These (and their starting times) are denoted in Chinese calendrics by the symbols J1, Z1, J2, Z2, ..., J12, Z12. The two 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 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, depending on how "equal" (above) is defined. It used to be defined so that the duration of each solar term was exactly 1/24th of an astronomical solar year, i.e., 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 along its orbit (starting from the winter solstice). 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 closer to the Sun, and fastest at perihelion) this means that in the true Sun variation the solar terms are of unequal durations. Since the Earth's perihelion currently occurs in January, the time between Z11 and Z12 is slightly less than the time between Z5 and Z6.
This software can use either the True Sun or the Mean Sun method to calculate the solar terms. The True Sun method is the one currently used to calculate the Chinese Calendar, the Mean Sun method being only of historical interest, although it is relevant to dates in Chinese texts occurring before the 17th Century.
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 (Chinese time) at the start of the day during which the solar term (in the first sense occurs) to the midnight (Chinese 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 Z11 begins at midnight (Chinese 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, ... A date in the solar calendar consists of 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, ...
Dates in the Chinese solar calendar are marked by CHS, as in "2-01-01-01 CHS".
(b) The Chinese lunar calendar
The first day of a lunar month begins at midnight (Chinese 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" When a year contains a thirteenth month one of the months is labelled with a numeral-plus-asterisk, e.g., "9*".
The way the series of lunar months is partitioned into lunar years is as follows:
First the series of lunar months is partitioned into sui. The first month of a sui is always a month containing a winter solstice. A sui largely overlaps a year in the Common Era Calendar, but can begin up to nearly a month before the CE year begins (as happens when the winter solstice occurs close to the end of the first month of the sui). A sui may have either 12 or 13 months.
The months in a particular sui are labelled as follows: If it has twelve months then the months are numbered "11", "12", "1", "2", ..., "10". Suppose 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 in the sui 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, beginning with the first month in the sui, are numbered "11", "12", "1", ..., "10". The leap month has the same number as its preceding month. Leap months are distinguished by an asterisk, so that, e.g., month "4" may be followed by leap month "4*", which is followed by month "5". If the leap month is the last in the sui then it is numbered "10*".
A year in the Chinese lunar calendar, called a nian, is then a sequence of months beginning with a month numbered "1" and running up to (but not including) the next month numbered "1" A nian consists of 12 or 13 months.
A date in the Chinese lunar calendar consists of 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 series of dates in the Chinese lunar calendar looks like this:
1-57-11-29, 1-57-11-30, 1-57-11*-01, ..., 1-57-11*-29, 1-57-12-01, ..., 1-59-12-30, 1-60-01-01, ...
As noted in the preceding section, the position-in-cycle number can be replaced by an element-animal combination.
Dates in the Chinese lunar calendar are marked by CHL, as in "1-60-01-01 CHL".
Overseas Chinese (Chinese people living outside of mainland China) often use a year number instead of a cycle-position combination to uniquely denote a particular day. So, e.g., "4713-09-25 CHL" denotes the same day as "79-32-09-25 CHL". When 'China' is selected as the reference longitude, this software displays the Overseas Chinese year, and also allows input of dates in year-month-day format (see Date Conversion).
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