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The Chinese Solar Calendar

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 equal parts known as "solar terms" (each about half the time of a lunation). These (and their starting times) are denoted 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:

There are two variations on the Chinese solar calendar, depending on how "equal" is defined above. 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 it is closest to the Sun) this means that in the true Sun variation the solar terms are of unequal durations.

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...
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".

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