Determining leap years Chinese Calendar has 12 “principal  terms”- zhongqi- in a year. Each month starts on the day of the new moon (as  seen from the meridian 1200 East) and the numbering of  the months depend on which “principal term” it coincides with. In any case, the winter solstice must fall on the 11th  month. Since there could be 13 lunations  in a solar year, there are some years that have 12 lunations, thus 12 months from one winter solstice to the next. When such a phenomenon happens, the Chinese calendar inserts an intercalary month to make sure that  the winter solstice still falls on the month coinciding with  the 11th  “principal term”. This  month is inserted on the lunation  that does  not coincide with any “principal term”. It would take the number of the preceding month with an added designation to  show that it is  an intercalary month. If there are two months that do not coincide with any “principal term”, only  the first month is considered the intercalary month.Intercalary months will be encountered roughly 7 out 19 years.

Determining Blue Moon
In a year with 13 lunations, one  of the 13 full moons is called Blue Moon. This  full moon looks  exactly  like  any other full moons, just that it is given the name: Blue Moon. The other  12 full moons  have their own special names, but they all appear  yearly, according to the  season. Only  Blue Moon is rather erratic, not only because of when they appear, but  also because of the rules in  determining which one of  the 13 full moons should be called the Blue Moon. The purpose of adding a  Blue Moon is  to ensure  that other moons fall correctly with respect to the equinoxes and solstices; the marker of seasons. The original rule in  determining  Blue Moon, according to  the Maine Farmer’s  Almanac, Blue Moon is the third full moon in a season of four full moons.  The newer way  to  determine a blue moon, apparently  caused by  an error in an article published by Sky &  Telescope, Blue Moon is the second full moon in a month.

Comparing the occurrence of the Chinese calendar intercalary months and Blue Moon
According to an article in “The Moon Book” by Kim Long, the author stated, “The traditional Chinese and Hindu calendars are based on a lunisolar system, balancing the cycles of both the Moon and the Sun. In order not to get out of step, these calendars must periodically adjust dates and the adjustment periods are the same months in which there are blue moons.” Is the above quotation accurate? That is what we shall investigate. Looking at the similar ways of how Blue Moons and intercalary months in Chinese calendar are defined, we can expect them to be one and the same thing. They both depend on the appearance of the 13th moon in the year, even though there are some differences in determining when which of them occur. Let’s take a look at the following table:
However,  looking at the table above, we can conclude that the intercalary months of the Chinese  calendar does not coincide with the appearances of any of the Blue Moons.  In order to find the possible explanation to this unexpected result, we need to take a look  at the differences in determining intercalary months and the Blue Moons.

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