Chinese calendar

Chinese calendar

The Chinese calendar is lunisolar, so a leap year has an extra month, often called an embolismic month after the Greek word for it. In the Chinese calendar the leap month is added according to a complicated rule, which ensures that month 11 is always the month that contains the northern winter solstice. The intercalary month takes the same number as the preceding month; for example, if it follows the second month then it is simply called "leap second month".
Hebrew calendarThe Hebrew calendar is also lunisolar with an embolistic month. In the Hebrew calendar the extra month is called Adar Alef (first Adar) and is added before Adar, which then becomes Adar Sheni (second Adar). According to the Metonic cycle, this is done seven times every nineteen years, specifically, in years, 3, 6, 8, 11, 14, 17, and 19.
In addition, the Hebrew calendar has postponement rules that postpone the start of the year by one or two days. The year before the postponement gets one or two extra days, and the year whose start is postponed loses one or two days. These postponement rules reduce the number of different combinations of year length and starting day of the week from 28 to 14, and regulate the location of certain religious holidays in relation to the Sabbath.
Hindu CalendarIn the Hindu calendar, which is a lunisolar calendar, the embolismic month is called adhika maas (extra month). It is the month in which the sun is in the same sign of the stellar zodiac on two consecutive dark moons.
Iranian calendarThe Iranian calendar also has a single intercalated day once in every four years, but every 33 years or so the leap years will be five years apart instead of four years apart. The system used is more accurate and more complicated, and is based on the time of the March equinox as observed from Teheran. The 33-year period is not completely regular; every so often the 33-year cycle will be broken by a cycle of 29 or 37 years.
Long term leap year rulesThe accumulated difference between the Gregorian calendar and the vernal equinoctial year amounts to 1 day in about 8,000 years. This suggests that the calendar needs to be improved by another refinement to the leap year rule: perhaps by avoiding leap years in years divisible by 8,000.
(The most common such proposal is to avoid leap years in years divisible by 4,000 [1]. This is based on the difference between the Gregorian calendar and the mean tropical year. Others claim, erroneously, that the Gregorian calendar itself already contains a refinement of this kind [2].)
However, there is little point in planning a calendar so far ahead because over a timescale of tens of thousands of years the number of days in a year will change for a number of reasons, most notably:
Precession of the equinoxes moves the position of the vernal equinox with respect to perihelion and so changes the length of the vernal equinoctial year. Tidal acceleration from the sun and moon slows the rotation of the earth, making the day longer. In particular, the second component of change depends on such things as post-glacial rebound and sea level rise due to climate change. We can't predict these changes accurately enough to be able to make a calendar that will be accurate to a day in tens of thousands of years.