Intercalation is the insertion of an extra day or month into some calendar years to make the calendar follow the seasons.
The solar year does not have whole number of days, but a calendar year must have a whole number of days. The only way to reconcile the two is to vary the number of days in the calendar year.
In many calendars, this is done by adding to a common year of 365 days, an extra day (leap day or intercalary day): this makes a leap year of 366 days.
The solar year does not have a whole number of lunar months either, so a lunisolar calendar must have a variable number of months in a year. This is usually 12 months, but sometimes a 13th month (an intercalary or embolismic month) is added to the year.
Intercalation can also refer to the insertion of a molecule (or group) being inserted between two other molecules (or groups). Ethidium bromide, e.g., intercalates between adjacent nucleotide side chains.
Whether or not an embolismicmonth (a second Adar) was needed depended on the condition of roads used by families to come to Jerusalem for Passover, on an adequate number of lambs which were to be sacrificed at the Temple, and on the earing of barley needed for first fruits.
Months are numbered from Nisan (reflecting the injunction in Exodus "This month shall be to you the beginning of months".
Twelve lunar months are about 354 days while the solar year is about 365 days so an extra lunar month is added every two or three years in accordance with a 19-year cycle of 235 lunar months (12 regular months every year plus 7 extra or embolismicmonths every 19 years).
Consequently, since this month always began with that new moon of which the fourteenth day occurred on or next after the vernal equinox, Christ arose from the dead on Sunday, the seventeenth day of the so-called paschal moon.
As in the Julian calendar the months had lost all their original reference to the moon, the early Christians were compelled to use the Metonic Lunar Cycle of the Greeks to find the fourteenth day of the paschal moon.
The divergence is removed by assigning to the seven embolismicmonths (which would otherwise have contained 7 times 29.5, or 206.5, days) 209 days, 30 days being assigned to each of the first six and 29 to the seventh.
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