A lunisolar calendar usually comes with a leap rule that determines when, how often, how many and where leap items have to be inserted into the common year in order to keep it in sync with the seasons.
The leap item can be any calendaric unit:
- leap quarter – non known
- leap month, especially in lunar calendars
- leap week
- leap day, as in the Gregorian calendar, or leap days
- leap hour – non known
- leap minute – non known
- leap second
Intercalary items can be considered a special kind of leap item that occurs every year, i.e. the leap cycle is one year.
A common leap cycle – sometimes also called solar cycle – for a single leap day in ancient calendars, e.g. the Julian calendar, is 4 years, because 365.25 days approximates the length of the solar year much better than 360, 365 or 366 would.
The Gregorian calendar has a leap cycle of 400 years containing 97 leap days (and leap years), which results in a mean year length of 365.2425 days. Its rule of determining whether a given year is leap is easy enough to remember and calculate in ones head, but in doing so it does not distribute leap days as evenly as possible across the cycle, therefore nominal dates of equinoxes and solstices deviate more than necessary from their actual occurrence. Some alternative leap rules work better than that.
years | days | weeks | leap days | leap weeks | mean days/year | mean weeks/year | lunations |
---|---|---|---|---|---|---|---|
400 | 146097 | 20871 | 97 | 71 | 365.2425 | 52.1775 | 4947.311… |
231 | 84371 | 12053 | 56 | 41 | 365.(24) | 52.177489… | 2857.071… |
293 | 107016 | 15288 | 71 | 52 | 365.242321… | 52.177474… | 3623.903… |
817 | 298403 | 42629 | 198 | 145 | 365.242350… | 52.177479… | 10104.878… |
A leap cycle with c years which contains both, a whole number d leap day years (365/366 days) and w leap week years (364/371 days), must conform to the formula c = 7·w − d and should fulfill 0.24 ≤ d/c = 7·w/c - 1 ≤ 0.25 to approximate the solar year.