Editing Lunisolar calendar (section)

===Determining leap months===
{{More citations needed|section|date=July 2021}}
A [[tropical year]] is approximately 365.2422 [[mean solar day|days]] long and a [[synodic month]] is approximately 29.5306 days long,<ref>{{cite book | title=Explanatory Supplement to the Astronomical Almanac |year=1992 | editor=P. Kenneth Seidelmann |page=577 |url=https://archive.org/details/131123ExplanatorySupplementAstronomicalAlmanac/page/n302/mode/1up | quote=For convenience, it is common to speak of a lunar year of twelve synodic months, or 354.36707 days.}} (which gives a mean synodic month as 29.53059 days or 29 days 12 hours 44 minutes and 3 seconds)</ref> so a tropical year is approximately {{nowrap|365.2422 / 29.5306 ≈ 12.36826}} months long.  Because 0.36826 is between {{1/3}} and {{1/2}}, a typical year of 12 months needs to be supplemented with one intercalary or leap month every 2 to 3 years.  More precisely, 0.36826 is quite close to {{frac|7|19}} (about 0.3684211): several lunisolar calendars have 7 leap months in every cycle of 19 years (called a '[[Metonic cycle]]'). The [[Babylonians]] applied the 19-year cycle in the late sixth century BCE.<ref>{{Cite web |first=R.H. |last=van Gent |date=July 2021  |url=https://webspace.science.uu.nl/~gent0113/babylon/babycal.htm |title=The Babylonian Calendar |publisher=Utrecht University}}</ref>

Intercalation of leap months is frequently controlled by the "[[epact]]", which is the difference between the lunar and solar years (approximately 11 days). The classic Metonic cycle can be reproduced by assigning an initial epact value of 1 to the last year of the cycle and incrementing by 11 each year. Between the last year of one cycle and the first year of the next the increment is 12{{snd}} the {{langnf|la|'''saltus lunae'''|leap of the moon}}{{snd}} which causes the epacts to repeat every 19 years. When the epact reaches 30 or higher, an intercalary month is added and 30 is subtracted. The Metonic cycle states that 7 of 19 years will contain an additional intercalary month and those years are numbered: 3, 6, 8, 11, 14, 17 and 19. Both the Hebrew calendar and the Julian calendar use this sequence.{{citation needed|date=July 2021}}

The Buddhist and Hebrew calendars restrict the leap month to a single month of the year;{{citation needed|date=July 2021}} the number of common months between leap months is, therefore, usually 36, but occasionally only 24 months. Because the Chinese and Hindu lunisolar calendars allow the leap month to occur after or before (respectively) any month but use the true apparent motion of the [[Sun]],{{citation needed|date=July 2021}} their leap months do not usually occur within a couple of months of [[perihelion]], when the apparent speed of the Sun along the [[ecliptic]] is fastest (now about 3 January). This increases the usual number of common months between leap months to roughly 34 months when a doublet of common years occurs, while reducing the number to about 29 months when only a common singleton occurs.{{citation needed|date=July 2021}}