Calendars that follow the Moon

A calendar has to juggle three cycles that do not fit together: the day, the month of the Moon’s phases, and the year of the seasons. A year holds neither a whole number of days nor a whole number of lunar months.¹ There are three ways out. Ignore the Moon, and you get a solar calendar, like the Gregorian one we use. Ignore the seasons, and you get a lunar calendar. Follow both, and you get a lunisolar calendar, with extra months now and then.¹

Islamic: the Moon alone

The Islamic calendar is purely lunar: twelve months that follow the phases.¹ A lunar month lasts about 29.53 days and a year of seasons about 365.24,² so twelve months come out some eleven days short of the solar year. The months therefore slide backwards through the seasons and go all the way round in about 33 years: Ramadan can fall in winter or in summer.¹

For religious purposes, a month begins with the first sighting of the thin crescent after new moon. The instant of new moon can be computed exactly; the moment someone first sees the crescent cannot.¹

Chinese: new moons and solar terms

The Chinese calendar follows both the Moon and the Sun. Each month starts on the day of a new moon, so it has 29 or 30 days. A year normally has twelve months; about every three years a thirteenth, a leap month, is added to stay in step with the seasons.²

The modern rules are precise. The winter solstice always falls in the eleventh month. When thirteen months separate two of them, the leap month is the first one that contains no “major solar term”, a rule that dates from the calendar reform of 1645. The new year begins with the second month after the eleventh. Since 1929, the new moons and solar terms are computed for the meridian 120° East.³

Hebrew: computed, with a second Adar

The Hebrew calendar is lunisolar too, but it is computed rather than observed. Its rules were made public by the patriarch Hillel II; later Jewish writers date the fixing of the calendar to 359 CE.⁴⁵ It rests on a cycle described by the Greek astronomer Meton in the fifth century BCE: 19 solar years hold almost exactly 235 lunar months.⁵ Nineteen years of twelve months make only 228, so seven years in each cycle need a thirteenth month. In those years the month of Adar is doubled: Adar, then a second Adar.⁴ Passover always begins on the same date of the Hebrew calendar, the 15th of Nisan.⁵

Easter: a Moon from the tables

Christian Easter is the best-known lunar date inside a solar calendar. Its rules go back to the Council of Nicaea, in 325, which wanted the same Sunday everywhere.⁶

The usual summary, “the first Sunday after the first full moon after the spring equinox”, is only approximate. The equinox is fixed on 21 March, and the full moon is an “ecclesiastical” one, read from tables that keep more or less in step with the real Moon. Easter therefore falls between 22 March and 25 April.⁶

The Gregorian reform of 1582 produced new Easter tables. Western churches use the Gregorian tables; many Eastern churches still use the older ones based on the Julian calendar. That is why the two Easters can fall on different Sundays.⁶