The arithmetic behind the drift
A lunation — new moon to new moon — averages 29.53 days. Twelve of them come to 354.37 days. A tropical year, the sun’s round trip through the seasons, is 365.24 days. The gap is not subtle:
| Year | Length | Against the solar year |
|---|---|---|
| Lunar (12 lunations) | 354.37 days | 10.88 days short |
| Tropical (solar) | 365.24 days | — |
| Lunisolar, common year | 353–355 days | short, and corrected later |
| Lunisolar, leap year | 383–385 days | long, and that is the correction |
Drift is a decision, not an oversight
It would be easy to read the drift as a flaw someone failed to fix. It is the opposite. The Islamic calendar is deliberately untethered from the solar year, so its observances are not tied to a season — Ramadan in high summer and Ramadan in midwinter are both ordinary.
A calendar that has to keep an agricultural year cannot afford that. Planting and harvest are solar events, so any calendar used to schedule them must be pinned to the sun, whatever it does with the moon.
The lunisolar compromise
A lunisolar calendar wants both: months that begin at the new moon, and a year that stays with the seasons. The two are incompatible, so it cheats — periodically inserting a thirteenth month to absorb the accumulated shortfall.
The Hebrew calendar does this seven times in nineteen years, on the Metonic cycle — nineteen solar years being almost exactly 235 lunations. The Chinese calendar reaches the same end by a different route, inserting a leap month whenever one is needed to keep the solstice in the eleventh month.
- Lunar — twelve moons, no correction, drifts about eleven days a year.
- Lunisolar — moon months, plus a leap month every few years to hold the solar year.
- Solar — the year is the unit; months are administrative divisions of it, and the moon is ignored.