[wolf550e]

This is the same as the early Jewish calendar. The Jewish calendar has adjustments to make it not fully lunar, so that holidays would be during the same season every year, unlike in the simpler Muslim calendar which is fully lunar.

The bible says the new moon must be observed, but the formula for the calendar was calculated in 389CE and that requirement was not observed. I was taught they switched to the calculated calendar right then, but wikipedia says newer sources show the switch was a gradual process that lasted until the 9th century CE.

https://en.wikipedia.org/wiki/Hillel_II