The Hebrew calendar uses lunar months, which are based on the phases of the moon, e.g. the new moon is always the first day of the month, and months are always 29 or 30 days long. The Gregorian calendar’s months are fixed to the solar year, so the two never line up 1:1.
Since there aren’t a whole-number of lunar months in a solar year (or even a whole number of days in one lunar month) the Hebrew calendar adds a thirteenth leap month in seven out of every 19 years to keep it roughly in sync with the solar calendar. That’s why Rosh Hashana (or the first day of Tishrai) always falls between September 5 and October 5.
The Hebrew calendar is based on the lunar cycle instead of the solar cycle. So instead of the normal year having 365 days the Hebrew calendar have about 354 years with leap months added to make up the difference. This means that each month starts with a new moon. You can see remnence of this in the Cristian holidays related to Easter. In the Hebrew calendar the Cristian Easter selebration takes place on the same day every year.
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