The Jewish calendar is generally said to have been set down by the Sanhedrin president Hillel II in approximately C.E. 359. The original details of his calendar are, however, uncertain. The Jewish calendar is the official calendar of Israel and jews all over the world.
Rosh Hashana shofer
The Jewish calendar is a combined solar/lunar calendar, in that it strives to have its years coincide with the tropical year and its months coincide with the synodic months. Lunisolar calendars use months to approximate the tropical year. Examples are the Jewish and Chinese calendars. Since 12 months are about 11 days shorter than the tropical year, a leap month (also called intercalary month) is inserted about every third year to keep the calendar in tune with the seasons.
The first day of the calendar year, Rosh HaShanah, on 1 Tishri is determined as follows:
- The new year starts on the day of the new moon that occurs about 354 days (or 384 days if the previous year was a leap year) after 1 Tishri of the previous year.
- If the new moon occurs after noon on that day, delay the new year by one day. (Because in that case the new crescent moon will not be visible until the next day.)
- If this would cause the new year to start on a Sunday, Wednesday, or Friday, delay it by one day. (Because we want to avoid that Yom Kippur (10 Tishri) falls on a Friday or Sunday, and that Hoshanah Rabba (21 Tishri) falls on a Sabbath (Saturday)).
- If two consecutive years start 356 days apart (an illegal year length), delay the start of the first year by two days.
- If two consecutive years start 382 days apart (an illegal year length), delay the start of the second year by one day.
Note: Rule 4 can only come into play if the first year was supposed to start on a Tuesday. Therefore a two day delay is used rather than a one day delay, as the year must not start on a Wednesday as stated in rule 3.
http://www.webexhibits.org/calendars/calendar-jewish.html
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