In our Sedra, Nisan – in deference to it being the month of our liberation from Egypt and our start as a nation - is declared by Hashem to be the first month in the Hebrew year. This is despite the strong opinion that the world was created in Tishrei (there is a minority opinion that the world was created in Nisan). In ancient and classical times, the months of the year began with the observation by at least two witnesses of the crescent moon; leap months could be added by the Yerushalayim authorities as the need arose. The fixing of the calendar by human means is derived from the phrase, Ha-Chodesh hazeh lachem; "this month is for YOU" (i.e. humanity is empowered to declare and coordinate the calendar). The permanent, fixed calendar, attributed to the 4th-century sage Hillel II, is based on a mean month of 29d, 12h, 44m and 3 1/3s. The average year length is 365.2468 days, which is slightly longer than the mean tropical year. On account of the discrepancy between solar and lunar years, Pesach - which must be celebrated in the Spring - would often occur more than a month after the vernal equinox; and so the 19-year Metonic cycle comprises 7 leap years, each containing 13 months. In this fixed calendar, common years have 353-355 days, leap years have 383-385 days, and Pesach never begins on a Monday, Wednesday, or Friday. Additionally, Rosh Hashana can never come out on a Sunday, Wednesday or Friday. The details of the fixed calendar were finalized by the 10th century.
Beit Midrash Shabbat and Holidays The Essence of the Holidays