The term Rosh HaShana appears only once in the Bible, in the book of Yehezkel (40:1). Here, Rosh HaShana is the first month of the year, rather than a specific day. If Rosh HaShana refers to the first month of the year, however, then it should refer not to Tishrei, but to Nisan. The Torah consistently lists months as the first, the second, etc., counting from Nisan.
The Sages resolved this apparent contradiction by distinguishing between four different New Years, each on a different date, depending on what type of year is being discussed. They also defined four different times when the world is judged. Nisan marks the New Year for historical dating. The agricultural year begins in Tishrei. Tractate Rosh HaShana lists the various New Years and explains which calendars should be used for various counts, e.g., dating documents, interpreting vows, and giving tithes.
The Jewish calendar is based to a large degree on the lunar cycle, which is approximately twenty-nine and one-half days. The Jewish calculation of months is based on the appearance of the new moon. However, certain times of the year must also correspond to certain seasons, which are related to the solar year. Since most of the Festivals and events in the Jewish calendar are connected to specific days in the lunar month, the Gemara grapples with questions such as: To what extent must the court rely on the natural, heavenly cycles? Is it possible to create a fixed calendar based solely on mathematical calculations, or must it be based entirely or at least somewhat on direct observation?
There is only one New Year in the Jewish calendar that is called simple Rosh HaShana. This is the first of Tishrei. This Festival is described by the Torah as “A day of blowing the shofar,” (Bamidbar 29:1), and “A memorial proclaimed with the blast of shofar” (Vayikra 23:24). Sounding the shofar is the unique and central mitzva of the day. Unlike the sounding of the shofar in the Temple accompanying the choir of Levites, the shofar blasts on Rosh HaShana are not intended to create a pleasant, musical sound. Their essence combines elements of remembrance, proclamation, warning and majestic coronation. These shofar blasts must be done in a specific manner. The Gemara discusses the precise details of fulfilling this mitzva, including the specifications of the shofar itself, the timing of the blasts, and the manner in which they are sounded.
Since the shofar of Rosh HaShana is not sounded solely in the Temple, but in every place for every Jewish person, rabbinic decrees were instituted to prevent unintentional transgression of Torah laws. For this reason, the Sages decreed that the shofar may not be sounded on Shabbat, except for inside the borders of the Temple or the central court.