Rosh Hashanah

Rosh Hashanah falls on the first of Tishrei, and Tishrei is the seventh month. The Torah counts Nisan as the first month, so the Jewish new year is celebrated at the start of the seventh, which looks like an error and is not.

Rabbinic tradition resolves it by recognising four new years for different purposes: the first of Nisan for kings and festivals, the first of Elul for the tithe of cattle, the first of Tishrei for years, sabbatical cycles and jubilees, and the fifteenth of Shevat for trees. This is a calendar with multiple year-starts serving different functions, which is not unusual in the ancient world and is not unusual now, fiscal, academic and civil years routinely differ.

The Torah does not call the day a new year. Leviticus and Numbers name the first of the seventh month as a day of rest, of memorial proclaimed with blast of horns, and of holy convocation. The name Rosh Hashanah, and the day's character as the anniversary of creation and the day of judgement, are rabbinic developments, and the Mishnah's discussion is where they are set out.

The shofar is the day's defining act. It is a ram's horn, and the sounds are prescribed: a long blast, a broken one, a series of short ones, and a very long one, in fixed sequences totalling a hundred notes in most customs. The obligation is to hear it, not to blow it.

The day begins the ten days of repentance that end at the Day of Atonement, and the liturgical language throughout is judicial: books opened, a decree written, and the possibility of it being changed.

The Gregorian date of Rosh Hashanah moves within roughly a five-week band, and the movement is the visible output of the intercalation described for Passover.

In an ordinary Hebrew year of 354 days, the festival falls about eleven days earlier in the Gregorian calendar than the year before. In a leap year, with a thirteenth month of thirty days added, it jumps about nineteen days later. The result is a sawtooth: three or two years of drifting earlier, then a correction back. Over the nineteen-year cycle the average holds, and Rosh Hashanah stays in September or early October indefinitely.

There is a slow residual drift. The Hebrew calendar's mean year is about 365 days, 5 hours and 55 minutes, roughly six and a half minutes longer than the mean tropical year, so the festivals creep later against the Gregorian calendar by about a day every 216 years. This is a known feature and is discussed in rabbinic and scientific literature; it will eventually require attention, on a timescale of millennia.

The four postponement rules also produce a visible effect: Rosh Hashanah never falls on a Sunday, Wednesday or Friday. Anyone checking a range of years will find those weekdays simply absent. The rule exists so that the Day of Atonement does not fall on a Friday or Sunday, which would produce two consecutive days on which no cooking or burial is permitted, and so that a particular festival does not land on a sabbath.

The calendar is therefore constrained by liturgical practicality as well as by astronomy, and the constraints are visible in the output.