One-Page Learn · The Halachos at a glance
קִדּוּשׁ הַחֹדֶשׁ
Sanctification of the New Month 6
Sefer Zemanim · The hour divided into 1080 parts, the constants of the mean conjunction, and the nineteen year cycle that brings moon and sun almost even
1080
Units in an hour, chosen so the fractions come out whole
793
Units of the thirteenth hour in a mean lunar month
7
Leap years within each cycle
Part 1The unit and the constants
- The court reckons before it listens. Where the month was sanctified on the testimony of witnesses, the court first calculated the conjunction of sun and moon in the manner of the astronomers in order to know whether the moon could be sighted at all; the first level of these calculations is an approximation based on mean rates of movement. (6:1)
- Why 1080. Day and night are treated as a fixed composite of twenty four hours, twelve and twelve on average, and the hour is divided into 1080 units because that number divides into halves, quarters, eighths, thirds, sixths, ninths and tenths, each fraction still containing many whole units. (6:2)
- The mean lunar month. The interval from one mean conjunction to the next is twenty nine full days, twelve hours of the thirtieth day, and 793 units of the thirteenth hour. (6:3)
- The years, and the true drift. An ordinary lunar year of twelve such months runs 354 days, 8 hours and 876 units; a leap year of thirteen runs 383 days, 21 hours and 589 units; a solar year is 365 days and 6 hours, exceeding the ordinary lunar year by ten days, twenty one hours and 204 units. (6:4)
RememberNothing in the sky produces 1080; it was chosen because it leaves no remainders.
Part 2Remainders, and stepping forward
- Cast out the weeks. Counted in sevens, a lunar month leaves 1-12-793, an ordinary year leaves 4-8-876 and a leap year leaves 5-21-589; these are the remainders that carry the calculation. (6:5)
- Add the remainder, get the next conjunction. Knowing the conjunction of any month, adding 1-12-793 yields the conjunction of the month that follows, and the same addition may be repeated month after month without end; knowing a year's conjunction and adding its own remainder yields the following year's. (6:6, 6:8)
- The carrying rules. Every 1080 units becomes an hour, every twenty four hours becomes a day, and multiples of seven days are subtracted away, because the object is not the number of days but the weekday, hour and unit on which the conjunction falls. (6:9)
- From Tishrei outward. The conjunction of a year means the conjunction of Rosh Chodesh Tishrei; adding 1-12-793 gives Marcheshvan, adding it again gives Kislev, and so on through every subsequent month. (6:13, 6:15)
RememberThe whole apparatus exists to answer one question: which weekday, and how far into it.
Part 3The cycle, and the anchor
- The molad of creation. The first conjunction, from which all reckoning begins, is that of the first year of creation: Monday night, 5 hours and 204 units after nightfall. (6:8)
- Why nineteen years. Twelve ordinary years and seven leap years, summed with their hours and units, equal nineteen solar years of 365 days and 6 hours, with a residue of only one hour and 485 units; this cycle is called a machzor. (6:10)
- Which years are full. The seven leap years of every cycle are the third, sixth, eighth, eleventh, fourteenth, seventeenth and nineteenth. (6:11)
- Cycle to cycle. Summing the twelve ordinary remainders and the seven leap remainders and casting out sevens leaves 2-16-595, the remainder of a cycle, by which one steps from the start of one machzor to the start of the next, and so to any year past or future. (6:12, 6:14)
RememberHe prints the leftover hour instead of hiding it, and anchors everything in a night nobody witnessed.