Because Rosh Hashanah (the 1st day of the month of Tishrei), Sukkot (15 Tishrei) and Shemini Atzeret (22 Tishrei) all start on the same day of the week, Jews often find that day quite busy during the fall holiday season. Some years, fall weekends are swamped with Jewish holidays. Other years, it’s three out of four Mondays. It turns out, though, that there are only four days of the week on which this can happen. Because of the intentional design of the Jewish calendar, the first day of Rosh Hashanah (and therefore also Sukkot and Shemini Atzeret) can only fall on a Monday, Tuesday, Thursday or Saturday. Today’s daf explains why.
The Jewish calendar is lunar; new months begin with the appearance of a new moon. Because the lunar cycle is about 29.5 days, some months are 29 days, others are 30. As we’ll learn when we get to Tractate Rosh Hashanah, eyewitness testimony was originally used to confirm the arrival of a new moon. Under this system, the day of the week on which the holidays fell was not known in advance — it depended on when the new moon was spotted in the sky.
Over time, this practice of declaring a new month according to witness testimony fell by the wayside and the calendar was established ahead of time based on the predictable appearance of a new moon. But there was still disagreement about how this should be done.
The Gemara shares a proposal by a group of rabbis (labeled aherim, “others,” which often implies that their view will not ultimately be accepted) who advocate for a fixed cycle of months that alternate between 29 and 30 days. It’s a reasonable plan — straightforward, easy to remember, and it creates a balanced calendar.
If implemented, this system would create a fixed 354 day year (six 29-day months and six 30-day months) and it would be possible for Jewish holidays to begin on any day of the week, and the day of the week would shift by four each year. So if Rosh Hashanah were to fall on a Thursday one year, it would fall on a Monday the next, Friday the next, and so forth. Since 4 and 7 share no prime factors — since they are, in math speak, “relatively prime” — eventually Rosh Hashanah would fall on every day of the week. But some days are really inconvenient:
When the first festival day of Sukkot would happen to occur on Shabbat eve (i.e. Rosh Hashanah falls on a Friday), we postpone it by adding a day to the month of Elul (which precedes Rosh Hashanah) and observing both Rosh Hashanah and the first day of Sukkot on Shabbat. What is the reason for doing so? The reason is this: If the first festival day occurs on Shabbat eve, when is Yom Kippur that year? It is on Sunday.
If Rosh Hashanah were to fall on Friday, then Yom Kippur would fall on a Sunday — and that is the real problem. If Yom Kippur were to fall on a Sunday (or Friday), there would be two consecutive days when there is a severe prohibition against performing labor (festival labor prohibitions are less severe than Shabbat labor prohibitions) and it would be difficult to observe the first day and prepare for the next.
To prevent this from happening, the rabbis suggest, we adjust the number of days in the prior year (and deviate from the pattern suggested by the aherim). Nowadays, we make this adjustments by adding an extra day to Heshvan, the second month (making it 30 days long) or by deleting one from Kislev, the third month (making it 29 days long). As a result, a regular Jewish year can be 353, 354 or 355 days.
Of course, none of this quite aligns with the approximately 365.25 days in a solar year. To solve this problem, the rabbis also instituted a rotation of leap years that contain an extra 30-day month, another Adar; these years are 383, 384 or 385 days.
By the way, in addition to fixing Rosh Hashanah so that it does not fall on Friday or Wednesday so that Yom Kippur is not adjacent to Shabbat, Rosh Hashanah is also prevented from falling on a Sunday so that Hoshanah Rabbah, the last day of Sukkot, does not fall on a Shabbat — but that’s a story for another day.
If you are interested in taking a deep dive into the Jewish calendar, check out Sacha Stern’s Calendar and Community: A History of the Jewish Calendar, 2nd Century BCE to 10th Century CE. If you just want to know what day it is on the Jewish calendar or when the holidays fall, hebcal.com (or My Jewish Learning’s holiday calendar) will do the trick.
Read all of Sukkah 54 on Sefaria.