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There are 4 rules that would cause the postponement of the 1st day of Rosh Hashanna from being on the day of the molad. One of the most commonly implemented rules is called Lo Ad'u Rosh, meaning that Rosh Hashanna cannot occur on the 1st, 4th or 6th day of the week.

The reason for not allowing it to occur on Wednesday or Friday is to prevent Yom Kippur from occurring on Friday or Sunday. I've been able to locate the Talmudic discussion on this.

I understand that the reason to prevent it from occurring on Sunday is to prevent Hoshannah Rabba from occurring on Shabbat so that we could beat the aravot. I haven't been able to locate the Talmudic discussion on this. I found a web site that referred me to Bavli Talmud Succah 43b and 44a. To me it seems to focus on whether and why using the aravot were forbidden on Shabbat in the 1st place. But, I don't see any mention of adjusting the calendar to make sure it doesn't happen. Did I miss it, or is this discussed elsewhere?

  • Here you go (and spec. 509-10). Forgive me, but time constricts elaboration. – Oliver Oct 11 at 20:00
  • פסיקתא זוטרתא (לקח טוב) ויקרא פרשת אמור 23:4 has it, and I found an interesting quote (שכל טוב (בובר) בראשית פרשת לך לך פרק יז) ומשום תקנה איתיה כדאמרינן במס' ר"ה but I'm not sure what it refers to though this site points to R"H 20a individual.utoronto.ca/kalendis/hebrew/postpone.htm#swf – rosends Oct 11 at 20:10
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    I think that Lo ADU Rosh is the conclusion, not an apriori rule. After discussing various implementations and their drawbacks, this conclusion was accepted. As our calendar is synthetic, it was made in accordance with this conclusion. – Al Berko Oct 12 at 16:50
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    I suggest that as usual with our Halachah, the formal calendar wasn't accepted and kept up until hundreds of years later because it wasn't practical for the masses and they used foreign calendars everywhere. – Al Berko Oct 12 at 16:58
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    @AlBerko You're diverging, here, I'm afraid. I'm pretty knowledgeable of what Sanhedrin did with witnesses, the two-day Yom Tov "doubt" issues, and why HIllel 2 created the calendar and designed it the way that it is, now. And I am basing my question solely on finding the written source of the reason of specifically the postponement to accommodate Hoshanna Rabbah. So, my question is narrowly focused on just that. – DanF Oct 13 at 0:11
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Sukkah 43b does indeed briefly discuss it:

אינהו דידעי בקיבועא דירחא לידחי כי אתא בר הדיא אמר לא איקלע

They [in Eretz Yisrael] who know the establishment of the months, let [Aravah] push off [Shabbos]! When Bar Hedya came, he said, it does not fall out [on Shabbos].

As Rashi there explains:

לא איקלע - הם מעברים את אלול או אחד מן החדשים כשרואין שיארע שביעי בשבת:

It does not fall out - They would make Elul, or another month, longer when they saw that the seventh day would occur on Shabbos.

But the main Gemara you want isn’t in Bavli, but rather Yerushalmi Sukkah, end of 4:1:

ר' סימון מפקד לאילין דמחשבין יהבון דעתכון דלא תעבדין לא תקיעתה בשבת ולא ערבתא בשבתא. ואין אדחקון עבדון תקיעתה ולא תעבדון ערבתא:

R’ Simon charged those who calculate [the calendar]: Take care not to make the Shofar on Shabbos nor Arava on Shabbos. If you’re forced, make Shofar on Shabbos and don’t make Arava on Shabbos.

  • If you’re interested in exploring R’ Simon further, check out the Pnei Moshe to that Yerushalmi and the Ran and Tosfos to that Bavli. I assume the reason we can’t have Rosh Hashanah avoid Shabbos and Sunday in our calendar is because in a year where Rosh Hashanah falls out bezemano on a Monday (like this year), the next year will fall out on a Friday - and, unlike in practice, it can’t be pushed off to Shabbos, but rather Monday, violating the rules set forth in Arachin 8b-9b. – DonielF Oct 16 at 2:38

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