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Our Sources give the impression that Shabbat is the holiest of the yamim tovim. On Shabbat, we rest, eat and drink of the best, sleep, rejoice, have sex with the spouse, wear nice clothes, etc. It trumps many other things, such as mourning.

But Shabbat does not trump Yom Kippur. Yom Kippur frequently falls on Shabbat, and does not allow most things mentioned above.

I know the Mishna [Taanit 26b] says that the two most joyous days are Yom Kippur and Tu b'Av, but I have the impression many Jews do not feel that way. (Maybe they haven't learned enough.)

Why was the calendar not arranged so that Yom Kippur never falls on Shabbat?

  • You said it yourself: Yom Kippur is a joyous day. The fact that we don’t feel that way is our problem, not Yom Kippurs – Lo ani Jun 3 at 4:39
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    I thought you would ask why not multiply those joyous days and not let them overlap. – Al Berko Jun 3 at 11:58
  • The Hebrew calendar was improved so as to avoid objectively life-threatening situations, such as risk of starvation due to the Sabbath falling near a day of fasting. – Lucian Jun 5 at 22:22
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The fixed calendar already prevents Yom Kippur from falling on a Friday or Sunday, to avoid two consecutive days where all melachot are forbidden. (See Shulchan Aruch Orach Chaim 428:1 with e.g. Magen Avraham, Biur HaGra, Biur Halachah.)

If we were to also prevent Yom Kippur from falling on Shabbat, that would lead to a situation where the new moon of Tishrei could appear on Tuesday night, but Rosh Hashanah wouldn't start until Friday night (a full three days later) in order to avoid Yom Kippur falling on Friday, Shabbat or Sunday. To my mind, the Rabbis would not have wanted to set up the calendar in such a way that would lead to this ridiculous-seeming outcome.

As noted by @DonielF in a comment, there is precedent for this line of thinking in Arachin 8b-9a:

אמר רב הונא לא נראה לחכמים לעבר יתר על שמונה מאי שנא תשעה דלא אם כן קדים אתי סיהרא תלתא יומי

Rav Huna says: It did not seem appropriate to the Sages to extend more than eight months in a year [and establish them as full, thirty-day months].

What is different about nine months [in that the Sages did not deem it appropriate to establish that many full months in one year]? If so [i.e. if there were that many full months] then the new moon [of Tishrei] would arrive three days before [Rosh HaShana].

Rashi comments:

קדים [אתי] סיהרא - חדתא ג' ימים קודם ראש השנה שהמולד ביום ד' וראש השנה בשבת ומרנני עלמא בתר רבנן למימר כל מה דבעו עבדי

The new moon would arrive three days before Rosh HaShana because the molad will fall on Wedenesday but Rosh HaShana would only fall on Shabbat, and people will mock the Rabbis, saying that they do what they want.

  • All the same, radically changing the character of Shabbat is a high price to pay to avoid what you described. – Maurice Mizrahi Jun 3 at 14:40
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    @Maurice As per Arachin 8b-9b, I think they would rather have the character of Shabbos changed, than people come to denigrate Rosh HaShanah entirely, or worse, the calendar as a whole. Joel - might even be worth adding this Gemara into your answer. – DonielF Jun 3 at 15:56
  • Just so I get a feel for how prevalent this is, how many of you feel in your kishkas that"Yom Kippur is the most joyous day on the Jewish calendar"? – Maurice Mizrahi Jun 3 at 18:53
  • @DonielF Thanks. Good call. I added it in to the answer... – Joel K Jun 4 at 13:42
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Yom Kippur is described in Vayikra 23 as a kind of Shabbat, a "Shabbat Shabbaton", as it is written:

אַ֡ךְ בֶּעָשׂ֣וֹר לַחֹדֶשׁ֩ הַשְּׁבִיעִ֨י הַזֶּ֜ה י֧וֹם הַכִּפֻּרִ֣ים ה֗וּא ...
שַׁבַּ֨ת שַׁבָּת֥וֹן הוּא֙ לָכֶ֔ם וְעִנִּיתֶ֖ם אֶת־נַפְשֹׁתֵיכֶ֑ם בְּתִשְׁעָ֤ה לַחֹ֙דֶשׁ֙ בָּעֶ֔רֶב מֵעֶ֣רֶב עַד־עֶ֔רֶב תִּשְׁבְּת֖וּ שַׁבַּתְּכֶֽם׃

Mark, the tenth day of this seventh month is the Day of Atonement... It shall be a sabbath of complete rest for you, and you shall practice self-denial; on the ninth day of the month at evening, from evening to evening, you shall observe this your Sabbath.

As such, it would stand to reason that, as a kind of very special Shabbat in and of itself, there is no incompatibility between the two holidays. You might also want to check out this video by the OU, "Yom kippur is referred to as Shabbat Shabbaton, a double Shabbat. What about Yom Kippur makes it a “double Shabbos”? How does this manifest itself?

Shabbat Shabbaton – Thoughts on Shabbos & Yom Kippur."

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