Rosh Hashana On Shabbos

 The Minchas Ani on Ha'azenu (translation from Gemini AI) says: Although regarding a good year, it must be analyzed whether Rosh Hashanah falling on Shabbat is a good sign. Regarding this, we find that the worst years and the best years both had Rosh Hashanah on Shabbat.

For the two years in which the Holy Temple was destroyed, Rosh Hashanah fell on Shabbat, as stated in the Jerusalem Talmud (Taanit, Chapter 4): the day the First Temple was destroyed was the 1st of Av, and it was the first day of the week (Sunday); and the Second Temple was also destroyed on the 9th of Av on the first day of the week, and both were at the conclusion of a Sabbatical year (Moztzei Shevi'it), as stated in the Babylonian Talmud.

According to this calculation, for the First Temple, if the 1st of Av was Sunday (Day 1), then the 1st of Tammuz was Saturday (Day 7) or Friday (Day 6); 1st of Sivan was Thursday (Day 5); 1st of Iyar was Wednesday/Tuesday (Days 3–4); 1st of Nisan was Monday (Day 2); 1st of Adar was Sunday/Saturday (Days 7–1); 1st of Shevat was Friday (Day 6); 1st of Tevet was Wednesday/Thursday (Days 4–5); 1st of Kislev was Tuesday (Day 3); 1st of Marcheshvan was Sunday/Monday (Days 1–2); and 1st of Tishrei was Saturday (Day 7).

Similarly, regarding the Second Temple, which was destroyed on the 9th of Av on Sunday, the 1st of Av was Saturday (Day 7). According to this calculation, Rosh Hashanah would have fallen on Friday (Day 6). However, this is impossible, as stated in Rosh Hashanah (page 20b), because if so, Yom Kippur would fall directly after Shabbat (on Sunday). Therefore, they must have made two months deficient (29 days) so that Rosh Hashanah would fall on Sunday (Day 1). (And we cannot resolve this by assuming it was a leap year, because the year after a Sabbatical year is not made into a leap year).

Conversely, regarding the best years, we find that the forgiveness for the sin of the Golden Calf occurred in a year where Rosh Hashanah fell on Shabbat, as did the inauguration of the Tabernacle (Mishkan)—since Israel left Egypt on a Thursday, as derived in Shabbat (Chapter 9)—as Tosafot wrote in Mekhilta / Kamma (page 82b; see there). Likewise, the year they entered the Land of Israel also had Rosh Hashanah on Shabbat, since Moses died on Shabbat, the 7th of Adar, meaning the 1st of Adar was on Sunday (see Tosafot in Menachot, page 30b, and the Rosh in Arvei Pesachim).

He explains this phenomenon that when RH falls on Shabbos and we don't have shofar, the Shabbos is our zechus. However, it can only be our zechus if we keep Shabbos properly, if not, then it can't be a merit for us. It is the degree of shmerus shabbos in general which justifies canceling the shofar in order to avoid chillul Shabbos, עיי"ש a mashal to explain this concept.