Passover is followed seven weeks later by the holiday of Shavu’ot [“Weeks”]. Although the months of the Jewish year are numbered from Nisan, the years are counted as beginning on the first day of Tishrei, the seventh month. The first of Tishrei is thus Rosh HaShanah, “the Beginning of the Year.” This holiday is marked by the sounding of the shofar, a ram’s horn – except when it coincides with the Sabbath.
Spiritual Heights of the Sabbath
בַּחֹדֶשׁ הַשְּׁבִיעִי בְּאֶחָד לַחֹדֶשׁ יִהְיֶה לָכֶם . . . זִכְרוֹן תְּרוּעָה וגו': (ויקרא כג:כד)
[G‑d told Moses,] “The first day of the seventh month [Tishrei] will be . . . a remembrance of the shofar blast.” Leviticus 23:24

The sounding of the shofar on the first day of the year elicits new Divine energy that will sustain all creation, spiritual and physical, for that year. However, when Rosh HaShanah coincides with the Sabbath, the shofar is not sounded; we only “remember” it by mentioning it in our prayers.

This is because blowing the shofar on the Sabbath is not only superfluous but pointless. G‑d’s sovereignty over us is the primary theme of Rosh HaShanah. Sounding the shofar at G‑d’s “coronation” is our declaration of our renewed selfless and voluntary submission to His sovereignty. The need for such a declaration, however, implies that we are conscious of ourselves as independent beings who must submit to G‑d intentionally. Such self-awareness characterizes our consciousness on weekdays. On the Sabbath, in contrast, when we are inherently absorbed in our heightened Divine consciousness, such a declaration is redundant.1