The month of Elul and the Ten Days of Repentance are particularly auspicious for repentance, as this is the period when God agreed to forgive the Jewish people for the sin of the Golden Calf. Forty days after the Torah was given, when Moshe had not yet descended from Mount Sinai, a group of sinners persuaded the people to make a golden calf as a replacement for God’s authority. At that moment, a great anger was kindled against Israel. It was serious enough that God said to Moshe, “Now, let Me be, that My anger may blaze forth against them and that I may destroy them, and make of you a great nation” (Shemot 32:10). Moshe prayed fervently and reminded God of the merits of the patriarchs and matriarchs, thus delaying the punishment. Then he descended the mountain, shattered the Tablets, and, together with the tribe of Levi, executed the sinners. He melted down and pulverized the calf, mixed the ash with water, and made all the Israelites drink from it. The water served as a litmus test, and those who had worshipped the calf died. Nevertheless, the threat of destruction still hovered over Israel. Displaying a spirit of self-sacrifice, Moshe stood before God and declared, “Now, if You will forgive their sin [well and good]; but if not, erase me from the record which You have written” (ibid. v. 32). Following this declaration, the decree was lifted. However, Israel was still disgraced and distant from God. It was as if they were no longer His children, His servants, or His special nation. Furthermore, the first Tablets lay in pieces.
On Rosh Ḥodesh Elul, Moshe once again ascended Mount Sinai to pray as Israel’s emissary, asking God to have mercy upon them and forgive them. On Yom Kippur, their repentance was fully accepted. Moshe descended to give the Jews the second set of Tablets and to inform them that they were forgiven. As an indication of their renewed closeness and specialness, God commanded them to erect a Mishkan (Tabernacle), through which the Shekhina would be revealed to them. Since the timing of important events is not accidental, we see that the forty days from Rosh Ḥodesh Elul until Yom Kippur are particularly auspicious for repentance.
This accords with the following midrash:
On Rosh Ḥodesh Elul, God said to Moshe, “Come up to Me on the mountain” (Shemot 24:12). The shofar was then blown in the camp, to let it be known that Moshe was ascending the mountain again and that Israel must not repeat their mistake. God ascended on that day through those same shofar blasts, as we read, “God ascends with a blast (teru’a); the Lord, with the sound of a shofar” (Tehilim 47:6). Therefore, the Sages ordained that the shofar be blown each year on Rosh Ḥodesh Elul. (Pirkei De-Rabbi Eliezer 46)
They chose to have the shofar serve as a wake-up call for the people, because it has the power to discourage people from sinning and to awaken the masses to repent (Tur and Beit Yosef, OḤ 581:1).
Accordingly, Jewish communities customarily blow the shofar during the month of Elul. Ashkenazic custom is to blow each day at the end of Shaḥarit. Sephardim, who recite Seliḥot all month, blow the shofar when they recite the concluding Kaddish of Seliḥot. Many Sephardim also blow the shofar when reciting the Thirteen Attributes of Mercy. Blowing the shofar in Elul is not obligatory, but it is proper for communities to try to do so. Nevertheless, an individual who did not hear the shofar blown does not need to search for someone to blow the shofar for him.