The foundation for the shofar blasts lies in three Torah passages that each use the word תְּרוּעָה in connection with the seventh month: Vayikra 23:24 prescribes a "memorial of blasts," while the Gemara (Rosh Hashanah 34a) derives from this verse alongside Bamidbar 29:1 and Vayikra 25:9 that the Torah mandates three teruot, each preceded and followed by a tekiah — yielding the basic unit of nine blasts.
Because the precise character of the Torah's terua is uncertain — whether it resembles the wail called shevarim, the staccato notes called terua, or both combined — the Shulchan Arukh (Orach Chayim 590:1) rules that one must sound the sequence תשר"ת three times, תש"ת three times, and תר"ת three times, to cover every possibility, a position elaborated in parallel by the Tur (Orach Chayim 590), the Shulchan Arukh HaRav (Orach Chayim 590), and Tosafot (Rosh Hashanah 33b).
The Beit Yosef (Orach Chayim 590) explains the Gemara's resolution that each set must be blown as a complete, independent unit to address the doubt, and considers why it is insufficient simply to combine sequences — affirming that the full tripling is required.
The Arukh HaShulchan (Orach Chaim 590:2) makes explicit that three teruot entail three tekiot before them and three after, producing nine base sounds, and then raises directly the question of why we therefore blow thirty sounds three times over — pointing toward the total of one hundred blasts as the operative practice.
The Kabbalistic rationale for that total of one hundred is articulated by the Pri Etz Chaim (Sha'ar HaShofar 1), which states that the sound emerging from the shofar corresponds to the secret of the divine name of numerical value sixty-three together with its expansion (הב"ל), and that together these sum to one hundred — the precise number of blasts we sound.
רבינו בחיי, כד הקמח ראש השנה א ב situates the blasts within a broader theological framework, explaining that the Sages instituted ten Kingship verses, ten Remembrance verses, and ten Shofar verses for this day, and that the tekiah itself corresponds to the attribute of mercy while the terua corresponds to the attribute of judgment — so that the shofar service as a whole expresses the interplay of those two divine attributes under which the world was created.
The Gemara itself provides the theological purpose behind the entire shofar service: the Gemara (Rosh Hashanah 34b) records Rabba's teaching that God commands Israel to recite Kingship, Remembrances, and Shofar verses before Him on Rosh HaShana — so that they crown Him as King, so that their remembrance rises before Him for good, and the instrument through which all this is accomplished is the shofar.
