The Torah establishes the obligation in Bamidbar 29:1 — "a day of sounding the horn" — and Vayikra 23:23–25 describes the day as "commemorated with loud blasts," while the Rambam (Mishneh Torah, Shofar 1:1) derives from the parallel language of Yovel that this sounding must be specifically with a shofar; together these passages ground the biblical positive commandment that underlies the entire discussion.
The two verses themselves already hint at a tension: the Torah Temimah (Vayikra 23:24) cites a baraita that resolves the apparent contradiction between "zikaron teru'ah" (Vayikra 23:24) and "yom teru'ah" (Bamidbar 29:1) by teaching that the former describes Rosh Hashanah when it falls on Shabbat — a day of remembering the blast rather than sounding it — while the latter describes Rosh Hashanah on a weekday.
The Sifra already establishes the principle at its source: the Sifra (Behar 2:5) derives from the Yovel verses that while the Yom Kippur shofar of the Jubilee overrides Shabbat everywhere, the Rosh Hashanah shofar does not override Shabbat throughout the land — it may be sounded only in the Beit Din.
The Mishnah in Rosh Hashanah 32b–33b operationalizes this by listing the Shabbat-related restrictions: one may not travel beyond the Shabbat limit, clear rubble, climb a tree, ride an animal, or swim — nor cut the shofar — all in order to obtain or prepare a shofar on this day; and Rosh Hashanah 30a records that where sounding was permitted it was only in the presence of the Beit Din, with Rava raising a challenge from a baraita that the Rosh Hashanah shofar overrides Shabbat in the outlying areas.
Rashi (Rosh Hashanah 29b) clarifies the Mishnah's structure: the Temple sounded without restriction because rabbinic decrees of shevut do not apply there, while the provinces — including Jerusalem outside the Temple — did not sound; after the destruction, Rabban Yochanan ben Zakkai instituted sounding wherever there is a Sanhedrin, meaning a court of twenty-three, not merely three.
Tosafot (Rosh Hashanah 29b) probe why after the destruction Rabban Yochanan ben Zakkai was more lenient about the shofar than about the lulav, and conclude that because the shofar serves to raise Israel's remembrance before their Father in Heaven the Sages did not wish to suppress it entirely, so once they permitted it in one court they permitted it in every place that has a Beit Din.
The Jerusalem Talmud (Rosh Hashanah 4:2) adds a further distinction: Jerusalem in Temple times was more expansive than Yavneh in that any town which could see, hear, and reach Jerusalem was permitted to sound, whereas in Yavneh sounding was confined to the court alone.
The Tur (Orach Chayim 588) records a dispute about whether any Beit Din of three suffices for the post-destruction dispensation or whether only a court of twenty-three qualifies, noting that the Rif himself sounded in his own court but that all the commentators understood the institution to require a court of twenty-three; the Tur also notes that one may tell a minor who has not yet reached the age of chinuch to sound on Shabbat for practice purposes.
The Rambam (Mishneh Torah, Shofar 2:6–10) explains the legal architecture: sounding the shofar itself is forbidden only as a rabbinic shevut — a weekday-like act — and by rights a biblical positive commandment should override it; the reason it does not is a rabbinic decree lest someone carry the shofar four cubits in the public domain to find an expert, thereby incurring a capital prohibition, since everyone is obligated but not everyone is skilled; and the Shulchan Arukh HaRav (Orach Chayim 588:4–8) restates this reasoning explicitly: the Torah-level positive commandment does not override even this mild shevut because of that decree.
The Levush (Orach Chayim 588:5) synthesizes the ruling: sounding is not forbidden because it constitutes prohibited labor — it is a skill, not a melachah — but the Sages decreed against it outside a court of twenty-three, and the shofar itself becomes muktzeh so that even handling it is forbidden unless needed for its own use or to clear its place.
The Shulchan Arukh (Orach Chayim 588:5) states the final ruling plainly — when Rosh Hashanah falls on Shabbat the shofar is not sounded — and the Rema adds that it is even forbidden to handle the shofar unless needed for its own use or to free its space.
The Levush (Orach Chayim 584:4) notes the liturgical consequence: on a Shabbat Rosh Hashanah the circumcision that normally precedes the shofar blowing is instead followed by Ashrei and the return of the Torah scroll, since there is no sounding at all, with the full reasoning deferred to a later siman.
The Shem MiShmuel (Rosh Hashanah 5:10) offers a conceptual dimension: on Shabbat there is no need to arouse divine mercy through the shofar because Shabbat is itself a fixed and permanent state of divine love and will, making the shofar functionally unnecessary — though he notes in brackets that this does not itself create a prohibition, comparing it to women who are permitted to sound even though they are not obligated; it is the rabbinic shevut, not an inherent unfittingness, that suspends the mitzva, and the Shem MiShmuel (Rosh Hashanah 5671) elaborates that on Shabbat the external forces that the shofar is needed to repel withdraw of their own accord, so the primordial light can shine without the shofar's aid.