The fourth and last chapter of Masechet Rosh Hashanah focuses on the mitzvah of shofar and the special davening—malchiut, zichronot and shofarot—for this special day. These two mitzvoth were joined together with the blowing of shofar taking place during the recital of the amidah. In fact, as far as the Mishnah is concerned, the shofar was blown only during the amidah. Our practice of blowing before mussaf is either post-Talmudic—the Ba'al Hamaor, living in 12th-century Provence, claims that they were instituted for people who could not stay in shul until the end of mussaf—or is based on a passage in the first chapter of the masechet. "Why do we blow when we sit (i.e., before mussaf) and blow when we are standing (i.e., the amidah)? In order to confuse the Satan" (Rosh Hashanah 16a-b).
This additional blowing of the shofar, while not part of the original mitzvah, demonstrates our love of mitzvoth and quiets those who would argue that the Jewish people are a bunch of sinners who should be punished (Rashi 16b). Yet this additional blowing of the shofar was an outgrowth of the original aspect of shofar. As Rav Soloveitchik often discussed, and is evident from the Mishnah above, shofar is fundamentally a form of prayer. We first pray using words—yet words can never fully express our innermost thoughts and feelings. We thus move from words to sounds, to the cry of the shofar, a sound more powerful than any words could ever be. This inarticulate form of prayer was so central that we even prayed, i.e., blew shofar, before we prayed. Thus, the original 30 sounds of the shofar during mussaf became 60, and eventually 100 with the extra blasts of the shofar added at the end of davening. We introduce and conclude prayer with prayer.
Rosh Hashanah as a day of prayer may help offer further insight into the opening of the fourth chapter of the tractate, which begins: "Yom Tov of Rosh Hashanah that falls on a Shabbat, in the Temple they would blow [the shofar], but not in the country" (Rosh Hashanah 29b). In a relatively well-known Talmudic passage, the Gemara explains that it was a rabbinic decree to disallow shofar on Shabbat outside of the Temple: "Rabba said: all are obligated in the blowing of the shofar, but not all are expert in the blowing of the shofar—a decree that perhaps someone will carry it in his hand and go to an expert to learn, and will carry it four cubits" in a place where there is no eiruv, violating the laws of Shabbat. There is little point in crying out to G-d to answer our prayers if we have just flouted His will—even inadvertently. In the awe-inspiring atmosphere of the Temple, there was little fear that the kohanim would be careless regarding the law, and hence, rabbinic decrees needn't apply.
What is less well-known is that the Gemara initially claimed that the distinction between the Temple and the country was rooted in the Biblical text itself. "One verse says, 'a day of rest to remember the shofar' and one verse says, 'a day of blowing it shall be for you'? There is no contradiction, here (remembering) is when Yom Tov falls on Shabbat; and here (blowing) is when Yom Tov falls on a weekday" (29b). Yet the Babylonian Talmud rejects this answer. "Ravah said: if it is from the Torah, how could they blow in the Mikdash?" While rabbinic decrees may not apply in the Temple, biblical laws surely do.
However, the Jerusalem Talmud accepts this distinction. As Rav Soloveitchik explains, the Beit HaMikdash is "a house of prayer" and thus, its special status allows the blowing of the shofar, the ultimate prayer, even on Shabbat.
Yet if prayer is so integral to Rosh Hashanah, why should blowing be proscribed outside of the Temple on Shabbat? Yom teruah, a day of blowing, is defined by the Targum, the Aramaic translation of the Bible, as Yom Yebabah, a day of crying (Bamidbar 29:1). The shofar is more than prayer--it is the crying of prayer, like an infant crying for help. Such crying has no place on Shabbat. On Rosh Hashanah, we acknowledge G-d's creation of the world; but on Shabbat, we celebrate such creation.
Apparently, the cry of the shofar—when expressed in the Temple, the place where the Divine presence dwells—is a cry of joy. While a crying baby is a most bothersome nuisance at most times and in most places, when a baby cries out at home, it is a call for the parent to express their love of their child. May our Father in heaven hear our cries with joy, and may we merit to soon hear the sound of the great shofar of joy: "And it shall come to pass in that day, that a great shofar shall be blown; and they shall come that were lost in the land of Assyria, and they that were dispersed in the land of Egypt; and they shall worship the Lord in the holy mountain at Jerusalem" (Yishayahu 27:13).
 The use of the term Yom Tov in regard to Rosh Hashanah is most deliberate. While we do not recite Hallel on Rosh Hashanah, it is a day of joy celebrated with good food, nice clothes, and all the other trappings of a Yom Tov. While, as the Rambam (Megillah and Chanukah 3:6) notes, it is not a day of simcha yeteirah, excessive joy, it is a Yom Tov. Even the fact that we are judged, while adding an element of trepidation (one hopes), adds much joy. It is only because we are G-d's children that He cares enough to judge us.
 While Rashi and many others assume "the Temple" means just that, the Rambam (Shofar 2:8) explains that all of Jerusalem is regarded as the Temple.
 Perhaps it is noteworthy that in Parshat Emor, which gives the basic laws of the holidays, the Torah refers to Rosh Hashanah as zichron teruah, "a day to remember", but not necessarily to blow the shofar. It is in Parshat Pinchas, which details the sacrifices of the day brought in the Temple, that the Torah uses the expression yom teruah, "a day of (actual) blowing".