There is an ancient custom, dating back to Geonic times, to blow a hundred blasts. During the times of the Rishonim, most communities did not follow this practice. Rather, they blew thirty blasts before Musaf, and during Musaf itself, some blew an additional ten blasts, while others blew an additional thirty. During the time of the Aḥaronim, following Arizal’s prescription of mystical meditations (kavanot) for each of the hundred blasts, the custom of blowing a hundred blasts spread, and today it is almost universal.
The hundred blasts are arranged as follows. Before Musaf, we blow thirty blasts: three sets of tashrat, three sets of tashat, and three sets of tarat. During the repetition of the Musaf Amida, another thirty blasts are blown: one set each of tashrat, tashat, and tarat after each of Malkhuyot, Zikhronot, and Shofarot.
Regarding the silent Amida, there are different customs. Some blow the shofar during the silent Amida as they do during the repetition. By integrating the blasts and the prayers, both are more readily accepted. This is the custom of Sephardim and Ḥasidim. For those who follow this custom, the shofar-blower sets the pace of prayer, and worshippers do their best to pray at his pace so that they hear the blasts at the proper place, at the end of a berakha. To that end, the shofar-blower must pray at a steady pace. Anyone who finishes a berakha before he does should wait for him to blow the shofar before continuing, but those who wish to pray a bit faster or slower may do so. Those who choose to do this recite the paragraph “Ha-yom Harat Olam” following their conclusion of each berakha. Then, when the shofar is blown, even if they are in the middle of a different berakha, they stop to listen to the blasts and then continue with their prayers. (See Mateh Ephraim 592:13.)
Others do not blow during the silent Amida. (This is the custom of Ashkenazim.) They feel that the primary ordinance is to blow the shofar during the communal prayer, i.e., during the ḥazan’s repetition. Additionally, the need for the individual to coordinate the pace of his prayer with that of the shofar-blower is likely to distract the focus of the worshipper.
Those who blow the shofar during the silent Amida will have blown ninety blasts by the end of the ḥazan’s repetition; they blow the last ten during the full Kaddish. Those who do not blow during the silent Amida are still forty teki’ot short at the end of the ḥazan’s repetition. They blow thirty blasts after Aleinu and another ten following An’im Zemirot (MB 592:4).
The first two customs are problematic for, as we have seen, the teki’ot blown during Musaf are primary, and due to uncertainty, we must blow three sets of each of the three types of teru’a. Yet, according to the first custom, each type of teru’a is sounded only once, and, according to the second custom, only one type of teru’a is blown three times. Two possible arguments in support have been suggested. Rabbeinu Ḥananel explains, based on the view of R. Hai Gaon, that even nowadays one fulfills the Torah obligation with any type of teru’a. Rif and Rambam explain that once all three types of teru’ot were blown three times each before Musaf, fulfilling the Torah obligation, it is not necessary to burden the congregation by requiring them to hear them all again during Musaf (cited in Beit Yosef 590:2). The custom to blow a hundred blasts is cited by Arukh (s.v. “erev”) in the name of the Yerushalmi, which in turn is cited by Tosafot (Rosh Ha-shana 33b), Raavya, and Shibolei Ha-leket. Arizal bases his kavanot on this, and this is also the opinion of Shlah.
. Ashkenazic custom is not to blow the shofar during the silent Amida (MA; MB 592:1; Avnei Nezer OḤ §445). The reason is that since people do not pray at the same pace, it is distracting and difficult for them to try to adjust their pace to that of the ḥazan. According to the Geonic custom (of R. Sherira and R. Hai) that only seven berakhot are recited in the silent Amida, the shofar clearly was not blown then. Even among those who follow the majority opinion (of R. Yitzḥak ibn Gi’at, Tur, and SA 591:1) that nine berakhot are recited in the silent Amida, many do not blow during the silent Amida, as is explained in SA 592:1-2. This is also the position of Radbaz and Knesset Ha-gedola. However, among those who blow a hundred blasts (following Arukh), many do blow the shofar during the silent Amida. This is what Arizal and Shlah recommend, and this is the custom of Sephardim and Ḥasidim.