Halakhah zu Schemot 19:13

After the conclusion of Ne'ilah, even if it is Shabbos, and Ne'ilah ended while it is still daytime, nevertheless, we say Avinu Malkeinu. We then say "Shema Yisrael" one time, Baruch sheim kevod malchuso le'olam va'ed, [Blessed is His name, whose glorious kingdom is forever and ever] is said three times; Hashem hu haElokim [Hashem is God] is said seven times, to honor the departure of the Divine Presence as it ascends to the spiritual heights upward of above the seven heavens. The Chazzan then sings the whole kaddish with a joyous melody. After that,²³In some places the shofar is sounded before the Kaddish is said. (Ramah 623:6) one Tekiah is sounded on the shofar, as a sign that the Shechinah has risen on high, as was done at the Giving of the Torah. For when the Shechinah ascended, it is said, "When the ram's horn is blown" etc. (Exodus 19:13), and it is also said, "God ascended amidst Teruah sounds." It is also a reminder of the blowing of the shofar on the Yom Kippur of the Jubilee Year. It is permitted to blow the shofar even though the stars have not yet appeared and it is still twilight, even on Shabbos. But when it is yet daytime, the shofar should not be blown. After the Tekiah everyone says three times,²⁴In many places it is said only once. (Mateh Ephraim) Leshanah haba'ah birushalayim [Next year [may we be] in Jerusalem].

At the end of the prayers of forgiveness²¹⁷Prayers of forgiveness, seliḥot, סליחות; see footnote 14. we say seven times, “He is the God,” (and one time the “שמע ישראל”), and three times the, “Blessed be His glorious kingdom forever and ever,”²¹⁸See the end of the footnote on the Ne'ilah Service, number 191. This is how the Ne'ilah Service ends. (see above section 61,²¹⁹In the Shulḥan Arukh, Oraḥ Ḥayyim, chapter 61, there are twenty-six paragraphs which contain the laws concerned with how one is to pronounce it and what is to be one's personal conviction when reciting the Shema prayer. (מנהגים).²²⁰Minhagim, מנהגים; see footnote 13.) and we blow the shofar, (תקיעה, שברים, תרועה, תקיעה).²²¹The shofar, שופר, is a ram's horn which has been prepared to use as a musical instrument. The word is mentioned sixty-nine times in the Bible as well as numerous times in talmudic and post-talmudic literature.
The shofar was used to proclaim significant events in Judaism. It proclaimed the Jubilee Year (Leviticus 25:9-11) every fiftieth year proclaiming freedom throughout the land. Its most noted use is on Rosh HaShanah which is also called yom teru'ah, "a day of blowing", (Numbers 29:1). It was also used to declare war (Judges 3:27) and to induce fear (Amos 3:6).
In Temple times the shofar was not exclusively a ram's horn. Any curved animal's horn from a sheep, goat, mountain goat, antelope, or a gazelle was possible. The use of the ram's horn became popular because of its association with the Akedah, the sacrifice of Isaac read on Rosh HaShanah when the shofar is sounded. A ram was substituted for Isaac in the biblical account (Genesis 22) which is read on the second day of Rosh HaShanah. The shofar may have carved designs on it as long as the mouthpiece is natural. It may not be painted. It may not have a hole.
The Bible only refers to two trumpet sounds, teki'ah and teru'ah (Numbers 10: 5-8) the Mishna (RH. 4:9) describes teki'ah as one long blast and teru'ah as three wavering crying blasts. It prescribes three sets of shofar sounds since the word teru'ah is mentioned three times in the Bible, (Leviticus 23:24, 25:9, and Numbers 29:1). In talmudic times there was a disagreement about what exactly the sounds of the shofar should be and Rabbi Ahbahu decided the issue by compromise. The shofar was to be sounded three times which included different notes of shevarim, which are broken sounds and teru'ah, nine staccato notes. The sounding is one set of teki'ah, shevarim - teru'ah, teki'ah, and two sets of the following: teki'ah, shevarim, teki'ah, and teki'ah, teru'ah, teki'ah. The teki'ah begins as a low note swelling to a higher one. The teru'ah is a series of staccato blasts and the shevarim alternates higher and lower notes. The concluding note of each of the two series is a teki'ah gedolah, a great, long blast, which derives its origin from Exodus 19:13, "When the ram's horn soundeth long, they shall come up to the mount."
The shofar used to be sounded on the second day of the month of Elul marking the beginning of the penitential season. Today it is sounded daily except for the last day of the month of Elul at the Morning Service until Rosh Ha-Shanah is over and it is sounded at the end of the Ne'ilah Service at the conclusion of Yom Kippur.
On Rosh HaShanah, Psalm 47 is recited seven times before the shofar is sounded. This is a reminder of the walls of Jericho being circled seven times before they fell to the sound of the shofar.
The shofar may only be sounded during the day. It is not sounded when Rosh HaShanah falls on the Sabbath, lest one violate the laws of the Sabbath by carrying the shofar into the synagogue. When the Temple was in existence the shofar was blown there on the Sabbath.
Throughout Jewish history the shofar was blown to announce a death, on fasts, at excommunications (see footnote 29), and at funerals. On Friday afternoons it was sounded six times to announce various work stopping times and the times to light the candles and usher in the Sabbath. Today it is used to inaugurate a new president in Israel.
According to the Sephardi rite the shofar is sounded at the end of the Ne'ilah Service as follows: teki'ah, one rising blast; shevarim, three blasts alternating high and low; teru'ah, seven staccato blasts; and teki'ah, one rising note.
Albert L. Lewis, E. J., v. 14, pp. 1442-47.
The following comment is given by Magen Avraham, (see footnote 33.): 623:4 - "And they blow (the shofar)": Even though they still have not "separated" (said Havdalah, see footnote 226) in the prayer (and it is still not actually night), nevertheless since (the blowing of the shofar is a matter of) wisdom (art and know-how) and not work, and the rabbis were not too strict about it, (did not prohibit it at this occasion), since the day has already passed (Tur, טור, see footnote 23). And even though he wrote that one should complete it (the shofar blowing) close to sunset, this should complete it (the shofar blowing) close to sunset, this means that the stars still have not come out (indicating nightfall), nevertheless this is twilight, and see the end of chapter 299, (in the Shulḥan Arukh, Oraḥ Ḥayyim).
Hagah: There are those who say that we only blow the shofar once (תקיעה),²²²The Ashkenazi rite states that at the end of the Ne'ilah Service only one long shofar blast is sounded, teki'ah gedolah, תקיעה גדולה. (מרדכ והגהות מיימוני סוף הלכות ואגור י״כ),²²³Mordekhai and Hagahot Maimuniyyot, the end of the Laws of Yom Kippur, and Agur, מרדכי והגהות מיימוניי סוף הלכות י״כ ואגור.
For Mordekhai, מרדכי; see footnote 24.
For Hagahot Maimuniyyot, הגהות מיימוני; see footnote 27.
Agur, אגור, is a halakhic work that deals basically with the subject matter found in Tur Oraḥ Ḥayyim and Yoreh De'ah, (see footnote 23). It was written by Jacob b. Judah Landau, a fifteenth century German talmudist. He was educated in Germany by his famous father Judah who died in 1464. Judah was a favorite pupil of Jacob Moellin (see footnote 8) and a relative of Jacob Weil (see footnote 27) who was the head of a large yeshivah and a well respected posek, an halakhic decision maker.
Jacob emigrated at some time in his life to Italy along with the great wave of Jewish emigration from Germany and in Pavia in 1460 he met Joseph Colon from whom he drew many rulings and quotes. While in Pavia he wrote Ḥazon a work introduced by the words "How could it be?" In 1487 Jacob went to Naples. He worked there as a proofreader for the new Hebrew Press established there, which published his work, Ha-Agur along with Ḥazon.
Ha-Agur is an anthology and a summation of German-Jewish scholarship on the laws contained in Oraḥ Ḥayyim and Yoreh De'ah down to Jacob's own time. He based himself on the Tur of Jacob b. Asher (see footnote 23). Jacob wanted to assemble all the data on a particular halakhah, (but omitted the arguments), lay down the halakhah, and then include any new rulings by people such as Israel Isserlein (see footnote 96), Jacob Weil (see footnote 27), Joseph Colon, and particularly his father Judah. The work is organized similar to the Tur and is distinguished by the interweaving of varied material from many different works. Landau, who was well versed in Kabbalah interlaced those theories together with the halakhic material as an aid to arriving at decisions. The work reveals a great deal of the teachings of the German scholars in the fourteenth and fifteenth centuries.
Israel Moses Ta-Shma, E. J., v. 10, p. 1393. and thus we do it in these lands, we sound the shofar after we say the Kaddish²²⁴Kaddish, קדיש; see footnote 177. after the Closing Service, but in a few places the custom is to blow the shofar before the Kaddish.