Midrasch zu Bamidbar 29:1

8) Whence is derive three of three and three (i.e., that he blows three teruoth, each of which is accompanied by a plain blast before and a plain blast after)? From (Vayikra 25:9) "And you shall cause to pass a shofar of teruah," (Vayikra 23:14) "a remembrance of teruah, a holy calling," (Bamidbar 29:1) "A day of teruah shall there be for you."

9) And whence is it derived that what applies to Yovel (vis-à-vis shofar) applies to Rosh Hashanah, and that what applies to Rosh Hashanah applies to Yovel? From the identity (gezeirah shavah) of "in the seventh month" (stated in respect to each).

12 Rabbi Yochanan and Reish Lakish were sitting and having difficulties and saying, "We heave learned [regarding] Rosh Hashanah that comes out to be on Shabbat, we blow in the Temple, but not in the country. If it is the word of the Torah, [blowing the shofar] should override [Shabbat even with]in the borders; if it is not the word of the Torah (but merely rabbinic), it should not override [it] even in the Temple." While they were sitting and having difficulties, Kahana passed by. They said, "The author of the teaching came. Let us go and ask him." They went and asked him. He said to [them], "One Scripture (Leviticus 23:24) states, 'a memorial of blowing'; and another Scripture (Numbers 29:1) states, 'it shall be a day of blowing for you.' How is this? When it comes on Shabbat, it is 'a memorial of blowing.' We mention (remember) [it], but we do not blow." Rabbi Shimon ben Yochai said, "Let it be overridden in the Temple, as they know the time of the new moon (and will be blowing on the right day); but let it not be overridden in the country, as they do not know the time of the new moon." For Rabbi Shimon ben Yochai said, "'It shall be a day of blowing for you. And you shall make a fire-offering' (Numbers 29:1-2) - in the place that they are sacrificing." Rabbi Tachlifa [of] Caesarea said, "In all of the additional offerings, it is written, 'And you shall offer'; but here it is written, 'And you shall make a fire-offering.' How is this? The Holy One, blessed be He, said to Israel, 'My children, I will count it for you as if you were made in front of Me today; as if I created you [as] a new creature today.' This is [the understanding of] that which is written (Isaiah 66:22), 'For as the new heaven and the new earth.'"

… And He said to him ‘go away to the land of Moriah and bring him up there for a burnt offering’ (Bereshit 22:2) What is the land of Moriah? There is a whole bundle of Sages here, each saying their own answer. R’ Yanai says ‘what is Moriah? The place from which awe and fear (morah and yirah) go out to the world,’ “You are feared, O God, from Your Sanctuary…” (Tehillim 68:36) R’ Chiya the elder says ‘the land from which instruction (hora’ah) goes out to the world,’ as it says “…for out of Zion shall the Torah come forth…” (Yeshayahu 2:3) Another explanation: the land from which, in the future, the Holy One will teach that the wicked should descend to gehinnom, as it says “Like sheep, they are destined to the grave; death will devour them, and the upright will rule over them in the morning, and their form will outlast the grave…” From where? “…his dwelling place (zevul).” (Tehillim 49:15) Another explanation of the land of Moriah. R’ Yehoshua ben Levi said ‘the land from which the righteous teach (morim) and make decrees upon the Holy One which He does,’ as it says “…and David and the elders, covered with sackcloth, fell upon their faces. And David said to God, "Did I not say to count the people?…I beg that Your hand be against me and against my father's house, but not against Your people for a plague." (Divre HaYamim I 21:16-17) Another explanation of the land of Moriah. R’ Yehudah bar Padiiya said ‘Moriah - he said to Gd, where is it? He replied – to the land which I will show (mareh) you.’ Another explanation of Moriah. Avraham said to Gd, Master of the World! But am I fit to offer sacrifices? Am I a kohen? Let Shem the High Priest come and receive him from me. The Holy One replied to him – when you arrive at the place I will sanctify you and make you into a kohen. What is the meaning of Moriah? In exchange (temurah) for Shem. His replacement, as it says “He shall not exchange it or offer a substitute for it…” (Vayikra 27:10) Another explanation. What is Moriah? R’ Pinchas said ‘the land in which the master (maruto) of the world dwells,’ as it says “…and My eyes and My heart shall be there at all times.” (Melachim I 9:3) Another explanation. What is Moriah? R’ Shimon bar Yochai said ‘the land which was adorned opposite the altar above “…or cast down… (yaro yireh)” (Shemot 19:13) Another explanation. The land in which the incense is offered – “I will go to the mountain of myrrh (mor)…” (Shir HaShirim 4:6)

(Bamidbar 10:5) "And you shall sound a blast" ("Utekatem teruah"): A teruah (a rapid succession of three notes, tremolo) by itself, and tekiah (a long, sustained sound) by itself. You say, a tekiah by itself and a teruah by itself. But perhaps (in this context) tekiah and teruah are one and the same? (This cannot be, for) (7) "And when the people are to be gathered, you shall sound a tekiah and not a teruah" indicates that tekiah and teruah are distinct sounds. "utekatem teruah": We are hereby taught that a tekiah precedes a teruah. Whence is it derived that a teruah (also) follows a teruah? From (Ibid. 6) :"teruah yitkeu" ("a teruah shall they blow.") R. Yishmael the son of R. Yochanan b. Beroka says: This (derivation) is not needed. It is written (Ibid.) "And when you blow a second teruah." Let "second" not be written. Why is it written? To serve as a prototype (binyan av) for the tekiah, that it be second (i.e., after) the teruah — whence we learn that (in sum he blows) tekiah-teruah-tekiah. This tells me only of (the order in) the desert. Whence do I derive (the same for the order on) Rosh Hashanah? It is written "teruah" here and it is written "teruah" elsewhere (re Rosh Hashanah). Just as "teruah" here — tekiah-teruah-tekiah, so, "teruah" there — tekiah-teruah-tekiah. Three "teruoth" are written in respect to Rosh Hashanah: (Vayikra 23:24) "Shabbaton zichron teruah," (Ibid. 25:9) "Veha'avarta shofar teruah," (Bamidbar 29:1) "Yom teruah yihiyeh lachem" — two tekioth for each (teruah). In sum, on Rosh Hashanah there are three teruoth and six tekioth — two (sets of tekiah-teruah-tekiah) prescribed by the Torah, and one by the scribes: "Shabbaton zichron teruah," "veha'avarta shofar teruah" — by the Torah. "Yom teruah yihiyeh lachem" — This comes for its teaching (that the shofar is blown in the daytime ["yom"], and not at night). R. Shmuel b. Nachmani says in the name of R. Yonathan: One prescribed by the Torah; two prescribed by the scribes. "Shabbaton zichron teruah" — by the Torah. "veha'avarta shofar teruah" and "yom teruah yihiyeh lachem" — These come for their teachings, ("veha'avarta") to teach that there is an unbroken sound (tekiah) before the teruah, and "yom," to teach that the shofar is blown in the daytime.