זכרון תרועה - The memory of a Teruah

Speak to the Israelite people thus: In the seventh month, on the first day of the month, you shall observe complete rest, a sacred occasion commemorated with loud blasts.

MISHNA: With regard to the Festival day of Rosh HaShana that occurs on Shabbat, in the Temple they would sound the shofar as usual. However, they would not sound it in the rest of the country outside the Temple. After the Temple was destroyed, Rabban Yoḥanan ben Zakkai instituted that the people should sound the shofar on Shabbat in every place where there is a court of twenty-three judges. ...

GEMARA: The Gemara asks: From where are these matters; from where is it derived that the shofar is not sounded on Shabbat? Rabbi Levi bar Laḥma said that Rabbi Ḥama bar Ḥanina said: One verse says, with regard to Rosh HaShana: “A solemn rest, a memorial of blasts” (Leviticus 23:24), which indicates that one should merely remember the shofar without actually sounding it. And another verse says: “It is a day of blowing for you” (Numbers 29:1), i.e., a day on which one must actually sound the shofar. This apparent contradiction is not difficult: Here, the verse in which the shofar is only being remembered but not sounded, is referring to a Festival that occurs on Shabbat; there, the verse in which the shofar is actually sounded, is referring to a Festival that occurs on a weekday.

זכרון תרועה, “a remembrance with the blast of the Teruah.” [...] A Midrashic approach based on Vayikra Rabbah 29,7 understands the verse in terms of the patriarchs, suggesting that G’d is telling us that if we want to be found deserving when examined by G’d, our relationship to our patriarchs is the key. The words באחד לחודש is reminiscent of Avraham who was one of a kind as we know from Ezekiel 33,24 אחד היה אברהם, “Avraham was only one man.” The words זכרון תרועה are a reference to Yitzchak, whereas the words מקרא קודש, “a holy convocation,” are a reference to Yaakov. What the Midrash means is that the shofar blasts of Rosh Hashanah, i.e. the blasts of the teruah, are an allusion to certain attributes. Just as the attribute of fear pervading the celestial regions is surrounded by the attribute of Mercy, so our teruah sounds which are fear-inspiring are preceded and followed by the sounds known as tekiah, to parallel what occurs in heaven. Were this not so the earth would collapse completely as soon as G’d would commence sitting in judgment of mankind. If we would only blow the תרועה sounds this would be heresy of the first order, [i.e. as if we denied the presence of the attribute of Mercy. Ed.] Keeping this in mind we can understand that what is written here means that the Day of Judgment is the Day of the Teruah which is surrounded by the attribute of Mercy, called here זכרון. Having understood this it follows that the meaning of the words זכרון תרועה is equivalent to שופר תרועה and יום תרועה. (Compare 25,9 and Numbers 29,1 respectively).