- Peninei Halakha
On the Shabbat preceding Rosh Ĥodesh (known as Shabbat Mevarkhim), it is customary to announce when Rosh Ĥodesh will take place and recite Birkat Ha-ĥodesh (“blessing the new month”), a prayer that God “renew this month for us and for all His people, the house of Israel, for good and blessing.” In a certain way, this prayer also commemorates the sanctification of the new moon by the beit din of old. Therefore, it is customary to announce the exact time at which the new moon will appear. This event is known as the molad, signifying the moon’s “rebirth.” This is also why we stand during the ceremony, as people used to stand before the beit din when it would perform the mitzva of sanctifying the new moon. The only month before which we do not recite Birkat Ha-ĥodesh is Tishrei. The reason for this is that everyone knows when Rosh Ĥodesh Tishrei is coming, as it is also the holiday of Rosh Ha-shana.
We announce the coming of the new month specifically on Shabbat because that is when the entire congregation is gathered in the synagogue, and everyone will hear when Rosh Ĥodesh is set to take place. Furthermore, all the days of the week receive blessing from Shabbat, and even the sanctity of Rosh Ĥodesh flows from the Shabbat that precedes it. Therefore, we bless the new month on that day. Because of this, on Shabbat Mevarkhim we already begin to feel the festiveness of the forthcoming Rosh Ĥodesh.
 mb 417:1 and Igrot Moshe, oĥ 1:142. Sefer Rosh Ĥodesh ch. 1 nn. 4-8 quotes Yerei’im, Shibolei Ha-leket, and Or Zaru’a, which state that we recite Birkat Ha-ĥodesh to let people know when Rosh Ĥodesh is going to take place. Raavya writes that it is in commemoration of the sanctification of the new moon. For this reason, some communities give the rabbi the honor of blessing the new moon (Sefer Rosh Ĥodesh 1:7). What I wrote concerning our omission of Birkat Ha-ĥodesh before Tishrei is found in sht 417:2.).
 This is why Ashkenazim refrain from reciting memorial prayers for the dead on Shabbat Mevarkhim (Rema 284:7, mb 284:17). They even omit the Av Ha-raĥamim prayer, which is said in memory of those killed in sanctification of God’s name. The only exceptions are the Shabbatot prior to Rosh Ĥodesh Iyar and Rosh Ĥodesh Sivan, because the holy martyrs were killed mainly during these two months. My teacher and master, Rav Zvi Yehuda Kook, would recite Av Ha-raĥamim even on an ordinary Shabbat Mevarkhim. He maintained that after the Holocaust it should be said on every Shabbat, just like it is said on Shabbat Mevarkhim before Rosh Ĥodesh Iyar and Rosh Ĥodesh Sivan.