What do we learn from "ba'Chodesh"?
Rashi: B'Chidush ha'Levanah (when there is a new moon; this refers to Rosh Hashanah).
Radak: The first day of the month is called Chodesh, e.g. "Machar Chodesh" (Shmuel I, 20:18). Then the moon is new. The entire month is called Chodesh due to Chidush ha'Levanah.
Why does it say "Tik'u... Shofar"?
Radak: This is like Tik'u... b'Shofar, like the Torah commands. It seems that the reason for the Mitzvah is because the slavery stopped that day; Teru'ah is a sign of freeing slaves, just like Hashem commanded to blow the Shofar in Yovel, for a sign that [Ivri] slaves leave their masters' Reshus. On Rosh Hashanah, it recalls that the slavery stopped; it was the beginning of our freedom.
Why does it say "ba'Keseh"?
Rashi: It is the Mo'ed fixed for this. Also "l'Yom ha'Keseh Yavo Veiso" (Mishlei 7:20) is the fixed time.
Malbim: It is a day special for Mishpat.
What is "l'Yom Chagenu"?
Radak: It is one of the Chagim known to us.
Malbim: It is a day fixed to be a festival and a Mo'ed.
