a. The verse states (Psalms 81:4), “Blow the shofar at the moon's renewal, at the time appointed (bakeseh) for our festive day.” The word bakeseh also means “hidden.” From this our sages infer that the time of the holiday of Rosh Hashanah is meant to be shrouded in secrecy. This is also one of the reasons why we do not bless the month of Tishrei on the Shabbat beforehand, and why Rosh Chodesh is barely alluded to in the entire Rosh Hashanah services.

(One explanation for this secrecy is that we are trying to confuse and confound the Satan by not revealing the the date of Rosh Hashanah.)

b. Rosh Hashanah is the first and second days of Tishrei. But only the first day of Rosh Hashanah is Rosh Chodesh. The rabbis were concerned that if Rosh Chodesh prayers and practices were followed on the first day of Rosh Hashanah, people would erroneously assume that these customs and prayers are to be continued on the next day as well.