Leviticus 23:24 reads,
Speak unto the children of Israel, saying, In the seventh month, in the first day of the month, shall ye have a sabbath, a memorial of blowing of trumpets, an holy convocation.
But the Bible gives us no clue as to what the purpose of this festival is, and which function it is supposed to serve. For example, Passover commemorates the Exodus and is the festival of the Abib (an agricultural spring festival when the Israelites planted their fields). The festival of Shavuoth (weeks) is a festival of the קציר--a time of reaping the crops. And the festival of Sukkoth (booths) serves a similar function, it celebrates the final harvest of the year. But what is the purpose of the festival of the trumpets?
Furthermore, 10 days later there is the "Day of Atonement" יום כיפורים (see verse 27-33). Are these festivals related in any way? Jews nowadays call the festival of the trumpets "Rosh Hashana" which means "New Year", and they regard this day as a Day of Judgement (God judges everyone for good or for bad for the upcoming year), a "Day of Remembrance" and a prelude to the Day of Atonement; they both serve a similar function, they involve praying all day (well not exactly the whole day but a nice part of it) and asking god for forgiveness, and regard them propitious times for atonement. But i'm wondering is this an invention of the Rabbis, or does it have any biblical basis? The text doesn't say anything about the function of this festival so it is reasonable to assume that this festival is somehow related to the Day of Atonement 10 days later, and that this festival may be regarded as a day of judgement as the Jews understood it for thousands of years. (But of course finding evidence for the New Year idea will be a harder task). But i'm not satisfied with that, since the text is silent and doesn't mention any of the aforementioned descriptions, and doesn't say why we should celebrate that day at all.
So what is going on here. I'm looking for any clarifications (on the function of this festival) on the text itself, or some theories that may shed some light on this obscure holiday. And of course extra-biblical evidence is always a bonus for me.