The Mishnah is ordered and very structured. That being the case, the beginning of the third perek of Rosh Hashanah is surprising. The second perek completes the discussion of kiddush ha'chodesh -- how Rosh Chodesh was determined and publicised. The third perek begins discussing the laws of the shofar followed by the mitzvah of blowing the shofar on Rosh Hashanah. The first Mishnah however appears to be a hangover from the previous perek. It discusses the process of kidush hachodesh when beit din itself saw the new moon. We shall try to understand why this Mishnah is placed here. This is the question posed by the Melechet Shlomo.
The Tifferet Yisrael explains that the Mishnah is in this perek because it is necessary for the Rosh Chodesh that is Rosh Hashanah. He cites Rashi (30b) who explains that during the time when Rosh Chodesh was determined by witness testimony, they would already treat the night after the twenty-ninth of Elul as if it was Rosh Hashanah in case witnesses came the following day. In other words, the tefillot would be those of Rosh Hashanah and they would blow shofar. If we learn the Mishnah assuming that it is referring to the beginning of Tishrei we gain deeper understand. The Mishnah first discusses the case where everyone saw the new moon but beit din did not have a chance to say "mekudash" (declaring the thirtieth day as Rosh Chodesh) before nightfall. The Mishnah teaches that the previous month is considered a thirty-day month (meuberet) and Rosh Chodesh is pushed off until the next day. If we are however dealing with Rosh Chodesh Tishrei, one might think that since everyone is already treating that day as Rosh Hashanah, it should be considered publicized enough such that that day should be Rosh Chodesh (and the previous month a twenty-nine-day month). The Mishnah is therefore needed to teach that even in that case, Elul would be meuberet.
It would seem from the Tifferet Yisrael, that we learn that beit din's declaration of "mekudash mekudash" is critical, and without it, the previous month would be meuberet. That sounds similar to the Bartenura, who explains that the law in our Mishnah was necessary, since one might have thought that since everyone saw the new moon, it is significantly publicized that that days is Rosh Chodesh and that their declaration is not necessary.
Based on the above, one would find the Ramban surprising (Sefer HaMitzvot 157). He explains that the declaration of "mekudash, mekudash" is not critical. What is critical is that the Beit Din come to an agreement whether the day should be Rosh Chodesh.
Based on the Ramban's position, we must understand our Mishnah different. The reason why the Mishnah rules that if they did not declare "mekudash, mekudsha" the previous month is meuberet is not because the declaration itself is vital. Instead, the Mishnah was using the declaration in this case as a marker of whether the Beit Din had reached an agreement. Consequently, the Mishnah is teaching that even though it may appear to everyone that the day should be Rosh Chodesh, without the agreement of Beit Din it is not.
With this understanding, the explanation of the Tifferet Yisrael is even sharper. In other words, despite the fact that everyone saw the new moon and the day is already being treated like Rosh Hashanah, that is still not enough for the day to be considered Rosh Chodesh, without Beit Din "calling" it so.
The Ahavat Eitan however provides two other suggestions for why this Mishnah appears in this perek. The first is that the laws of a shofar are very much dependent on kiddush ha'chodesh. That is because if the months falls out such that Rosh HaShannah coincides with Shabbat the shofar was not blow. Alternatively, he explains that they would blow shofar as part of kidush ha'chodesh []{dir="rtl"} (Niddah 38a). Consequently, what qualifies as a shofar is not only important for Rosh Hashanah, but also for the very subject matter of the first Mishnah. Accordingly this Mishnah is a suitable bridge between the two halves of the masechet.
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