Full Or Abridged?
‘One Is Obligated To Recite Hallel’
We recite Hallel on every Yom Tov, on Rosh Chodesh, and on Chanukah. Let us examine the nature of Hallel and the reason for saying it. On Yom Tov we say the full Hallel, whereas on Rosh Chodesh we say an abridged Hallel, omitting two chapters. The Gemara (Arachin 10b) explains that the halacha of saying Hallel is derived from Yeshayahu 30:29: “The song will be yours as on the night of the sanctification of the chag” – indicating that one should praise Hashem on days sanctified as festivals.
On Rosh Chodesh we say an abridged Hallel to emphasize that saying Hallel on Rosh Chodesh is a custom and not a din (Mishnah Berurah 422:2). The Sephardic custom is not to say a berachah on an abridged Hallel (Shulchan Aruch, Orach Chayim 422:2).
The Difference Between Pesach And Sukkos
On Sukkos we say the full Hallel every day whereas on Pesach we say the full Hallel only on the first two days. The Gemara (Arachin 10a-b) explains that the days of Sukkos differ from one another since each day a different number of sacrifices is offered in the Holy Temple. Therefore, each day is like a Yom Tov unto itself meriting its own recital of Hallel. On Pesach, however, the same number of sacrifices is offered each day. There is thus no reason to recite Hallel every day.
‘At Your Enemy’s Downfall, Do Not Rejoice’
The Beth Yosef (Orach Chayim 490:4) mentions a completely different reason for not reciting Hallel every day of Pesach. He cites Shibbolei HaLeket, which quotes a Midrash stating that we only say full Hallel on the first [two days] of Pesach because the Egyptians drowned in the sea and we are told: “At your enemy’s downfall, do not rejoice” (Mishlei 24:17).
The Maharsha (Berachos 9b) wonders why the Beth Yosef ignores the Gemara about the different number of sacrifices offered each day of Sukkos (as opposed to Pesach). Indeed, the Beth Yosef mentions this Gemara when discussing the laws of Sukkos (Orach Chayim 844). Why, then, does he cite a Midrash and ignore the Gemara when discussing the laws of Pesach?
Two Reasons For Saying Hallel
The Yeshuos Yaakov (on Shulchan Aruch 490, ibid.) explains that there are two reasons for saying Hallel: 1) because of the Yom Tov and 2) because a miracle occurred that day.
There are holidays that do not commemorate a miracle – Shavuos and Sukkos – and saying Hallel is required only because they are Yamim Tovim. And then there are days that commemorate a miracle but which aren’t proper Yamim Tovim – such as Chanukah.
The seventh day of Pesach seems to be an anomaly. A miracle occurred on this day and yet we don’t say the full Hallel. The Gemara in Arachin only explains why we say full Hallel on every day of Sukkos. It doesn’t explain why we don’t say full Hallel on the seventh day of Pesach. That’s why, when discussing the laws of Pesach, the Beth Yosef had to cite the Midrash about not rejoicing at one’s enemies’ downfall.