Siman 659

In the morning they enter the beit knesset, and they do not arrive as early as on Shabbat. And they pray the Yom Tov prayer. And they recite piyut, each place according to its custom. And if the first day falls on Shabbat – they switch the piyut of the second day to the first, because in the first the liturgical poet speaks regarding the arba'ah minim, and in the second regarding the sukkah. And they complete Hallel, and afterward he says "Kaddish Shalem." And they take out two Sifrei Torah; in one they read five men in the parashah of "Shor O Kheshav," and the Maftir reads in the second Sefer Torah in the Musaf offerings in "Pinhas." And they read the Haftarah in Zechariah: "Behold, a day is coming," because the matter of Sukkot is mentioned there. And they pray Musaf, and they say in Kedushah "Adir Adirenu," and they perform Nesiat Kapayim, and the Kohanim say Birkat Kohanim, and the Shliach Tzibbur finishes "Sim Shalom."

And regarding the matter of the Hoshanot – there are differing customs. Rav Saadia Gaon wrote to say them after Hallel, and such is the custom of the Sephardim. And his reason is simple: since they are holding the lulav and the etrog in their hands – they should say the Hoshanot with them as well. And according to this, the shliach tzibbur does not say "Kaddish Shalem" after Hallel, but rather after the Hoshanot. But the Tur wrote to say the Hoshanot after Musaf, and such is the custom of Ashkenaz. And the reason: since the hakafot are a remembrance of the Mikdash, where they would circle the Altar, and in the Mikdash the circling was after the Musaf offerings – therefore we also do so (Bach). And there are those who say "Kaddish Shalem" after Musaf before the Hoshanot, and after the Hoshanot they also say Kaddish. But we do not practice this, rather after Musaf we say Hoshanot, and afterwards "Kaddish Shalem." And the matter of the Hoshanot – will be explained in the next siman with the help of Heaven.