A number of curious points in the discussion of shaking the lulav (the naanuim) in the Gemara, Rishonim and Poskim encourage taking a closer look at the issue and  point to a complex picture of the naanuim. 

3 Questions
1.  Common practice is to shake the lulav immediately following the brakha over the 4 minim -- before Hallel.  This seems to go against an explicit Mishna (Sukka 37b) that asks when to shake the lulav but answers during “Hodu Lashem ki tov” and “Ana Hashem hoshia na” in Hallel -- but not, “After the brakha” (like we do).  Tosafot and others bring a number of sources pointing to another set of naanuim preceding Hallel.  This gives textual support for our custom, but begs the question, “Why are there naanuim both inside and outside of Hallel?”

2. Common practice is to move the lulav in 6 directions both before and during Hallel.  This is the way most Rishonim rule.  However, the Raavia (quoted in the Rosh Sukka 3:26) rules that we only move the lulav in 6 directions before Hallel, but that during Hallel we shake the lulav while holding it in one place.  Why the distinction?

3.  Rava in the Gemara (Sukka 37b) compares shaking a lulav to waving a sacrifice (tenufa).  This model does not seem to be followed completely.  A sacrifice is only waved, moving it to and fro, up and down. The lulav’s is also shaken, according to many (Ritva, R’ah, Ran and others).  They hold that the lulav is moved (for instance, to the east) and then also shaken so the leaves rustle.  Why stray from the sacrificial model?

Two Sources
At least two acharonim -- Hagaon Rav Moshe Soloveitchik, zt”l (quoted in Reshimot Shiurim, Rav Tzvi Reichman’s presentation of Hagaon Rav Yosef Soloveitchik zt”l’s shiurim on Sukka) and Hagaon Mordechai Kalina zt”l (in his correspondence wtih the Rogotchover Gaon zt”l, Michtevei Torah) -- assume that the naanuim are a complex phenomenon, drawing from more than one halakhic source. 

1. Part of the Mitzva of the 4 Minim
The most basic nature of the naanuim is, in line with the Tosafot’s approach, part of the mitzva of taking the lulav.  A number of gemaras quoted as support for pre-Hallel naanuim point to this:

A. A child should start the mitzva of lulav when he knows how to shake it (Sukka 42b) -- chinuch on the mitzva of  lulav is contingent on ability to do naanuim;

B. The Gemara refers to the naanuim as the essential act done with the lulav on Berakhot 30a. For  one who must leave very early in the morning, says the gemara,  we bring a lulav and he shakes it, a shofar and he blows it, a megilla and he reads it.  Shaking the lulav is tantamount to blowing the shofar or reading the megilla.

C. The size of the lulav is 4 handbreadths (tefachim), not three like the aravot and hadasim, so naanuim can be done with the extra tefach of the lulav (Sukka 32b).  If a lulav lacks the physical ability to do naanuim it is invalid (Even though the mitzva can be fulfilled without doing the naanuim, the ability to do them is essential).

Shaking the lulav is, says the Shibulei Haleket (366), a rabbinic level of taking the lulav.  On a biblical level we take the lulav, and the Sages added shaking it.  He compares the relationship between netilat lulav and the naanuim to destroying the chametz (biur),  and checking for it (bedika).  Just like bedikat chametz is a rabbinical level of the mitzva, so are the naanuim.

2. Naanuim During Hallel
Shaking the lulav in Hallel, says the Tosafot, is based on the verse, “All of the trees of the forest  will then sing out before G-d” (Divrei Hayamim 16:33).  The trees, represented by the lulav, etrog, hadasim and aravot, join us in our Hallel.  Shaking at those particular points in Hallel, Hodu and at Ana Hashem Hoshia (and not Ana Hashem Hatzlicha) is based on the verses immediately following the above one:  “Hodu Lashem Ki Tov” (34) and “V’imru Hoshieinu LaHashem Elokeinu” (35).  The second side of the naanuim is as a form of prayer. 

Through shaking the lulav we express two different types of prayer -- praise during Hodu and request during Ana Hashem.  This is reflected in the two aggadot explaining waving and shaking on Sukka 37b.  The first, “Rabbi Yochanan says, We wave back and forth to He who the four directions are His and we wave up and down to He who the heavens and the earth are His,” relates to the naanuim as praise.  The second, “In the West (Israel, west of Bavel) they learned, Rav Chama son of Ukva quoted Rabbi Yosi son of Chanina who said that we wave back and forth to counter dangerous winds (from the four directions) and up and down against dangerous dews,”  relates to the naanuim as request. 

The Duality of the Naanuim
This duality of the naanuim -- both 1. a rabbinic level of the mitzva of taking the lulav and 2. a physical form of prayer joined by the trees of the 4 species -- explains the curious points we mentioned above. 

1.  The Mishna was referring to the most powerful prayer aspect of the naanuim, as it appears during Hallel.  Tosafot brought out the additional side -- that they are part of the mitzva of lulav.

2.  The Raavia took the duality a step further and saw the naanuim in Hallel as physically reflecting their different role.  The essential naanuim, he holds, are done immediately after the brakha.  There the rabbinic level of the mitzva elevates the four species to the level of a sacrifice and demands waving.  During Hallel we shake the lulav to counter the forces of evil and do not require moving the lulav in the four directions and up and down.

3.  Shaking the leaves of the lulav, not only moving the lulav as a whole, stems from the prayer aspect of the naanuim.  How can the lulav sing if its leaves do not rustle?  That additional element, “All of the trees of the forest  will then sing out before G-d,” does not apply to a waving sacrifice, so there is no additional shaking.  The lulav’s leaves, though, must  also make a noise, a group of Rishonim say.

Rav Moshe Soloveitchik zt”l: Rambam vs. Tosafot
Rav Moshe Soloveitchik zt”l saw the duality of the naanuim as a point of contention between the Rambam and Tosafot.  The Rambam does not mention shaking the lulav before Hallel, only during it, yet describes the naanuim when presenting the mitzva of taking the 4 minim.  According to him, shaking the lulav is the method of fulfilling the mitzva of taking the lulav, but it is done in the context of Hallel.  The Tosafot differ and see the naanuim done right after the brakha as part of the mitzva of lulav and those during Hallel as a separate act, prayer along with the trees, as developed above.  Rav Moshe suggests that the requirement of owning the lulav on the first day does not apply to the naanuim of Hallel according to the Tosafot, only to those before it, because they are a separate mitzva of prayer without any ownership requirement.  According to the Rambam, though, since the essential mitzva of lulav is fulfilled through the naanuim of Hallel, ownership is still a requirement.

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