• Offerings which require תנופה

The next Mishnah lists the offerings which require תנופה but not הגשה: the לוג שמן of a metzora, and his אשם, ביכורים according to Rebbe Eliezer ben Yaakov, the אימורים and חזה ושוק of a private shelamim, and the שתי הלחם with the שני כבשים of Shavuos. The מנחת העומר and מנחות קנאות (sotah’s minchah) require both הגשה and תנופה. The לחם הפנים and מנחת נסכים (brought with a korban) do not require either. Rebbe Shimon says: ג' מינין טעונין ג' מצות – there are three types of offerings requiring between them three different mitzvos, שתים בכל אחת ואחת ושלישית אין בהן – but there are only two of the three mitzvos for each one, and not the third: (1) A private שלמים requires סמיכה while it is alive, and תנופה after it is shechted, but no תנופה while it is alive. (2) The שלמי ציבור (of Shavuos) require תנופה while they are alive and after they are shechted, but do not require סמיכה. (3) The אשם of a מצורע requires סמיכה and תנופה while it is alive, but does not require תנופה after shechitah.

• Opinion that ביכורים require תנופה

The Mishnah stated that Rebbe Eliezar ben Yaakov holds that ביכורים require תנופה. He derives this from the passuk: ולקח הכהן הטנא מידך – and the Kohen shall take the basket (of ביכורים) from your hand, and darshens a gezeirah shavah (יד יד) from שלמים to require תנופה by ביכורים. He also derives: מה כאן כהן אף להלן כהן – Just as here, the Kohen waves the bikkurim, there too the Kohen waves the shelamim portions. ומה להלן בעלים אף כאן בעלים – And just as there, the owner waves the shelamim portions, so too here, the owner waves the ביכורים. The Baraisa explains how they wave it together: כהן מניח ידו תחת ידי בעלים ומניף – the Kohen places his hands under the owner’s hands and waves it together with him. The Gemara wonders why our Mishnah did not mention that Rebbe Yehudah also holds that ביכורים require תנופה, which he darshens from the superfluous word "והנחתו" – and you shall place it. Rava explains: הואיל ופתח בו הכתוב תחלה – because the passuk opened first with it, i.e., Rebbe Eliezer ben Yaakov’s derashah appears earlier in the פרשה. Rav Nachman bar Yitzchak answers: הואיל ורב גבריה – because [Rebbe Eliezer ben Yaakov’s] power in Torah wisdom is great.

• תנופה of korbanos of idolators and women is performed alone by the Kohen 

A Baraisa darshens the phrase "בני ישראל" written before the passuk of תנופה to teach: בני ישראל מניפין – the sons of Yisroel perform the waving, ואין העובדי כוכבים מניפין – but idolators do not perform the waving. Similarly, בני ישראל מניפין – the (male) sons of Yisroel perform the waving, ואין הנשים מניפות – but women do not perform the waving. Rebbe Yose says that since the Torah differentiated between the korbanos of male Jews and the korbanos of idolators and women regarding סמיכה (i.e., that their korbanos do not require סמיכה at all), one would think the same differentiation would apply to תנופה, and their korbanos would not require any תנופה. However, they cannot truly be compared, because סמיכה is performed only by the owner, so once idolators and women were excluded from סמיכה, their korbanos are entirely excluded from סמיכה. In contrast, תנופה is performed by the Kohen, who may also act as the שליח of idolators and women. Therefore, we darshen "בני ישראל" to exclude idolators and women from performing the תנופה, and it is performed by the Kohen alone.

Siman – Saw. While the man put down the saw he used to cut off the חזה ושוק from a שלמים in order to pick them up and do תנופה, and another man who used a saw to cut reeds to make a basket for ביכורים put his down in order to doתנופה together with the כהן, a goy was told by the Kohen that even if he would wave his saw at them all day long they still can’t allow him to do תנופה, and theכהן will do it alone.