We are up to Menachos chapter 5, mishnah 6. In the previous mishnah we dealt with menachos that require hagashah but do not require tenufah, and here the mishnah comes to list the remaining combinations. The mishnah opens: "Eilu te'unin tenufah v'ein te'unin hagashah" - the following offerings require tenufah, waving, but do not require hagashah, meaning bringing the minchah until it touches the southwest corner of the mizbe'ach.
It is worth noting the change in wording: in the previous mishnah the term was "te'unos" in the feminine, and here "te'unin" in the masculine. The reason is that the previous mishnah listed menachos alone, since hagashah is unique to menachos; here, however, the mishnah lists categories of offerings that are not necessarily menachos, including animal offerings, and therefore it uses the masculine form.
These require tenufah but do not require hagashah:
"Log shemen shel metzora v'ashamo" - the metzora, at the conclusion of his purification process, brings several offerings, the central one being the asham, which is accompanied by a log of oil. Some of the oil is placed on the lobe of his right ear, on the thumb of his right hand and on the big toe of his right foot. The verse requires that the asham and the log that comes with it be waved before the slaughtering.
"V'habikkurim" - the first fruits of Eretz Yisrael from the seven species. The farmer brings them in a basket to the Beis HaMikdash, recites the verses, and the kohen takes hold of the basket together with him and waves it. The waving is done before the basket is set down before the mizbe'ach, and in the end the kohen eats the fruits. This is the opinion of Rabbi Eliezer ben Yaakov, and in practice the bikkurim are waved.
"V'eimurei shalmei yachid" - shelamim brought by a private individual. In fact all shelamim come from an individual, except for one exception that will be discussed below. The eimurim, such as the innards, are waved before they are burned on the mizbe'ach, and along with them the breast and the thigh - the right hind leg - which are given to the kohen as the priestly gifts. The order of placement is: the eimurim on top, beneath them the breast and the thigh, beneath them the hands of the owner who brings the shelamim, and beneath those the hands of the kohen, and they all wave together. The kohen and the owner wave in the manner of all wavings, in the six directions, like the shaking of the lulav.
"Ushtei halechem ushnei kivsei atzeres" - the two loaves of bread that accompany the two sheep offered on Shavuos. These too are shelamim (communal shelamim), and the two loaves and the two sheep are all waved together before the sheep are slaughtered. We will return to discuss the waving that is done after the slaughtering.
The mishnah continues: "Echad anashim v'echad nashim" - the waving is performed whether the one bringing the shelamim is a man or a woman. "B'Yisrael aval lo b'acheirim" - however, only the Yisrael, the male Jew, is the one whose hands are placed upon the hands of the kohen and support the eimurim and the breast and the thigh together with him. A woman, and likewise a non-Jew who brings shelamim according to the view of the mishnah here (even though this is not the halachah), do not take part in the waving, and the kohen waves alone.
Most of the offerings listed here are not menachos, and the only minchah on the list is the two loaves that come with the sheep of Shavuos. The mishnah therefore focuses on them, since it is with regard to them that the matter is relevant to Maseches Menachos.
"Keitzad hu oseh":
How did the kohen perform the waving of the two loaves on Shavuos? "Nosen shtei halechem al gabei shnei kevasim" - according to the wording of the verse the two loaves are placed on top, and halachically the meaning is that they are placed alongside the two sheep. "Umaniach shtei yadav milmatan" - the hands of the kohen are placed beneath the two sheep and the two loaves, and apparently his forearms as well, since the young sheep are not large in size.
"Molich u'meivi, ma'aleh u'morid" - the plain meaning is that he moves them back and forth and likewise up and down, but according to most commentators it is done in the manner of the shaking of the lulav: his face toward the east, and he waves before him to the east, to his right to the south, behind him to the west, to his left to the north, and upward and downward. "Shene'emar: asher hunaf va'asher huram".
Those that require both tenufah and hagashah:
The minchas ha'omer and the minchas kena'os require both tenufah and hagashah. The minchas ha'omer is the barley offering brought on the second day of Pesach, and the minchas kena'os is the minchah that the husband of the suspected woman, the sotah, brings, and she carries it. Both of these require tenufah, as stated explicitly in the verses, and also hagashah like all menachos, to the corner at the southwest of the mizbe'ach.
Those that require neither tenufah nor hagashah:
The lechem hapanim and the minchas nesachim require neither tenufah, which is waving, nor hagashah, which is bringing the offering up against the altar. "Lechem hapanim" - the twelve loaves of the showbread that rest on the Table and are eaten every Shabbos. It is true that two bowls of frankincense are brought together with them, but they have no kometz and no hagashah.
"U'minchas nesachim" - the accompanying meal offerings that come with every olah and with every shelamim, and the wine along with them. The meal offering is made of fine flour, oil and frankincense, and even so it does not require hagashah; rather, the whole of it goes up directly onto the altar without any kemitzah.