In the previous sections we dealt with the ingredients that go into making the menachos, and we saw that they are all built upon flour. Now we will deal with two additional ingredients that are added to most menachos: olive oil, and the frankincense placed on top. As we will see, there are menachos that require both, there are those that require only one of them, and there are those that have neither, but consist of dry flour alone. The Mishnah lists all the menachos and specifies what is included in each one.
The four categories the Mishnah lists:
"Yesh te'unos shemen u'levonah" - menachos that contain both olive oil and frankincense.
"Shemen v'lo levonah" - menachos that require olive oil alone.
"Levonah v'lo shemen" - menachos that require frankincense alone.
"Lo shemen v'lo levonah" - menachos that contain no olive oil and no frankincense at all.
"V'eilu te'unos shemen u'levonah" - the primary list:
Minchas ha'soles - the voluntary minchah that is neither fried nor baked, but raw flour as it is. Even though soles is the dry type of flour, this minchah is mixed with olive oil, and the frankincense is placed on top.
The machavas - the first of the two fried voluntary menachos, made on a flat pan.
The marcheshes - a minchah fried in a deep pan.
The challos - literally loaves, referring to a baked item that is not leavened and also not as thin as a wafer (similar to Sephardic matzah).
The rekikin - thin wafers (similar to Ashkenazic matzah).
These are the five types of the voluntary minchah, and olive oil is mixed into all of them. In the fried and baked menachos, water is also kneaded in for the purpose of making the dough, before the frying and baking, and finally the frankincense is placed on top.
The continuation of the list:
Minchas kohanim - this is not a type of minchah in its own right, but rather a kohen who brings one of the menachos already listed. Unlike a Yisrael who brings a minchah, there are no leftovers here to be eaten by a kohen; rather, the whole thing is burned. One might have thought that because of this the manner of its preparation would change as well, but the Mishnah teaches that its preparation is identical: oil and frankincense.
Minchas kohen mashiach - this refers to the minchas chavitin brought every day by the Kohen Gadol, half of the twelve loaves in the morning and half in the evening, as we learned in the previous chapter. Even though it has its own procedure, including a large amount of oil, the point is that it contains oil as well as frankincense.
Minchas goyim - a non-Jew who brings a minchah, it has the status of a voluntary offering like the minchah of a Yisrael, and he brings it as one of the five voluntary menachos, and it contains oil and frankincense. This is the opinion of Rabbi Yosi HaGelili. Rabbi Akiva disagrees and holds that non-Jews may bring specifically an olah alone, an animal offering that is entirely burned, and not a minchah - and according to his view there is no such thing as a minchah of non-Jews at all, and it would not belong in this Mishnah. The halachah is decided like Rabbi Akiva, as the Rambam rules, so the minchas goyim in our Mishnah follows Rabbi Yosi HaGelili and is not the halachah according to the Rambam.
Minchas nashim - a woman who brings a minchah, her law is the same as that of a man, and there is no reason to say otherwise. The Mishnah spells this out just as it set apart the kohanim on their own, and teaches that a woman's minchah too includes oil and frankincense.
Minchas ha'omer - the minchah brought on the second day of Pesach from the new grain, from the new barley crop. Although it differs somewhat, essentially it is barley flour mixed with olive oil, with the frankincense on top.
The one that requires oil but not frankincense:
The Mishnah continues: "Minchas nesachim te'unah shemen v'einah te'unah levonah". This is the only type of minchah that has oil but no frankincense. The minchas nesachim, as we have already explained, is the accompanying minchah that comes with every olah and every shelamim. The flour is mixed with oil, and their quantities depend on the type of animal being brought. In any case, it has oil and it has no frankincense.
The one that requires frankincense but not oil:
The third category is the lechem ha'panim: "Ta'un levonah v'eino ta'un shemen". The loaves that are placed on the Table in the Sanctuary from Shabbos to Shabbos have no oil mixed into their preparation, only flour and water. On top of them are placed the two bowls of frankincense - so they have frankincense and no olive oil at all.
"She'ein bahen lo shemen v'lo levonah" - Those that contain neither oil nor frankincense:
Shtei HaLechem - the two loaves of bread that are waved on Shavuos together with the two lambs of Atzeres. They are chametz, they are not brought on the altar, and they are eaten.
Minchas Chotei - the meal offering brought as part of the korban oleh v'yored, the sliding-scale sin offering, when the sinner cannot afford even two birds. For the transgressions listed in Vayikra chapter 5 he brings a minchas chotei in their place, and it is nothing but plain fine flour, dry flour, without oil and without frankincense.
Minchas Kena'os - the meal offering brought by the husband of a woman suspected of adultery, the sotah. He brings the offering and she holds it. This offering is made of barley flour, and it has neither olive oil nor frankincense placed upon it.
To summarize: This Mishnah lists all of the meal offerings according to four categories: those that require both oil and frankincense - the five voluntary meal offerings (fine flour, pan, deep pan, loaves and wafers), the meal offering of kohanim, the meal offering of the anointed kohen, the meal offering of gentiles, the meal offering of women and the omer offering; the one that requires oil alone - the meal offering that accompanies the libations; the one that requires frankincense alone - the show bread; and those that require neither oil nor frankincense - the two loaves, the meal offering of a sinner and the meal offering of jealousy. This is the complete list of all the meal offerings.