פירוש על מנחות 5:3

מנחת סולת – a person who vows a mere free-will meal-offering, brings fine flour and oil and frankincense and mixes it and takes a handful as it is prior to baking it. And for which it is written (Leviticus 2:1): “he shall pour oil upon it, lay frankincense on it,” all of these others we derive from the meal-offering of fine flour where it is written regarding the meal-offering of fine flour (Leviticus 2:1): “when a person,” that implies that all meal-offerings of an individual require oil and frankincense.

Some [minhahs] require oil and frankincense, some require oil but not frankincense, some frankincense but not oil, and some neither oil nor frankincense.
These require oil and frankincense: the minhah of fine flour, that prepared on a griddle, that prepared in a pan, the cakes and the wafers, the minhah of the priests, the minhah of the anointed high priest, the minhah of a gentile, the minhah of women, and the minhah of the omer.
The minhah offered with the drink-offerings requires oil but not frankincense.
The showbread requires frankincense but not oil.
The two loaves, the sinner's minhah and the minhah of jealousy require neither oil nor frankincense.
This mishnah teaches which minhah requires oil and frankincense, which requires one of the two, and which require neither.
Section one: As the mishnah typically loves to note, all of the possible combinations can actually occur. I shall give references for each of these types of minhahs.
Section two:
The minhah of fine flour; that prepared on a griddle; that prepared in a pan: Leviticus 2:1.
The cakes and the wafers: Leviticus 2:4.
The minhah of the priests: A priest who volunteers to bring one of these minhahs.
The minhah of the anointed high priest: See above 4:5.
The minhah of a gentile; the minhah of women: who volunteered to bring one of these minhahs.
And the minhah of the omer: Leviticus 2:14-15.
Section three: Numbers 15:4ff.
Section four: Leviticus 24:7.
Section five: The two loaves are those brought on Shavuot. The sinner’s minhah is referred to in Leviticus 5:11 and the minhah of jealousy is that brought by the suspected adultress (the Sotah (Numbers 5:15). In both cases the Torah specifically states not to put frankincense or oil on them.

והחלות והרקיקין – a meal-offering of grain that is baked in an oven is called, the loaves [of bread] and the wafers. For if he requires loaves [of bread], he brings them and if he requires wafers, he brings wafers.

ומנחת כהנים – a Kohen who volunteers to donate one from these five meal-offerings.

מנחת כהן משיח – the meal-offering of unleavened cakes (see Tractate Menahot, Chapter 4, Mishnah 5).

גוי – [a heathen] who freely donates a meal-offering as we derive from "איש איש"/anyone (Leviticus 17:8 – “If any one of the house of Israel or of the strangers who reside among them offers a burnt-offering or a sacrifice”) which teaches that heathens bring votive offerings and free-will offerings like Israelites.

ומנחת נשים – a woman who vowed to donate a meal-offering.

ומנחת נסכים – which does not require frankincense, for oil is stated with it but not frankincense (see Numbers 15:4-5).

ולחם הפנים – it is written regarding it (Leviticus 24:7): “With each row you shall place pure frankincense, [which is to be a token offering for the read, as a gift to the LORD].” But oil is not written there.

שתי חלות – of Atzeret/Shavuot, but it is not mentioned on them neither oil nor frankincense (see Leviticus 5:11: “he shall not add oil to it or lay frankincense on it, [for it is a purification offering].”

מנחת חוטא ומנחת קנאות – it is written explicitly regarding them (Leviticus 5:11): “he shall not add oil to it or lay frankincense to it” (and Numbers 5:15: “No oil shall be poured upon it and no frankincense shall be laid upon it for it is a grain offering of jealousy.”).