We now turn to Mishnah 6 in the third chapter of Maseches Horayos. The Mishnah seemingly departs from its subject and returns to it at the end, since it comes to answer the question: if both the bull of the anointed Kohen and the bull brought for a mistaken ruling of the community are before us, which one takes precedence? Before we discuss that, let us set out the general principles governing the order of precedence among offerings: when two offerings are due to be brought at one and the same time, which comes first. This principle extends to mitzvos in general as well: when two mitzvos present themselves to a person at once, which one takes precedence.
"Kol hatadir mechaveiro kodem es chaveiro":
The first rule is "Kol hatadir mechaveiro kodem es chaveiro" - of two items, the one that is more frequent and more common takes precedence. This rule is familiar in its common formulation: "Tadir v'she'eino tadir, tadir kodem" - the more frequent one comes first.
The important point here is that we are speaking of frequency based on the halachic obligation. For example:
The daily morning offering versus the Mussaf of Shabbos - the daily offering comes first, since it is brought on all seven days of the week, whereas the Mussaf is brought on only one day of the week.
The Mussaf of Shabbos versus the Mussaf of Rosh Chodesh - Shabbos comes first, because it occurs more often.
And likewise Rosh Chodesh versus Rosh Hashanah, by the same logic.
Frequency, then, is measured by the number of times the obligation applies, and not by how many times the act is actually performed. An example: a person who has two berachos to recite, Asher Yatzar and Birkas HaMazon. Even if in practice he will recite Birkas HaMazon ten times in a day while saying Asher Yatzar only five times, Birkas HaMazon is not considered the more frequent one, since there is no obligation during the day to eat and recite Birkas HaMazon, whereas saying Asher Yatzar is required at least once a day. Asher Yatzar is therefore considered the more frequent one, because of the frequency of its halachic obligation.
"V'chol hamekudash mechaveiro kodem es chaveiro":
The second rule is "V'chol hamekudash mechaveiro kodem es chaveiro" - when two items are due to be performed at once, and one of them is holier than the other in some respect, it takes precedence. The Gemara illustrates this with two cases:
Sprinkling the blood: if we have before us the blood of a chatas and the blood of an olah, the chatas comes first, because its blood atones even for a negative commandment - a Torah prohibition that carries the punishment of kareis when transgressed intentionally; the olah, by contrast, atones only for a positive commandment, and its power is not as great as that of the chatas.
Burning the emurim: here the olah comes first, because in an olah everything is burned - not only the emurim, but also the limbs, the extremities and the innards; whereas in a chatas only the emurim are burned, those specific inner portions that are offered, and not the rest of the animal. The completeness of the burning gives the olah a kind of elevation in its sanctity in this respect.
And what is the law when the two rules conflict - one item is more frequent while the other is holier? The Gemara raises this question and leaves it unresolved, and therefore the Rambam rules that one is permitted to give precedence to either one as he wishes.
The bull of the anointed Kohen precedes the bull of the congregation:
Finally the Mishnah returns to the subject of the chapter and states: "Par HaMashiach kodem l'far ha'edah b'chol ma'asav" - the offering of the Kohen Gadol for his mistaken ruling that he then followed unwittingly precedes the bringing of the bull for a mistaken ruling of the community. The reason, as emerges from Maseches Sukkah, is that the Kohen Gadol is a kind of representative of the community, as expressed on Yom Kippur, and therefore it is important that he receive his atonement first, before attending to the atonement of the people. His atonement precedes the atonement of the community, and there is even a verse to this effect.
Interestingly, the Rambam understands this not merely as a general principle but as a specific law, since it appears from his words that at least ideally, it is the Kohen Gadol who must offer the bull for a communal error in judgment. On this basis it becomes perfectly clear why his atonement must come first: he is the agent for offering the bull for a communal error, and therefore he must receive atonement first.
Yet it is not clear that this is an absolute requirement. The Rambam does suggest as much, but other sources in the Oral Torah indicate that the service need not be performed specifically by a Kohen Gadol, and an ordinary kohen is fit for it as well. It may therefore be only an ideal requirement. In any case, it seems that the Kohen Gadol must receive his atonement, or at the very least bring his bull, first.
In summary: In this mishnah we learned two rules of precedence among offerings - "kol hatadir mechaveiro kodem es chaveiro" - whatever is more frequent than its counterpart takes precedence over it, with frequency measured by how often the halachic obligation occurs, and "kol hamekudash mechaveiro kodem es chaveiro" - whatever is more sanctified than its counterpart takes precedence over it, as explained regarding the blood of the sin offering versus the blood of the burnt offering, and the burning of the burnt offering's fats versus those of the sin offering. Where the two rules collide, the Gemara reached no decision, and so the choice is left open. Finally, we learned that the bull of the anointed kohen precedes the bull of the congregation in all its procedures, because the atonement of the Kohen Gadol, the representative of the community, comes before the atonement of the people.