Bechoros, Chapter 9, Mishnah 5. The Mishnah discusses the designated dates for actually separating the animal tithe from the flock and the herd.
Unlike agricultural produce - wine, oil, and grain - which a person must tithe for that year, and which retains the strict status of untithed produce (tevel) as long as it has not been tithed, carrying a penalty of premature death at the hands of Heaven for eating it, the animal tithe is different: a person is permitted to slaughter and eat, or sell the animal, before the tithe has been separated from it.
Therefore, in the distant past, the practice was to tithe the animals approximately once a year: they would wait until toward the end of the year (our Mishnah contains a dispute regarding when the end of the year falls), separate the tithe, and from then on eat, slaughter, and sell.
The Sages were concerned that this system was flawed. Why? The pilgrims to Jerusalem need animals for their sacrifices, and we want there to be a good supply of animals for the three pilgrimage festivals. Therefore, the Sages established a deadline before each of the holidays, by which a person must tithe the animals born to him up to that point in that year. In this way, the animals will be permitted and ready to be brought to Jerusalem for eating, slaughtering, and the like, guaranteeing an abundant supply for all who need them.
Our Mishnah comes to establish exactly when these deadlines fall, presenting three opinions of Tannaim who disagree on several points.
The Opinion of Rabbi Akiva - Three Granos:
The first opinion is that of Rabbi Akiva, which is the halachah: "Shalosh granos lema'asar behemah" - three groups, each with its own deadline, during which a person tithes his flock and herd. The literal meaning of the word 'goren' is a threshing floor. This is a borrowed term referring to the batch of grain that a person tithes, and from there it was borrowed again to refer to the batch of animals that a person tithes.
These are: "Bifros HaPesach, bifros HaAtzeres u'vifros HaChag" - fifteen days before Pesach, before Shavuos, and before Succos. This ensures an abundant supply of animals to bring to all the holidays and to the Beis HaMikdash, and this is the halachah.
The Meaning of the Word "Peros":
'Peros' - from the word peras, meaning a half; and as a verb, to divide in half, the way one slices (pores) bread. Even split hooves are called 'parsah', since a parsah is something halved. This relates to the halachah - according to Rabbi Akiva and also in practice - that for thirty days before a holiday we inquire and expound upon its laws. One must learn the laws of Pesach during the thirty days prior to Pesach, and the same applies to Shavuos and Succos. Therefore, they said that in the middle of this period, fifteen days before each of the holidays, is the time to tithe the animals born from the beginning of the period until now.
In practice, the dates work out as follows:
Before Pesach: The last day of Adar.
Before Shavuos: The thirty-fifth day of the Omer, since Shavuos is the fiftieth day of the Omer. This day falls toward the end of Iyar, although this may vary slightly, give or take a day.
Before Succos: The last day of Elul.
The Opinion of Ben Azzai:
"Ben Azzai omer: be'esrim vetishah beAdar" - the first designated time is the twenty-ninth of Adar, which is actually the last day of Adar. This seemingly matches the words of Rabbi Akiva, who specified the last day of Adar, fifteen days before Pesach. However, Ben Azzai wishes to emphasize that the month of Adar (at least the Adar in which Purim falls, the Adar closest to Pesach when there are two months of Adar) is always exactly twenty-nine days long. Rabbi Akiva disagrees and maintains that Adar can even be thirty days long, which is why he did not explicitly state the twenty-ninth day. Ben Azzai, on the other hand, emphasizes that the designated time is specifically the twenty-ninth of Adar, which is fifteen days before the start of Pesach.
"Be'echad beSivan" - here Ben Azzai specifies the first of Sivan and not fifteen days before Shavuos, which is the thirty-fifth day of the Omer, a difference of about ten days. Why? Because he is concerned that not many animals are born in the spring, and he wants to, so to speak, widen the time window so that there will be more animals to tithe. This achieves the required amount to ensure there are enough tithed animals to bring to the Beis Hamikdash and so forth. By saying "the first of Sivan," it turns out that a person has all of the month of Nisan and all of the month of Iyar, and afterward he will tithe everything that was born up to that point.
"Be'esrim vetishah beAv" - the month of Av is the month before Elul. Rabbi Akiva specified the last day of Elul, while Ben Azzai specifies the last day of the previous month, Av. The reason for this: there is a dispute, as we will see later in the Mishnah, whether the new year for the animal tithe begins on the first of Elul or the first of Tishrei. Ben Azzai is in doubt and does not know which side to lean toward, so he seeks to avoid the uncertainty: the animals born in Elul will be tithed by themselves, so that they will not be tithed for the wrong year (since, as we learned in the first Mishnah of the chapter, we do not tithe from this year for the past year). Since he is unsure whether the animals born in Elul belong to the coming year or the previous year, he set a separate cutoff point before the first of Elul.
The Opinion of Rabbi Eliezer and Rabbi Shimon:
"Rabbi Eliezer veRabbi Shimon omerim: be'echad beNisan" - they specify the first of Nisan and not the last day of Adar, because they disagree with the very assumption that there is a halachah of inquiring and expounding the laws of the festival thirty days before the festival. In their opinion, the halachah is not like the Sages, but rather like Rabban Shimon ben Gamliel, who holds that the time is only fourteen days before the festival. Therefore, fourteen days before Pesach, which is the first day of Nisan, is the time when we begin the process of studying the laws of Pesach, and we begin it by tithing the animals. Hence their establishment of the first of Nisan.
"Be'echad beSivan" - here this is the first day of Sivan, just a few days before Shavuos, and the logic is the same logic stated in the opinion of Ben Azzai: we want a larger time window, the two months (Nisan and Iyar) in which the animals were born, and thus a larger quantity to tithe and bring to the Beis Hamikdash, instead of advancing it by ten days when there would be fewer animals.
"Uve'esrim vetishah beElul" - Rabbi Eliezer and Rabbi Shimon are the ones who hold that the new year for the animal tithe begins on Rosh Hashanah itself, on the first of Tishrei. They have no doubt about the matter, and this is their approach, and therefore they hold that we must tithe the third harvest right before that day, on the last day of Elul before Rosh Hashanah. However, according to their calculation, they should have said fourteen days before Succos, which is the first of Tishrei, just as fourteen days before Pesach is the first of Nisan.
Regarding this, the Mishnah asks: "Velamah amru be'esrim vetishah beElul velo amru be'echad beTishrei? Mipnei shehu yom tov" - and it is impossible to tithe on a yom tov. The first of Tishrei is Rosh Hashanah, and on Rosh Hashanah we certainly do not tithe animals, due to a rabbinic law, because the matter looks like fixing something. Since we do not tithe animals or produce and the like on yom tov and on Shabbos, they had to move it early to the day before it, and they established the determining day for tithing on the day before Rosh Hashanah.
The Halachah:
These are the three opinions, and the halachah is in accordance with Rabbi Akiva: fifteen days before each of the three festivals, and the Rambam rules this way. Additionally, the Rambam rules that the determining date itself, the time when the new year begins regarding the tithe, is on the first of Tishrei, and not as the Bartenura learns that it is on the first of Elul, and he explicitly stated this in Tractate Rosh Hashanah.
The Words of Rabbi Meir and Ben Azzai in the Seifa:
Rabbi Meir holds the opinion that the first of Elul is the new year for animal tithes, unlike Rabbi Eliezer and Rabbi Shimon. However, Rabbi Eliezer and Rabbi Shimon do not state this explicitly here, but rather it is implied from their words, and they state it explicitly in Tractate Rosh Hashanah; whereas Rabbi Meir states it explicitly here.
Ben Azzai, as explained above, maintains that animals born in the month of Elul must be tithed by themselves, because he is uncertain what the correct ruling is: whether the halachah follows Rabbi Meir that the new year for animal tithes is the first of Elul, or Rabbi Eliezer and Rabbi Shimon that it is the first of Tishrei. Since he does not know, he says that any animal born in Elul is a case of doubt, and therefore they must be treated independently and tithed together as a separate group.
In practice, as mentioned, the Rambam rules that the halachah is the first of Tishrei, and there is no doubt here, so this is our practical halachah.