The problem is that this case might not really be an omission. It is possible that the mishnah holds like R. Judah who said that the third group was always a smaller group and they would offer all of their sacrifices even before the first reading of Hallel was complete. So according to R. Judah, there never were 48 blasts on erev Pesah.
The problem is that earlier we had stated that this mishnah does not agree with R. Judah, who holds that a set of tekiah, teruah, tekiah counts as only one blast. So how could the mishnah disagree with R. Judah about that point, and count the three notes as three, but agree with him that on erev Pesah the third group never read Hallel three times.
This question is easily answerable—the mishnah indeed agrees with R. Judah about one issue but disagrees with him on the other.
This now means that the case of erev Pesah was not an omission for the mishnah might hold like R. Judah that the third group never read Hallel three times. So we still need to find another case of 48 blasts that the mishnah did omit.
The other omission was erev Pesah that fell on erev Shabbat. The mishnah could agree with R. Judah who holds that the third group only read Hallel once. This would cause us to lose six blasts. But then we could add in six more for erev Shabbat, the six blasts that would cause the people to stop working and then distinguish between the week day and Shabbat. This would leave the total at 48.
Today’s section deals with the assertion of the mishnah that there were a maximum of 48 blasts in the Temple. There were indeed cases in which there were more.
The mishnah stated that there were never more than 48 blasts. But on erev Pesah which falls on Shabbat there would have been 51 according to R. Judah (21 regular, 9 for musaf, 21 for the Hallel of the three groups offering their pesah sacrifices) or 57 according to the rabbis (27 for the Hallel of the three groups—all three groups recited Hallel three times). So why would the mishnah state that there were only 48?
The answer is that the mishnah only teaches occasions that occur every year. Erev Pesah which falls on Shabbat is a rare occurrence so it was not taught in the mishnah.
The problem with the above resolution is that erev Shabbat does not fall during Hol Hamoed Sukkot every year either. If the Festival of Sukkot begins on Friday, then there will be no erev Shabbat during Hol Hamoed Sukkot. The next Friday will be Shemini Atzeret, no longer Hol Hamoed Sukkot.
The Talmud resolves this by stating that the rabbis who shape the calendar never let the first day of Sukkot fall on erev Shabbat. This is because if the 15th of the month of Elul (Sukkot) falls on Friday, then the tenth of the month, which is Yom Kippur, falls on Sunday. Yom Kippur can never fall on Sunday because the sages didn’t want erev Yom Kippur to be on Shabbat, for this would mean two days in a row of a biblical holiday. There are two problems with this scenario. One, on erev Shabbat people would have to gather their vegetables for the break fast meal two days later. During times when they didn’t have refrigeration, this would have presented a problem. The second problem is that there would be two days in a row in which a person couldn’t be buried. Again, without refrigeration, this would cause a problem.
They would postpone Yom Kippur by a day by making sure that they made Elul a full month, meaning a month of thirty days.
At the end of yesterday’s section we learned that the rabbis intercalate (add a day) to Elul to make sure that Yom Kippur never falls on Sunday. Our section questions this assertion.
The Talmud now cites several pieces of evidence that Yom Kippur could fall on Sunday (or Friday, where it also no longer can fall). First of all, there is a mishnah that states that if they don’t have enough time to burn all of the forbidden fats on the altar on Shabbat, they can do so the next day, even if the next day is Yom Kippur. Clearly, Yom Kippur could fall on Sunday. Second of all, R. Zera relates a baraita that discusses various issues related to a case where Yom Kippur fell either immediately before or after Shabbat. R. Zera thought that all agree with that baraita, but R. Judah corrected him and related it only to R. Akiba. In any case, all seem to agree that Yom Kippur can fall on Friday or Sunday.
There is a dispute between tannaim over whether the rabbis can add a day to a month (intercalate it) for some ulterior motive, such as making sure that Yom Kippur never falls on Friday or Sunday. The rabbis of our mishnah in Sukkah do allow for this to be done (that’s why the first day of Sukkot is never on erev Shabbat). However, there are “others” who say that there are always four days between the day on which a holiday occurs in one year, and the day in which it occurs in the next. For instance, if Rosh Hashanah begins on Sunday this year, next year it will be Thursday. This is because there are always 354 days in the year, 50 weeks plus four days. The months always alternate between 30 and 29 days, 59 days in two months. So there are always four extra days. During a leap year, another month is added, and this month has 29 days. So that would push next year’s holiday back another day of the week (4 weeks plus one day). The important issue is that according to these “others” the rabbis never manipulate the calendar in order to cause a holiday to fall on a specific day. The year cannot have 355 days.
I should note that today’s calendar is fixed and has been since the fourth century. It was arranged so that Yom Kippur would never fall on Friday or Sunday.
Earlier on this daf, R. Aha had stated that on days of multiple holidays they would have blasts for each musaf offering. The Talmud raises a difficulty on this position.
A baraita teaches that if Rosh Hodesh falls on Shabbat, the Levites sing the psalm of Rosh Hodesh and not the psalm for Shabbat. But if we sound shofar blasts for each musaf sacrifice, as R. Aha holds, why not sing a separate psalm for each as well.
R. Safra interprets the baraita to mean that the psalm for Rosh Hodesh doesn’t set aside the psalm for Shabbat. It simply comes first. But both are recited.
Normally in halakhah, if something is performed frequently, it is done before something that is performed less frequently. Since Shabbat is more frequent than Rosh Hodesh, it is a bit puzzling why the psalm for Rosh Hodesh is recited first.
R. Yohanan answers by stating that the psalm takes precedence to let people know that the court established Rosh Hodesh at the proper time. Since most people do not actually witness the new moon, it is important for them to be assured that this day is actually Rosh Hodesh.
The problem is that there is another distinguishing sign to let people know about the new month—the fats were placed in a spot on the way up to the altar different from the other additional offerings. This refers to where they the fats were put before the priests would bring them up to be burned on the altar. In any case, what is important is that there was another distinguishing sign done in the Temple to let people know that it was Rosh Hodesh.
The Talmud answers that there were two distinguishing signs—some people noticed one and some noticed another. In any case, both psalms were recited on Shabbat Rosh Hodesh, just as both musaf offerings had their own set of trumpet blasts.