[San 13a.1: We begin on the next to the last line of San 12b.]
[The rabbis wished to ensure that synchronization of the lunar and solar calendars would be in line with the agricultural features of the major holidays. (Exodus 23:16-17) In the previous sections the Talmud considered the effect on Pesach, which must occur in Nisan"the month of Aviv (ripening grain)", of intercalating a second Adar before it. They now look six months ahead to Sukkot, the "feast of in-gathering".
The following dates in Tishrei should be kept in mind:
1: Rosh Hashana
15: Sukkot
16: First day of Hol haMoed Sukkot
21: Last day of Hol haMoed Sukkot (Hoshana Rabbah")
22 Shemini Atzeret]
[The work of in-gathering cannot be performed on Sukkot or on Shemini Atzeret, but only on "hol hamoed", between the 16th and 21st of Tushrei, inclusive.]
Rav Yehudah said in the name of Shmuel: We do not intercalate [add a month to create a leap year] unless the (summer) season would be incomplete until most of the month had passed. [The end of the summer is marked by the autumnal equinox. The court would meet in Adar to determine when during Tishrei the equinox would occur. Sukkot must fall in the autumn, i.e. after the equinox, so if the equinox is scheduled to occur before he middle of Tishrei -- Sukkot -- the court would declare a leap year.]
And how many days are "most of the month?" Sixteen days; these are the words of R. Yehudah. R. Yosei says twenty-one days. And both derive their positions from a single verse (Ex 34:22): "the feast of in-gathering at the turn of the year". One [R. Yehudah] holds that all of the days of Hol haMoed (16-21) must fall in the new season [i.e., autumn], and one [R. Yosei] holds that only some of the days must fall during the new season. [It is enough that the 21st falls in the autumn.]
What do they hold? If they hold that the day of the equinox ends the old (summer) season, in either case you have not met the requirement (of Sukkot falling in the autumn), either according to the one (R. Yehudah) who requires "all the days" or according to the one (R. Yosei) who requires "some of the days."
[If the day of the equinox is part of the summer, autumn begins on the following day. Therefore, R. Yehudah should have set the fifteenth day of Tishrei as the cutoff in order to ensure that all the days of Hol haMoed Sukkot were in the autumn. And R.Yosei should have set the twentieth day as the cutoff, which would have ensured that the last day of Hol haMoed Sukkot would be in the autumn.] Instead, (we must conclude that) both maintain that the day of the equinox is the beginning of the new season.
They challenged [Shmuel's account of R. Yehudah's position]. [A b'raita:] The day of the equinox is part of the previous season; these are the words of R. Yehudah. R. Yosei says that the day of the equinox is the start of the new season. [This clearly contradicts Shmuel's analysis of R. Yehudah's position, because then if the equinox falls on the 16th, the first day of Hol haMoed, it would still be summer.]
In addition, we learned in a b'raita: We do not intercalate unless the (autumn) season lacks most of the month (of Tishrei). And what is "most of the month?" Sixteen days. R. Yehudah says two parts (thirds) of a month. And what is two parts of a month? Twenty days.
[This b'raita contradicts Shmuel's account in that it interchanges the opinions of R. Yehudah and R. Yosei as reported by him. However, it is a citation from Tosephta Sanh. 2:3, where - in the version of the Tosephta available to us - the attributions are reversed, so that they agree with Shmuel's account, except for R. Yosei's requirement of 20 rather than 21 days.]
[Continuing the citation from the b'raita:] R. Yosei says we calculate: (If winter would extend into Nissan) sixteen days before Pesach, we intercalate [because then the second day of Pesach, on which the Omer offering is made, would not be "in the month of Aviv"]. But if (summer would extend) sixteen days into Sukkot, we do not intercalate. R. Shimon says: We also intercalate (if summer would extend into Tishrei) sixteen days before Sukkot Others [a euphemism for R. Meir, who having offended Rabban Shimon ben Gamliel, is often referred to in this way rather than by name {Horayot 13b}] say: Even [if it extended] for a smaller part of the month. And how much is a smaller part? Fourteen days.
[The gemara concludes:] These are indeed difficulties [i.e., the gemara cannot reconcile the two b'raitot].
[We examine a section of the previously cited b'raita.]
A master said: R. Yehuda said two parts of a month, which is twenty days. R. Yosei says that we calculate [how far the winter season would extend into Nissan; if it would extend] sixteen days before Pesach [i.e., if the vernal equinox falls on or after the 17th of Nissan] we intercalate.
If so, this [R. Yosei] is the same as R. Yehudah [in that both would require that only some of Hol haMoed Sukkot fall in the autumn season.] [The reference is to the dispute at the top of p.13a: "And how many days are `most of the month'? Sixteen days; these are the words of R. Yehudah. R. Yosei says "twenty-one days". It is argued that the dispute is only apparent. In the first b'raita they are referring to different months: R.Yehudah to 16 days into Nissan; R. Yosei to 21 days into Tishrei.]
[The interval between the vernal and autumnal equinoxes is taken to be 182 days (half a solar year to the nearest integer) but six lunar months are 177 (3x30 + 3x29) days. Therefore, if the vernal equinox falls on the 16th on Nissan, the autumnal equinox will fall on the 21st of Tishrei, which is the last day of Hol haMoed, so, according to R. Yosei we don't have to intercalate. However, if it falls on the 17th of Nissan, autumn would have begun on the 22nd of Tishrei, Shemini Atzeret, on which no "gathering" can be done, so we must intercalate.]
[The gemara answers that] the dispute is whether the day of the equinox is the end (of the previous season) or the start (of the new season). [R. Yehudah holds that the equinox is the end of the previous season; if summer extends twenty days into Tishrei, the equinox would fall on the last day of Hol haMoed, and we would have to declare a leap year. R. Yosei holds that the equinox is part of the new season, and would occur on the last day of Hol haMoed, so that a leap uear would not have to be declared.]
A master said [citing R. Yosei in our previously cited b'raita]: (If the summer season) before Sukkot (would extend) sixteen days (into Tishrei), we do not intercalate. [This was interpreted to mean that he agrees with R. Yehudah that it is sufficient if one day of Hol haMoed Sukkot falls in the autumn, and differs with him only as to whether the day of the equinox is considered to be still summer or already autumn.]
[This interpretation is now questioned.] This implies that, according to R. Yosei, it is only if the summer would extend sixteen days into Tishrei that we would not intercalate. But if it would extend seventeen or eighteen days, we would intercalate [even though several.days of Hol haMoed would be in autumn]
But didn't he (R. Yosei) say that if the winter before Pesach would extend sixteen days into Nissan, we do intercalate. (Doesn't this imply that) less than that, we would not (intercalate)? [If winter would extend fifteen days into Nissan, then summer would extend only twenty days into Tishrei -- but R. Yosei said that we would not intercalate, evidently because the 21st of Tishrei would still be Hol haMoed. Yet, as R. Yosei's opinion is interpreted above, he says that we _would_ intercalate! The two statements are contradictory.]
No. In both cases [summer extending sixteen days into Tishrei and summer extending twenty says into Tishrei], we would not intercalate. But since he wanted to teach in the first case that we would intercalate if winter before Pesach would extend sixteen days, he also referred to sixteen days before Sukkot [as a lower limit, but he would not intercalate for as many as twenty days of summer into Tishrei].
[The next part of the b'raita]: R. Shimon says: We intercalate even if summer would extend sixteen days (into Tishrei).
But that is the position of the Tanna Kamma [the anonymous author of the b'raita, who requires all of Hol haMoed to be in the autumn. So why cite R. Shimon if his position is the same]?
[The gemara answers:] There is indeed a difference between them, on whether the day of the equinox is the end of the old season or the start of the new season, but the b'raita does not specify [who holds which position].
[If the equinox is the start of the new season, and falls on the sixteenth day, which is the first day of Hol haMoed, all of Hol haMoed would be in the fall, and intercalation would be unnecessary. But if the equinox were part of the summer season, then the first day of Hol haMoed would be part of the summer season, and intercalation would be required.]
Others [a euphemism for R. Meir] say: Even [if the previous season extended before the equinox] for a smaller part of the month. And how much is a smaller part? Fourteen days. What do they ("others") hold? If they hold that the day of the (autumnal) equinox ends (the summer) and we require the entire holiday (to be in the autumn), didn't Rav Shmuel b. Rav Yitzhak say: "The `others' are referring to the _vernal_ equinox, for it was said (Deut 16:1) `Observe the month of Aviv'. Observe the season of Aviv (spring), that it fall in the month of Nissan, and intercalate Adar [the preceding month]'.
[Rashi: The vernal equinox is the beginning of spring by the solar calendar; Nissan is the first month of spring by the lunar calendar. According to this interpretation, "others" wanted to ensure that less than half - i.e., at most 14 days - of Nissan had elapsed before the equinox in order for most of the month to be in the spring.]
Rav Aha b. Yaakov [also referring to Nissan] says: ``The tanna (of `others', i.e. R. Meir ) was counting downwards, and this is what he said: '_until_ fourteeen days [exclusive]' ";. [If the vernal equinox is on the 14th, we do _not_ intercalate, because then Pesach {15 Nissan) would be in the spring.]
Ravina says: " `Others' may still be referring to (14 days in) Tishrei. `Others' hold that the entire holiday, including the first holiday [first day of Sukkot] must be in the autumn)".
[The gemara asks:] The first holiday?! It is; written (Ex. 24:16) "the feast of in-gathering". [Since no in-gathering can be performed on the holiday, why can't it fall in the summer, as autumn doesn't begin until the following day.] [The gemara replies:] The holiday that comes at the time of in-gathering (must fall in the autumn).
[We end at the colon on line 14 of p. 13b. This completes the section on intercalation.]