I'm implementing support for the Hebrew calendar in Noda Time, my date/time library for .NET. I think I'm mostly there aside from text support (although beta testers would be very welcome!) but one aspect still puzzles me.

The Wikipedia Hebrew Calendar entry states that in a leap year, the extra month is inserted before the "regular" Adar:

During leap years Adar I (or Adar Aleph — "first Adar") is added before the regular Adar. Adar I is actually considered to be the extra month, and has 30 days. Adar II (or Adar Bet — "second Adar") is the "real" Adar, and has the usual 29 days. For this reason, holidays such as Purim are observed in Adar II, not Adar I.

So according to this, Adar I is the leap month. However, the Microsoft method of Calendar.IsLeapMonth returns true for year 5502, month 7 - which is Adar II (using civil month numbering instead of ecclesiastical). By my reckoning, it should return true for month 6 instead of month 7.

This is also the way Microsoft handles Adar in Windows Store applications. From CalendarIdentifiers.Hebrew:

During leap years, Adar is replaced by Adar Alef with 30 days and Adar Beit with 29 days. Adar Beit is considered the leap month. The last day of Adar Alef and all the days in Adar Beit are considered leap days.

Currently this doesn't impact my implementation, but I can see that it might in the future - and I'd rather get things right than just follow Microsoft if they've got it wrong. So, who's right in this case? And does it have impact beyond that mentioned in Wikipedia?

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    Related: judaism.stackexchange.com/questions/35519/… – user4523 Apr 19 '14 at 19:24
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    Only Jon Skeet could get a +22 on his first question here. – Double AA Apr 23 '14 at 3:45
  • Consider if the Gregorian transition had involved going back 11 days instead of forward. Would people have celebrated their birthdays twice? Would their age have incremented twice? When would holidays be celebrated? Two Thanksgiving day parades? Or off both times but big parade once? Same sort of idea is going on here. The real month happens twice, just certain things happen in one round only for local/practical reasons. – Double AA Feb 2 at 3:00
up vote 13 down vote accepted

After some much Hebrew googling, it seems as though the rationale is the other way around.

Adar was doubled because it was the last month of the calendar (which started at Nisan with Passover) back then. The decision was to celebrate Purim (and all the other events) in the second Adar as to keep both redemption celebrations close (Purim and Passover). Because of that the first Adar was treated as the "extra" month.

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    Great - thanks very much :) – Jon Skeet Apr 19 '14 at 20:50
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    It still is the last month of the calendar. – Double AA Apr 23 '14 at 3:44
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    Citing any of the results of this Google search (regardless of its language) would improve the value of this post. – Double AA Apr 23 '14 at 3:45
  • @DoubleAA The Jewish civil year starts at Tishrei with Rosh Hashanah and ends in Elul. – i3arnon Apr 23 '14 at 8:35
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    @I3arnon Right. And the Jewish civil first month is Nissan and the last is Adar (II). Who said the year count and month count must start at the same time? – Double AA Apr 23 '14 at 21:07

There is some discussion in the Jerusalem Talmud (M'gilla 7a-b) regarding which of the two Adars is considered the leap month (incidentally, halachic ramifications are discussed ad loc.). Medieval commentators interpret the Talmud as concluding that Adar I is the extra month (see Rashi to Rosh HaShana 19b, s.v. kamma ibbur hashana; see also Tosafos ibid., s.v. Adar hasamuch l'Nisan l'olam chaseir).

Interestingly, there is a separate debate over the meaning of an unqualified reference to "Adar" during a leap year. This debate traces from the Tanaitic era (with a difference in opinion between Rabbi Meir and Rabbi Yehuda mentioned in a b'raisa in N'darim 63a) to the medieval era, with the Rosh (N'darim 8:2) ruling in accordance with R' Yehuda that an unspecified reference refers to Adar I, and the Rambam (Hil. N'darim 10:6) ruling in accordance with R' Meir that an unspecified reference refers to Adar II. Although some later authorities rule in favor of the Rosh (Tur OC 428, Rema OC 427:1), multiple later decisors view this debate as unsettled and insist that important legal documents should explicitly specify which Adar is being referenced (see, for example, Bach EH 126:4 and Mishna B'rura 427:3).

The extra month is Adar I. That's because Purim (the holiday) is in Adar II, in a leap year. As Purim is celebrated also in non-leap year, the conclusion is that Adar II is the month that is always present whereas Adar I is present only in leap years.

My guess is that the MS implementation is wrong.

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    This seems to be the same reasoning as the bit of Wikipedia I quoted, but in reverse. (Wikipedia reasons that Purim is celebrated in Adar II because Adar I has been added before Adar II, which is the "real" Adar.) I can understand that the two decisions could be so intertwined as to be indistinguishable, but is there anything other than Purim (and similar holidays) which can either indicate when the extra month occurs, or that would be affected by it? Does any scripture explicitly say that the extra month is added before Adar? – Jon Skeet Apr 19 '14 at 17:57
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    @JonSkeet no scripture that I know of, but the month length kinda seems to imply it. vbm-torah.org/purim/purim65-bt.htm is an overview of some related issues, though nothing directly helpful to you. – msh210 Apr 20 '14 at 5:21
  • Maybe in leap years, Purim is celebrated in a different month. – Double AA Apr 25 '14 at 20:34

http://parsha.blogspot.com/2011/03/yu-purim-to-go-5771.html Rabbi Mordechai Willig - "When is a Bar Mitzvah in a Leap Year?

The Jewish calendar has 12 months. In a leap year, there are 13 months. Each month has either 29 or 30 days, and the first month is the month of Nissan (Shemos 12:2.) If a boy is born on the 29th of Cheshvan (in a year when Cheshvan has 29 days) he becomes a bar mitzvah on his birthday even if that year Cheshvan has 30 days. The fact that it isn’t the last day of the month is halachically irrelevant.
Born in a Regular Year, Bar Mitzvah in a Leap Year
What if a boy is born in the 12th month, Adar, in a year that has 12 months, and becomes a bar mitzvah in a year that has 13 months? Logically, he should become a bar mitzvah in the 12th month, just as the boy in the previous example becomes a bar mitzvah on the 29th day of the month. The fact that it isn’t the last month of the year should be irrelevant. In fact, the Pri Chadash (OC 55:10) quotes the Maharash HaLevi who rules that he does become a bar mitzvah in the first month of Adar, the 12th calendar month. However, the Rama rules that he becomes a bar mitzvah in the second month of Adar, the 13th month of the year. The Mishna Brurah (55:45) states that the gemara (Megillah 6b) supports the ruling of the Rama. The Gemara there discusses whether, in a leap year, the megillah should be read in Adar I, the first opportunity to do so, or Adar II, based on the reasoning of celebrating the redemption of Purim and Pesach in consecutive months, and concludes to read it in the second Adar. Therefore, just as the megillah is read in Adar II and not Adar I, so too a boy doesn’t become a bar mitzvah until Adar II. This proof is questionable, as the plain reading of the gemara is that both months have the status of Adar. In fact, the Rama himself rules (568:7) that a yahrtzeit for one who passed away in Adar during a 12-month year is observed at the first possible opportunity, in Adar I, in a leap year, while the Gra (568:16) rules that it should be observed in both months. Therefore, if a boy born in Adar becomes a bar mitzvah in Adar, it should occur in Adar I, the first opportunity, according to the Rama. In fact, since the months in the Torah are numbered and not named, the paradigm of 29 and 30 day months should apply. This, too, indicates that the bar mitzvah should occur in month 12, Adar I, parallel to the 29th day of Cheshvan. The existence of a subsequent day, or month, in the bar mitzvah year should be irrelevant. The Pri Chadash suggests a support for the opinion of the Rama from the Yerushalmi (Megillah 1:5) which suggests, in the context of the requirement to bring an animal as a korban within a year of its birth, that Adar I is the added month, and therefore an animal born in Adar can be brought until Adar II of the following year. So too, he writes, the 13th year of a boy born in Adar isn’t reached until Adar II. How can this be explained? Perhaps there is a set number of 12 months in a year, and in a leap year the 12th month occurs twice, 12a and 12b. Since, according to the Yerushalmi, 12a is the additional month, the bar mitzvah status is not conferred until 12b, otherwise known as Adar II. This innovative definition of a year may help answer another question as well. The Mishna Brurah (55:45) rules that a boy born on the 30th day of Cheshvan who becomes a bar mitzvah in a year where Cheshvan has 29 days becomes a bar mitzvah on the 1st day of Kislev and not on the 29th day of Cheshvan. The fact that Kislev is the next month is irrelevant for this case

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