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During my shul's annual *Tikun Leil Shavuot", I plan to give a short lecture about the "seasonal drift" affect of the Judaic calendar. See this Mi Yodeya answer for additional info.

I could use some additional help. The Wikipedia article gives an overview. Other articles that I have found delve into too much math for me to digest the full concept of what is really occurring. I need some balance between these two extremes, by seeing visibly, how this works. Ideally, I'd like one of these options, if they exist:

  • The exact year that the current Hebrew (fixed) calendar occurred
  • An online interface where I can enter a Hebrew year and it would display the corresponding Gregorian dates of the Hebrew holidays, particularly the Gregorian date of Passover. What I'm trying to discover is at what points Passover becomes too early to necessitate a Judaic leap year. Recall, that currently, years 8 and 19 in the cycle push Passover to be "later" than needed (i.e, w/o the leap year that year Passover would still be after the equinox.)
  • In lieu of an online interface, if there is computer code that I can easily compile (preferably Visual Basic), this may work for me as well.
  • Re "An online interface where I can enter a Hebrew year and it would display the corresponding Gregorian dates of the Hebrew holidays": wwwx.uwm.edu/cgi-bin/corre/calendar – msh210 May 16 '16 at 16:51
  • What will happen to the calendar if the Sanhedrin is re-instituted talks about hte current effect of the seasonal drift on Pesach and how going back to witnesses will affect the calendar. – sabbahillel May 16 '16 at 18:58
  • I know Jon Skeet was working on something related to the Jewish calendar. See judaism.stackexchange.com/q/37308/1713 – Daniel Jun 14 '16 at 19:50
  • I would highly recommend going through Shvili d'Rakia, the Tiferes Yisrael's explanation of how the calendar works, complete with what's probably the first-ever pop quiz, plus an answer key, in the front of any Moed Aleph mishnayos that has the Tiferes Yisrael. Also take a look at the Tur's 247-year chart (in Orach Chaim - the exact volume varies by edition, but it's between hilchos Rosh Chodesh and hilchos Pesach, or between Simanim 428 and 429), which gives the exact year type for any year in the cycle. The aforementioned pop quiz emphasizes the points you need to know to find the molad. – DonielF Jul 26 '16 at 21:56
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Check out hebcal.com -- it has exactly what you need for the second option.

There's also code you can use to script something that will tell you whenever Pesach lands before the Equinox. I'm personally partial to hebcal-js, having written it myself. ;)

  • Didn't think of Hebcal. I'll try it out, b"n. What Hebrew year did the fixed calendar begin? – DanF May 16 '16 at 15:46
  • I can't answer that part, so i didn't. – Scimonster May 16 '16 at 15:47
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I will give you the figures for calculation.

The "molad" period is 29 days, 12 hours, 44 minutes and 1/18th of a minute 3.3333 seconds).

The calendar we use contains 235 months over a period of 19 years. So multiple that timespan above by 235 and divide by 19. That will give you the time period we have as an average "year".

The Gregorian calendar uses 365.2425 days in an average year. There are a few leap-seconds if you need a totally accurate calculation. And you will see that our average year is slightly longer, which means our calendar will gradually drift forward.

You will find that if we could get a more "accurate" calendar using 353 years, 18*19 + 1*11, 18 years with 7 extra months, 11 years with 4 extra months, so a total of 130 extra months, 4366 months in total.

That was not implemented, probably not because they didn't know it would be more accurate / could not calculate, but more likely because it would be too complicated for most people to calculate and the calendar was supposed to be "accessible" so people could work out when yom tov is.

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I speak about the drift at What will happen to the calendar if the Sanhedrin is re-instituted

Calendrical Calculations 3rd Edition by Nachum Dershowitz (Author), Edward M. Reingold (Author) gives the algorithms for a number of calendars using Lisp. The fixed calendar of Hillel II is one of the algorithms presented.

The Jewish Encyclopedia states that Hillel II instituted the fixed calendar officilly in the year 4119 (359 CE). However, it also states that the Sanhedrin had been using it for the previous generation.

As @Scimonster said, Date Converter will give the translation from the year 3761 (1 CE) to 13760 (9999 CE)

Note that even though the Gregorian calendar was not instituted until October 1582, the site appears to use the Gregorian calculation only. This means that the Julian calendar used before that will diverge the farther back that the calculation is taken.

The Jewish Calendar: An Overview states that

In the fourth century, Hillel II established a fixed calendar based on mathematical and astronomical calculations.

CALENDAR, HISTORY OF states

Under the patriarchate of Rabbi Judah III. (300-330) the testimony of the witnesses with regard to the appearance of the new moon was received as a mere formality, the settlement of the day depending entirely on calculation.

The persecutions under Constantius finally decided the patriarch, Hillel II. (330-365), to publish rules for the computation of the calendar, which had hitherto been regarded as a secret science. The political difficulties attendant upon the meetings of the Sanhedrin became so numerous in this period, and the consequent uncertainty of the feast-days was so great, that R. Huna b. Abin made known the following secret of the calendar to Raba in Babylonia: Whenever it becomes apparent that the winter will last till the 16th of Nisan, make the year a leap-year without hesitation.

Later Jewish writers agree that the calendar was fixed by Hillel II. in the year 670 of the Seleucidan era; that is, 4119 A.M. or 359 C.E. Some, however, as Isaac Israeli, have fixed the date as late as 500. Saadia afterward formulated calendar rules, after having disputed the correctness of the calendar established by the Karaites. That there is a slight error in the Jewish calendar — due to inaccuracies in the length of both the lunar and the solar years upon which it is based — has been asserted by a number of writers.

  • Thanks. I'll sift through this. Yes, I got the idea that Rosh Hodesh is already after the molad, and Rosh Hashanna further compounds the problem. All this carries over into each year and subsequent years. I'd just like to get a better visual sense of how quickly the placement of the leap years within the cycle occurred. Your last citing is particularly useful. – DanF May 16 '16 at 19:45

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