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The current Judaic calendar allows for three types of year lengths:

  • Chaser ("missing") - 353 days
  • Kesidra ("in order") - 354 days
  • Shalem ("full") - 355 days

(Add 30 to each of the above for leap years.)

Is there a set of rules that explain the sequence / possibilities of the year types? For example, I noticed that this year, 5779 is a leap year / shaleim and 5780 will be a non-leap year shaleim . Offhand, I don't recall two maleh years concecutively, and I assume that this can occur only if one is a leap year and the other is not. (I.e., you wouldn't see two consecutive non-leap shleimim.)

I gather that the sequence depends mainly on the day of week that Rosh Hashanna begins as there are a limited number of kviyot allowed for each possible weekday. But, I haven't been able to locate something that explains the possible sequence of the year types.

  • You can figure this all out by yourself with 10 minutes, a pencil, and paper. judaism.stackexchange.com/a/75798/759 – Double AA Aug 7 '19 at 16:18
  • It's not so common, but you can have two non-leap shleimah years consecutively, for example 5739 and 5740 were בשה and זשג. – Meir Aug 7 '19 at 18:12
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    Are you looking for the chart in the Tur OH 428 ? – פרי זהב Aug 7 '19 at 18:33
  • @פריזהב, note that the standard printing of that chart has mistakes in it. The one in Pri Chadash, same siman, is much more accurate. – Meir Aug 7 '19 at 20:52
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    @Meir - Good point. The Biur Halacha beginning of 428 notes that, but the new Tur Machon Shiras Devorah has a corrected one based on earlier printings of the Tur. – פרי זהב Aug 7 '19 at 21:01
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An excellent work, written by a major Torah authority but geared for the layman, is "The Jewish Calendar: It Structures and Laws" by Rav David Feinstein.

From the Product description (linked above):

When the Syrian-Greeks - in the time of Chanukah - wanted to undermine and eventually destroy Jewish life, one of the three commandments they tried to abolish was the proclamation of Rosh Chodesh. They knew that without a calendar as ordained by the Torah, the festivals could not be observed and major components of Jewish life would come to a standstill.

Today, there is no Sanhedrin, no means of establishing Rosh Chodesh according to sightings of the new moon. How is our present-day calendar designed? What are its complex computations? Why can't Rosh Hashanah fall out on Sunday, Wednesday, or Friday? How are the leap years determined, and how is it that the solar years and lunar years are kept in equilibrium?

These are only a few of the many problems that are analyzed and clarified in this brilliant presentation by HaGaon Harav David Feinstein, Rosh Yeshivah of Mesivtha Tifereth Jerusalem, and one of the world's great poskim.

There is much more in this stellar book. It presents the Rosh Yeshivah's insights into all the special days of the Jewish calendar, explanations of their laws, and reasons for many of our familiar but sometimes mysterious customs.

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  • Thanks. I bought this book a few months ago. It is well organized and excellent reading. I haven't yet found an answer to my question within this book, but, I have to search a bit. – DanF Sep 10 at 1:38
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There is a Hakirah journal article here that describes how the calendar works. The leap years, year sequences, and which days yom tov can't fall out and such things.

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    A short summary of what it says would improve this answer. Thanks for posting! – robev Jul 13 at 14:39

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