**מַה-נִּשְׁתַּנֵּית הַשָּׁנָה הַזֹּאת מִכָּל-הַשָּׁנִים?**

**An essay about the Jewish calendar in honour of the New Year 5765 ****תשס”ה**** **

© Copyright 5765/2004 by Ari Meir Brodsky. All rights reserved. Permission is given to copy, forward or print this document for personal use, provided this copyright notice is included. You may not print or distribute this document or any part of it for profit or for commercial purposes. For any other form of distribution please request permission by e-mail to ari.brodsky@utoronto.ca.

This essay is available on the internet at http://individual.utoronto.ca/aribrodsky

**A. ****INTRODUCTION**

**What’s so special about the year 5765?**

I’m glad you asked.

A casual glance at a Jewish calendar for the year 5765 (September 2004 through October 2005 on the civil calendar) should be enough to identify a few interesting features of the year, such as: Erev Pesach falls on Shabbat, Pesach falls so “late” that it extends into May (except in Israel), and the Jewish calendar year ends in October 2005 rather than September. If you pay close attention to detail, you may also notice that there are **no “double parashiyyot” the whole year**, something which hasn’t happened (except in Israel) since 5741 (1980-81).

What I have compiled here is a **collection of calendrically fascinating events of the year 5765**. This essay is divided into sections. In most cases, the section title describes an important event occurring during the year 5765. At the beginning of each section, there is general information about the important event, including **how often it happens**. Each section then contains a list of many interesting events that occur **only in years when the important event in the section title occurs**.

As you will see, the essay is quite long. If you don’t want to read the whole thing, that’s fine – **you can skim through the (lettered) section headings and individual (numbered) items **to see which facts you find most interesting. **As you read the details of a particular item, make sure to look at the information given at the beginning of the section containing the item, in order to find out how often the event occurs.**

It would probably help your understanding of what I’ve written if you **follow along with your Jewish calendar for 5765 as you read**, so that you can better understand and verify the events for yourself as you read them.** **

I’d be thrilled to receive **feedback **from anyone who has any comments, corrections, questions, clarifications, or additions to anything written here or to anything about the Jewish calendar in general. Also, there are several places in this essay where I have left questions open as “**Exercises for the reader**”. Feel free to submit any answers you come up with. My e-mail address is ari.brodsky@utoronto.ca. (Note that some of the exercises are there because I have not yet figured out the answers myself. Enjoy!)

When I indicate **halakhic sources **for the information presented, here are the abbreviations I use:

**SA **stands for **Shulchan Arukh**, the Code of Jewish Law by Rav Yosef Karo, section Orach Chayyim.

**Rama **refers to the additional comments of Rav Moshe Isserlis to the Shulchan Arukh.

**MV **refers to the **Mishna Verura**, the famous commentary to SA by the Chafetz Chayyim, Rav Yisrael Meir (Hakkohen) Kagan of Radin. (Most people would call this MB for Mishna Berura, but grammatically there should probably not be a dot in the letter vet, so I’ll use MV.)

In addition, at the end of this essay there is a **suggested reading list **for general information about the Jewish calendar.

Thanks to my many friends who have provided various insights that I have included in this essay. I have tried to acknowledge them by name in the body of the essay, where their contribution is included. I apologize if I have forgotten anyone. Special thanks go to Henry Segal, Tzvi Goldman, Zvi Golish, Rabbi Y. M. Gross, and my parents, who have read parts of this essay and offered valuable comments. Thanks to Rabbi Yosef Simon for his technical assistance. Thanks also to those who have provided general encouragement during the time I’ve been writing this essay – usually in the form of “Ari, is your calendar essay done yet?”

This essay is dedicated in honour of my dear parents

Elaine and Marten H. Brodsky

מרדכי צבי ואסתר יוטא בראדסקי

who have always encouraged me to pursue excellence both in Torah study and in general knowledge.

Also dedicated in memory of my beloved grandparents

Mary and Jack A. Silverberg

אברהם ירחמיאל בן ישראל שלמה הלוי ע”ה

מרים רבקה בת שמחה בונים ע”ה

Gertrude and Morris O. Brodsky

משה אשר בן מרדכי אייזיק ע”ה

גיטל בת יוסף ע”ה

whose lives and accomplishments always remain a source of inspiration to me.

**B. ****GENERAL INFORMATION ABOUT 5765**

The Jewish calendar year **תשס”ה **(tav-shin-samach-hei) – **5765 from Creation **– runs from Thursday, September 16, 2004 until Monday, October 3, 2005 on the civil (Gregorian) calendar.

The year **5765 is a Jewish leap year**, meaning that the calendar year contains 2 months of Adar, for a total of 13 months in the year, rather than 12.

Every Jewish calendar year is assigned a three-letter “**keviut**” or “**year-type**” symbol. The year-type has nothing to do with the 19-year cycle of leap years, and does not determine the relationship between the Jewish calendar and the civil calendar. **The year-type simply characterizes the features of the Jewish calendar year **itself, such as the length of each month, the day of the week on which each holiday and calendar date falls, and the distribution of the Torah readings throughout the year. Based on the rules for setting up the Jewish calendar, it turns out that there are **14 possible different year-types**. 7 of them represent leap years (with 13 months) and the other 7 represent regular years (with 12 months).

**The year-type of the year 5765 is החא **(hei-chet-aleph). The three letters of the year-type are interpreted as follows: The first letter ה (hei) means that the first day of Rosh HaShana falls on Thursday. The second letter ח (chet) means that the year is “**ch**aseira” – both of the two variable months, Cheshvan and Kislev, are “short” months having only 29 days each. The third letter א (aleph) means that the first day of Pesach falls on Sunday. A year with this year-type must be a leap year.

The החא (hei-chet-aleph) year-type occurs extremely rarely, **in only 3.9% of all years**. That means about 4 times every 100 years on average, although there is no reason for the occurrences to be equally spaced. **The last time we had one was 24 years ago, in 5741 (1980-81). **The next one after 5765 will be only **3 years later**, in 5768 (2007-08). But the next one after that won’t be until **44 years later**, in 5812 (2051-52).

Sections C through P of this essay contain events determined by the החא (hei-chet-aleph) year-type, in increasing order of rarity, as follows:

Section **C** describes events occurring **only **in years when there is no Shabbat between Yom Kippur and Sukkot (60.5%).

Section **D** describes events occurring **only **in years when Cheshvan has 29 days (55.1%).

Section **E** describes events occurring **only **in years when there is no Shabbat during the Intermediate Days of Pesach (39.5%).

Section **F** describes events occurring **only **in leap years (36.8%).

Section **G **describes events occurring **only **in years when Rosh HaShana falls on Thursday (31.9%).

Section **H** discusses the surprising fact that Parashat Vayyeilekh is not read during the whole calendar year (29.6%).

Section **I** describes events occurring **only **in “chaseira” years (25.5%).

Section **J** describes events occurring **only **in years when the first day of Kislev falls on Sunday (21.9%).

Section **K** discusses the exact length of a “chaseira” leap year (15.5%).

Section **L** discusses the fact that Haftarat Tzav is read this year (13.9%), and contains a general discussion of rarely read haftarot.

Section **M **describes events occurring **only **in years when the first day of Pesach falls on Sunday (11.5%).

Section **N **describes events occurring **only **in leap years with Rosh HaShana on Thursday (10.5%).

Section **O **describes events occurring **only **in years with the first day of Tevet falling on Monday (3.9%), and discusses various characterizations of the החא (hei-chet-aleph) year-type.

Section **P** discusses the effect of the החא (hei-chet-aleph) year-type on preceding and following years.

Sections Q through S describe events characteristic to the 8^{th} year of the 19-year cycle:

Section **Q** discusses the fact that the Jewish calendar dates and holidays seem to fall very late on the civil calendar during most of this year.

Section **R** discusses the possibility of having a bar mitzva in Adar I of a leap year.

Section **S** contains my novel analysis of the correspondence (or lack thereof) between Easter and Pesach.

Sections T through V describe events involving both the Jewish and civil calendars:

Section **T** describes the correspondence between the Jewish and civil calendar dates for this year, including the implications for birthday coincidences.

Section **U **describes rare events that depend on some unusual combinations of the Jewish date, the civil date and the day of the week, and occur with unpredictable frequencies.

Section **V **analyzes the fact that Good Friday falls on Purim, which hasn’t happened since 95 years ago.

Section **W **describes events relating to the precise time of the Molad for a particular month, and includes discussion of the various “dechiyyot” used to determine the year-type.

Section **X **is the conclusion. (Feel free to skip to it at any time!)

Section **Y **contains suggested references for further reading.

Wow, I’ve almost run out of letters in the alphabet!

**C. ****NO SHABBAT BETWEEN YOM KIPPUR AND SUKKOT**

In years when Rosh HaShana begins on either Thursday or Shabbat, there is no Shabbat between Yom Kippur and Sukkot. This occurs in 8 out of the 14 possible Jewish calendar year-types, including our year-type, החא (hei-chet-aleph). These year-types account for**60.5% **of all years.

There can be up to 3 consecutive years with no Shabbat between Yom Kippur and Sukkot. In fact, this year 5765 is the 3^{rd} year in a row with this property.

Here are the **events that occur only in years when there is no Shabbat between Yom Kippur and Sukkot**:

1. **HAAZINU**** ****ON**** SHABBAT SHUVA: **Last year’s cycle of Torah readings must end on Simchat Torah with the reading of Vezot Habberakha. The second-last parasha, Haazinu, must be read on the last available Shabbat before Sukkot. Since there is no Shabbat between Yom Kippur and Sukkot, we read Haazinu on the Shabbat before Yom Kippur. See also G.4. The haftara begins “Shuva Yisrael” (Hoshea chapter 14), relating to the theme of repentance. This haftara is sometimes listed as Haftarat Vayyeilekh, but it should really be called the haftara for the Shabbat before Yom Kippur. We read it more often with Parashat Haazinu than with Vayyeilekh.

2. **HAFTARAT HAAZINU NOT READ:** Since we read Haazinu on Shabbat Shuva, the regular haftara for Haazinu (the Song of David in Samuel II) is not read. Note that it is the same as the haftara for the 7^{th} day of Pesach. So we read it only once this year, rather than twice.

3. **NITZAVIM-VAYYEILEKH COMBINED AT END OF PREVIOUS YEAR: **In order to make up for the missing Shabbat, Nitzavim and Vayyeilekh must be combined at the end of the previous year, on the last Shabbat before Rosh HaShana. See section H for the peculiarity of Parashat Vayyeilekh. Note that in some classical sources, such as Sefer HaChinnukh, the combination is treated as a single parasha; in other words Vayyeilekh is not listed at all as a separate parasha.

4. **BIRKAT HACHODESH DURING CHANUKKA:** In such years, we bless the month of Tevet on a Shabbat during Chanukka. See also G.26 and J.5. In other years we bless the month of Tevet before the beginning of Chanukka.

**D. ****CHESHVAN HAS 29 DAYS**

8 out of the 14 possible Jewish calendar year-types correspond to years in which Cheshvan has 29 days, including our year-type, החא (hei-chet-aleph). These year-types account for **55.1% **of all years. This is not rare at all, and in fact it happens more often than not, but I’m writing in “increasing order of rarity”, so you can forgive me for starting with this year’s events that are not rare.

Note that in a year when Cheshvan has 29 days, Kislev may also have 29 days (the year is “chaseira”) or Kislev may have 30 days (the year is “kesidrah”, meaning that the months alternate in length between 29 and 30 days).

There can be up to 2 consecutive years with Cheshvan having 29 days, such as this year and next year (5765 and 5766). There can also be up to 2 consecutive years in which Cheshvan has 30 days, such as last year and the previous year (5764 and 5763). This means the last time Cheshvan had 29 days was 3 years ago, in 5762 (2001).

Here are the **events that occur only in years in which Cheshvan has 29 days**:

1. **ROSH CHODESH KISLEV HAS ONLY ONE DAY: **Since Cheshvan has only 29 days, there is only one day of Rosh Chodesh Kislev. This one day can fall on any one of Sunday (as in this year), Tuesday, Thursday or Friday. Note that even when Rosh Chodesh Kislev has 2 days, no day of Rosh Chodesh Kislev can ever fall on Shabbat.

2. **CHANUKKA BEINGS ONE DAY EARLIER IN THE WEEK THAN ROSH HASHANA: **Because Chanukka falls in Kislev, the day of the week on which it begins **cannot be determined uniquely by referring only to the other holidays**. (That is why it is not included in the “At-Bash” mnemonic of SA 428:3.) But once we know that Cheshvan has 29 days, it follows that Chanukka begins one day earlier in the week than did Rosh HaShana. As MV 428:2 puts it, when Cheshvan has 29 days, Chanukka begins on the same day of the week as the previous year’s Shavuot. There are other mnemonics given for determining the day of the week on which Chanukka begins (see for example Beiur Halakha 428 d.h. “Bemidbar” at the very end of the paragraph), but **my general opinion of mnemonics **is that it’s often harder to remember and apply the mnemonic than to figure out whatever the mnemonic is supposed to help you remember. (Remember SOH-CAH-TOA or CAST from high school trigonometry?)

**E. ****NO SHABBAT DURING INTERMEDIATE DAYS OF PESACH**

When the first day of Pesach falls on either Shabbat or Sunday, there is no Shabbat during the Intermediate Days of the holiday (Shabbat-Chol Hammoed). So there is a **maximum number of “weekdays” during Pesach **– 5 in Israel, 4 in the Diaspora. This occurs in 6 out of the 14 year-types, including our year-type, החא (hei-chet-aleph). These year-types account for **39.5% **of all years. The last time we had such a year was 4 years ago, in 5761. The next time after 5765 will be 3 years later, in 5768.

There can be up to 2 consecutive years with no Shabbat during the Intermediate Days of Pesach.

Here are the **events that occur only in years when there is no Shabbat during the Intermediate Days of Pesach:**

1. **BREAK BETWEEN ZAKHOR AND ****PARA****: **In such years, there is one Shabbat after Parashat Zakhor on which we do not read a special maftir, before continuing with Para the following week. See section L regarding the haftara read that week. There may or may not also be a break between Shekalim and Zakhor. See M.2 regarding possible breaks among the 4 Special Parashiyyot in Adar.

2. **SEDER**** ****ON**** SATURDAY NIGHT:** In the Diaspora, either the first or the second Seder will be on Saturday night. See M.18 for the halakhic details.

3. **YOM HAATZMAUT ADVANCED TO THURSDAY:** 5 Iyyar itself never falls on Thursday, but in years such as these, Yom HaAtzmaut is celebrated on Thursday, since 5 Iyyar falls on Friday or Shabbat. See M.26 for details. This also means that Yom HaZikaron is observed on Wednesday, even though 4 Iyyar never falls on Wednesday.

4. **BIRKAT HACHODESH ON FIRST SHABBAT OF THE 3 WEEKS:** We bless the month of Menachem Av on the first Shabbat after the Fast of 17 Tammuz, rather than the second. See also M.32.

5. **TISHA B’AV AND 17 TAMMUZ OBSERVED ON SUNDAY:** The fast days are observed on Sunday, either because they actually fall on Sunday, or because they fall on Shabbat and are postponed to Sunday. See also M.34. For halakhot regarding Tisha B’Av beginning at the end of Shabbat, see SA 551:4, 552:10, Rama 553:2, SA 556 (re Havdala), 559:1-2.

6. **SELICHOT MORE THAN A WEEK BEFORE ROSH HASHANA:** Rosh HaShana of the following year will begin on Monday or Tuesday. Since we must have at least 4 days of Selichot before Rosh HaShana, Ashkenazim begin saying Selichot a week before the last Shabbat of the year, after Shabbat Parashat Ki Tavo (Rama 581:1). See also M.40.

7. **NITZAVIM AND VAYYEILEKH SEPARATE AT END OF YEAR:** Since the following year there will be a Shabbat between Yom Kippur and Sukkot, we read only Nitzavim on the last Shabbat of this year. It’s quite a short parasha, with only 40 pesukim. (Vayyeilekh is even shorter, with 30 pesukim!) Compare what happened at the end of last year – see C.3. Also see section H for the peculiarity of Parashat Vayyeilekh.

**F. ****LEAP YEAR**

I’ve mentioned this already in the introduction, but I don’t want you to forget it. This year 5765 is a Jewish leap year, meaning that it contains 2 months of Adar, for a total of 13 months in the year, rather than 12. (Incidentally, the literal translation of the Hebrew expression “shana meubberet” would be “pregnant year”, but I’ll stick to the more common usage, which is “leap year”.) Leap years are necessary in order to resolve what I call the “**Fundamental Problem of Calendar Making**”. This refers to the fact that the month is determined by the lunar cycle, while the year is a solar concept, and there is no whole number of lunar months whose total length corresponds to a solar year. The solution is that our calendar years are usually 12 months long, but we add a 13^{th} month when necessary, in order to ensure that the holidays fall in the appropriate seasons.

It turns out that 19 solar years are almost exactly the same length as 235 lunar months. Therefore, the leap years in the fixed Jewish calendar are arranged based on a cycle of 19 years, containing 12 ordinary years of 12 months each, and 7 leap years of 13 months each. The 7 years in each 19-year cycle that are **leap years **are the ones numbered **3, 6, 8, 11, 14, 17, and 19**. The position of any year in the19-year cycle is determined by simply dividing the year number by 19 and taking the remainder. For example: The current 19-year cycle began with the year 5758 (1997-98) and continues until 5776 (2015-16). Since 5776 is equal to 304 times 19, we often say that the current cycle, from 5758 to 5776, is the 304^{th} 19-year cycle of the Jewish calendar. When we divide the current year number, 5765, by 19, we get a remainder of 8, meaning that **5765 is the 8 ^{th} year of the **304

^{th}

**19-year cycle, and is therefore a leap year.**

Leap years are the only calendrical events that **do **occur in a predictable, repeating pattern, as distinct from the other events described in the various sections of this essay. Jewish leap years happen once every 2 or 3 years, for a total of **7 times every 19-year cycle**. This means that leap years account for 7/19 or **36.8% **of all years. The last leap year was 2 years ago, the year 5763, which was the 6^{th} year of the current cycle. The next leap year after this year will be 3 years from now, the year 5768, which will be the 11^{th} year of the cycle.

In a later section (section Q), I will have more to say about the leap-year cycle. In particular I will discuss why the holidays seem to fall very “late” this year relative to the civil calendar. In this section, I will just mention some calendrical **events that occur only in leap years**:

1. **PURIM IN ADAR II: **Purim is observed in Adar II of a leap year, so as to celebrate the redemption of Purim adjacent to the redemption of Pesach. (See discussion in Talmud Megilla 6b-7a.)

2. **FOUR SPECIAL PARASHIYYOT IN ADAR II: **The 4 special parashiyyot centred on Purim and leading up to Pesach are read just before and during the month of Adar II. See SA 685:1 and 685:5.

3. **PURIM KATAN IN ADAR I: **The 2 days in Adar I of a leap year that would otherwise have been Purim (14 and 15 Adar I) are observed as Purim Katan. See SA 697 (the very last chapter of Orach Chayyim!) for details. See also event O.9.

4. **WHICH ADAR IS EXTRA? **What is the status of the two months of Adar? Which one is the “real” Adar, and which one is extra? I’ll leave this for you to ponder. See Talmud Yerushalmi Megilla 7a. For a recent contribution, see Rav David Kav, “Haggeder hahilkhati shel shnei haAdarim” in *Yod’ei** Binah* vol. 2 (Drazin Institute for Kiddush Hachodesh Studies, Yeshivat Kerem B’Yavneh, Nisan 5764), pp. 60-63. Thanks to my brother Avi for buying this volume for me on his way back from yeshiva there.

5. **TWO NEW YEARS ON SAME DAY OF THE WEEK: **Tu BiShvat (15 Shevat – the New Year for Trees) falls in a leap year on the same day of the week as the following 1 Tishrei (Rosh HaShana – the New Year for year-count and other things – see the first Mishna in Rosh HaShana).

6. **MOST OF THE DOUBLE PARASHIYYOT ARE SEPARATE:** Because of the extra month, a leap year contains at least 4 Shabbatot more than a non-leap year. **Vayyakhel-Pekudei, Tazria-Metzora, Acharei Mot-Kedoshim, and Behar-Bechukkotai are always read separately in a leap year. **They are usually combined in non-leap years (with possible exceptions). For more about parashiyyot being read separately, see events E.7, N.10, and especially O.1 which contains a surprise for this year.

7. **ULKHAPPARAT PASHA:** The common custom is that we add the words “ulkhapparat pasha” to the Musaf of Rosh Chodesh during a leap year, from Rosh Chodesh Cheshvan through Rosh Chodesh Adar II. See MV 423:6 for alternative customs. I am always amused by the sight of people wondering, during Musaf of the first day of Rosh Chodesh Cheshvan, whether or not the year is going to be a leap year. I was once at an aufruf on this date, when after Kedusha of Musaf, the chatan ran over to me and said “Ari! Quick! The chazzan needs to know whether it’s a leap year!” At least he knew to ask the right person! See also the end of section K.

**G. ****ROSH HASHANA ON THURSDAY**** **

The first day of Rosh HaShana falls on Thursday in the following 4 year-types: הכז (hei-kaf-zayin), השא (hei-shin-aleph), החא (hei-chet-aleph), and השג (hei-shin-gimel). Altogether, these year-types account for **31.9%** of all years. That is still not rare at all, but as with most calendrical events the distribution is irregular. **The last time Rosh HaShana fell on Thursday was 7 years ago, in 5758 (1997).**

There can be up to 2 consecutive years with Rosh HaShana on Thursday.

Here is the list of **events that occur only in years with Rosh HaShana on Thursday**. In addition to these, all the events of section C occur in such years, as explained there.

1. **THREE-DAY MIKRA KODESH FOR HOLIDAYS IN TISHREI:** Colloquially known as a “**3-day yom tov**”, in the Diaspora we will have 3 of them in Tishrei. The two days of Rosh HaShana, first two days of Sukkot, and Shemini Atzeret/Simchat Torah all fall on **Thursday-Friday**. This requires an **“eiruv tavshilin” on Wednesday **for each occasion. **Even in Israel **where most holidays are only one day, **there will still be a “3-day yom tov” for Rosh HaShana**. This is the only possible occurrence of a “3-day yom tov” in Israel, and also **the only possibility in ****Israel**** for an “eiruv tavshilin” on Wednesday. **Note that Israelis never have a Shabbat-Sunday-Monday type of 3-day yom tov, the way Diaspora Jews sometimes have for Pesach or Shavuot. See also M.19 regarding Pesach this year. In 5765 there are 4 occurrences of a 3-day Mikra Kodesh throughout the year – the 3 in Tishrei, as well as Pesach. Having four occurrences of a 3-day Mikra Kodesh in the same calendar year happens in 25.2% of years.

^{th}Independence Day of the State of Israel, the Government of Israel legislated that Friday 5 Iyyar 5758 would be a national holiday, in addition to Yom HaAtzmaut which was celebrated on Thursday 4 Iyyar according to the usual advancement rules. See www.knesset.gov.il/laws/special/heb/chok_yom_haatzmaut.htm

So one could say that for the first time in history, Israelis had two “3-day yom tov”s in the same calendar year 5758 – Rosh HaShana and Yom HaAtzmaut!]

2. **NO AVINU MALKEINU ROSH HASHANA AFTERNOON: **The 2^{nd} day of Rosh HaShana falls on Friday, so we don’t say Avinu Malkeinu at Mincha that day (MV 584:4).

3. **RECORD NUMBER OF CONSECUTIVE WEEKS WITH ABRIDGED KABBALAT SHABBAT: **For **4 **consecutive Friday nights in the Diaspora (only 3 in Israel), Kabbalat Shabbat will be abridged:

3 Tishrei – conclusion of Rosh HaShana

10 Tishrei – Yom Kippur

17 Tishrei – Sukkot

24 Tishrei – conclusion of Simchat Torah (Diaspora only)

On all of these dates Kabbalat Shabbat is abridged. (See SA 270:2 regarding Bamme Madlikin.) When we resume the full Kabbalat Shabbat on 1 Cheshvan (Diaspora) or 24 Tishrei (Israel), we will not have sung (the complete) Lekha Dodi since 5 or 4 weeks earlier, respectively, on 25 Elul. This is the only scenario in which this can happen. In all other years, we say the full Kabbalat Shabbat on Shabbat Shuva.

4. **HAAZINU ON EARLIEST POSSIBLE DATE:** We read Parashat Haazinu on 3 Tishrei, the earliest possible date. See also C.1 and C.2 regarding Shabbat Shuva.

5. **RECORD NUMBER OF VEZOT HABBERAKHA ****READINGS****: **The beginning of Vezot Habberakha is read on **7 **occasions, more than in any other year: Shabbat 3 Tishrei at Mincha, Monday 5 Tishrei, Thursday 8 Tishrei, Monday 12 Tishrei, Shabbat 17 Tishrei at Mincha, and both the evening and the morning of Simchat Torah.

6. **VIHI NOAM ON MOTZEI SHABBAT SHUVA: **After Shabbat Shuva, there will be a full 6-day halakhic workweek, so we do say Vihi Noam at Maariv, 4 Tishrei. In all other years, Yom Kippur would preclude saying Vihi Noam at the end of Shabbat Shuva, and there are usually 4 consecutive weeks of omitting Vihi Noam because of the Tishrei holidays. This year, there are only 2 consecutive omissions.

7. **FAST OF GEDALIA POSTPONED: **3 Tishrei falls on Shabbat, so the Fast of Gedalia is observed on Sunday, 4 Tishrei. Otherwise, it’s always on the same day of the week as Yom Kippur, exactly one week earlier. Note that **3 Tishrei never falls on Sunday**, so the only way the Fast of Gedalia can be observed on Sunday is when 3 Tishrei falls on Shabbat.

8. **AVINU MALKEINU ON FRIDAY EREV YOM KIPPUR: **When Erev Yom Kippur falls on Friday, we do say Avinu Malkeinu at Shacharit even though we don’t say Tachanun. See Rama 604:2. This is the only calendrical occasion on which we say**Avinu Malkeinu without Tachanun**, except for the yom tov days (Rosh HaShana and Yom Kippur). Thanks to David Cashman for noticing the error in my original formulation.

9. **YOM KIPPUR ON SHABBAT: **No cholent to eat that day. There’s a halakhic issue about how to fulfill the Biblical commandment of “**Remembering Shabbat**” if we can’t say the usual Kiddush on wine. We should intend to fulfill the Kiddush obligation with the Amida at Maariv. I recall hearing this somewhere but I can’t find the source for it. Note also that this is the only occasion where the Torah reading at Mincha on Shabbat is not taken from the regular weekly cycle of parashiyyot. For other halakhot relevant to Yom Kippur on Shabbat, see SA 610:1; MV 618:29; SA 619:3 and MV #7, 9-11; SA 621:1 and MV #3, 5; SA 622:1, 2, 3, and Rama and MV there; SA 623:3 and MV #4-6, 10, 12; SA 624:3 and MV #5, 7.

10. **DON’T NEED SPECIAL CANDLE AFTER YOM KIPPUR: **The end of Yom Kippur is also the end of Shabbat, so we say the full Havdala as on any Saturday night. No need for special candle that was burning since before Yom Kippur. (See discussion in MV 624:7.) However, note SA 624:3 saying that we don’t use **spices **after Yom Kippur even on Saturday night. MV (#5) disputes this, so we do use spices. What do Sephardim do?

11. **NO ABRIDGED HAVDALA IN TISHREI: **In the Diaspora, because all the holidays are followed by Shabbat, every Havdala is a full one – there is no Havdala other than on a Saturday night.

12. **3 ^{rd} DAY OF **

**SUKKOT**

**ON**

**SHABBAT – HOSHANA POSTPONED:**The Hoshana of “

**E’erokh Shui**” contains references to repentance and Yom Kippur. We usually say it on the 3

^{rd}day of Sukkot, either because it is the first weekday during the holiday (Levushei Serad to SA 663) or because it falls on the same day of the week as Yom Kippur. But the 3

^{rd}day falls on Shabbat, and on the Shabbat of Sukkot we always say “Om Netzura”, so E’erokh Shui is postponed to Sunday, the 4

^{th}day. (If you are concerned that part of this description does not apply correctly to Israel, make sure to read the Levushei Serad all the way to the end of the paragraph.)

13. **HOSHANA RABBA ON WEDNESDAY: **Hoshana Rabba is always on the same day of the week as Shavuot of the previous year.

14. **RECORD NUMBER OF CONSECUTIVE MUSAF DAYS: **In the Diaspora we say Musaf on **10 **consecutive days, from Thursday 15 Tishrei through Shabbat 24 Tishrei. This is a record number of consecutive days, and this is the only scenario in which it occurs. Note that in Israel it is not even possible to have 9 consecutive Musaf days. The most there can be is 8.

15. **SIMCHAT ****TORAH**** ****ON**** FRIDAY:** In the Diaspora, Simchat Torah is celebrated on Friday. For those who are careful about not dancing on Shabbat, this means that hakkafot must end before sunset on Friday afternoon. Thanks to Yisroel Meir DovidFremes for bringing this to my attention. See SA 339:3, but see also Rama there for leniency. Note also MV #8 regarding allowance for Simchat Torah.

16. **NO TIME TO LEARN BEREISHIT: **We complete the cycle of Torah reading on Simchat Torah, which falls on Friday (Diaspora) or Thursday (Israel), so there is very little time to study Bereishit before it is read on Shabbat morning, 24 Tishrei. It’s a long parasha, too, and certainly not a simple one. Bereishit is the only parasha **never to be read at Shabbat Mincha **(except some years in Israel), and this year it is not read on any weekday morning either.

17. **EARLIEST DATE FOR ALL PARASHIYYOT UNTIL TOLEDOT: **As Simchat Torah falls on Friday or Thursday, we read Bereishit on the earliest possible calendar date, 24 Tishrei. Similarly, all parashiyyot until the end of Cheshvan are read on their earliest possible calendar dates:

24 Tishrei – Bereishit

1 Cheshvan – Noach (with maftir and haftara for Shabbat Rosh Chodesh)

8 Cheshvan – Lekh-Lekha

15 Cheshvan – Vayyeira

22 Cheshvan – Chayyei Sara

29 Cheshvan – Toledot (with Haftarat Machar Chodesh)

**Exercise for the reader: **Why is the same not necessarily true for the month of Kislev and further?

18. **BIRKAT HACHODESH FOR CHESHVAN ON EARLIEST POSSIBLE DATE:** We bless the month of Cheshvan on Shabbat 24 Tishrei, the earliest possible date. (This is on Shabbat Bereishit, as always.) **Rosh Chodesh Cheshvan will fall on Friday and Shabbat.** Friday is 30 Tishrei, and Shabbat is 1 Cheshvan. For an interesting surprise about the timing of the molad this month, see W.3.

19. **SHABBAT ROSH CHODESH CHESHVAN: **We read the special Maftir for Shabbat Rosh Chodesh from the 2^{nd} sefer Torah. We also read the special Haftara for Shabbat Rosh Chodesh from the end of Isaiah (HaShamayim Kis’i), rather than the regular haftara for Noach (also from Isaiah). See item P.5 for more information about this haftara.

20. **BAHAB**** ****ON**** LATEST POSSIBLE DATES: **For those who observe the fasts of “BaHaB” (Monday, Thursday, and Monday) after Rosh Chodesh Cheshvan, they occur on the latest possible dates, since we must wait until the Shabbat after Rosh Chodesh to announce them, which falls on 8 Cheshvan. (See MV 492:3.) The fasts would be on 10, 13, and 17 Cheshvan.

21. **YOM KIPPUR KATAN ADVANCED IN CHESHVAN: **For those who observe the day before Rosh Chodesh as Yom Kippur Katan, it must be advanced from Shabbat 29 Cheshvan to Thursday 27 Cheshvan. See also M.9.

22. **MACHAR CHODESH FOR KISLEV: **Rosh Chodesh Kislev falls on Sunday, so we read the special Haftara called “Machar Chodesh” on Shabbat 29 Cheshvan, rather than the regular haftara for Toledot. See item P.6 for more information about this haftara.

23. **BIRKAT HACHODESH ON TOLEDOT: **We bless the month of Kislev on Shabbat Parashat Toledot, 29 Cheshvan. In other years it would be on Chayyei Sara. See also W.5 regarding the molad for this month.

24. **DAYS OF THE WEEK DETERMINED FOR TISHREI AND CHESHVAN:** Each calendar date from 1 Tishrei until 29 Cheshvan can fall on any one of 4 days of the week, depending on the weekday on which Rosh HaShana falls. The fact that RoshHaShana falls on Thursday determines the day of the week of each calendar date in these 2 months.

25. **MIKKETZ READ ON MONDAY MORNING: **There will be a Monday morning reading of the beginning of Parashat Mikketz. In other years, the Monday of Mikketz is already Chanukka. Note that the Thursday (and Friday) of Mikketz is always Chanukka so **Mikketz is never read on a Thursday**.

26. **BIRKAT HACHODESH ON MIKKETZ: **We bless the month of Tevet on Shabbat Parashat Mikketz. In other years it would be on Vayyeishev. See also C.4 and J.5.

**H. ****VAYYEILEKH NOT READ THE WHOLE YEAR**

The cycle of Torah readings is such that Parashat Vayyeilekh can be read either before or after Rosh HaShana. This causes Vayyeilekh to have the peculiar property that it can be read either twice, once, or not at all in any Jewish calendar year, depending on whether it is read before or after Rosh HaShana, both at the beginning and at the end of the year.

We read Vayyeilekh combined with Nitzavim on the last Shabbat of the year 5764, just before Rosh HaShana 5765 (see event C.3). A year later, we will read Vayyeilekh by itself on Shabbat Shuva 5766, just after Rosh HaShana (see event E.7). Combining these two events, it follows that we do not read Vayyeilekh at all during the calendar year 5765!

Well, let’s be careful about that. A significant portion of Vayyeilekh (almost half!) is read on the last Shabbat afternoon of the year, after we have read Nitzavim in the morning. So to be precise, what we mean is that **Vayyeilekh is not read on any Shabbat morning during the calendar year**. We can also say that the last section of Vayyeilekh, Devarim 31:14-30, is never read publicly during the entire calendar year.

There are 4 year-types corresponding to years in which this occurs: הכז (hei-kaf-zayin), השא (hei-shin-aleph), זחא (zayin-chet-aleph), and החא (hei-chet-aleph). These year-types account for **29.6% **of all years. The last time we had such a year was 4 years ago, in 5761. The next time after 5765 will be 3 years later, in 5768.

**I. ****“CHASEIRA” YEAR – CHESHVAN AND KISLEV HAVE 29 DAYS EACH**

The term “chaseira” or “missing” refers to the fact that both of the two variable months, Cheshvan and Kislev, are “short” months having only 29 days each. As explained earlier (section D), Cheshvan has 29 days more often than not, but it is less common for Kislev to be shortened to 29 days from its usual length of 30 days. **If Kislev has 29 days then Cheshvan must also have 29 days. **This means that a “chaseira” year is characterized by the fact that Kislev has 29 days.

There are 5 year-types which correspond to “chaseira” years: זחא (zayin-chet-aleph), בחג (bet-chet-gimel), החא (hei-chet-aleph), זחג (zayin-chet-gimel), and בחה (bet-chet-hei). The “chaseira” year-types account for **25.5% **of all years. This is the **least common **of the 3 possible configurations for the Cheshvan-Kislev month lengths.

The last time we had a “chaseira” year was 4 years ago, in 5761 (2000-01). The next one after this year 5765 will be 3 years from now, in 5768 (2007-08).

There **cannot be 2 consecutive “chaseira” years**. Successive occurrences of “chaseira” years can be as close together as 2 years apart (very rarely) or as far as 6 years apart.

In section D, we described calendrical events that occur in years when Cheshvan has 29 days. In this section, we describe **events that occur only in “chaseira” years, when Kislev also has 29 days:**

1. **ROSH CHODESH TEVET HAS ONLY ONE DAY: **Since Kislev has only 29 days, there is only one day of Rosh Chodesh Tevet. This day is the **6 ^{th} day of Chanukka**. In years when Kislev has 30 days, both the 6

^{th}and 7

^{th}days of Chanukka are Rosh Chodesh.

2. **FEWEST MUSAF DAYS DURING CHANUKKA: **There are only two days during Chanukka on which we say Musaf – one Shabbat and one day of Rosh Chodesh. This gives us the **minimum number of 26 times saying “Al Hannissim” during Chanukka **– 3 tefillot each of 8 days plus 2 times Musaf. If there were a second day of Rosh Chodesh we would (usually) have an extra Al Hannissim. **Exercise for the reader:** Consider all cases carefully and figure out why I added the word “usually” to the previous sentence.

3. **6 ^{th} DAY OF CHANUKKA IS 1^{st} DAY OF TEVET: **It is very important to realize that events occurring on the 6

^{th}, 7

^{th}or 8

^{th}days of Chanukka (such as

**birthdays, anniversaries, yortzeits, etc.) must not be remembered by the day of Chanukka on which they happened**. This is because these days of Chanukka can fall on different calendar dates each year, depending on whether Kislev has 29 or 30 days. The 1

^{st}day of Tevet can fall on either the 6

^{th}or 7

^{th}day of Chanukka; this year it is the 6

^{th}.

4. **7 ^{th} DAY OF CHANUKKA IS 2 TEVET: **See comment above. 2 Tevet can be either the 7

^{th}or 8

^{th}day of Chanukka. Yochanan Shrira Melnick (Jeremy and Diana’s baby boy) has his birthday on 2 Tevet, which is the 7

^{th}day of Chanukka this year, even though he was born on the 8

^{th}day of Chanukka last year.

5. **8 ^{th} DAY OF CHANUKKA IS 3 TEVET: **See comment above. 3 Tevet has the distinction of sometimes being the 8

^{th}day of Chanukka and sometimes not being Chanukka at all. Mr. Melech Goldman was born on 3 Tevet, so he celebrates his birthday some years by saying Hallel and some years not. This year it will be a Hallel day. For more about Mr. Goldman’s birthday, see section O.

6. **10 TEVET SAME DAY OF THE WEEK AS CHANUKKA: **Since the last day of Chanukka is 3 Tevet, the Fast of 10 Tevet will be exactly one week later, on the same day of the week as the first and last days of Chanukka. In other years, 10 Tevet would be one day later in the week than the first and last days of Chanukka.

**J. ****1 KISLEV ON SUNDAY**** **

The first day of Kislev falls on Sunday in the following 2 year-types: הכז (hei-kaf-zayin) and החא (hei-chet-aleph). Kislev begins on Sunday precisely in years when Rosh HaShana falls on Thursday and Cheshvan has 29 days. These year-types account for **21.9%** of all years.** **The last time Kislev began on Sunday was **7 years ago, in 5758 (1997).**

Here are the **6 possible days of the week on which Kislev can begin**, along with their corresponding frequencies:

**1 Kislev on Sunday (= first day of Chanukka on Wednesday): 21.9% of years**

1 Kislev on Monday (= first day of Chanukka on Thursday): 10.0% of years

1 Kislev on Tuesday (= first day of Chanukka on Friday): 10.1% of years

1 Kislev on Wednesday (= first day of Chanukka on Shabbat): 18.4% of years

1 Kislev on Thursday (= first day of Chanukka on Sunday): 11.5% of years

1 Kislev on Friday (= first day of Chanukka on Monday): 28.0% of years

Kislev cannot begin on Shabbat. In fact, even when Rosh Chodesh Kislev has 2 days, **no day of Rosh Chodesh Kislev can ever fall on Shabbat**.

When Kislev begins on Sunday, it may have either 29 or 30 days. Sunday is the only day of the week with this distinction. (When Kislev begins on Monday, Wednesday or Friday it must have 30 days, and when it begins on Tuesday or Thursday it must have 29 days. Note however that when Kislev begins on Sunday, it may have 29 days only in a leap year, or 30 days only in a non-leap year.)

The possible interval lengths between occurrences of 1 Kislev on Sunday are 3, 4, 7, 10, 11, or 14 years.

All of the events listed in sections C, D, E, G, and H occur in years with Kislev starting on Sunday, as explained in each section. **The following calendrical events occur only in years with 1 Kislev on Sunday**:

1. **ROSH CHODESH ****KISLEV**** ****ON**** SUNDAY ONLY:** As opposed to both Sunday and Monday, as could happen in some other years. See D.1 and G.22.

2. **PARASHIYYOT DETERMINED FOR KISLEV:** Here are the dates on which each parasha is read:

7 Kislev – Vayyeitzei

14 Kislev – Vayyishlach

21 Kislev – Vayyeishev

28 Kislev – Mikketz (with maftir and haftara for Shabbat Chanukka)

3. **FIRST AND LAST DAYS OF CHANUKKA ON WEDNESDAY: **(This follows from item D.2 combined with section G.) We light the first Chanukka candle on Tuesday evening. We light 8 Chanukka candles the following week on Tuesday evening. In general, the first day of Chanukka can fall on any day of the week except Tuesday. We never light the first candle on Monday night.

4. **SHABBAT CHANUKKA ON 4 ^{th} DAY OF CHANUKKA:** We read the dedication of the tribe of Reuven as maftir from the 2

^{nd}sefer Torah. In general, any day of Chanukka except the 5

^{th}can fall on Shabbat.

5. **BIRKAT HACHODESH FOR ****TEVET**** ****ON**** LATEST POSSIBLE DATE: **We bless the month of Tevet on Shabbat 28 Kislev, the latest possible date. See also C.4 and G.26. Rosh Chodesh Tevet will be on Monday, although in some years it may be Tuesday as well.

6. **DAYS OF THE WEEK DETERMINED FOR KISLEV:** Each calendar date from 1 through 29 Kislev can fall on any one of 6 days of the week, depending on the weekday on which 1 Kislev falls. The fact that 1 Kislev falls on Sunday determines the day of the week of each calendar date this month (in addition to the days of the week for dates in Tishrei and Cheshvan, which are already determined from G.24).

**K. ****“CHASEIRA” LEAP YEAR – 383 DAYS LONG**

Combining the information in sections F and I, we see that this year is a “chaseira” year that is also a leap year. That is, the months of Cheshvan and Kislev have 29 days each, and there are 2 months of Adar. All of the other months have fixed lengths, as described in chapter 8 of Rambam, Hilkhot Kiddush HaChodesh. This means that the year contains 7 29-day months (Cheshvan, Kislev, Tevet, Adar II, Iyyar, Tammuz and Elul) and 6 30-day months (Tishrei, Shevat, Adar I, Nisan, Sivan, and Av), for a **total of 383 days **in the year, which amount to **54 weeks and 5 days**.

There are 3 year-types which correspond to 383-day years: החא (hei-chet-aleph), זחג (zayin-chet-gimel), and בחה (bet-chet-hei). These year-types account for **15.5% **of all years. It is interesting to note that **it is relatively common for “chaseira” years to be leap years, and for leap years to be “chaseira” years**.

What I mean is this: Although only 25.5% of all years are “chaseira” years (see section I), it turns out that **42.0% of leap years are “chaseira”**. So although the “chaseira” year represents, in general, the least common configuration of the Cheshvan-Kislev month lengths, in the particular case of leap years this is not so. Leap years are more likely to be “chaseira” than “kesidrah” (where Cheshvan has 29 days and Kislev has 30 days).

Similarly, although only 7/19 or 36.8% of all years are leap years (see section F), it turns out that **60.6% of “chaseira” years are leap years**. So “chaseira” years are more likely to be leap years than non-leap years, which is somewhat surprising.

I can give a partial explanation for this statistical anomaly: In a leap year, the “extra” month of Adar I adds 30 days to the year length. This is longer than the average month length in the Jewish calendar, which is slightly more than 29½ days. To compensate for this extra length, it is more likely in a leap year than in a non-leap year that a day will have to be removed from Kislev, making the year “chaseira”.

In any event, here is a list of recent and upcoming years that are 383-day years, i.e. “chaseira” leap years: 5662 (1901-02), 5668 (1907-08), 5670 (1909-10), 5679 (1918-19), 5687 (1926-27), 5695 (1934-35), 5703 (1942-43), 5706 (1945-46), 5714 (1953-54), 5719 (1958-59), 5722 (1961-62), 5730 (1969-70), 5733 (1972-73), 5741 (1980-81), 5746 (1985-86), 5749 (1988-89), 5757 (1996-97), **5765 (2004-05)**, 5768 (2007-08), 5784 (2023-24), 5790 (2029-30), 5793 (2032-33), 5801 (2040-41), 5812 (2051-52), 5817 (2056-57), 5820 (2059-60), 5828 (2067-68), 5831 (2070-71), 5839 (2078-79), 5844 (2083-84), 5847 (2086-87), 5855 (2094-95).

Note that the “chaseira” leap year is the shortest possible leap year, and in fact has fewer Rosh Chodesh days than any other leap year. There are 18 Rosh Chodesh days during a “chaseira” leap year. There are only 9 Rosh Chodesh days from the beginning of the year until Adar II, so we add “ulkhapparat pasha” on these 9 occasions. (See F.7.) This is the **fewest number of times we can say “ulkhapparat pasha” in a leap year**. In other leap years there would be 10 or 11 such days.

**L. ****HAFTARAT TZAV IS READ**

This year, we read the regular haftara listed for Parashat Tzav, which is a rare occurrence. In all non-leap years, we read Parashat Tzav on Shabbat Haggadol. In most leap years, we read Tzav on a Shabbat when there is a special maftir and haftara – either Zakhor orPara. The only time Tzav gets its own haftara (from Yirmeyahu chapter 7) is during a leap year that has a **“break” between Zakhor and ****Para**** **(see item E.1). There are only 3 such year-types – החא (hei-chet-aleph), בשז (bet-shin-zayin), and גכז (gimel-kaf-zayin). These year-types account for **13.9% of all years**. The last time we read Haftarat Tzav was 10 years ago, in 5755 (1995), but after this year we will read it again 3 years from now, in 5768 (2008). Note that all of the events of sections E and F necessarily occur in years when we read Haftarat Tzav.

Here is a list of recent and upcoming years in which we read Haftarat Tzav: 5660 (1900), 5670 (1910), 5681 (1921), 5684 (1924), 5687 (1927), 5698 (1938), 5708 (1948), 5711 (1951), 5714 (1954), 5725 (1965), 5738 (1978), 5741 (1981), 5752 (1992), 5755 (1995), **5765 (2005)**, 5768 (2008), 5776 (2016), 5779 (2019), 5782 (2022), 5803 (2043), 5806 (2046), 5809 (2049), 5812 (2052), 5833 (2073), 5836 (2076), 5839 (2079), 5850 (2090), 5860 (2100).

The possible interval lengths between years when we read Haftarat Tzav are 3, 8, 10, 11, 13, or 21 years.

Note that the years in which Haftarat Tzav is read are precisely the years in which there are no “double parashiyyot” read in Israel the whole year. See the comments at the end of event O.1, as well as the note at the end of section N, for more details about this.

Note also that in walled cities such as Yerushalayim, Haftarat Tzav is NOT read in a החא (hei-chet-aleph) year-type, as the Shabbat of Parashat Tzav is Shushan Purim. See event M.7. So **in walled cities, Haftarat Tzav is read in only 10.0% of years, and this year is not one of them.**

While on the topic of **rarely read haftarot**: There are two other rare haftarot which we do read this year – Haftarat Vayyakhel (see item N.2) and Haftarat Pinechas (see item N.9). Some examples of rare haftarot which we do NOT read this year are: Mikketz, Tazria, and Acharei Mot. **Exercise for the reader:** For each of these 3 rare haftarot, verify why we don’t read it this year, and then figure out which year-types are the ones in which we do read it, how often it is read, and what are the possible interval lengths between occurrences of its reading. Since this is a multi-part exercise, partial credit is available. Warning: The haftara for Acharei Mot is tricky, as there are different minhagim involving the haftarot for Acharei Mot and Kedoshim. **Super-duper extra credit exercise:** Repeat the above exercise not only for the rarely read haftarot, but for all haftarot in the book. This is a project which I might like to do at some point but probably will never get around to it. If you plan to work on this one (or even if you don’t), I’ll be happy to send you a copy of B.Alperin’s “Permanent Haftarah Calendar” (found in the back of some chumashim, published in 1928 by the Hebrew Publishing Company), which would be helpful. Thanks to Ethan Rotenberg for sending it to me.

**M. ****PESACH ON SUNDAY**

A whole book could be written on the halakhot of Erev Pesach on Shabbat. In fact, I think several such books have been written. One booklet I happen to have come across is “What to do when Erev Pesach falls on Shabbos”, by Rabbi Simcha J. Weissman, first published in 5710 (1950) and then revised in 5734 (1974) and 5737 (1977). Thanks to Chaim Greenspan for showing me this one. I’m sure there are others, and new ones will become available in a few months. In any event, my goal here is not to examine the halakhic details. For that, consult your Local Orthodox Rabbi. All I want to do is point out various calendrical events that occur in this situation.

The first day of Pesach falls on Sunday in the following year-types: השא (hei-shin-aleph), זחא (zayin-chet-aleph), and החא (hei-chet-aleph). Altogether, these year-types account for **11.5% of all years**. In fact, **Sunday is the least common of the possible days of the week on which the first day of Pesach can fall.** The other possible days are Tuesday, Thursday, and Shabbat.

Why is it so rare for the first day of Pesach to fall on Sunday? In a sense, the basic answer is relatively simple: We know that according to our fixed calendar system, Pesach cannot fall on Monday, Wednesday or Friday – in mnemonic form, “La BaDU Pesach”, where בדו(bet-dalet-vav) stands for Monday, Wednesday and Friday. So what happens in years when Pesach should have been on a Monday, Wednesday or Friday? In a certain sense, the calendar is adjusted so that Pesach is observed on the following day of the week. (This adjustment is made by varying the lengths of the preceding and following Cheshvan and Kislev.) For the purpose of this question, the important point is that Pesach falls on Tuesday whenever it “should have been” on either Monday or Tuesday; it falls on Thursday whenever it “should have been” on either Wednesday or Thursday; and it falls on Shabbat whenever it “should have been” on either Friday or Shabbat. This explains why the first day of Pesach is twice as likely to fall on each of Tuesday, Thursday or Shabbat as it is to fall on Sunday.

Of course all this must be taken with a grain of salt, as the calculations determining the year-type are more complex than this. In fact, the day of the week on which Pesach begins in any year depends on the day on which the following Rosh HaShana falls. Here are the various possibilities and their corresponding frequencies:

Rosh HaShana on Monday (= previous Pesach on Shabbat): 28.0% of years

Rosh HaShana on Tuesday (= previous Pesach on Sunday): 11.5% of years

Rosh HaShana on Thursday (= previous Pesach on Tuesday): 31.9% of years

Rosh HaShana on Shabbat (= previous Pesach on Thursday): 28.6% of years

I will have more to say about year-type frequencies in a later section. Well, I may or I may not get around to writing more about year-type frequencies later in this essay, depending on how much time I have. This essay must be finished before Rosh HaShana in order to be useful, and I’m supposed to be working on a Ph.D. now, but this essay is taking up way too much of my time.

Here is a list of recent and upcoming years in which the first day of Pesach falls on Sunday: 5663 (1903), 5670 (1910), 5683 (1923), 5687 (1927), 5690 (1930), 5710 (1950), 5714 (1954), 5734 (1974), 5737 (1977), 5741 (1981), 5754 (1994), 5761 (2001), **5765 (2005)**, 5768 (2008), 5781 (2021), 5785 (2025), 5805 (2045), 5808 (2048), 5812 (2052), 5832 (2072), 5835 (2075), 5839 (2079), 5859 (2099).

The possible interval lengths between occurrences of Pesach on Sunday are 3, 4, 7, 13, 16, 17, or 20 years.

As you can see from the list above, **the current decade is extremely unrepresentative with regard to the frequency of Pesach on Sunday**. Pesach falls on Sunday 3 times within 8 years, in 5761, 5765 and 5768! Kids growing up nowadays will not appreciate how rare is the experience of Pesach on Sunday. In my childhood I was deprived of the experience, as it did not happen for 13 years, between 5741 (1981) when I was too young to appreciate it and 5754 (1994) when I was already in Grade 12.

Note that in a year when the first day of Pesach falls on Sunday, the previous Rosh HaShana must have been on either Thursday or Shabbat. Therefore, all of the events of sections C, E, and H occur in years with Pesach beginning on Sunday. Here is the list of **events that occur only in years with the first day of Pesach on Sunday**. Recall that these events occur in 11.5% of years.

1. **3 SIFREI TORAH FOR SHABBAT-ROSH CHODESH-SHEKALIM: **Rosh Chodesh Adar (II) falls on Shabbat, so we read from 3 sifrei Torah (see SA 685:1). The sections usually read as “shishi” and “shevii” from the regular parasha are combined into one, and the 7^{th} person called to the Torah reads the Rosh Chodesh reading in Pinechas from the 2^{nd} sefer Torah. The Maftir is Parashat Shekalim, read from the 3^{rd} sefer Torah. The usual haftara for Shabbat Rosh Chodesh (HaShamayim Kis’i) is replaced by the haftara for Shekalim (see MV 685:3). [Some communities read the first and last verses of HaShamayim Kis’i after the haftara for Shekalim.] See O.12 for an extra twist on this event for this year. See item P.5 for more discussion about Shabbat-Rosh Chodesh and the omitted haftara.

2. **NO BREAK BETWEEN SHEKALIM AND ZAKHOR: **SA (685:6) gives mnemonics to remember when the breaks are between the Four Special Parashiyyot of Adar. This year’s mnemonic is זטו (“zayin-tet-vav” or “zatu”), meaning that Rosh Chodesh Adar (II) falls on Shabbat (=zayin) so the “break” when we don’t read a special parasha falls on 15 (=tet-vav) Adar (II), between Zakhor and Para. [Of course that day is Purim in Yerushalayim (see M.6) so one might argue it’s not much of a “break”.] This is the only configuration where there is no break between Shekalim and Zakhor. The only break this year is between Zakhor and Para. See also E.1. (Some years there are two breaks, or else a break only between Shekalim and Zakhor.)

3. **PARASHAT ZAKHOR ON EARLIEST POSSIBLE DATE: **Since Purim falls on Friday, we read the special maftir called Zakhor from the 2^{nd} sefer Torah (as well as the corresponding haftara) on the previous Shabbat, 8 Adar (II), which is the earliest possible calendar date. This means that inevitably there will be more than 12 months from now until next year’s reading of Parashat Zakhor, and so a certain extrapolation from an analysis of the Chatam Sofer implies that we should make sure to hear Parashat Zakhor again properly when we read Parashat Ki Teitzei in the summer, on 13 Elul. See Eliezer Bulka’s Weekly Shtikle at www.geocities.com/ez_bulka/shtikle.html#Zachor although I’m pretty sure I came up with this extrapolation independently. Note that this is a chumra not required by halakha so don’t worry too much about it.

4. **FAST OF ESTHER ON THURSDAY: **Note that the Fast of Esther [13 Adar (II)] **actually falls on Thursday this year**, as opposed to last year when it was observed on Thursday because 13 Adar fell on Shabbat. The Fast of Esther is observed on Thursday in 43.4% of years – 11.5% with Purim immediately following as in this year, and 31.9% with Purim on Sunday.

5. **PURIM ON FRIDAY: **The regular Purim for non-walled cities [14 Adar (II)] falls on Friday, which makes observances somewhat constrained because of Shabbat. Rama 695:2 advises making the Seuda in the morning. If you’re concerned about the day being an extremely busy workday, see section V for an unusual surprise.

6. **SHUSHAN PURIM ON SHABBAT: **Purim for walled cities such as Yerushalayim [15 Adar (II)] falls on Shabbat. This scenario is known as “**Purim Meshullash**” or Triple Purim, because the observances are spread over 3 days – Friday, Shabbat and Sunday, in order to avoid chillul Shabbat. This also means that everyone reads the Megilla on the same day, both in walled and non-walled cities. For the detailed halakhot see SA 688:6.

7. **SAME HAFTARA TWO CONSECUTIVE SHABBATOT: **Since Purim in walled cities falls on Shabbat, the Torah reading for Purim (from Beshallach) is read as maftir from the 2^{nd} sefer Torah. The haftara for Purim on Shabbat is the same as the haftara for Parashat Zakhor the previous week (the story of King Shaul and Amalek in Samuel I). **Exercise for the reader: **There is one other situation where the same haftara can be read on two consecutive Shabbatot. Figure out what it is. Thanks to Tzvi Goldman and Danny Hershtal for bringing this to my attention, and also to David Woolf who I think used it as a riddle one year.

8. **PARA**** ON 22 ADAR (II):** We read the special maftir called Para from the 2^{nd} sefer Torah on 22 Adar (II), as well as its corresponding haftara.

9. **YOM KIPPUR KATAN ADVANCED IN ADAR (II), TAMMUZ AND AV: **Those who observe the day before Rosh Chodesh as Yom Kippur Katan must advance the observance from Shabbat 29 Adar (II) to Thursday 27 Adar (II); from Friday 29 Tammuz to Thursday 28 Tammuz; and from Shabbat 29 Av to Thursday 27 Av. See also G.21.

10. **BIRKAT HACHODESH FOR ****NISAN**** ****ON**** LATEST POSSIBLE DATE:** We bless the month of Nisan on Shabbat 29 Adar (II), the last day of the month. See also the next item, as well as N.4. See also W.6 regarding the molad for this month.

11. **MACHAR CHODESH OMITTED BECAUSE OF HACHODESH: **We read the special maftir called HaChodesh from the 2^{nd} sefer Torah on 29 Adar (II). This maftir is taken from Shemot chapter 12, and describes the preparations for the exodus fromEgypt, **beginning with the mitzva to establish a Jewish calendar. It is my favourite parasha in the Torah. **Although **Rosh Chodesh Nisan falls on Sunday**, the usual haftara “Machar Chodesh” is replaced by the special haftara for HaChodesh. [Some communities read the first and last pesukim of “Machar Chodesh” after the haftara for HaChodesh.] See item P.6 for more discussion about the omitted haftara, Machar Chodesh.

12. **RECORD CONSECUTIVE NO AV HARACHAMIM WEEKS: **What’s the greatest number of consecutive Shabbatot on which we don’t say Av HaRachamim (before Ashrei)? That’s a difficult question, because there are **many different minhagim**regarding when to say Av HaRachamim, especially regarding Nisan and Sefira. See Rama 284:7. (If I’m not mistaken, Sephardim don’t say it at all, so their answer would be infinity.) The record seems to occur this year, and depending on custom, the answer may be 10, although I think **9 **is more likely. Here is the sequence of consecutive Shabbatot on which we don’t say it: (Note that in all other years, there would be one Shabbat in Adar (II) when we do say it.)

24 Adar I (or 24 Shevat if not a leap year) – Blessing the month of Adar (II)

1 Adar (II) – Rosh Chodesh and Parashat Shekalim

8 Adar (II) – Parashat Zakhor

15 Adar (II) – Shushan Purim

22 Adar (II) – Parashat Para

29 Adar (II) – Blessing the month of Nisan and Parashat HaChodesh

7 Nisan – No Av HaRachamim in Nisan

14 Nisan – Erev Pesach

21 Nisan – 7^{th} day of Pesach, but note that in Israel this is a Yizkor day, so Israelis would say Av HaRachamim at the end of Yizkor, thereby limiting the record to 8

28 Nisan – this is the controversial one. MV (284:18) says we say Av HaRachamim because of Sefira, thereby limiting the record to 9 (Diaspora), even though it is still Nisan and also Blessing the month of Iyyar. But from discussion with Rabbi Yacov Felder it seems that Shomrai Shabbos in Toronto does not say Av HaRachamim on this day, so the record there becomes 10 consecutive weeks of not saying Av HaRachamim.

**Exercise for the reader: **Let me know if you know anything further about different minhagim and how they affect this record.

13. **RECORD CONSECUTIVE NO TACHANUN: **What’s the greatest number of consecutive days on which we don’t say Tachanun? For the question to be meaningful, we must exclude personal situations such as weddings, britot and mourning, and agree to count **only calendrical considerations**. Otherwise someone could get married every week and never have to say Tachanun. So, let’s work it out. We never say Tachanun in Nisan, nor on 1 Iyyar which is Rosh Chodesh. That’s 31 consecutive days every year. But this year 29 Adar (II) falls on Shabbat, so we get **32 consecutive Tachanun-free days**. That seems to be the record. If you enjoyed that, here’s an **exercise for the reader**: What’s the record number of consecutive days of no Tachanun at**Mincha**? If you think that’s too easy, don’t forget to consider the various possible configurations of Yom HaAtzmaut. (Does anyone have any authoritative information as to whether or not we say Tachanun at Mincha the day before Yom HaAtzmaut?)

14. **DERASHA A WEEK AHEAD: **Shabbat Haggadol falls on Erev Pesach, so the usual Derasha would be given a week ahead of time, on Shabbat 7 Nisan (MV 430:2).

15. **FAST OF FIRSTBORN MOVED TO THURSDAY: **Since Erev Pesach falls on Shabbat, the Fast of the Firstborn (or, more likely, the seudat mitzva held to break the fast) is observed on Thursday, 12 Nisan (SA 470:2). Note that Erev Pesach never falls on Thursday, so the only way the Fast of the Firstborn can be observed on Thursday is when Erev Pesach falls on Shabbat.

16. **SEARCH FOR CHAMETZ EARLY: **Since Erev Pesach falls on Shabbat, we search for chametz on Thursday evening, the night of 13 Nisan. We do say a berakha on this search (see SA 444:1 and MV #1), despite the fact that if the search is done early for any other reason there would be no berakha. We then burn the chametz on Friday morning, 13 Nisan.

17. **SHABBAT HAGGADOL EREV PESACH: **I won’t belabour the point. Just see SA 444. For more about this Shabbat, see O.13.

18. **FIRST SEDER SATURDAY NIGHT: **The Seder begins with the Kiddush-Havdala combination known as “YaKNeHaZ” (see SA 473:1). There’s also a controversial issue about reversing the order of the words “min hazzevachim umin happesachim” in the berakha “Asher gealanu” before drinking the second cup. See Shaar Hatziyyun 473:80. Thanks to Eliezer Bulka who discussed this in his Weekly Shtikle for Pesach 5761. (Note that in Israel, this is the only way there can be a Seder on Saturday night.)

19. **THREE-DAY MIKRA KODESH FOR BEGINNING OF PESACH: **In the Diaspora we have Shabbat-Sunday-Monday for the first days of Pesach. It’s the kind of 3-dayer that **never happens in ****Israel**. (See also G.1 regarding other cases of 3-day Mikra Kodesh this year.) Note that if Pesach starts on a Thursday we also get a 3-dayer, so in 40.1% of years the beginning of Pesach forms a “3-day yom tov” in the Diaspora. Note **that the last days of Pesach can never form a “3-day yom tov”**. (Every other holiday can, in the Diaspora.)

20. **AT-BASH MNEMONIC WORKS BEST**: SA 428:3 (quoting the Tur) gives a mnemonic for determining the day of the week on which each holiday falls in any year, according to the days of Pesach. The letters of the aleph-bet counting from the beginning are matched in sequence to the letters counting backward from the end. The mnemonic is known as “**At-Bash**”, meaning **A**leph corresponds to **T**av, **B**et to **Sh**in, etc. The correspondence is interpreted to mean that the **first **day (aleph) of Pesach falls on the same day of the week as **T**isha B’Av (tav); the **second **day (bet) of Pesach falls on the same day of the week as **Sh**avuot (shin); etc. (See SA and other sources for the remaining details.) **The “At-Bash” mnemonic applies to all years. **However, this year, since the first day of Pesach falls on Sunday, the number of each day of Pesach is the same as the number of the day of the week on which it falls. In other words, **for this year only**, we can reinterpret “At-Bash” to mean aleph (the **first **day of the week – Sunday) matches with tav (**T**isha B’Av), etc., making the days of the week easier to determine for the various holidays.

21. **7 ^{th} DAY OF PESACH ON SHABBAT**: This riddle comes from the Yiddish newspaper “Der Yid”, on 2 Iyyar 5764: Q: How can it happen that we read

**4 different “songs” on one Shabbat?**A: When the 7

^{th}day of Pesach falls on Shabbat, we read the

**Song of Moshe**(“Az yashir”), the

**Song of Miriam**(“Vattaan lahem Miriam”), both from the Torah reading in Beshallach; the

**Song of David**in the haftara from Samuel II; and the

**Song of Songs**(Shir HaShirim), as it is the Shabbat during Pesach. Thanks to Rabbi Yisroel Meir Gross for bringing this riddle to my attention.

22. **8 ^{th} NIGHT OF PESACH – “YAKNEHA” WITHOUT “Z”: **When yom tov falls on Saturday night, the usual mnemonic for the

**Kiddush/Havdala combination**is known as “YaKNeHaZ”, referring to the order of the berakhot – “Yayin, Kiddush, Ner, Havdala, Zeman” (SA 473:1, MV #3). But on the 7

^{th}and 8

^{th}nights of Pesach we

**don’t say Shehecheyanu**(SA 490:7). This year the 8

^{th}night falls on Motzei Shabbat, so the usual mnemonic doesn’t quite work. We have Kiddush and Havdala without the Zeman at the end. This situation is unique to the Diaspora because the 7

^{th}night of Pesach cannot fall on Motzei Shabbat.

**Exercise for the reader:**There is one other Kiddush/Havdala combination that is unique to the Diaspora. Figure out what it is.

23. **OMER COUNT BEFORE KIDDUSH/HAVDALA: **Another issue with the 8^{th} night of Pesach, unique to the Diaspora: In general, we count the Omer after Kiddush in shul on Friday night and yom tov night, but before Havdala on Saturday night and motzei yom tov. So what happens when the 8^{th} day of Pesach falls on Saturday night and we say Kiddush and Havdala combined? SA (489:9) says that we count the Omer before the Kiddush/Havdala combination, because the holiness of the (exiting) Shabbat is greater than the holiness of the (incoming) yom tov day (MV #43).

24. **YOM HASHOAH ADVANCED TO 26 NISAN: **Because 27 Nisan falls on Friday, Knesset law stipulates that Yom HaShoah is observed on Thursday, 26 Nisan. See the relevant legislation at www.knesset.gov.il/shoah/heb/memorial_law.htm . I found one source stating that this adjustment was introduced in 5761 (2001) [“Errata and Notes for Calendrical Calculations: The Millennium Edition”, available from www.calendarists.com, referring to page 110 of the book, by Edward M. Reingold and NachumDershowitz]. I found another source implying that the adjustment has existed for longer than that [“Shearim LaLuah HaIvry” by Rahamim Sar-Shalom, page 88]. I suppose I need a “katuv shelishi lehakhria beineihem”. (**Exercise for the reader: **Please find me an authoritative source indicating when this and other similar adjustments were introduced.) If the first source is correct, then this year is the 2^{nd} time in history that we observe Yom HaShoah on 26 Nisan.

25. **ROSH CHODESH ****IYYAR**** ****ON**** MONDAY AND TUESDAY:** Monday is 30 Nisan, and Tuesday is 1 Iyyar. We bless the month of Iyyar on the previous Shabbat, 28 Nisan.

26. **YOM HAATZMAUT ADVANCED TO 3 IYYAR: **Because 5 Iyyar falls on Shabbat, Knesset law stipulates that Yom HaAtzmaut is celebrated on the previous Thursday, 3 Iyyar, and Yom HaZikaron is observed on Wednesday, 2 Iyyar. See the relevant legislation at www.knesset.gov.il/laws/special/heb/chok_yom_haatzmaut.htm and www.knesset.gov.il/laws/special/heb/chok_yom_hazikaron.htm . My understanding is that this adjustment has been in effect for as long as Yom HaAtzmaut has existed. As you can see from the years listed at the beginning of this section, this year is the **8 ^{th} time in history that we celebrate Yom HaAtzmaut on 3 Iyyar**. The first one was 5710 (1950). For other comments regarding Yom HaAtzmaut, see events E.3, G.1, M.13, section Q, and event T.4. Wow, someone could probably write a whole book about the Calendrical Complications of Yom HaAtzmaut, especially after last year’s episode. Maybe that will be my Ph.D. thesis.

**Can one get a Ph.D. in Calendars?**

27. **PESACH ****SHEINI**** ****ON**** BAHAB**: For those who observe the fasts of “BaHaB” (Monday, Thursday, and Monday) after Rosh Chodesh Iyyar, the fasts would be on 7, 10, and 14 Iyyar. The last one coincides with Pesach Sheini (14 Iyyar). The guide “Devaryom beyomo” by Rav Shlomo Tal, at the back of Siddur Rinnat Yisrael, says that the fast is not observed on Pesach Sheini, but it does not say whether the fast should be made up at a later date. **Exercise for the reader:** Find out what is done in this case.

28. **LAG BAOMER ON FRIDAY – HAIRCUTS FOR EVERYONE**: Sephardim generally do not get haircuts until after Lag BaOmer, as opposed to the Ashkenazic custom of allowing haircuts on Lag BaOmer day itself. However, since Lag BaOmer falls on Friday, all agree that haircuts are allowed in honour of Shabbat (SA 493:2).

29. **ROSH CHODESH SIVAN ON WEDNESDAY:** We bless the month of Sivan on the previous Shabbat, 26 Iyyar.

30. **SHAVUOT ON MONDAY:** Also Yom Yerushalayim (28 Iyyar) is on the previous Monday, as it is exactly one week before Shavuot.

31. **ROSH CHODESH ****TAMMUZ**** ****ON**** THURSDAY AND FRIDAY:** Thursday is 30 Sivan, and Friday is 1 Tammuz. We bless the month of Tammuz on the previous Shabbat, 25 Sivan.

32. **BIRKAT HACHODESH FOR MENACHEM AV ON EARLIEST POSSIBLE DATE:** We bless the month of Menachem Av on Shabbat 23 Tammuz, the earliest possible date. Rosh Chodesh will be on Shabbat.

33. **SHABBAT ROSH CHODESH AV – HAFTARA OMITTED: **We read the special Maftir for Shabbat Rosh Chodesh from the 2^{nd} sefer Torah. However, the usual haftara for Shabbat Rosh Chodesh (HaShamayim Kis’i) is omitted, as we read the second Haftara of Tragedy (from Yirmeyahu) for the “3 weeks” before Tisha B’Av (see Rama 425:1 and MV #8). [Some communities read the first and last verses of HaShamayim Kis’i after the haftara from Yirmeyahu.] See also O.15 for more about this day’s Torah reading this year. See item P.5 for more discussion about Shabbat-Rosh Chodesh and the omitted haftara.

34. **17 TAMMUZ AND TISHA B’AV ON SUNDAY:** The fast days actually fall on Sunday, as opposed to falling on Shabbat and being postponed to Sunday. See E.5 for the halakhot.

35. **15 ****AV**** ****ON**** SHABBAT:** The holiday known as “Tu B’Av” falls on Shabbat.

36. **DATES DETERMINED FOR PARASHIYYOT IN DEVARIM AS WELL AS HAFTAROT OF TRAGEDY AND CONSOLATION:** Here are the dates on which each parasha and/or haftara is read. (The earlier parashiyyot depend more subtly on the year-type – see O.2.)

23 Tammuz – 1^{st} Haftara of Tragedy

1 Av – Masei (either with or without Mattot) – 2^{nd} Haftara of Tragedy – see item 33 above

8 Av – Devarim – 3^{rd} Haftara of Tragedy (Chazon)

15 Av – Vaetchannan – 1^{st} Haftara of Consolation (Nachamu)

22 Av – Eikev – 2^{nd} Haftara of Consolation

29 Av – Re’ei – 3^{rd} Haftara of Consolation

6 Elul – Shofetim – 4^{th} Haftara of Consolation

13 Elul – Ki-Teitzei – 5^{th} Haftara of Consolation

20 Elul – Ki-Tavo – 6^{th} Haftara of Consolation

27 Elul – Nitzavim – 7^{th} Haftara of Consolation

5 Tishrei of following year – Vayyeilekh – Haftarat Shuva

12 Tishrei of following year – Haazinu

37. **BIRKAT HACHODESH FOR ****ELUL**** ****ON**** LATEST POSSIBLE DATE: **We bless the month of Elul on Shabbat 29 Av (Parashat Re’ei), the latest possible date. Rosh Chodesh Elul will fall on Sunday and Monday.

38. **MACHAR CHODESH OMITTED BECAUSE OF CONSOLATION:** Although Rosh Chodesh Elul falls on Sunday, the usual haftara “Machar Chodesh” is omitted, as we read the 3^{rd} of the 7 Haftarot of Consolation after Tisha B’Av, from Isaiah (see Rama 425:2). [Some communities read the first and last pesukim of “Machar Chodesh” after the haftara from Isaiah.] See item P.6 for more discussion about the omitted haftara, Machar Chodesh.

39. **3 WEEKS COMBINED PIRKEI AVOT, EVEN IN ****ISRAEL****: **There are just over 22 weeks from the end of Pesach until Rosh HaShana. For those who observe the minhag of studying one chapter of Pirkei Avot each Shabbat throughout the summer, this should be enough for three 6-week cycles, with 4 weeks remaining to complete the cycle a fourth time. This means we must cover 2 chapters on each of the last 2 weeks before Rosh HaShana. This year, however, since Tisha B’Av falls on Sunday, we do not study a chapter of Avot on Shabbat afternoon, Erev Tisha B’Av (Rama 553:2, MV #9). So we lose a week – there are only 21 Shabbatot available to complete the 4 cycles, so we must double-up on each of the last 3 weeks of the year. Let’s see what happens in other years: When Tisha B’Av falls on Shabbat we would have the same problem, as there would not be a chapter assigned to that Shabbat. But in such years, the 8^{th} day of Pesach falls on Shabbat, which would be a regular Shabbat in Israel. In Israel there would be 23 Shabbatot from the end of Pesach until Rosh HaShana, so even omitting Tisha B’Av there would still be 22 Shabbatot available for Pirkei Avot. So although Diaspora Jews would have only 21 Shabbatot available and would have to double-up for 3 weeks, Israelis would have 22 Shabbatot available and would double-up only 2 weeks. Similarly, in years when Pesach begins on Thursday, Diaspora Jews will lose one Shabbat due to the 2^{nd} day of Shavuot falling on Shabbat. So again, Diaspora Jews would have only 21 Shabbatot available and would have to double-up for 3 weeks, while Israelis would have 22 Shabbatot available and would double-up only 2 weeks. Finally, in years when Pesach begins on Tuesday there are no difficulties, as there are exactly 22 Shabbatot available, so all communities would double-up the last 2 weeks.

40. **LONGEST POSSIBLE SELICHOT PERIOD:** Better start catching up on your sleep now. Rosh HaShana of the following year will begin on Tuesday. Since we must have at least 4 days of Selichot before Rosh HaShana, Ashkenazim begin saying Selichot on Motzei Shabbat (or Sunday morning), 21 Elul. This is the earliest possible date to begin Selichot. This means (at least in theory!) that unlike most years, we say everything in the book – we get all the way to “Selichot for the 7^{th} day” before continuing with “Selichot for Erev Rosh HaShana”.

41. **TORAH ****READING**** ****ON**** EREV ROSH HASHANA AT THE END OF THE YEAR:** So you’ve made it through all those days of Selichot, and you finally get to Erev Rosh HaShana. Not only is there a very long Selichot for the day, but it will be a Monday so there’s a Torah reading too. At least there’s no Tachanun at Shacharit! Note also that this is the **only situation in which we can read Vayyeilekh on a Monday morning**. It is also the **only situation in which we read Vayyeilekh on a weekday morning in Elul**.

42. **DAYS OF THE WEEK DETERMINED FOR ADAR (II) THROUGH ELUL:** Each calendar date from 1 Adar (II) until 29 Elul can fall on any one of 4 days of the week, depending on the weekday on which Pesach begins. The fact that the first day of Pesach falls on Sunday determines the day of the week of each calendar date in these 7 months. Even more is true: **the fact that Pesach begins on Sunday determines the day of the week for all calendar dates until the end of Shevat of the following year! **This is because Rosh HaShana of the following year must begin on Tuesday, and when Rosh HaShana begins on Tuesday it turns out that the year must be kesidrah, i.e. Cheshvan must have 29 days and Kislev must have 30, so there is only one possible day-of-the-week configuration for all dates until the end of Shevat.

**N. ****LEAP YEAR WITH ROSH HASHANA ON THURSDAY:**

Leap years in which Rosh HaShana falls on Thursday are years with the following year-types: החא (hei-chet-aleph) and השג (hei-shin-gimel). These year-types account for **10.5% **of all years. The last time we had a leap year with Rosh HaShana on Thursday was **21 years ago**, the year 5744 (1983-84).

Here is a list of recent and upcoming years that are leap years with Rosh HaShana on Thursday: 5670 (1909-10), 5673 (1912-13), 5676 (1915-16), 5687 (1926-27), 5700 (1939-40), 5714 (1953-54), 5717 (1956-57), 5727 (1966-67), 5741 (1980-81), 5744 (1983-84), **5765 (2004-05)**, 5768 (2007-08), 5771 (2010-11), 5774 (2013-14), 5795 (2034-35), 5798 (2037-38), 5812 (2051-52), 5822 (2061-62), 5825 (2064-65), 5839 (2078-79), 5852 (2091-92).

The possible interval lengths between these years are 3, 10, 11, 13, 14, 21, or 24 years.

In sections C and G, we described calendrical events that occur in years in which Rosh HaShana falls on Thursday. In section F, we described events occurring in leap years. In this section, we describe additional events that **occur only in leap years beginning with RoshHaShana on Thursday. Recall that the last time these events occurred was 21 years ago, in 5744.**

1. **29 SHABBATOT BETWEEN SIMCHAT TORAH AND PESACH: **The number of Shabbatot between Simchat Torah and Pesach **affects the distribution of the parashiyyot**. In most non-leap years, there are **24 **Shabbatot during this period. We combine Vayyakhel and Pekudei, so we read Tzav on the Shabbat before Pesach. (Count the parashiyyot, and you’ll see it works!) There is one year-type (השא – hei-shin-aleph) where there are **25 **Shabbatot during this period, so we separate Vayyakhel and Pekudei and we still read Tzav on the Shabbat before Pesach. In leap years, of course, there is an extra month, so we get at least 4 extra Shabbatot. In most leap years there are **28 **Shabbatot during this period, so with all the parashiyyot separated we get to Metzora before Pesach. But this year, since Simchat Torah was on Friday (or Thursday), we effectively squeezed in an extra Shabbat between then and Pesach, so there are **29 **Shabbatot. This means we read Acharei Mot on Shabbat Haggadol, the Shabbat before Pesach. This is essentially the cause for all of the other events described in this section.

2. **HAFTARAT VAYYAKHEL IS READ: **We read Parashat Vayyakhel by itself this year on an ordinary Shabbat, so we also read the haftara assigned to the parasha. In non-leap years, Vayyakhel is either combined with Pekudei or on Parashat Para, and in other leap years it is on Parashat Shekalim, so we don’t usually read the haftara for Vayyakhel. **There are no years in which both haftarot for Vayyakhel and Pekudei are read. **This leads me to wonder why we don’t simply have the same haftara assigned to both parashiyyot Vayyakhel and Pekudei, since their content is similar and we never need to read 2 different haftarot the same year. In fact, B. Alperin’s “Permanent Haftarah Calendar” lists only one haftara, “Vayyaas Chirom” (Melakhim I 7:40-50), to be read whenever Vayyakhel or Pekudei is not on a special Shabbat. For more about rare haftarot, see section L.

3. **SHEKALIM**** ****ON**** PARASHAT PEKUDEI: **Parashat Shekalim is always read **exactly 6 weeks before Shabbat Haggadol**. Based on the number of weeks as described in item 1 above, Parashat Shekalim is read on Shabbat Parashat Pekudei this year. In other leap years it would be Vayyakhel. For further significance of the events on this date, see O.12.

4. **BIRKAT HACHODESH FOR ****NISAN**** ****ON**** TAZRIA: **We bless the month of Nisan on Parashat Tazria. In other leap years it would be on Shemini. See also M.10.

5. **ACHAREI MOT BEFORE PESACH: **As described in item 1 above, because of the 29 Shabbatot between Simchat Torah and Pesach, Acharei Mot is read on Shabbat Haggadol. This is in violation of the mnemonic “sigru ufischu”, stating that Metzora should be read immediately before Pesach in a leap year (SA 428:4). In other leap years it would be Metzora, and in non-leap years it’s always Tzav. For more about this Shabbat, see O.13.

6. **KEDOSHIM 5 TIMES: **The beginning of Parashat Kedoshim is read 5 times, because of the (extra) Shabbat Mincha during Pesach.

7. **BIRKAT HACHODESH ON KEDOSHIM: **We bless the month of Iyyar on Parashat Kedoshim. In other leap years it would be Acharei Mot.

8. **NASO BEFORE SHAVUOT: **Parashat Naso is read on the Shabbat before Shavuot. This is in violation of the mnemonic “minu veitzru”, stating that Bemidbar should be read on the Shabbat before Shavuot (SA 428:4). In all other years, Bemidbar is read on the Shabbat before Shavuot.

9. **HAFTARAT PINECHAS IS READ: **We read Pinechas on the Shabbat **before 17 Tammuz**, so we read the haftara corresponding to the parasha (from Melakhim I). This is the only way Haftarat Pinechas can be read. In all other years, Pinechas is read on the first Shabbat after 17 Tammuz, so its haftara is replaced by first Haftara of Tragedy for the “3 Weeks” (often listed as the haftara for Parashat Mattot). For more about rare haftarot, see section L.

10. **MATTOT AND MASEI SEPARATE: **What a relief for the baal keria. The 244 pesukim of Mattot-Masei are not read all at once, for the first time in 21 years (only 10 years in Israel – see note below). We read Mattot alone, on the first Shabbat after 17 Tammuz. **The haftara “listed” for Mattot is actually read for Mattot**, because it is the first Shabbat after 17 Tammuz. (The haftara should really be listed as “the First Haftara of Tragedy”, or the “haftara for the Shabbat after 17 Tammuz”, rather than “the haftara for Mattot”. In most years it is read on Parashat Pinechas, not Mattot.) On the second Shabbat after 17 Tammuz we read Masei. Note that when Masei is read alone, there are **different customs regarding the division of the aliyyot**. KafHaChayyim writes that we should not interrupt in the middle of the listing of the various **camping locations in the desert**. Therefore, the Sephardic custom is for the Kohen to read all the way until 33:49. However, the Ashkenazic custom is for the Kohen to read only until 33:10. See also O.15 for more about the events of this Shabbat. See O.1 for more about parashiyyot being separate this year.

**SPECIAL NOTE REGARDING TORAH ****READINGS**** ****IN**** ****ISRAEL****:** In Israel, the last 4 events listed in this section (items 7 through 10) actually occur more often than the other events. In **leap years with Pesach beginning on Shabbat**, Israelis read a regular parasha on the Shabbat that is celebrated as the 8^{th} day of Pesach in the Diaspora, causing a discrepancy in the parashiyyot which is not corrected until Mattot-Masei. Events N.7 through N.10, which happen because of an “extra” Shabbat at some point during the year, will occur in Israel in these years also. These additional year-types, in which events 7 through 10 occur in Israel but not in the Diaspora, account for **10.0% **of years. Some recent and upcoming such years are 5660 (1900), 5681 (1921), 5684 (1924), 5698 (1938), 5708 (1948), 5711 (1951), 5725 (1965), 5738 (1978), 5752 (1992), 5755 (1995), 5776 (2016), 5779 (2019), 5782 (2022), 5803 (2043), 5806 (2046), 5809 (2049), 5833 (2073), 5836 (2076), 5850 (2090), and 5860 (2100). Therefore, **events 7 through 10 are not so rare in ****Israel****, **as altogether, **they occur in 20.5% of years**. The last time these events happened in Israel was **10 years ago, in 5755**. Regarding the other events of this section, there is no discrepancy between Israel and the Diaspora.

**HISTORICAL NOTE: **It seems that the current system of division of the parashiyyot, leading to the special events listed in this section, was **not always universally practiced**. According to the system described by Rabbi Avraham bar Chiyya Hannasi in his SeferHaIbbur (4883 / 1123 CE), Parashat Metzora was always read immediately before Pesach in all leap years. This means that most of the events in this section would not apply under the system of the Sefer HaIbbur: Shekalim would always be read on Parashat Vayyakhel in a leap year; Shabbat Haggadol would always be Metzora in a leap year; Acharei Mot would always be the Shabbat after Pesach in a leap year; Bemidbar would always be read on the Shabbat before Shavuot; Pinechas would never have its “own” haftara as it would always be read after 17 Tammuz; Mattot and Masei would always be combined. But wait a minute – how would we deal with the fact that in leap years with Rosh HaShana on Thursday there are 29 Shabbatot from Simchat Torah until Pesach, but only 28 parashiyyot from Bereishit until Metzora to read on those 29 Shabbatot (see item 1 in this section)? Apparently, the custom in such years was to split up one of the early parashiyyot (possibly one of “Vayyeira”, “Mikketz”, “Vaeira”, “Mishpatim”, or “Ki Tissa”), and spread its reading over 2 Shabbatot. See “Shearim LaLuah HaIvry” by Rahamim Sar-Shalom, page 112. Sar-Shalom doesn’t seem to explain what would happen in Israel in leap years when Pesach is on Shabbat. Maybe they would have to split up Parashat Emor (or Bemidbar?) in order to make sure that Naso is read after Shavuot. **Exercise for the reader: **Check the original source (Sefer HaIbbur) to see whether it deals with this issue.

**O. ****1 TEVET ON MONDAY**

Tevet begins on Monday in only 1 out of the 14 different calendar year-types. This is the year-type החא (hei-chet-aleph), the one corresponding to our current year 5765. This means that **the description “Tevet beginning on Monday” completely characterizes the structure of this Jewish calendar year. **In particular, a year in which 1 Tevet falls on Monday must be a leap year that began with Rosh HaShana on Thursday and contains Pesach beginning on Sunday.

As described earlier (section B), this year-type occurs vary rarely, **only in 3.9% of all years**. The last time it happened was **24 years ago, in 5741 (1980-81). **After this year 5765 it will happen again **3 years later**, in 5768 (2007-08), but after that it won’t happen until**44 years later**, in 5812 (2051-51).

Most calendar dates can fall on 4 different days of the week (see G.24 and M.42), and any of the four can occur in a leap year or a non-leap year. Dates in Kislev can fall on 6 different days of the week (see J.6), but again each of the 6 can occur in a leap year or a non-leap year. Dates in Tevet and Shevat are different: they can fall on 5 different days of the week, but one of them can occur only in a leap year. In particular, 1 Tevet cannot fall on Monday in a non-leap year, nor in any year other than this year-type. It turns out that it is**more than 4 times as likely for 1 Tevet to fall on any other legal day of the week as for it to fall on Monday**.

Here are the 5 possible days of the week on which Tevet can begin, along with their corresponding frequencies:

1 Tevet on Sunday: 28.0% of years

**1 Tevet on Monday: 3.9% of years (must be a leap year)**

1 Tevet on Tuesday: 18.0% of years (must be a non-leap year)

1 Tevet on Wednesday: 20.1% of years

1 Tevet on Friday: 30.0% of years

A similar observation is correct for the month of Adar I. When Tevet begins on Monday, Adar I will begin on Thursday (see below, item 8). Neither Adar II of a leap year nor the single Adar of a non-leap year can begin on Thursday. Only Adar I of a leap year can begin on Thursday, and it can do so only in this year-type. This means that **Thursday is by far the least likely of the possible days of the week for any Adar to begin**.

As a result of this analysis, it follows that **anyone who was born in Tevet, Shevat or Adar I of a החא (hei-chet-aleph) year will celebrate their birthday very rarely on the same day of the week as when they were born**. See below for a list of such years. In particular, the last time this year-type occurred was 24 years ago, in 5741 (1980-81). So anyone who was born in Tevet, Shevat or Adar I of 5741 will celebrate their Hebrew birthday this year on the same day of the week as when they were born, for the first time in their lives, as they turn 24 years old. This includes my sister Sara, who was born on Wednesday, 21 Adar I, 5741. This year will be the first time since she was born that her Hebrew birthday falls on Wednesday. For an example from a different year, Mr. Melech Goldman was born on Wednesday, 3 Tevet, 5714. This year will be the second time since he was born that his birthday falls on Wednesday. Mr. Goldman’s birthday is interesting for another reason – see item I.5. (Of course the same is true for anniversaries or yortzeits, etc.)

There are other characterizations of the year-type החא (hei-chet-aleph), obtained by combining pairs of events described in the preceding sections. For example, **each of the following descriptions can refer only to this year-type and no others:**

“Leap year with first day of Pesach on Sunday”

“Leap year with 1 Kislev on Sunday”

“Chaseira year with Rosh HaShana on Thursday”

“Chaseira year with 1 Kislev on Sunday”

“1 Kislev on Sunday and first day of Pesach on Sunday”

Based on the first one of these alternate characterizations, we can easily derive the list of years in which 1 Tevet falls on Monday. It is simply the intersection of the lists of years from section M (first day of Pesach on Sunday) and section N (leap years with Rosh HaShana on Thursday). Here is a list of recent and upcoming years in which 1 Tevet falls on Monday: 5592 (1831-32), 5616 (1855-56), 5643 (1882-83), 5670 (1909-10), 5687 (1926-27), 5714 (1953-54), 5741 (1980-81), **5765 (2004-05)**, 5768 (2007-08), 5812 (2051-52), 5839 (2078-79), 5863 (2102-03), 5890 (2129-30), 5917 (2156-57), 5961 (2200-01), 5988 (2227-28).

The possible interval lengths between occurrences of 1 Tevet on Monday are 3, 17, 24, 27, 44, or 47 years.

Note however that the description “Rosh HaShana on Thursday and Pesach on Sunday” does **NOT **characterize this year-type. There is another year-type, השא (hei-shin-aleph), sharing this description. (It is a non-leap year and is the rarest of all the 14 year-types, occurring only 3.3% of all years.)

All of the events listed in the preceding sections (C through N) occur in years with 1 Tevet on Monday, as explained in each section. **The following calendrical events occur only in this year-type החא (hei-chet-aleph), that is, they occur only in years with 1 Tevet on Monday. Recall that the last time these events occurred was 24 years ago, in 5741.**

1. **NO “DOUBLE PARASHIYYOT” THE WHOLE YEAR! **This is the ultimate dream for any baal keria (unless they pay you double for a double parasha – thanks to Gershie Deutsch for pointing this out). See also events E.7, F.6, and N.10. Let’s add up the number of Shabbatot during the year’s Torah reading cycle and see what we get. There are 29 Shabbatot between Simchat Torah and Pesach (see N.1), 6 Shabbatot between Pesach and Shavuot, 6 Shabbatot between Shavuot and 17 Tammuz, 3 Shabbatot between 17 Tammuz and 9 Av, and 7 Shabbatot from 9 Av to the end of the year. Then there is Shabbat Shuva at the beginning of the following year, followed by one more Shabbat between Yom Kippur and Sukkot. This adds up to 53 Shabbatot, which is enough to read each parasha on its own Shabbat, except for the 54^{th} one, Vezot Habberakha, which is read on Simchat Torah in all years. The important factor here is that there is a minimum number of holidays falling on Shabbat – only one during Sukkot, one during Pesach, none on Shavuot, and next year’s Rosh HaShana and Yom Kippur are not on Shabbat. Combined with the “extra” Shabbatot between Simchat Torah and Pesach (N.1), this gives us the maximum number of available Shabbatot for Torah readings. Note that **in ****Israel**, there are no “double parashiyyot” also in leap years when Pesach falls on Shabbat, for an **additional 10.0% **of years – see explanation in the “Note” at the end of section N. So this event is not so rare in Israel, as it occurs in a total of 13.9% of years. The last time there were no “double parashiyyot” in Israel was 10 years ago, in 5755 (1994-95). See also section L for characterization of years with no double parashiyyot in Israel.

2. **PARASHIYYOT FROM VAYYIGGASH TO MASEI HAVE DATES DETERMINED:** These parashiyyot are read on the corresponding calendar dates in **this year-type only**. (The dates of all other parashiyyot are specified in sections G.17, J.2, and M.36.)

6 Tevet – Vayyiggash

13 Tevet – Vaychi (chazak!)

20 Tevet – Shemot

27 Tevet – Vaeira

5 Shevat – Bo

12 Shevat – Beshallach (Shabbat Shira)

19 Shevat – Yitro

26 Shevat – Mishpatim

3 Adar I – Teruma

10 Adar I – Tetzavve

17 Adar I – Ki Tissa

24 Adar I – Vayyakhel

1 Adar II – Pekudei (chazak!) (with 3 sifrei Torah – see item 12 below)

8 Adar II – Vayyikra (with maftir and haftara for Zakhor)

15 Adar II – Tzav (see M.7 regarding walled cities)

22 Adar II – Shemini (with maftir and haftara for Para)

29 Adar II – Tazria (with maftir and haftara for HaChodesh)

7 Nisan – Metzora

14 Nisan – Acharei Mot (with Haftarat Haggadol)

28 Nisan – Kedoshim

5 Iyyar – Emor

12 Iyyar – Behar

19 Iyyar – Bechukkotai (chazak!)

26 Iyyar – Bemidbar

4 Sivan – Naso

11 Sivan – Behaalotekha

18 Sivan – Shelach-Lekha

25 Sivan – Korach

2 Tammuz – Chukkat

9 Tammuz – Balak

16 Tammuz – Pinechas

23 Tammuz – Mattot (see also M.36)

1 Av – Masei (chazak!) (see item 15 below)

3. **ROSH CHODESH TEVET ON MONDAY ONLY:** This is Monday, 1 Tevet, the 6^{th} day of Chanukka. See also item I.3.

4. **FAST OF 10 TEVET ON WEDNESDAY: **The other possible days for the Fast of 10 Tevet are Sunday, Tuesday, Thursday, and Friday, each occurring more than 4 times as often as Wednesday.

5. **BIRKAT HACHODESH ON 27 TEVET:** We bless the month of Shevat on Shabbat 27 Tevet (Parashat Vaeira). Other possible dates are 23, 25, 26, or 28 Tevet, each occurring more than 4 times as often as 27 Tevet.

6. **1 SHEVAT AND TU BISHVAT ON TUESDAY: **The other possible days for Rosh Chodesh Shevat and Tu BiShvat are Monday, Wednesday, Thursday, and Shabbat, each occurring more than 4 times as often as Tuesday.

7. **BIRKAT HACHODESH ON 26 SHEVAT:** We bless the month of Adar I on Shabbat 26 Shevat (Parashat Mishpatim). Note that we never bless Adar of a regular year on 26 Shevat.

8. **ROSH CHODESH ADAR I ON WEDNESDAY AND THURSDAY: **Wednesday is 30 Shevat, and Thursday is 1 Adar I. Neither Adar II of a leap year nor the single Adar of a non-leap year can ever begin on Thursday. See further explanation at the beginning of this section regarding birthdays in Adar I.

9. **PURIM ****KATAN**** ****ON**** WEDNESDAY AND THURSDAY:** We observe 14 and 15 Adar I as Purim Katan. See F.3. The “real” Purim can never fall on Wednesday.

10. **DAYS OF THE WEEK DETERMINED FOR TEVET, SHEVAT AND ADAR I:** As explained at the beginning of this section, the fact that 1 Tevet falls on Monday determines the day of the week of each calendar date in Tevet, Shevat and Adar I. This is in addition to dates throughout the rest of the year, whose days of the week are already determined from G.24, J.6, and M.42. Actually, the fact that 1 Tevet falls on Monday determines the day of the week for calendar dates farther away than you would expect. See section P for more about this.

11. **BIRKAT HACHODESH FOR ADAR II ****NOT**** ****ON**** SHEKALIM:** We bless the month of Adar II on Shabbat 24 Adar I, the earliest possible date in Adar I to do so. This day is not Parashat Shekalim, as Shekalim will be read the following week, on Shabbat Rosh Chodesh. In all other leap years, we bless the month of Adar II on the same day we read Shekalim. **Rosh Chodesh Adar II will fall on Friday and Shabbat. **Friday is 30 Adar I, and Shabbat is 1 Adar II.

12. **PEKUDEI – ROSH CHODESH – SHEKALIM – SHISHI IS CHAZAK: **Combining the events described in M.1 and N.3, we see that we have 3 sifrei Torah for Parashat Pekudei – Shabbat Rosh Chodesh – Parashat Shekalim. In order to read from 3 sifrei Torah, the person called up for **“shishi” **reads all the way to the end of Pekudei, which is the **end of the book of Shemot**. Consider the following interesting scenario: Suppose one synagogue member bought the honour of “shishi” for the entire year, and another member bought the honour of “chazak” for the whole year. **This week there will be a conflict.** This is the only calendrical situation in which this can happen. Thanks to Rav Dovid Pam of Zichron Shneur (Toronto) for bringing this scenario to my attention.

13. **ACHAREI ****MOT**** ****ON**** SHABBAT HAGGADOL EREV PESACH:** Combining events M.17 and N.5, we see that we read Acharei Mot on Shabbat morning, Erev Pesach. Maybe there’s some strange plot going on. Not only is it the first time in 21 years that we read Acharei Mot before Pesach, but we’re hiding it by reading it so early in the morning that everyone will miss it!

14. **HAFTARAT CHUKKAT ON EARLIEST POSSIBLE DATE:** We read Parashat Chukkat on Shabbat 2 Tammuz. Although there are some other years in which we read Chukkat on 30 Sivan, that date is Rosh Chodesh, and so the regular haftara would be replaced by “HaShamayim Kis’i”. So 2 Tammuz is the earliest possible date on which we read the haftara for Chukkat.

15. **MASEI**** ****ON**** ROSH CHODESH WITHOUT MATTOT:** Combining the events described in M.33 and N.10, we see that Rosh Chodesh is on Shabbat when we read Parashat Masei without Parashat Mattot. In other year-types when Rosh Chodesh Av falls on Shabbat, the parashiyyot may be combined, giving a total of 251 pesukim for the double-parasha-plus-maftir combination. This time we’re lucky.

**P. ****NEIGHBOURING YEARS DETERMINED BY YEAR-TYPE**

In this section we will consider the effect of this year’s year-type on the years preceding and following it. As we have emphasized, the year-type החא (hei-chet-aleph) is rare, and it turns out that the fact that **1 Tevet falls on Monday is enough information to determine the year-types of the preceding and following years**, and even some information about calendar dates farther into the past or future.

In order to clarify the presentation (I hope!) when referring to various years before and after the current year, I will use the symbol “X” to refer to the principal year under discussion, i.e. the year with year-type החא (hei-chet-aleph) (i.e., the year with 1 Tevet on Monday). So year X could refer to the year 5765, or to any other year with 1 Tevet on Monday (see the list at the beginning of section O for examples). Then, “X – 1” refers to the year prior to the year with 1 Tevet on Monday (for example, 5764), and so on.

Here are various effects determined by the fact that the year X has 1 Tevet on Monday. Note that I do not claim that the events in this section cannot happen in any other case. I just say that they will necessarily happen when 1 Tevet of year X is on Monday.

1. **PRECEDING YEAR HAS YEAR-TYPE זשג: **Since year X is a leap year, it is clear that year X – 1 must be a **non-leap year**. However, since year X has 1 Tevet on Monday, it turns out that the year X – 1 (for example, 5764) must have year-type זשג(zayin-shin-gimel). That represents a non-leap year that is “sheleima”, with Rosh HaShana on Shabbat and the first day of Pesach on Tuesday. I will not describe all the features of the year-type, as that would require another whole essay.

2. **FOLLOWING YEAR HAS YEAR-TYPE גכה: **Since year X is a leap year, it is clear that year X + 1 must be a **non-leap year**. However, since year X has 1 Tevet on Monday, it turns out that the year X + 1 (for example, 5766) must have year-type גכה(gimel-kaf-hei). That represents a non-leap year that is “kesidrah”, with Rosh HaShana on Tuesday and the first day of Pesach on Thursday. Again, I will not describe all the features of the year-type, as that would require another whole essay. Maybe I’ll write another essay next year in honour of the year 5766.

3. **YEAR X + 2 HAS YEAR-TYPE זש_: **The year X + 2 may or may not be a leap year, but either way it must be a sheleima year with Rosh HaShana on Shabbat. This means that all calendar dates until Adar (I) of year X + 2 (for example, 5767) are on fixed days of the week. The year-type must be either זשה (zayin-shin-hei) or זשג (zayin-shin-gimel) respectively, depending on whether the year is or is not a leap year.

4. **YEAR X – 2 HAS PESACH ON THURSDAY: **The year X – 2 may or may not be a leap year, and it may have any one of 4 different year-types, but it must have Pesach on Thursday. This means all calendar dates from Adar onward in year X – 2 (for example, 5763) are on fixed days of the week.

**The point of all this is: **Not only does the fact that 1 Tevet falls on Monday determine the features of the current Jewish calendar year, but it also determines the year-types of the immediately preceding and following years (X – 1 and X + 1), and it determines the day of the week for every calendar date from Adar of year X – 2 until Adar of year X + 2. In addition, if we know the year number of year X in the 19-year cycle (so that we know whether X – 2 or X + 2 is a leap year), then the year-types are determined for years X – 1 through X + 2, and so are the days of the week for every calendar date from 1 Tevet of year X – 2 until Cheshvan of year X + 3.

5. **19-MONTH INTERVAL WITHOUT HASHAMAYIM KIS’I: **The haftara beginning “HaShamayim Kis’i” is usually read when Rosh Chodesh falls on Shabbat, which tends to happen once every 4 or 5 months. We read it this year on Shabbat Rosh Chodesh Cheshvan (see G.19). However, it will be 19 months until we read it again, on Shabbat Rosh Chodesh Iyyar of year X + 1. There are 3 occasions during this interval when Rosh Chodesh falls on Shabbat but HaShamayim Kis’i is omitted for various reasons: Rosh Chodesh Adar II falls on Shabbat, but the haftara is replaced by the special haftara for Parashat Shekalim (see M.1). Rosh Chodesh Av falls on Shabbat, but the haftara is replaced by one of the special Haftarot of Tragedy for the “3 weeks” (see M.33). Next year, Rosh Chodesh Tevet will be on Shabbat (and Sunday), but the haftara will be replaced by the haftara for Shabbat Chanukka. [Note that in all these cases, some communities read the first and last pesukim of “HaShamayim Kis’i” after the competing haftara.] 19 months is NOT the longest possible interval during which we don’t read HaShamayim Kis’i – **there can be intervals of up to 29 months **where we don’t read it.

6. **19-MONTH INTERVAL WITHOUT MACHAR CHODESH:** The haftara known as “Machar Chodesh” is usually read on Shabbat when Rosh Chodesh falls on Sunday, which tends to happen once every 4 or 5 months. We read it this year on Shabbat 29 Cheshvan, Erev Rosh Chodesh Kislev (see G.22). However, it will be 19 months until we read it again, on Shabbat 29 Iyyar (Erev Rosh Chodesh Sivan) of year X + 1. There are 3 occasions during this interval when Rosh Chodesh falls on Sunday but Machar Chodesh is omitted for various reasons: Rosh Chodesh Nisan is on Sunday, but Machar Chodesh is replaced by the special haftara for Parashat HaChodesh (see M.11). Rosh Chodesh Elul is on Sunday, but Machar Chodesh is replaced by one of the special Haftarot of Consolation (see M.38). Next year, Rosh Chodesh Tevet will be on (Shabbat and) Sunday, but Machar Chodesh will be replaced by the haftara for Shabbat Chanukka. [Note that in all these cases, some communities read the first and last pesukim of “Machar Chodesh” after the competing haftara.] 19 months is the **longest possible interval **during which we don’t read Machar Chodesh.

This concludes the description of all calendrical events that depend on the year-type of the current year. All events described from section C until this point occur in all years whose year-type is החא (hei-chet-aleph). A list of such years was given at the beginning of section O.

From here on, we will discuss other events occurring this year, which are **independent of the year-type**. These events certainly do not occur in all החא (hei-chet-aleph) year-types, and generally may occur in other year-types as well. The important thing for us is that they all occur in the year 5765.

**Q. ****8 ^{th} YEAR OF THE 19-YEAR CYCLE – EVERYTHING IS “LATE”**

As explained in section F, a Jewish leap year contains 2 months of Adar, for a total of 13 months in the Jewish calendar year, rather than 12. The purpose of the extra month is to ensure that the Jewish holidays, including Pesach, fall in the appropriate seasons, rather than drifting earlier and earlier throughout the solar year. The years of the 19-year cycle that are Jewish **leap years **are the years numbered **3, 6, 8, 11, 14, 17, and 19.** This year 5765 is the 8^{th} year of the current 19-year cycle (5765 modulo 19 is 8), and so it follows that the year is a Jewish leap year.

The insertion of the extra month of Adar causes the subsequent Jewish calendar dates and holidays to fall “later” than they otherwise do, relative to the seasons and to the solar calendar year. In other words, in a leap year, Pesach (for example) falls later in April than it does in a non-leap year. However, you may have noticed that **the holidays in 5765 (from Adar onward) seem to fall a lot “later” than they fall even in other leap years**. Why is this? A glance at the sequence of leap years in the 19-year cycle (listed above) will help to explain.

As we have explained already, the 8^{th} year of the cycle is a leap year, and so the Jewish dates (from Adar onward) will be later relative to the seasons than in a non-leap year, because of the extra month. But there’s more: The 8^{th} year of the 19-year cycle is a **leap year which follows the previous leap year by only 2 years **(i.e., the 6^{th} year of the cycle is also a leap year). There is only one other year in the cycle, namely the 19^{th}, that shares this property. **Any other leap year, other than the 8 ^{th} and 19^{th} years of the cycle, follows the previous leap year by 3 years. **This means that holidays in the 8

^{th}or 19

^{th}year of the cycle will be later than in other years, because there have been 2 leap years in a shorter period of time than usual.

Furthermore, the 8^{th} year of the cycle concludes a span of **11 consecutive years containing 5 leap years **(the 17^{th}, 19^{th}, 3^{rd}, 6^{th}, and 8^{th} years of the cycle are leap years). This is the **only year in the cycle with this property**. Any other 11-year span contains only 4 leap years, even the span ending with the 19^{th} year of the cycle. This means that holidays will fall later in the 8^{th} year of the cycle than in all other years, because there have been 5 leap years in a shorter period of time than usual.

The result of all this is that **all Jewish calendar dates and holidays from Adar of the 8 ^{th} year of the cycle until Shevat of the following year will fall later in the solar year **(i.e. relative to the civil calendar)

**than they do in all other years of the 19-year cycle.**We will refer to this year-long period, from Adar of this year until Shevat of the next year, as

**the “late-year” period**. In our case, the “late-year” period runs from Adar of this year 5765 until Shevat 5766, i.e. (roughly) from March 2005 until February 2006.

Here is a list of recent and upcoming “late-years”. Remember that the late-year period runs from Adar (roughly March) of one year until Shevat (February) of the following year. The “late-year” period occurs in 5670-71 (1910-11), 5689-90 (1929-30), 5708-09 (1948-49), 5727-28 (1967-68), 5746-47 (1986-87), **5765-66 (2005-06), **5784-85 (2024-25), 5803-04 (2043-44), 5822-23 (2062-63), 5841-42 (2081-82), and 5860-61 (2100-01). Note that the interval from one “late-year” to the next is always 19 years.

So that’s why everything seems so late this year. The holidays haven’t been this late since 19 years ago, the year 5746 (1986). In particular, Purim this year falls on March 25 (March 26 in walled cities); the first day of Pesach falls on April 24 and Pesach extends until May 1 (Diaspora) or April 30 (Israel); and the following year’s Rosh HaShana 5766 begins on October 4, rather than in September as usual.

Now, the obvious question arises: **Why is the leap year cycle arranged the way it is? **If the purpose of the leap year is to ensure that Pesach falls in the spring season, it would seem that the 8^{th} year of the cycle should not need to be a leap year. After all, spring begins around March 21, and Pesach will be this year on April 24. Without the extra month, Pesach would begin on March 25, well after the beginning of spring. So why do we add the extra month this year?

I will not deal with this question further here, except to say that much has been written on this topic. The book “Al HaSheminit” by Yaaqov Loewinger (Tel Aviv, 5746 / 1986, now apparently out of print) deals exclusively with the question of **why the 8 ^{th} year in the 19-year cycle is a leap year**. (This year would be a good time for a second printing.) In addition, my friend Tzvi Goldman has written an essay on the topic, called “Al Hattekufa”, in

*Beit*

*Yitzchak*vol. 36, pp. 140-148 (published by Yeshiva University, 2004). See also “Alseder hashanim hammeubbarot balluach hakkavua” by Binyamin Albaum in

*Yod’ei*

*Binah*vol. 2 (Drazin Institute for Kiddush Hachodesh Studies, Yeshivat Kerem B’Yavneh, Nisan 5764), pp. 22-59.

**IMPLICATION FOR BIRTHDAYS, ANNIVERSARIES AND YORTZEITS:**

If you know both the Jewish and civil calendar anniversaries of a particular event (such as your birthday), it can be interesting to notice which one precedes the other in any given year, and by how much. For most people, there will be some years when their Hebrew birthday precedes their civil one, and some years in which the opposite is true. Similarly, in most years, there will be some people whose Hebrew birthday precedes their civil one that year, and other people for whom the opposite occurs.

(I am using birthdays as examples of events whose Hebrew and civil dates are likely to be known. Of course the same is true for anniversaries or yortzeits or all other events. By the way, if you don’t know what your Hebrew birthday is, now would be a good time to figure it out. There are many books containing calendars spanning long periods of time, such as 100 years or more, which you can use to determine the Jewish date corresponding to any civil date. Also, there are many computer programs as well as web sites that can do the same. One web site I’ve found to be useful is www.hebcal.com/hebcal, where you can get a Jewish calendar display for any desired year.)

**The period from Adar II of this year until Shevat of the next year is different. **As we have explained, this is the “**late-year**”, when all Hebrew dates fall later on the civil calendar than they do in any other year of the 19-year cycle. This fact has the following interesting consequences:

During the “late-year”, unless your age becomes a multiple of 19 years, **your Hebrew birthday will definitely fall later than your civil birthday**. Depending on which year you were born, your birthdays may even be close to a month apart. But there’s no chance your Hebrew birthday will be as early as, or earlier than, your civil birthday during this period.

Also, **anyone born during the “late-year” will have their Hebrew birthday precede their civil birthday in all other years**. The reason is that if you are born during the “late-year”, when the Hebrew dates fall later on the civil calendar than they do in other years, your civil birthday will be later than any other civil date on which your Hebrew birthday can fall.

As examples of this latter phenomenon, consider two events in modern Jewish history: the **Independence of the State of Israel **(5 Iyyar 5708 / May 14, 1948) and the **Liberation of Jerusalem **(28 Iyyar 5727 / June 7, 1967). Each of these events took place during a “late-year”. This is why, as you may have noticed, their Jewish calendar anniversaries (**Yom HaAtzmaut **and **Yom Yerushalayim**, respectively) **always seem to fall much earlier in the civil calendar than the original civil dates on which the events took place**. In any year other than a “late-year”, Yom HaAtzmaut cannot fall as late as May 14, and Yom Yerushalayim cannot fall as late as June 7. This year is a late-year, so the anniversary of Israel’s Independence – **5 Iyyar – actually falls on May 14 this year, as it did in 5708 (1948) **and 5746 (1986). In the year 5727 (1967), Yom HaAtzmaut fell on May 15. [Note that this year, since 5 Iyyar falls on Shabbat, Yom HaAtzmaut is advanced to Thursday, 3 Iyyar, which is May 12. So the only time Yom HaAtzmaut was ever actually celebrated on May 14, since 5708 (1948), was in 5746 (1986).] Yom Yerushalayim, on the other hand, has never fallen as late as its original civil date (June 7) – even this year it will fall on June 6, as it did in 5746 (1986). The first time Yom Yerushalayim will ever fall as late as its original civil date will be on its 76^{th} anniversary, in the year 5803 (2043).

**NOTE REGARDING BIRTHDAYS IN ADAR:**

If you were born either in Adar II of a leap year or in Adar of a non-leap year, then your Hebrew birthday will always fall on later civil dates in leap years (when it is celebrated in Adar II) than in non-leap years, and it will fall on its latest possible civil date in Adar II of the 8^{th}year of the cycle (e.g. this year 5765). As well, anyone born during Adar II of the 8^{th} year will have their Hebrew birthday precede their civil one in all other years. However, **if you were born in Adar I **of a leap year, then your Hebrew birthday will always fall on later civil dates in non-leap years (when it is celebrated in the single Adar) than in leap years (when it is celebrated in Adar I), and **it will fall on its latest civil date in Adar of the 9 ^{th} year of the cycle**.

For **yortzeits**, the situation is slightly different, as the Ashkenazic custom is that for someone who passed away in Adar of a non-leap year, the yortzeit is observed in Adar I of a leap year (Rama 568:7). (For Sephardim, the rules are the same as for birthdays, as above. The following results apply to Ashkenazim.) If someone passed away in Adar II of a leap year, their yortzeit will fall on later civil dates in leap years than in non-leap years, and it will fall on its latest possible civil date in Adar II of the 8^{th} year of the cycle (e.g. this year 5765). As well, if someone passed away during Adar II of the 8^{th} year, their yortzeit will precede their civil date of death in all other years. However, for someone who **passed away either in Adar I of a leap year or in Adar of a non-leap year**, their yortzeit will fall on later civil dates in non-leap years (when it is observed in the single Adar) than in leap years (when it is observed in Adar I), and it will fall on its **latest civil date during Adar of the 9 ^{th} year**. As well, if someone passed away during Adar of the 9

^{th}year, their yortzeit will precede their civil date of death in all other years.

**R. ****BAR MITZVA POSSIBLE IN ADAR I**

Have you ever noticed that **in many leap years you don’t get invited to a bar mitzva during the month of Adar I**? Here’s the story: If a boy is born in Adar of a non-leap year, and the year he turns 13 is a leap year, he becomes bar mitzva in Adar II (Rama 55:10). The only way a boy can become bar mitzva in Adar I of a leap year is if he was born in Adar I of a leap year as well.

For a particular leap year, if its position in the 19-year cycle is such that the year 13 years prior was not a leap year, then no boy will become bar mitzva during Adar I of that year – anyone born during Adar of 13 years prior will become bar mitzva during Adar II. On the other hand, if the year’s position in the 19-year cycle is such that the year 13 years prior was a leap year, then any boy born in Adar I will become bar mitzva in Adar I.

Looking at the list of leap years in the 19-year cycle (above in section Q), we can see that the leap years in positions 8, 11, and 19 of the cycle are such that 13 years prior there was a leap year as well, whereas the leap years in positions 3, 6, 14, and 17 are such that 13 years prior, the year was non-leap.

It follows that **in 3 years out of every 19-year cycle it is possible for a boy to become bar mitzva in Adar I**, namely in the 8^{th}, 11^{th}, and 19^{th} years of the cycle. The intervals between these years are **8 years, then 3 years, then 8 years**. In all other leap years, a boy cannot become bar mitzva in Adar I. Since this year 5765 is the 8^{th} year of the cycle, you may be invited to a bar mitzva this year in Adar I. The previous time there could have been a bar mitzva in Adar I was 8 years ago, in 5757 (1997), which was the 19^{th} year of the previous cycle. The next time will be 3 years from now, in 5768 (2008), the 11^{th} year of the cycle.

Note that **a girl can never become bat mitzva in Adar I **because there is no way to have two leap years exactly 12 years apart. Any girl born in a leap year will necessarily become bat mitzva in a non-leap year, and any girl becoming bat mitzva in a leap year must have been born in a non-leap year, so she will not become bat mitzva in Adar I.

**S. ****EASTER IS NOT ON PESACH**

In most years, the Christian holiday of Easter seems to fall some time during the 8 days of our Pesach holiday. This year it doesn’t. This has led me to wonder how often Easter falls during Pesach, and whether there is any pattern describing when it does. I have not yet seen any explicit analysis of this issue, and I am certainly not an expert on the rules for setting the date of Easter. Therefore, the results in this section are very tentative. **BIG Exercise for the Reader: Verify the analysis and conclusions in this section.** Here are the results of my limited research and analysis of the Easter/Pesach issue:

We know that Pesach starts approximately at the time of a full moon, being the middle of the Jewish month. Easter is supposed to be the first Sunday after the day of the first full moon on or after March 21 (the approximate day of the spring equinox). Most years, the first full moon after March 21 is the full moon during Nisan, so that Easter falls some time during the week of Pesach. But when Pesach falls very “late” in April, the full moon one month earlier than Pesach is used to set the date of Easter.

Now, it turns out (not surprisingly, I suppose) that the rules for determining the date of Easter use a sort of 19-year cycle to determine the solar date of the full moon. By the way, in the non-Jewish literature, the 19-year cycle correspondence between the lunar months and solar years is known as the **“Metonic” cycle**, named after the Greek astronomer Meton of Athens who apparently came up with the idea in 432 BCE. So, one might hypothesize (as I did) that the 19-year cycle should determine which years have Easter during Pesach, and which ones have Easter about a month before Pesach.

That hypothesis seems to be essentially correct, but there are a few complications. The first source of confusion is simply a question of convention. The year that we (Jews) consider to be the “beginning” of a 19-year cycle is not the same year as the beginning of the cycle for the Easter calculation. That’s not an essential difficulty once you realize how to deal with it. (Just add 3 (mod 19) to the year number in our cycle to get their “golden number”.) Another problem is that the Easter rules get adjusted every couple of hundred years because of the fact that the 19-year cycle isn’t a perfect correspondence. After all that, here’s what we get:

Most years, Easter falls some time during the 8 days of Pesach. The exceptions are the years that are the 8^{th}, 11^{th}, and 19^{th} years of our (Jewish) 19-year cycle. In those years, i.e. **3 times every 19 years, Easter will be approximately a month before Pesach**. (These correspond to years with “golden numbers” 11, 14, and 3, respectively.) The intervals between such occurrences in the cycle are **8 years, 3 years, then 8 years**. Since this year 5765 is the 8^{th} year of our cycle, it follows that Easter falls about a month before Pesach this year. The previous time this happened was 8 years ago, in 5757 (1997), which was the 19^{th} year of the previous cycle. The next time it will happen is 3 years from now, in 5768 (2008), the 11^{th} year of the cycle. (Incidentally, note that the years in which Easter falls a month before Pesach seem to be the same as the years in which a boy can become bar mitzva in the month of Adar I, as explained above.)

The above description works **from 5460 to 5959 (1700-2199 CE)**. Before that, i.e. from 5343 to 5459 (1583-1699 CE), there were only 2 times every 19 years that Easter would be a month before Pesach. These were the 8^{th} and 19^{th} years of our 19-year cycle (“golden numbers” 11 and 3, resp.). Starting with the year 5960 (2200 CE), there will be 4 times every 19 years that Easter will be a month before Pesach. They are the 3^{rd}, 8^{th}, 11^{th}, and 19^{th} years of our 19-year cycle (“golden numbers” 6, 11, 14, and 3, resp.).

All of this is **based on the Gregorian calendar **and its Easter rules. My understanding is that according to the Julian calendar rules (which all of Christianity used until 1582, and the Eastern Orthodox churches still use today), Easter can never fall earlier than Pesach, and it may sometimes be a month after Pesach. So, it seems that the first time in history that Easter was celebrated earlier than Pesach was in the year 5347 (1587), the 8^{th} year of a cycle, just over 4 years after the introduction of the Gregorian calendar.

Most of my information about the Easter rules comes from Chapter 13 of the book “Marking Time: The Epic Quest to Invent the Perfect Calendar”, by Duncan Steel (John Wiley & Sons, Inc., 2000). Thanks to Ephraim Stulberg for giving me his copy of the book. As I said earlier, the analysis is my own and it is somewhat tentative, so **I would be very happy for someone to corroborate it**.

See section V for an even more unusual correspondence between this year’s Easter and the Jewish calendar.

**T. ****CORRESPONDENCE BETWEEN CIVIL AND JEWISH BIRTHDAYS**

The correspondence between the Jewish and civil calendar dates depends roughly on the 19-year cycle of leap years in the Jewish calendar, but **there are many reasons why corresponding Jewish and civil dates may be a day or two apart even after 19 years**. The lengths of Cheshvan and Kislev vary from year to year, as does the length of February in the civil calendar. These are some of the reasons why the calendar dates may not correspond exactly after 19 years. In this section we examine the exact details of the calendar correspondence for this year. Note that the discussion in this section refers only to the correspondence between the Jewish and civil (Gregorian) calendar dates, and not to days of the week on which the calendar dates fall. Days of the week are determined by the year-type, as explained in sections C through P. The 19-year cycle has nothing to do with the days of the week on which calendar dates fall. Note also that these birthday correspondences work only if you were born during the day, i.e. before sunset. **If you were born after sunset, things get a little more confusing. **Thanks to Steven Tenenbaum for pointing this out.

First, here is a table listing all years from 5343 through 6000 (1582 through 2240) in which the dates in some portion of the year fall on the same civil dates as they do in the current year 5765. The “**YES**” in a particular spot means that **in those months of the year, all Jewish dates fall on the same civil dates as they do in 5765**. In other words, if you were born in any month and year indicated by a “**YES**”, then your Jewish and civil birthdays will coincide in the year 5765. (Your age is indicated in the “Age” column.) Also, anyone born during this year 5765 will have their Jewish and civil birthdays coincide in subsequent years if the relevant month and year is indicated by a “YES”.

Year | Pos | Civil year | Age | Tishrei-Cheshvan | Kislev | Tevet-Shevat | Adar II-Elul |

5355 | 16 | 1594-95 | 410 | YES | |||

5374 | 16 | 1613-14 | 391 | YES | YES | YES | |

5393 | 16 | 1632-33 | 372 | YES | YES | ||

5412 | 16 | 1651-52 | 353 | YES | YES | YES | |

5431 | 16 | 1670-71 | 334 | YES | |||

5450 | 16 | 1689-90 | 315 | YES | |||

5469 | 16 | 1708-09 | 296 | YES | |||

5480 | 8 | 1719-20 | 285 | YES | |||

5488 | 16 | 1727-28 | 277 | YES | YES | ||

5507 | 16 | 1746-47 | 258 | YES | |||

5526 | 16 | 1765-66 | 239 | YES | YES | YES | |

5545 | 16 | 1784-85 | 220 | YES | YES | ||

5556 | 8 | 1795-96 | 209 | YES | |||

5575 | 8 | 1814-15 | 190 | YES | |||

5583 | 16 | 1822-23 | 182 | YES | |||

5594 | 8 | 1833-34 | 171 | YES | YES | ||

5602 | 16 | 1841-42 | 163 | YES | YES | ||

5632 | 8 | 1871-72 | 133 | YES | YES | YES | |

5670 | 8 | 1909-10 | 95 | YES | YES | YES | YES |

5689 | 8 | 1928-29 | 76 | YES | |||

5700 | 19 | 1939-40 | 65 | YES | |||

5708 | 8 | 1947-48 | 57 | YES | YES | ||

5727 | 8 | 1966-67 | 38 | YES | |||

5746 | 8 | 1985-86 | 19 | YES | YES | YES | YES |

5754 | 16 | 1993-94 | 11 | YES | |||

5765 | 8 | 2004-05 | 0 | YES | YES | YES | YES |

5776 | 19 | 2015-16 | 11 | YES | |||

5784 | 8 | 2023-24 | 19 | YES | YES | YES | |

5795 | 19 | 2034-35 | 30 | YES | YES | ||

5803 | 8 | 2042-43 | 38 | YES | |||

5822 | 8 | 2061-62 | 57 | YES | |||

5830 | 16 | 2069-70 | 65 | YES | |||

5841 | 8 | 2080-81 | 76 | YES | YES | ||

5849 | 16 | 2088-89 | 84 | YES | YES | ||

5860 | 8 | 2099-2100 | 95 | YES | YES | ||

5898 | 8 | 2137-38 | 133 | YES | YES | YES | YES |

5917 | 8 | 2156-57 | 152 | YES | YES | YES | YES |

5928 | 19 | 2167-68 | 163 | YES | |||

5936 | 8 | 2175-76 | 171 | YES | |||

5947 | 19 | 2186-87 | 182 | YES | YES | ||

5955 | 8 | 2194-95 | 190 | YES | |||

5966 | 19 | 2205-06 | 201 | YES | YES | YES | YES |

5974 | 8 | 2213-14 | 209 | YES |

The column labelled “Pos” in the above table refers to the position of the year in the 19-year cycle of leap years. As this year 5765 is the 8^{th} year of a 19-year cycle, it seems reasonable that many of the years listed in the table are also the 8^{th} year of a cycle, as the dates tend to correspond after 19 years. However, **it is also possible for Jewish and civil dates to correspond after a period of 8 or 11 years**. This explains why there are many years in the table whose positions are either the 16^{th} or 19^{th} years of a cycle.

Now, let’s discuss some of the particulars. Don’t forget to glance at the chart above as you read the following descriptions:

1. **ROSH HASHANA**** ****ON**** “SEPARATION DATE”: **The New Year 5765 begins with 1 Tishrei falling on September 16, 2004. Note that of the years listed in the table, **some are leap years **(the ones that are the 8^{th} or 19^{th} year of a cycle, such as this year)**and some are not **(the ones that are the 16^{th} year of a cycle, such as 5754). **September 16 is the only civil calendar date in modern times on which both a leap year and a non-leap year can begin. **All leap years begin no later than September 16, and all non-leap years begin no earlier than September 16. This is true during the period from 5508 (1747) until 5878 (2117). Remy Landau refers to this date as a “Separation Date”, in his explanation at www.geocities.com/Athens/1584/divide.html (part of his website “Hebrew Calendar Science and Myths”).

The civil date of Rosh HaShana determines the civil date of all Jewish calendar dates and holidays until 29 Cheshvan, which falls on November 13 this year. As listed in the table above, anyone born between 1 Tishrei and 29 Cheshvan in any of the years 5670, 5746, or 5754 (i.e. between September 16 and November 13 of the years 1909, 1985, or 1993) will have their Jewish and civil birthdays coincide this year, as they turn 95, 19, or 11 years old, respectively. Their birthdays will coincide again 19 years from now, in 5784 (2023), as will happen to anyone born during this period this year.

2. **1 KISLEV ON NOVEMBER 14:** The civil date of 1 Kislev determines the civil date of all Jewish calendar dates from 1 through 29 Kislev, as well as the civil dates of the 8 days of Chanukka. This year, the 29 days of Kislev correspond to the dates from November 14 through December 12, and Chanukka runs from December 8 through 15. As listed in the table, this exact correspondence has been occurring regularly every 19 years for the past 5 cycles (95 years), and will continue to do so for the next 3 cycles (57 years). So anyone born between 1 and 29 Kislev in any of the years 5670, 5689, 5708, 5727, or 5746 (i.e. between November 14 and December 12 of the years 1909, 1928, 1947, 1966, or 1985) will have their Jewish and civil birthdays coincide this year, as they turn 95, 76, 57, 38, or 19 years old, respectively (all multiples of 19). Their birthdays will coincide again in the years 5784, 5803, and 5822 (2023, 2042, and 2061), as will happen to anyone born during this period this year.

3. **1 TEVET ON DECEMBER 13:** This determines the civil date of all Jewish calendar dates and holidays (except for Chanukka) from 1 Tevet until 19 Adar I, which falls on February 28. (The year must be a Jewish leap year unless it was more than 230 years ago.) As listed in the table, anyone born between 1 Tevet and 19 Adar I in any of the years 5670, 5700, or 5746 (i.e. between December 13 and February 28 of 1909-10, 1939-40, or 1985-86) will have their Jewish and civil birthdays coincide this year, as they turn 95, 65, or 19 years old, respectively. Their birthdays will coincide again several times in upcoming years – in the years 5776, 5784, and 5795 (2015-16, 2023-24, 2034-35), which are 11, 19, and 30 years from now, respectively.

4. **FIRST DAY OF ****PESACH**** ****ON**** APRIL 24:** As I explained earlier in section Q, this is about as “late” as it ever gets. (Note that 38 years ago, in 5727 (1967), Pesach fell even later, on April 25.) The fact that the first day of Pesach falls on April 24 determines the civil dates corresponding to all Jewish calendar dates and holidays from 20 Adar I (which falls on March 1) until the end of the Jewish year, 29 Elul (which falls on Oct. 3). As listed in the table, anyone born between 20 Adar I and the end of the year, during any of 5670, 5708, or 5746 (i.e., from March 1 until Oct. 3 of 1910, 1948, or 1986) will have their Jewish and civil birthdays coincide this year, as they turn 95, 57, or 19 years old, respectively. As I mentioned in section Q, note that the State of Israel is an example: its independence took place on 5 Iyyar 5708 (May 14, 1948), and this year 5 Iyyar will again fall on May 14 (although Yom HaAtzmaut will be celebrated two days earlier on 3 Iyyar, because 5 Iyyar falls on Shabbat – see M.26). The next time their birthdays coincide will not be until 30 years later, in 5795 (2035). Actually, all date correspondences are determined until 29 Cheshvan of the following year (in this case, 5766), which falls on Dec. 1. Note also that this correspondence causes my parents’ Hebrew wedding anniversary (13 Tammuz) to fall on the same day as my civil birthday (July 20).

5. **EXACT CORRESPONDENCE FOR THE WHOLE YEAR:** Looking at the table above, we can determine which years have their civil and Jewish dates correspond the way they do in 5765, for the whole year. These are the years with a “YES” in all 4 columns. The years in which all Jewish dates correspond to the same civil dates as they do in 5765 are: 5670 (1909-10), 5746 (1985-86), **5765 (2004-05), **5898 (2137-38), 5917 (2156-57), and 5966 (2205-06). So there are **only 6 years from the time of the introduction of the Gregorian calendar until the Jewish year 6000 in which all Jewish dates fall on the same civil dates as they do this year**. Note that all of these Jewish years must be “chaseira” leap years (see section K), and the corresponding civil calendar year must be a non-leap year (so that there is no February 29).

**U. ****SPECIAL EVENT COMBINATIONS DUE TO CIVIL AND JEWISH DATES AND DAYS OF THE WEEK**

In sections C through P we discussed events occurring in 5765 that depend on the year-type of the Jewish year, that is, events that depend (mostly) on the day of the week on which Jewish calendar dates fall. Those events do not depend on any correspondence with the civil calendar. In section T we discussed the correspondence between the Jewish and civil calendars for this year 5765. What about correspondences between the Jewish and civil calendars and days of the week, all at the same time?

In item T.5 we listed the years in which the Jewish and civil dates correspond the way they do in 5765, for the whole year. For the days of the week to correspond as well throughout the whole year, the year-type must be החא (hei-chet-aleph). Of the years listed in T.5, the only ones with the required year-type are the years **5670 (1909-1910), 5765 (2004-05), and 5917 (2156-57)**. So there are only 2 years other than the current year (from the time of the introduction of the Gregorian calendar until the year 6000) that have the exact same correspondence between Jewish and civil dates and days of the week as this year 5765. If you are a calendar publisher and you still have a supply of leftover Jewish calendars from the year 5670 (1909-10), then you can reuse them for this year 5765, without changing anything other than the year number. (Well, you may want to add some of the newer holidays like Yom HaAtzmaut that didn’t exist way back then. Be careful also with some of the civil holidays whose rules may have changed. Also, make sure the calendar you are using from 1909-10 was based on the Gregorian calendar, not the Julian calendar which was then still in use in many countries, including most of Eastern Europe.) And don’t forget to **save your calendars at the end of 5765**, because your great-great-…-grandchildren will be able to use them for the year 5917 (2156-57).

However, there are other years in which there are **partial correspondences**. 11 years ago, the months of Tishrei and Cheshvan (until 29 Cheshvan) of the year 5754 (1993) corresponded to the same civil dates and days of the week as they do this year – from Thursday September 16 until Saturday November 13. So the Jewish-civil calendar for those months this year looks exactly as it did in 5754. Thanks to Chaim Greenspan for pointing this out. (In 5754, Cheshvan had 30 days, so the correspondence doesn’t continue further.) In case you haven’t bought a calendar yet for this year, pull out your old one from 5754 to use for the first 2 months, and then ask to buy a calendar for this year starting with Kislev. Maybe you’ll get a discount by not taking the first two pages.

Now, there are many events on the civil calendar that don’t depend on a particular calendar date, but rather they depend on a day of the week. For example, Thanksgiving in Canada is on the 2^{nd} Monday in October. For these events to coincide with particular events on the Jewish calendar, we don’t necessarily need the Jewish date to fall on a particular civil date. Let’s examine some of this year’s calendar event correspondences:

1. **UNIVERSITY SCHEDULE ADJUSTED FOR ROSH HASHANA:** The University of Toronto maintains a resolution stating that “the first day of classes in the fall term in all teaching divisions should not be scheduled on the first and second days of Rosh Hashanah or on Yom Kippur”. Many divisions within the university, including the Faculty of Arts and Science, usually schedule classes to begin a week after Labour Day. This year, Rosh HaShana falls on the Thursday and Friday during what would have been the first week of classes, meaning that classes which meet only on Thursday or Friday (or Wednesday evening) would have their first meeting on Rosh HaShana, contrary to the university policy. To avoid this problem, some divisions simply cancelled classes on Rosh HaShana this year (such as the Faculty of Information Studies and some departments within the School of Graduate Studies). The Faculty of Arts and Science has adjusted the beginning of the semester so that classes begin the previous Thursday, Sept. 9. That way, it will be at least the second meeting of any class, not the first, that takes place on Rosh HaShana (except for Wednesday evening classes – I’m not sure what the story is with that). Thanks to Dr. Glen Weltman for bringing this to my attention. So how often does it happen that Rosh HaShana falls during what would ordinarily be the first week of classes? This would happen whenever Rosh HaShana falls on a Monday between September 8 and 14, or on a Tuesday between September 9 and 15, or on a Thursday between September 11 and 17. Some years in which this happens are 5711 (1950), 5722 (1961), 5727 (1966), 5738 (1977), 5741 (1980), 5749 (1988), 5752 (1991), 5754 (1993), **5765 (2004), **5768 (2007), 5776 (2015), 5779 (2018), 5790 (2029), 5795 (2034), and 5806 (2045). I don’t know how long this university policy has been in effect, nor for how long it has been customary for Arts and Science classes to begin a week after Labour Day.

2. **CLOCK CHANGE ON YOM TOV UNDER OLD RULES:** Until 5746 (1986), daylight saving time (DST) used to begin in Canada and U.S.A. on the **last Sunday of April**. The rules were then changed so that, since 5747 (1987), DST begins on the**first Sunday of April**. If the old rules were still in effect, the clock change would take place this year on the first Seder night. When does it happen that we actually do have a clock change on yom tov? Under the current rules, we would need a yom tov day to fall on the first Sunday in April, i.e. on a Sunday between April 1 and 7. Daylight saving time begins on the first day of Pesach (i.e., the night of the 1^{st} Seder) in the years 5805 (2045), 5832 (2072), 5859 (2099), 5930 (2170), 5957 (2197), and 5984 (2224). Daylight saving time begins on the 2^{nd} day of Pesach (the night of the 2^{nd} Seder) in the years 5748 (1988), 5775 (2015), 5778 (2018), 5789 (2029), 5802 (2042), 5816 (2056), 5829 (2069), 5843 (2083), 5870 (2110), 5873 (2113), 5897 (2137), 5900 (2140), 5927 (2167), 5941 (2181), 5954 (2194), 5965 (2205), 5968 (2208), 5995 (2235), and 5998 (2238). Daylight saving time begins on the 8^{th} day of Pesach in the years 5754 (1994), 5781 (2021), 5808 (2048), 5835 (2075), 5903 (2143), 5906 (2146), and 5933 (2173). Under the old rules, the clock change took place on the 8^{th} day of Pesach in the year 5741 (1981). If the old rules were still in effect, there would be clock changes on yom tov in **5765 **(**2005 **– 1^{st} day of Pesach), 5768 (2008 – 8^{th}day), 5776 (2016 – 2^{nd} day), 5803 (2043 – 2^{nd} day), 5860 (2100 – 2^{nd} day), 5863 (2103 – 8^{th} day), 5890 (2130 – 8^{th} day), 5917 (2157 – 1^{st} day), 5928 (2168 – 2^{nd} day), 5955 (2195 – 2^{nd} day), 5961 (2201 – 8^{th} day), 5985 (2225 – 2^{nd} day), 5988 (2228 – 8^{th} day). **Exercise for the reader: **Figure out **what proportion of years are such that Pesach begins before the clock change**, so that we are not yet on daylight saving time during the Sedarim. Now, what about the day we “fall back” to standard time on the **last Sunday of October**? Simchat Torah falls on the clock change date in the years 5747 (1986), 5815 (2054), 5842 (2081), 5872 (2111), 5899 (2138), 5937 (2176), 5967 (2206), and 5994 (2233). Of course, **other countries **may have different rules for the beginning and ending of DST, and this may lead to other occurrences of a yom tov on the clock change date. Note that in **Israel**, the tendency has been over the last several years to begin DST (known as “sheon kayitz” or “summer time”) on the night immediately following the first yom tov day of Pesach. For Diaspora Jews visiting in Israel and observing the 2^{nd} day of yom tov, this invariably leads to the clock change taking place on the 2^{nd} Seder night.

3. **MOTHERS’ DAY ON EREV ROSH CHODESH: **Mothers’ Day is celebrated (in Australia, Canada, and U.S.A.) on the 2^{nd} Sunday of May. This year May starts on a Sunday, so Mothers’ Day falls on May 8, the earliest possible civil date. Combining this with the fact that Jewish dates this year fall on civil dates that are much later than usual (see section Q), we see that Mothers’ Day will fall on a Jewish date that is much earlier than usual. Mothers’ Day this year falls on 29 Nisan, Erev Rosh Chodesh Iyyar. How often does this happen? We need Erev Rosh Chodesh to fall on a Sunday between May 8 and 14. The last time the 2^{nd} Sunday of May fell on 29 Nisan was in 5670 (1910) – but I doubt that Mothers’ Day existed way back then. So this year may be the first time in history that Mothers’ Day falls on Erev Rosh Chodesh. The next time will be in the year 5917 (2157). **This is the earliest Jewish date on which Mothers’ Day can fall**, unless we wait until the year 5974 (2214), when Mothers’ Day will fall on 27 Nisan. Note that Mothers’ Day can occasionally fall on 30 Nisan (the first day of Rosh Chodesh Iyyar), as in the years 5708 (1948 – if Mothers’ Day existed then), 5776 (2016), and 5803 (2043). Otherwise, Mothers’ Day falls during the month of Iyyar, or possibly at the beginning of Sivan. Last year Mothers’ Day fell on Lag BaOmer.

4. **VICTORIA DAY ON PESACH SHEINI:** Victoria Day is celebrated in Canada on the second-last Monday in May. This year it falls on Pesach Sheini. How often does this happen? We need 14 Iyyar to fall on a Monday, between May 18 and 24. Years in which this happens are 5741 (1981), **5765 (2005), **5768 (2008), 5863 (2103), 5890 (2130), 5917 (2157), 5961 (2201), and 5988 (2228).

5. **ROSH CHODESH ****ELUL**** ****ON**** LABOUR DAY:** Labour Day is the first Monday in September. This year it falls on Rosh Chodesh Elul. This happens in the years **5765 (2005), **5768 (2008), 5863 (2103), 5890 (2130), 5917 (2157), and 5988 (2228).

6. **4 CONSECUTIVE 3-DAY WORKWEEKS IN OCTOBER 2005: **This really belongs to 5766, but I couldn’t resist including it here. Thanksgiving in Canada is observed on the 2^{nd} Monday in October. (I think it’s the same day as Columbus Day in theU.S.A., but in Canada it’s a legal holiday.) All the yamim tovim in Tishrei 5766 fall on weekdays in October 2005, and combined with Thanksgiving falling during the same week as Yom Kippur, we get 4 consecutive weeks each having only 3 available working days (assuming a usual Monday-to-Friday workweek). In fact, there will be **only 13 working days in October 2005, no 3 of which are consecutive**. Better start saving up your vacation days now. Or, as someone once said, “I’ve run out of sick days so I’ll have to call in dead.”

**V. ****GOOD FRIDAY ON PURIM**

If you’re worried that Purim falling on Friday makes for an extremely busy workday (see M.5), you’ll be surprised to realize that the day is Good Friday, so depending on which country/province/state you live in, you probably won’t have to go to work or school. How often does this happen? Assuming my Easter analysis of section S is correct, **the last time it happened was 95 years ago**, in 5670 (1910), but it will happen again 3 years from now, in 5768 (2008).

For Good Friday to be on Purim, we need: (a) a year of the 19-year cycle that causes Easter to be a month before Pesach, as described in section S (the year is necessarily a Jewish leap year); and (b) Purim to be on a Friday (and since it is a leap year, the year-type must beהחא (hei-chet-aleph), as described in section O). These two conditions are clearly necessary, and I think they are also sufficient. **Exercise for the Reader:** Verify this.

As I explained earlier, this can only happen under the Gregorian rules for Easter, not the Julian rules. So here is this **complete list **of all years when Good Friday falls on Purim, until the year 6000: (The ordinal number indicates the year of the 19-year cycle.)

5396 – 19^{th} (1636), 5423 – 8^{th} (1663), 5518 – 8^{th} (1758), 5521 – 11^{th} (1761), 5616 – 11^{th} (1856), 5643 – 19^{th} (1883), 5670 – 8^{th} (1910), **5765 – 8 ^{th} (2005), **5768 – 11

^{th}(2008), 5863 – 11

^{th}(2103), 5890 – 19

^{th}(2130), 5917 – 8

^{th}(2157), 5988 – 3

^{rd}(2228)

So this year 5765 is the **8 ^{th} time in history that Good Friday falls on Purim**, and there will be 5 more until the year 6000. The possible interval lengths between occurrences seem to be 3, 27, 71, or 95 years.

**W. ****THE MOLAD AND THE DECHIYYOT**

In order to discuss any peculiarities resulting from the times at which the **molad (traditional mean lunar conjunction) **occurs each month, let us start with a table of the moladot for all months of the year 5765:

MONTH | CLASSICAL MOLAD | CLOCK FORMAT |

Tishrei 5765 | day 3, 19 hours 287 chalakim | Tuesday 1:15 p.m. 17 chalakim |

Cheshvan | day 5, 8 hours | Thursday 2:00 a.m. |

Kislev | day 6, 20 hours 793 chalakim | Friday 2:44 p.m. 1 chelek |

Tevet | day 1, 9 hours 506 chalakim | Sunday 3:28 a.m. 2 chalakim |

Shevat | day 2, 22 hours 219 chalakim | Monday 4:12 p.m. 3 chalakim |

Adar I | day 4, 10 hours 1012 chalakim | Wednesday 4:56 a.m. 4 chalakim |

Adar II | day 5, 23 hours 725 chalakim | Thursday 5:40 p.m. 5 chalakim |

Nisan | day 7, 12 hours 438 chalakim | Saturday 6:24 a.m. 6 chalakim |

Iyyar | day 2, 1 hour 151 chalakim | Sunday 7:08 p.m. 7 chalakim |

Sivan | day 3, 13 hours 944 chalakim | Tuesday 7:52 a.m. 8 chalakim |

Tammuz | day 5, 2 hours 657 chalakim | Wednesday 8:36 p.m. 9 chalakim |

Av | day 6, 15 hours 370 chalakim | Friday 9:20 a.m. 10 chalakim |

Elul | day 1, 4 hours 83 chalakim | Saturday 10:04 p.m. 11 chalakim |

Tishrei 5766 | day 2, 16 hours 876 chalakim | Monday 10:48 a.m. 12 chalakim |

The column “Classical Molad” gives the time of the molad the way the classical sources, including Rambam, would have described it. The “day” number refers to the day of the week, where the day begins at 6 p.m. the previous evening (so, for example, “day 3” in the first row begins at 6 p.m. on Monday). Each hour is divided into 1080 chalakim, rather than into minutes and seconds as we would do nowadays. Note that **each successive molad is determined by adding 1 day 12 hours 793 chalakim to the previous one **(and taking the result modulo 7 days), as described in chapter 6 of Rambam, Hilkhot Kiddush HaChodesh.

The column “Clock Format” gives the day and time in a more familiar format, the way it is usually announced at Birkat HaChodesh. The day of the week is given, the hours are given using a.m. or p.m., and the chalakim are converted into minutes (18 chalakim = 1 minute) with the remaining chalakim noted. Note that in this format, **we can determine each successive molad by adding 1 day 12 hours 44 minutes and 1 chelek to the previous one**. (Note also that 1 chelek is 3 1/3 seconds, so if you really want you can convert the times to h:mm:ss.)

Now, the question arises: According to whose clock does the molad occur at the time specified in the chart? One might guess that it is Jerusalem time. This should be correct, except that the clock time used in Israel today is based on the world’s system of standard time zones, which only came into being about 120 years ago, while the calculations used for the molad times have been around for a few millennia.

The consensus among those who have something to say about this issue seems to be that **the molad times are given in ****Jerusalem**** Mean Local Time **(JLT), which is UTC (GMT) + 2 hours 20 minutes 56 seconds. This is 20 minutes 56 seconds ahead of Israel Standard (Winter) Time (IST). So, in order **to convert from the given molad time in JLT to a time on any clock in the modern real world, the first step is to subtract 20 minutes 56 seconds to get IST**. Then you can add or subtract the correct number of hours for your local time zone, for example subtract 7 hours for EST, or only 6 hours for EDT if applicable. Rabbi Phil Chernofsky mentions this regularly in his Torah Tidbits at www.ou.org/torah/tt, as does the Luach Davar BeItto by Mordechai Genut (published annually). Personally, I’m not sure how one can prove that the intended time reference is mean local time rather than true (apparent) solar time, but I’ll have to discuss this with the experts at some point. For an entirely different point of view, see Melech Tanen’s essay “Equal Hours in Jewish Law”, available at www.molad.blogspot.com. His essay contains a wealth of information, analysis, and background source material, although I don’t necessarily agree with all of his conclusions.

Now, let’s discuss some of the interesting features of this year’s moladot. Don’t forget to glance at the chart above as you read the following descriptions:

1. **2-DAY POSTPONEMENT FOR ROSH HASHANA 5765: **The molad for Tishrei is on Tuesday afternoon. So why is the first day of Rosh HaShana on Thursday? In general, **the keviut (year-type) of the Jewish calendar year is determined based on the molad for Tishrei**. We set 1 Tishrei to be the day of the molad, except for several situations in which 1 Tishrei is postponed by one or two days, as explained in chapter 7 of Rambam, Hilkhot Kiddush HaChodesh. (The calendar is adjusted by varying the lengths of Cheshvan and Kislev of the previous year.) One of the postponement rules is known as “molad zaken”. This rule states that **if the molad falls after ****noon**** (****midday****) on a particular day, Rosh HaShana cannot be set for that day**, but must be postponed. Another postponement rule, known as “La ADU Rosh”, states that **Rosh HaShana cannot be set on Sunday, Wednesday or Friday**, so that if the molad falls on one of those days, Rosh HaShana must be postponed. In our case of 5765, the molad occurs just after noon on Tuesday. This is late enough that Rosh HaShana cannot be set for Tuesday, based on “molad zaken”. But Rosh HaShana cannot be on Wednesday either, by “La ADU Rosh”. So Rosh HaShana is postponed to Thursday, 2 days after the day of the molad.

How often does this happen? It turns out that **Rosh HaShana is 2 days after the molad in 14.0% of all years**. These are years when the molad is on Tuesday, Thursday or Shabbat, but Rosh HaShana is postponed to Thursday, Shabbat or Monday, respectively. In other words, **the molad for Tishrei falls on 28 Elul, 2 days before Rosh HaShana**. (For the advanced reader, note that this figure also includes instances of dechiyyat GaTRaD, which occurs in 3.3% of years.)

Here is a list of recent and upcoming years in which Rosh HaShana is 2 days after the molad: 5667 (1906), 5674 (1913), 5683 (1922), 5687 (1926), 5690 (1929), 5694 (1933), 5699 (1938), 5703 (1942), 5710 (1949), 5714 (1953), 5718 (1957), 5719 (1958), 5745 (1984), 5761 (2000), **5765 (2004), **5772 (2011), 5777 (2016), 5781 (2020), 5789 (2028), 5790 (2029), 5796 (2035), 5797 (2036), 5801 (2040), 5816 (2055), 5817 (2056), 5823 (2062), 5843 (2082), 5859 (2098).

2. **MOLAD ALMOST 29 HOURS BEFORE ROSH HASHANA:** The previous item describes the fact that the molad occurs on the calendar date which is 2 days before Rosh HaShana, i.e. on 28 Elul. The molad may occur any time from noon until the end of the day (or possibly even earlier than noon, in the case of dechiyyat GaTRaD which I will not explain here). However, in the case of this year 5765, the molad is very early in the afternoon on Tuesday – at 1:15 p.m. and 17 chalakim. That is almost 29 hours before the beginning of Rosh HaShana on Wednesday evening. So, we may ask, how often is the molad so far in advance? How often is the molad not only 2 calendar days before Rosh HaShana, but as early as 1:15 and 17 chalakim or earlier on that day?

It turns out that the molad for Tishrei is as early as it is this year or earlier on 28 Elul in **5.6% of years**. (Once again, this includes instances of dechiyyat GaTRaD.) Here is a list of recent and upcoming years in which this occurs: 5667 (1906), 5683 (1922), 5687 (1926), 5718 (1957), 5745 (1984), **5765 (2004), **5789 (2028), 5790 (2029), 5796 (2035), 5816 (2055), 5823 (2062). Note that the last time this happened before this year was 20 years ago, in 5745 (1984). The next time it will happen after 5765 will be 24 years from now, in 5789 (2028). Note also that 4 years ago, in 5761 (2000), the molad was **almost** as early as it is this year – it was on 28 Elul at 1:17 p.m. and 4 chalakim – less than 1½ minutes later than this year.

The point of all this is that the molad is very early this year relative to the beginning of Rosh HaShana. In fact, since the date of Rosh HaShana is set by adjusting the lengths of Cheshvan and Kislev, the unusually long discrepancy between the molad and Rosh Chodesh extends backward throughout most of the previous year (5764). You may have noticed that **the moladot for most months of 5764 were significantly earlier than Rosh Chodesh**. It all comes from the fact that the molad of Tishrei 5765 is very early on Tuesday afternoon.

3. **MOLAD AT WHOLE HOUR FOR CHESHVAN:** Notice that the molad for Cheshvan is on Thursday at 2:00 a.m. – with **no minutes and no chalakim**! How often does it happen that a molad occurs on the hour? There are 1080 chalakim in an hour (= 18 chalakim per minute times 60 minutes) and the molad cycles through all of them before repeating them in the same order. So the molad will occur on the hour **once every 1080 months**. 1080 lunar months are equal to **87 years and either 3 or 4 months**. The last time the molad was on the hour was Tammuz 5677 (1917), when the molad was Wednesday at 1:00 a.m. The next time after Cheshvan 5765 will be Adar I 5852 (2092), when the molad will be Friday at 3:00 a.m.

4. **KIDDUSH LEVANA FIRST SATURDAY NIGHT IN CHESHVAN SOME PLACES:** If you live far enough west, you may be able to say Kiddush Levana right after Shabbat, the night of 2 Cheshvan. The earliest time for Kiddush Levana is 3 days from the molad (MV 426:20), which takes us to Sunday at 2:00 a.m. (JLT), so in Israel you wouldn’t be able to say it that Saturday night. But that time is approximately 7:39 p.m. EDT on Saturday night, so depending on what time Shabbat ends in your location (and on what time the moon sets!), you may be able to say Kiddush Levana that night. Certainly people in most parts of western North America will likely be able to say it.

5. **MOLAD PRIOR TO ANNOUNCEMENT FOR KISLEV:** When we announce the molad during Birkat HaChodesh for Kislev, the molad will already have occurred in the past. Rosh Chodesh will be on Sunday, but we will announce that the molad has already taken place, on Friday at 2:44 p.m. and 1 chelek. This happens every once in a while, but it is especially prone to happen now, since the molad is so far in advance of Rosh Chodesh, as explained in item 1.

6. **MOLAD PRIOR TO ANNOUNCEMENT FOR NISAN:** The same thing will happen during Birkat HaChodesh for Nisan, unless you announce the month very early in the morning (in Israel) or you are in a location far east of Israel. Rosh Chodesh will be on Sunday, but we will announce that the molad has already taken place on Shabbat morning at 6:24 a.m. and 6 chalakim.

7. **SPECIAL POSTPONEMENT “BETU-TAKPAT” AT END OF YEAR: **The molad for Tishrei 5766 is on Monday morning. So why is Rosh HaShana 5766 on Tuesday? Based on what I’ve said earlier (see item 1 above), Rosh HaShana shouldn’t have to be postponed from the day of the molad, since the molad occurs before noon on Monday, which is a legal day of the week for Rosh HaShana. However, we have an exceptional situation which happens quite rarely. In order for Rosh HaShana 5766 to be on Monday rather than Tuesday, we would have to remove a day from the year 5765. But wait a minute, from which month can we remove a day if Cheshvan and Kislev already have only 29 days each? That’s the problem. The calendar is set up with only a certain number of possible year lengths. **A leap year cannot be shorter than 383 days. **If Rosh HaShana of this year is on Thursday, and the year is a leap year, then Rosh HaShana of next year cannot be less than 383 days later, on Tuesday, even if the molad is early enough on Monday for Rosh HaShana to be on Monday otherwise.

This special postponement is known as “dechiyyat BeTU-TaKPaT”. It applies only to **Rosh HaShana immediately following a leap year**, if the molad is on Monday at 15 hours 589 chalakim (= Monday 9:32 a.m. and 13 chalakim) or later, hence the name “BeTU-TaKPaT” (בטו תקפט) representing 2-15-589. The reason for this strange cut-off is that if the molad is at this time or later, then the molad at the beginning of the previous year, 13 months earlier, would have been on Tuesday at noon or later, causing the 2-day postponement of Rosh HaShana to Thursday, as we have described. This would cause the year to be too short, unless we postpone Rosh HaShana to Tuesday at the end of the year. Thus, when BeTU-TaKPaT occurs, it is always at the end of a החא (hei-chet-aleph) year-type, and it begins a גכה (gimel-kaf-hei) year, which would otherwise have been a בשה (bet-shin-hei) year if not for the postponement.

How often does this happen? BeTU-TaKPaT occurs very rarely, **only in 0.54% of years**, or approximately **once every 190 years**!

Here is a **complete list of all occurrences of dechiyyat BeTU-TaKPaT according to the rules of the fixed calendar, from the time of Hillel II **(who seems to have established the rules of the fixed calendar) **until the year 6000**: 4179 (418), 4257 (496), 4504 (743), 4602 (841), 4849 (1088), 5096 (1335), 5194 (1433), 5441 (1680), 5519 (1758), 5688 (1927), **5766 (2005)**. Notice that Tishrei 5766 will be the **last time before the year 6000 **that dechiyyat BeTU-TaKPaT occurs! The next occurrence according to the fixed calendar rules would be in the year 6013 (2252). The intervals between occurrences of BeTU-TaKPaT are 78, 98, 169, or 247 years. However, if we extend the fixed calendar far enough, we get an interval of 345 years from 6605 (2844) until 6950 (3189).

**X. ****CONCLUSION**

When I started writing this essay, my original title was **“How is this year different from all (or most) other years?”** Then I decided it would look better without the phrase “or most”. But is this change legitimate? Is this year, 5765, really different from **all** other years, and not just **most** other years?

Let us summarize what we have seen so far. The year-type החא (hei-chet-aleph) is quite rare, characterized by the fact that Tevet starts on Monday, as described in section O. What else distinguishes the year 5765? The exact correspondence between Jewish and civil calendar dates that occurs in 5765 occurs in only a small number of other calendar years, as described in section T (item T.5). Of these years, the only ones that are החא (hei-chet-aleph) years are **5670 (1909-1910), 5765 (2004-05), and 5917 (2156-57)**. As described in section U, these 3 years all seem to have the exact same calendar – **every Jewish date falls on the exact same Gregorian (civil) date and day of the week in 5765 as it fell in 5670 and as it will fall in 5917**. Even Good Friday falls on Purim in all of these 3 years. You can reuse your old 5670 calendars for this year 5765, and then reuse them again for 5917. Recycling is good, but it seems that I may be out of luck, and I may have to reinsert “or most” into the title of this essay.

But wait! The events of section W come to the rescue! In particular, the fact that the determination of the year-type involves the application of dechiyyat BeTU-TaKPaT at the end of the year (see event W.7) is extremely significant, as this occurs very rarely. In particular, it does not occur in either of 5670 or 5917! It turns out that **this year 5765 is the only year in all of history whose “keviut” (year-type determination) involves dechiyyat BeTU-TaKPaT at the end of the year, and whose Pesach falls on April 24. **Whew. This year really is different from all other years!

Wow, you made it all the way to the end of this essay! Okay, so you may have skipped a few details, or held the “Page Down” key for a while. I don’t mind. But if you really did read and enjoy a significant portion of this essay, then **I really want to know who you are!** Welcome to the club of calendar nerds! Please send me an e-mail and feel free to include any comments or corrections: ari.brodsky@utoronto.ca

Oh, and don’t forget to submit your solutions to the **exercises**. Speaking of exercises, here is **one more exercise for the reader:** In the Hebrew subtitle of this essay, I used the word **נִשְׁתַּנֵּית** (“nishtanneit”) as the feminine equivalent of **נִשְׁתַּנָּה** (“nishtanna”, familiar from the Pesach Seder), but I’m not sure that this is the correct feminine conjugation. My alternative option was **נִשְׁתַּנְּתָה** (“nishtanneta”). The problem is that these are not Biblical Hebrew verb forms, and so they don’t appear in the usual Biblical Hebrew grammar books. Can anyone with any expertise in Rabbinic (Mishnaic) Hebrew verb forms tell me which version (if either) is the correct conjugation?

**Y. ****REFERENCES FOR FURTHER ****READING**** **

In the body of this essay I have already indicated sources for many of the individual facts that I quote. For general background and information about the Jewish calendar, here are my recommendations:

The main **classical halakhic source **for the historical background and detailed calculations of the Jewish calendar is **Rambam (Maimonides), Hilkhot Kiddush HaChodesh**, included in the Zemanim volume of his halakhic code, Mishne Torah (approx. 4938 / 1178 CE). In the first 10 chapters, Maimonides gives all the theoretical background and calculations necessary to construct the Jewish calendar. (According to Maimonides (11:4), these calculations can be learned by schoolchildren in 3 or 4 days.) For the advanced reader, the last 9 chapters describe an algorithm for determining when the new moon will first be visible each month. I’ve used it and it works!

Another extremely valuable classical halakhic source is the Arba’a Turim (known simply as the “**Tur**”), by Rabbi Yaakov ben Asher, section **Orach Chayyim, chapters 427-428**. The Tur seems to be the earliest source to use the letter-codes to refer to each of the 14 different “keviut” year-types (although he uses 2-letter codes rather than the 3-letter codes that have become more common in modern writings). The Tur also gives rules for the distribution of the Torah readings throughout the calendar year, and most importantly gives tables for determining the year-type of any Jewish year from 5055 until after the year 6000. Be careful with the tables though – many old printings of the Tur contain an incorrect version of one of them. The correct version is printed in the 5753 (1993) edition, published by MachonYerushalayim. This edition also contains extensive footnotes, clarifying and elaborating on the various calculations.

**My favourite book on the Jewish calendar is Shearim LaLuah HaIvry **(Gates to the Hebrew Calendar), by **Rahamim**** Sar-Shalom**, Netanya 5744 (1984). This book contains **everything you could possibly want to know about the Jewish calendar**, but it will take you several lifetimes to read it. It is an excellent reference; in fact a lot of my statistical information and all of my lists of years in the various sections of this essay were taken from Shearim LaLuah HaIvry. The book also contains an extensive bibliography for further reference.

**References in English:**

The first source from which I learned about the details of the Jewish calendar was the “Calendar” entry in **Encyclopaedia Judaica** (Keter Publishing House Jerusalem Ltd., Jerusalem 1972 (5732), vol. 5 columns 43-53). It gives all the details necessary for the construction of the Jewish calendar.

A good book in English describing the Jewish calendar is **“Understanding the Jewish Calendar”, by Rabbi Nathan Bushwick **(Moznaim Publishing Corporation: New York 1989). It gives a very readable description of all the details of the calendar, based on Rambam and Tur.

When you finish all those, let me know and we’ll discuss them. J Really, even if you haven’t finished them, I’ll be happy to discuss calendar issues with anyone!