This year’s calendar

5786

How to understand it

How to calculate it

Michoel Reach

Contents

1. Introduction and overview
2. Choosing the calendar
3. Yomim Tovim and Sidros
4. Conclusion

Introduction

• Maharsha: The Bnei Esav’s calendar only follows the sun, the Bnei Yishmael’s calendar only follows the moon – but the Torah requires us to follow both.
• The Torah says that our calendar months should be set by the lunar cycle: החודש הזה לכם. A month begins with the sighting of the new moon. That happens approximately every 29 and a half days – but not exactly.
• The Torah also requires that the calendar year stay in synch with the sun: Pesach must be בחודש האביב: in the spring. Sukkos must be חג האסיף, the gathering-in festival: in the fall. The solar year is approximately 365 and a quarter days - but not exactly.
• These two time scales are independent, and are not multiples of one another. They are bound to get out of synch.

Introduction

• For the first half of our history, the solution was to adjust them by hand:
• Witnesses came to the Sanhedrin to establish the new month. Each month would be either 29 or 30 days long, whenever the new moon was sighted.�Since a lunar month is about 29 and a half days, they added an extra day about half the time.
• The Sanhedrin also decided each year whether to add Adar II, a thirteenth month, if it did not seem that spring would arrive before Pesach.�A solar year is a third of a month (about 11 days longer) longer than twelve lunar months, so they needed to do that every few years.
• In those days, there was no way to be sure ahead of time what the year’s calendar would be.

Introduction

• By the days of Abaye and Rava it was very difficult to establish the months and years directly (Rambam: “no permanent court was left in Eretz Yisroel”), so the nasi Hillel ben Yehudah established a permanent calendar instead.
• The Rambam says this is halacha l’Moshe b’Sinai. (Chazon Ish: the Rambam means doing it by calculation when needed – not the exact details.)
• The current calendar is based only on calculation, not observation. It cannot be exact, but the approximate values chosen for month and year are close enough that it has drifted very slowly - days - in the hundreds of years since.
• When we have a Sanhedrin again, we will be able to fix it.

References

• Rambam, Hilchos Kiddush Hachodesh
• Tur, Orach Chaim, 428. The chart there is the basis of the Keviyus web page.
• Tiferes Yisrael, Sh’vilei d’rakia (at end of Seder Moed)
• Rabbi Nathan Bushwick, Understanding the Jewish Calendar, Moznayim, 1989.
• Rav David Heber’s yearly shiur on the calendar at Yeshiva Ner Yisroel, Baltimore.

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• You can get this presentation and software tools at my website https://sites.google.com/site/miyminimichoel (along with other divrei Torah).

Overview

We are going to calculate the Jewish calendar for a year.

All we need to know is the number of the year. This year is תשפ"ו - 5786.

• Choose a calendar:
1. Decide if this is a regular year (פשוטה) or leap year (מעוברת).
2. Find the molad for this Tishrei.
3. Find the molad for the next Tishrei.
4. Find the calendar day for this Rosh Hashanah and for the next.
5. Choose the calendar.
• Arrange the chosen calendar:
6. Find all the days of Rosh Chodesh, and all the yomim tovim.
7. Determine the Torah readings (סדרות).
8. Connect the calendar to the civil calendar.

Overview, cont. – choose a calendar

1) Decide if this is a regular year (פשוטה) or leap year (מעוברת).

• The Torah requires the months to track the cycles of the moon.
• The Torah requires the years to track the seasons of the (solar) year.
• To keep them in synch, we sometimes add an extra month.
• There is a repeating nineteen-year cycle of regular and leap years – �(גו"ח אדז"ט).
• The number of the year we are calculating tells us which one it is.

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Overview, cont. – choose a calendar

2) Find the molad for this Tishrei

• That is, the astronomical moment of the new moon for Tishrei of this year.
• Chazal made the approximation that all months are exactly the same length, from one new moon to the next.
• That amount is not an exact number of days; they estimated it within a second. (אי"ב תשצ"ג)
• Knowing the number of years (and months) since Creation, knowing the starting point, and knowing the length of a month - calculate the moment of the molad.
• This is an exact time, not a day.

Overview, cont. – choose a calendar

3) Find the molad for the next Tishrei

• Repeat the process for the following year.
• To the result for this Tishrei, add twelve more months worth of time (for a regular year) - or thirteen (for a leap year) - to get the molad for next year.
• Again, this is an astronomical moment in time, not a day.

Overview, cont. – choose a calendar

4) Find the calendar day for each Rosh Hashanah.

• Very often Rosh Hashanah will be on the same day as the time that the molad we calculated falls – but not always!
• There are four situations that may cause it to be moved to the next day, or the day after.
• These are known as the Four Dechiyos (ד' דחיות).
• Each resulting Rosh Hashanah is a day of the week on the calendar now, not a moment in time.

Overview, cont. – choose a calendar

5) Choose the calendar

• From the weekday of the first Rosh Hashanah, and the second, we know the length of the year. (חסירה, כסידרה, שלימה)
• That length, plus the starting week-day, plus whether it’s a leap year or not, determines the full calendar.
• There are only fourteen possible calendars.
• Chazal already worked out every detail of each of them. We’re really done. The rest of the steps here will just describe how they got those details.

Overview, cont. – arrange the chosen calendar

6) Find all the days of Rosh Chodesh, and all the yomim tovim.

• Once we know whether the year is a regular or leap year, and which weekdays are Rosh Hashanah at the beginning and end, we know the total number of days in the year.
• That tells us the lengths of each of the months, and gives us the days of Rosh Chodesh for each month.
• Each of the yomim tovim is on a particular date in the calendar and is now determined as well.

Overview, cont. – arrange the chosen calendar

7) Determine the Torah readings (סדרות).

• Now that the calendar is set up, we can see how many weekly Torah readings are needed – just count available Shabboses.
• We decide how many parshiyos need to be doubled up to fit.
• This was already done by Chazal for every possible calendar, but they gave some principles for how they decided which ones to double up.
• The results can be different in Eretz Yisroel and in chutzah la’aretz.

Overview, cont. – arrange the chosen calendar

8) Connect the calendar to the English (civil) calendar.

• We are not actually going to do this step – just explain it.
• The קדמונים showed how to find the date when we start saying V’sein tal umatar, using the old Julian calendar.
• Convert to today’s Gregorian calendar (used since 1582).
• Use that to find any other date, like January 1.

Contents

1. Introduction and overview
2. Choosing the calendar
3. Yomim Tovim and Sidros
4. Conclusion

B) Choosing the calendar

Okay, let’s get started and really do it!

We’ll go through the steps to get the calendar for a year - and do it for this year.

1. Peshuta or m’uberes?
2. Introduction – how to calculate the molad
3. Find the molad�- for Tishrei this year�- and for next year
4. Find Rosh Hashanah - the four dechiyos
5. Choose the calendar

1) Peshuta or m’uberes?

B) Choosing the calendar

1. Peshuta or m’uberes?
2. Introduction – how to calculate the molad
3. Find the molad�- for Tishrei this year�- and for next year
4. Find Rosh Hashanah - the four dechiyos
5. Choose the calendar

2) Introduction – how to calculate

• We use day of the week (1-7), hours, chalakim (reverse order in Hebrew).
• All our calculations use this triplet of numbers.
• The hours are measured starting from 6 pm (not the more usual שעות זמניות, which are based on sunrise and sunset or darkness), so 18 = 12 noon, etc.
• 1 chelek = 3⅓ sec., 1080 chalakim = 1 hour, 24 hours = 1 day.
• Also 7 days = 1 week. But –�We don't normally need to worry about the weeks at all. Chazal set it up that it’s enough to determine the time for the molad within the week.

How to calculate - example

• If you'd want to add 4 days, 18 hours, 443 chalakim (די"ח תמ"ג) or (ד, יח, תמג) to 5 days, 20 hours, 742 chalakim (ה, כ, תשמב):

443+742 = 1185 = 1 hour (=1080 chalakim) + 105 chalakim.

18 + 20 + 1 (which was carried) = 39 = 1 day + 15 hours.

4 + 5 + 1 = 10 = 1 week (ignore) + 3 days.

The result: 3 days, 15 hours, 105 chalakim (ג, טו, קה).

• This is how all these calculations are done. Just keep carrying.

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How to calculate - standard shifts

• Basic procedure:�1) Find how many months there are, from creation till the molad of this year’s Tishrei. Remember that some years are leap years and some regular years.�2) From the calendar’s starting point, add the time for that many months.�3) Now: what day of the week and time of day is that?�Again: there have been thousands of weeks since creation, but we are only going to need to know the day of the week and the time of day. This is part of Chazal’s design to make things simpler.
• Instead of counting all those months, we can break the job into pieces:�1) 19-year cycles, 2) additional regular years, and 3) additional leap years.

How to calculate - standard shifts, cont.

• The starting point is set near the beginning of the _year_ one, but at בהר"ד: Monday, 5 hours, 204 chalakim.
• Amazingly enough, this is an imaginary time, before the world was created! Chazal could have started from their own time, call it 4200, and gone forward – but then you would have had to subtract 4200 from the number of this year in the calculations.
• For convenience, they tracked backward in time to zero, so you wouldn’t have to subtract.
• The time בהר"ד is arbitrary, just matches with whenever they really started. But adding one year to it, you do get Friday morning of 1 Tishrei the next year, year 2, the day when First Man was created.

How to calculate - standard shifts, cont.

To the starting point, we’ll add multiples of the following four shifts.

• One molad – shift for one lunar month = אי"ב תשצ"ג:�1 day (really 29 days - but we ignore the weeks), 12 hours, 793 chalakim
• Shana peshutah – built out of 12 of these months = ו"ח תתע"ד:�4 days, 8 hours, 876 chalakim
• Shana m'uberes - built out of 13 of these months = ט"א תקפ"הכ:�5 days, 21 hours, 589 chalakim
• 19 year cycle - 19 years with 7 m'ubaros and 12 peshutos = ה"ו תקצ"בי:�2 days, 16 hours, 595 chalakim.

Each of these tells how far the molad moves after that many months. No weeks!

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Calculator

So you don’t have to do this yourself:

B) Choosing the calendar

1. Peshuta or m’uberes?
2. Introduction – how to calculate the molad
3. Find the molad�- for Tishrei this year�- and for next year
4. Find Rosh Hashanah - the four dechiyos
5. Choose the calendar

3) Find the molad for this year’s Tishrei

3) Find the molad for this year’s Tishrei, cont.

3) Find the molad for this year’s Tishrei, cont.

3) Repeat: Find the molad for next year’s Tishrei

B) Choosing the calendar

1. Peshuta or m’uberes?
2. Introduction – how to calculate the molad
3. Find the molad�- for Tishrei this year�- and for next year
4. Find Rosh Hashanah - the four dechiyos
5. Choose the calendar

4) Find Rosh Hashanah – the four dechiyos

4) Find Rosh Hashanah – the Four Dechiyos

The ד' דחיות where they are moved later (never earlier):

1. מולד זקן
2. לא אד"ו ראש
3. ג"ט ר"ד
4. ט"ו תקפ"בט

4a) The four dechiyos - מולד זקן

4b) The four dechiyos – לא אד"ו ראש

4) The four dechiyos, cont.

Last two dechiyos – ג"ט ר"ד and בט"ו תקפ"ט

• There are two more rules ("dechiyos") that have to do with the length of the calendar year.

Some background first:

• Chazal only allowed three lengths to a year: short (חסרה), medium (כסדרה), and long (שלמה).
• Chaseirah is one day shorter than k'sidrah, sheleimah is one day longer. (We'll see how this works when we talk about the lengths of the months.)
• By comparing the day of this year's Rosh Hashanah to next year's, you can tell which it is.

Length of year - פשוטה

• The actual calendar doesn’t use times, i.e. hours and chalakim, just complete days.
• We saw that a regular year (פשוטה) has a molad shift of ו"ח תתע"ד: 4 days and 8+ hours.
• In the actual calendar - which uses days, not times - a short chaseirah year (353 days) has a shift of three days from one Rosh Hashanah to the next, say from Shabbos this year to Tuesday the next.
• A regular k'sidrah year (354 days) has a four day shift,�and a long sheleimah year (355 days) has a five day shift.
• These are all the choices that are allowed.

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Length of year - מעוברת

• A leap year (מעוברת) we saw earlier has a molad shift of הכ"א תקפ"ט: 5 days, 21+ hours. That was a shift in time-of-day within the week.
• In the actual calendar, a chaseirah leap year (383 days) has a shift of five days from one Rosh Hashanah to the next (such as from Monday to Shabbos).
• A k'sidrah (384) has a six day shift.
• A sheleimah (385) has a seven day shift - that is, the two Rosh Hashanos are on the same day of the week.
• These are all the choices that are allowed.

Length of year - summary

• You see now why we never worry about the weeks. That’s the easy part; we really just need to figure out the days: that tells us which of these years it is.

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4c) The four dechiyos – ג"ט ר"ד

4d) The four dechiyos – בט"ו תקפ"ט

4) The four dechiyos, cont.

B) Choosing the calendar

1. Peshuta or m’uberes?
2. Introduction – how to calculate the molad
3. Find the molad�- for Tishrei this year�- and for next year
4. Find Rosh Hashanah - the four dechiyos
5. Choose the calendar�- The Keviyus page�- Find this year’s calendar

Choose the calendar

• We can now choose the calendar for the year.
• It turns out there are only fourteen possible calendars, total: seven for regular years, seven for leap years.
• To help visualize this, this is a chart in the Tur, Orach Chaim, 428.�

Choose the calendar – the Keviyus page

• A maybe fancier version of that chart:

B) Choosing the calendar

1. Peshuta or m’uberes?
2. Introduction – how to calculate the molad
3. Find the molad�- for Tishrei this year�- and for next year
4. Find Rosh Hashanah - the four dechiyos
5. Choose the calendar�- The Keviyus page�- Find this year’s calendar

Choose the calendar – find this year’s calendar

Choose the calendar, cont. – ארבעה שערים

• The “Four Gates”: Chazal found a way to mechanize the process of picking a calendar, to handle the ד' דחיות automatically.
• All you need is �(a) the molad of this Rosh Hashanah, and�(b) which of last year, this year, and next year are m’ubaros.
• Then you look up the answer on the chart. The ד' דחיות are built in.

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(2d 18h 187ch)

Contents

1. Introduction and overview
2. Choosing the calendar
3. Yomim Tovim and Sidros
4. Conclusion

C) Yomim Tovim and Sidros

1. Establish the months
2. Yomim tovim
3. Sidros�- Introduction�- Arranging the sidros

Establish the months

We have our calendar. Now we determine the length of each of the months.

• Months can be either 29 days (חסר) with one day of Rosh Chodesh at the end, or 30 days (מלא), ending with two days of Rosh Chodesh.
• If there are two, the first day of Rosh Chodesh is the 30th day of the previous month. The last day of Rosh Chodesh is always the 1st of the next month.
• The months must combine to form the right length year: as we saw, 353, 354, or 355 for a regular year, 383, 384, or 385 for a leap year.
• Most months have a specific length, never vary. Roughly, they alternate:
• Tishrei 30, Teves 29, Shvat 30, Adar 29, Nisan 30, Iyar 29, Sivan 30, Tammuz 29, Av 30, Elul 29 – always.
• In a leap year, Adar I is added with 30 days and Adar II has 29.

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Establish the months, cont.

C) Yomim Tovim and Sidros

1. Establish the months
2. Yomim tovim
3. Sidros�- Introduction�- Arranging the sidros

Yomim Tovim

Establish the months, cont.

• We saw that only three things vary in the calendar (aside from which day you start): Cheshvan, Kislev, and whether there’s a second Adar.
• What that means: The entire calendar from the last Adar onward is always the same.�From Adar II and Purim, Nisan and Pesach, all the way through the next Rosh Hashanah (really right through Cheshvan) is an identical rigid span for all calendars (just shifted by the day it starts).
• The result: If you know the day of the week for any one of those days, you know all the rest.

Establish the months, cont.

• “If you know the day of the week for any one of those days, you know all the rest.”
• See Tur Orach Chaim 428 for a mnemonic using this ("את-בש"):
• 1st day of Pesach (א) same day as Tisha B’Av (ת)
• 2nd day of Pesach (ב) same day as Shavuos (ש)
• 3rd day of Pesach (ג) same day as Rosh Hashanah (ר)
• 4th day of Pesach (ד) same day as Krias HaTorah (Simchas Torah) (ק)
• 5th day of Pesach (ה) same day as Tzom (Yom Kippur) (צ)
• 6th day of Pesach (ו) same day as the previous Purim (פ)

Establish the months, cont.

C) Yomim Tovim and Sidros

1. Establish the months
2. Yomim tovim
3. Sidros�- Introduction�- Arranging the sidros

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Sidros - introduction

• On the home stretch!
• The last major job: we need to place the Sidros (parshiyos). It should be easy - they're in order!
• Three things make things more complicated.
1. Yomim Tovim
2. Counting parshiyos and deciding which ones to double
3. Eretz Yisroel and chutzah la’aretz

3a) Yomim Tovim

• If the major yomim tovim fall on Shabbos, they have their own reading�- and the weekly sidrah waits for the next week.
• This applies to:�Rosh Hashanah, Yom Kippur, all of Sukkos, all of Pesach, and Shavuos.
• Sukkos and Pesach can contain one or two Shabboses.

3b) Counting parshiyos

• Depending on
• when Rosh Hashanah falls at the beginning and end of the year, and
• how many yomim tovim interrupt,
• we find the total numbers of weekly readings that year. Count.
• There are 54 sidros (see the left-hand pane in the Keviyus page). Some may need to be doubled up, to fit the actual number of readings.
• [One of them is V’zos Habracha, and it is read on Simchas Torah – doesn’t count.]
• There are (about) four more weeks in a leap year (מעוברת) than in a regular year (פשוטה), so a regular year will need several more double parshiyos.

3c) Eretz Yisroel and chutzah la’aretz

• The one-day yomim tovim in Eretz Yisroel can mean that the second day of yom tov falls on Shabbos, and takes over the Torah reading in chutzah la’aretz -
• but not in Eretz Yisroel.
• That would mean that Eretz Yisroel has room for an extra parsha that year, compared to chutzah la’aretz. It will jump a week ahead then, and stay ahead until chutzah la’aretz has a double parsha and Eretz Yisroel not.

Sidros, cont.

C) Yomim Tovim and Sidros

1. Establish the months
2. Yomim tovim
3. Sidros�- Introduction�- Arranging the sidros

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Sidros – Arranging the sidros

We do this in stages, working between benchmarks.

1. Beginning the year
2. Pesach
3. Shavuos
4. Tisha B’Av
5. Nitzavim-Vayeilech

Plus - some changes between Eretz Yisroel and chutzah la’aretz

(A fuller description is in the separate Sidros.pptx)

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1) Arranging the sidros – beginning the year

2) Arranging the sidros – Pesach

3) Arranging the sidros – Shavuos

4) Arranging the sidros – Tisha B’Av

5) Arranging the sidros – Nitzavim-Vayeilech

6) Eretz Yisroel and chutzah la’aretz

Contents

1. Introduction and overview
2. Choosing the calendar
3. Yomim Tovim and Sidros
4. Conclusion
1. The civil calendar
2. Acknowledgements

The civil calendar

• One step remains – matching our Hebrew calendar with the civil (English) calendar.
• We aren’t going to go through it in detail.
• The Rishonim (Rambam, Tur, etc.) did not bother with this at all.
• It has become important in the last few centuries, as our connection with the non-Jewish society has grown, especially if we use the non-Jewish calendar for everyday living.
• Easiest way is to keep track from last year!

The civil calendar, cont.

• The two calendars do not match up well:

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Year 2017 2018 2019 2020 2021 2022

Days 365 365 365 366 365 365 …

Year 5777 5778 5779 5780 5781 5782

Days 353 354 385 355 353 384 …

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• They bounce back and forth, longer and shorter.
• It averages out.

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The civil calendar, cont.

• They aren’t even the same average length.

Mean solar year Gregorian year Tekufas Rav Adda (19-year cycle)

365.24219 days 365.2425 days 365.24677 days

Difference/year: .0003 days 0.0046 days/year

< 1/2 min ~ 6 minutes

• Our calendar has drifted around a week out of synch.
• Chazal could have made it more accurate (as they did with the months).
• Why, then? They chose to use the 19-year cycle, easier to calculate.

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The civil calendar, cont.

• The Rishonim did explain a related task: when to start saying ותן טל וברכה in חו"ל, 60 days after the autumnal (fall) equinox – a solar date.
• The calculation [“תקופת שמואל”] corresponds to the Julian calendar, where a year is exactly 365.25 days – a civil leap year (on Feb. 29) every four years.
• That was replaced in 1582 by today’s Gregorian calendar, which has a more complex rule for leap years. Also there was a one-time 11-day adjustment to get back in synch with the sun.
• You currently end up with Dec. 4^th (or 5^th before a civil leap year like 2020).
• Once that date is calculated, you can find all other corresponding civil dates. For example, Dec. 4 is the 338^th day of the solar year, 337 days from Jan. 1.

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D) Conclusion

• This year’s calendar is complete. Do it again next year!
• Thanks for watching!

References

• Rambam, Hilchos Kiddush Hachodesh
• Tur, Orach Chaim, 428. The chart there is the basis of the Keviyus web page.
• Tiferes Yisrael, Sh’vilei d’rakia (at end of Seder Moed)
• Rabbi Nathan Bushwick, Understanding the Jewish Calendar, Moznayim, 1989.

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• You can get this presentation and software tools at my website https://sites.google.com/site/miyminimichoel (along with other divrei Torah).
• This whole presentation (for 5780) is available on youtube, linked on that Google Site.