The Jewish Calendar, and the ’at<->bash' את-בש
1. The length of the year
We have no arbitrary addings of days, months or years (e.g. Julius, Augustus and Gregorius) to our calendar.
We have both G-od’s written and oral tora, teachings, and they simply teach that day, month and year, each
of them has a logically astronomic meaning unlike the christian “day” and “month” or the muslim “year”.
1.1 “Day”, yom
Our day starts when it is dark, evening: “vayhi ‘erev, vayhi voqer, yom ’echad”, “and there was evening,
and there was morning - day one” (bereishit, Genesis, 1,6), and not arbitrarily at 12 at night...
1.2 Month”, chodesh (or yerach - yerach - from the same three-consonants-root y'r'ch' as yareyach, moon)
The month, yerach or chodesh, is based on the moon, yareyach. Following the cycle of the moon around the world which is 29½ days (approximately!), and because one cannot, or better: sensibly may not, start a new day or a new date in the middle of a day or night (!), therefore ‘month’ ––the root of it in most languages is ‘moon’––, can contain only 29 or 30 days! We can never have an unscientific month of 28 or of 31 days!..
1.3 “Year”, shana
As a result of the above, a ‘regular lunar’, a 12-months’-year, should have: 6 months of 29 days
+ 6 months of 30 days = 6 x 29 + 6 x 30 = 354 days [indeed it is: = 12 x 29½ !].
- But: sometimes, a year can also have 355 or 353 days! (we will see more about it later)
1.4 “Leap Year”, shana-me‘uberet
The unit of the year, shana, is according to the sun and the seasons. Passover must be in the spring. The cycle of Earth around the sun lasts 365¼ days (approximately!). The difference between a solar year and 12 lunar months is: ~ 11 days [= 365 - 354]. Because adding days does not make any sense, we collect the days and we add some times a full month to the year! That year will have 13 months. In a cycle of 19 years, seven are “leap” years of 13 months. In Hebrew this kind of year is called: a ‘pregnant year’, shana-me‘uberet. The exact calculation and order is in 2. below. In order to keep the Passover in the spring, we are obliged to add a month before nisan. As it is written in devarim, Deuteronomy, 16:1 “Observe the month of aviv (= spring, which is the month nisan) and keep the pesach (Passover) unto the L-ord your G-od, for in the month of aviv the L-ord brought you forth out of Egypt by night”. The month added is ’adar 1st. Thus, a leap year consists of 384 days (= 354 + 30). - But: sometimes this leap year may have 385 or 383 days!
1.5 What causes these “little”changes?
The cycle of the moon around Earth is not exactly 29½, nor the cycle of Earth around the sun, the ‘year’, is exactly 365¼. There are fractions. In order to deal with them, we use the months marcheshvan (known more
in its shorter name: cheshvan) and kisleiv: the months, which come directly after the last tora’s festival within the Jewish year: sukot [their order in the tora is: pesach > shavu’ot > rosh-hashana > yom-kipur > sukot].
The reasonable regularity of a Jewish year thus should be: a ‘full’, ‘complete’, month, chodesh malé = 30 days, followed by a ‘lacking’ month, chodesh chaseir = 29 days. In fact, in all years (!) we have, this ‘set order’: 29, 30, 29, 30… for eight consecutive months starting from ’adar-hasamuch-lenisan = the month ’adar preceding nisan (in a regular year it is just - ’adar and in a leap year it is the 2nd ’adar), as follows;
I added for each month important dates of festivals, fasts etc.:
12/13 ’adar / ’adar sheini - always 29 purim is on 14th. shushan-purim (purim in Jerusalem): 15th
01 nisan - always > 30 chag-hamatzot, pesach, 15th to 21st. In Diaspora: 15th to 22nd
02 ’iyar - always > 29 yom-ha‘atzma’ut: 5th. la”g-ba‘omer, 33rd-day-in-‘omer-counting:18th
03 sivan - always > 30 shavu‘ot: 6th. In Diaspora: 6th and 7th
04 tamuz - always > 29 Fast shiv‘a-‘asar-betamuz: 17th
05 ’av - always > 30 tish‘a-be’av: 9th
06 ’elul - always > 29 no “special” days
07 tishrei - always > 30 rosh-hashanah: 1st and 2nd. Fast of gedalya: 3rd. yom-kipur: 10th
sukot: 15th to 21st. shemini-‘atzeret: 22nd. simchat-tora in Diaspora: 23rd
1.6 How do the other 4 months in a regular year and the 5 months in a leap year function
and how do they effect the changes in the length of the different years?
08 cheshvan no “special” days
09 and kisleiv chanuka from 25th for 8 days. Going into teiveit !
they alternate: each of them can have sometimes 29 days and sometines 30 days. Thus non-leap years:
If cheshvan is 29 and kisleiv is 29, the year is chaseira, lacking, = a year of 353 days.
If cheshvan is 29 and kisleiv is 30, the year is kesidrah, according to its order, = a year of 354 days.
If cheshvan is 30 and kisleiv is 30, the year is sheleima, complete, = a year of 355 days.
10 teiveit - has always 29 days. Fast ‘asara-be teiveit: 10th
11 shevat - has always 30 days. t”u bishvat: 15th
12 ’adar rishon, the first ’adar in a leap year, has always 30 days. Calendar rules instruct that in a leap year
the added 13th month, i.e. 1st ’adar, ’adar rishon, should always be of 30 days. Thus:
If cheshvan is 29 and kisleiv is 29, the year is chaseira, lacking, = a year of 383 days.
If cheshvan is 29 and kisleiv is 30, the year is kesidrah, according to its order, = a year of 384 days.
If cheshvan is 30 and kisleiv is 30, the year is sheleima, complete, = a year of 385 days.
2. Why and how seven leap years in a cycle, machzor, of nineteen?
The 7 leap years in a cycle of 19 are the 3rd, 6th, 8th, 11th, 14th, 17th and the 19th. We use Hebrew initials to
memorise them: gv”ch-’adza”t: gimel=3, vav=6, cheit=8, yud-’alef=11, yud-dalet=14, yud-zayin=17 and yud-teit=19.
We'll start the calculation from the moment G-od created Earth, the sun and the moon in order to serve us, humans, and not that we should, G-od forbid, serve, worship, them. I.e. the christian solar-calendar surely follows the ancient sun worshipers, and the muslim lunar-“year” surely follows the ancient moon worshipers...
Year 1 Y. 2 Year 3 > gimel < is the 1st leap year in the cycle of 19 years
365 365 365 = the number of days in a solar year’s
- 354 - 354 - 354 = the number of days in 12 lunar months: 12 x 29½
11 + 11 + 11 = 33 days. We now add a month! Thus the 3rd year, gimel, is a leap
year. But we are left now with 3 “extra” days, and we wait - - -
Y. 4 Y. 5 Year 6 > vav < is the 2nd leap year in the cycle of 19 years
365 365 365
- 354 - 354 - 354
11 + 11 + 11 +3 = 36 days. The 6th year is leap, vav. We have now 6 extra days.
Y. 7 Year 8 > cheit < is the 3rd leap year in the cycle of 19 years
- 354 - 354
11 + 11 +6 = 28 days. The 8th year is leap, cheit. But now: 2 days minus!!
Y. 9 Y. 10 Year 11 > yud-’alef < is the 4th leap year in the cycle of 19 years
365 365 365
- 354 - 354 - 354
11 + 11 + 11 -2 = 31 days. The 11th year is leap, yud-’alef. 1 extra day.
Y. 12 Y. 13 Year 14 > yud-dalet < is the 5th leap year in the cycle of 19 years
365 365 365
- 354 - 354 - 354
11 + 11 + 11 +1 = 34 days. The 14th year is leap, yud-dalet. 4 extra days.
Y. 15 Y. 16 Year 17 > yud-zayin < is the 6th leap year in the cycle of 19 years
365 365 365
- 354 - 354 - 354
11 + 11 + 11 + 4 = 37 days. The 17th year is leap, yud-zayin. 7 extra days.
Y. 18 Year 19 > yud-teit < is the 7th leap year in the cycle of 19 years
- 354 - 354
11 + 11 + 7 = 29 days. The 19th year is leap, yud-teit. All ’adar rishon's we added to the 6 leap years till now were of 30 days. But all the fractions collected add up to one 24-hour-day. By adding this day to the 29 we keep the rule that the added month, ’adar rishon is always a full month of 30 days.
We also have to indicate that the above calculation is based on a “365-days year”. The ~5 [19 x ¼ = 4¾] “extra”days caused by the true solar cycle of 365 + ~¼ days, is being solved by “playing” with the months cheshvan and kisleiv, as shown in 1.6 above.
From all what we saw above, we can derive clearly, that only the eight months from ’adar, or 2nd ’adar,
to tishrei, are set in a permanent regular order. Therefore, our Sages made for us the signs to know, from
the first tora-Festival, pesach, on which days-of-the-week (later: weekdays) the future Festivals of that year will occur. A “year” for this purpose, begins in nisan: “hachodesh haze lachem rosh chodashim, rishon hu lachem lechodshey hashana”, “This month [i.e. nisan] shall be unto you the beginning of months: it shall
be to you the first of the months of the year”. (shemot, Exodus, 12,2). The signs, simanim, are: ’at, bash,
gar, daq, hatz, vap, za‘, chas, tan, yam, kal. The ’at<–>bash is based on a simple structure of the ’alef-beit.
It is found in tana”ch, Bible, yirmeyahu, Jeremiah, 25:26: sheishach = babel!
’alef <–> tav ’at
beit <–> shin bash
gimel <–> reish gar
dalet <–> quf daq
hei <–> tzadi(q) hatz
vav <–> pei vap
zayin <–> ‘ayin za‘
cheit <–> samech chas
ťeit <–> nun ťan
yud <–> mem yam
kaf <–> lamed kal
’at ’alef, the weekday on which the 1st day of pesach occurs F tav: tish‘a-be’av
i.e. 9th ’av of that same calendar-year, will ‘fall’ on the same weekday as the 1st day of pesach.
bash beit, the weekday on which the 2nd day of pesach occurs F shin: shavu‘ot
i.e. 6th sivan of that same year will ‘fall’ on the same weekday as the 2nd day of pesach.
gar gimel, the weekday on which the 3rd day of pesach occurs F reish: rosh hashana
i.e. 1st tishrei of the next calendar-year will ‘fall’ on the same weekday as the 3rd day of pesach.
daq dalet, the weekday on which the 4th day of pesach occurs F quf: qeri’at hatora
i.e. 23rd of tishrei, simchat-tora, in galut, Diaspora, of the next calendar year will ‘fall’ on the same
weekday as the 4th day of pesach.
hatz hey, the weekday on which the 5th day of pesach occurs F tzadi(q): tzom-kippur
i.e. 10th tishrey of next Jewish calendar-year will ‘fall’ on the same weekday as the 5th day of pesach.
vap vav, the weekday on which the 6th day of Pesach occurs F pei: purim (a month before !!)
Here we add to the ’at, bash: pa-la”g: the 6th day pesach = purim before, and = la”g ba‘omer after.
za‘ zayin, the weekday on which the 7th day of pesach occurs F ‘ayin: ‘atzma’ut
i.e. 5th (!) iyar of that same year will ‘fall’ on the same weekday as the 7th day of pesach.
How do we find out simply if e.g the year AM 5771 (Anno Mundi, the Year of G-od’s Universe),
2010-2011, is a leap year, shana ne‘uberet, or not:
We take 5771 > years from Creation
dividing it by 19 > the number of years in a machzor, cycle
we get = 303 > with the remains of 14
Looking above ( 2. ) teaches us that the 14th, yud-dalet, year in the cycle should be a leap year,
shana ne‘uberet of 13 months, and indeed 5771 is one, and it is the 14th year in the 304th cycle;
the 5th of the “7-leap-years-in-a-cycle-of-19”. The 6th leap year will be the 17th, yud-zayin, 5774.
We shall end this 304th cycle with the 7th one, the 19th year in the-19-years-cycle, in 5776, 2015-2016.
5771 is also shana sheleima, i.e. tishrei, cheshvan, kisleiv, teiveit, 1st ’adar, nisan, sivan and ’av,
total 8 months of the 13, are of 30 days. Thus it is the longest Jewish year possible: 385 days!
shana tova ! Wishing to all a good year and many happy and healthy years to come !! M.D.