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[[File:Jewish calendar, showing Adar II between 1927 and 1948.jpeg|thumb|right|Jewish calendar, showing Adar II between 1927 and 1948]]
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The '''Hebrew''' or '''Jewish calendar''' ({{hebrew|הַלּוּחַ הָעִבְרִי}}, ''ha'luach ha'ivri'') is a [[lunisolar calendar]] used today predominantly for [[Jew]]ish religious observances. It determines the dates for [[Jewish holiday]]s and the appropriate [[Torah reading|public reading]] of [[Weekly Torah portion|Torah portion]]s, ''[[yahrzeit]]s'' (dates to commemorate the death of a relative), and daily [[Psalm]] readings, among many ceremonial uses. In [[Israel]], it is used for religious purposes, provides a time frame for agriculture and is an official calendar for civil purposes, although the latter usage has been steadily declining in favor of the [[Gregorian calendar]].
 
The calendar used by Jews has evolved over time. The basic structural features of the early calendar are thought to have been influenced by the [[Babylonian calendar]], including the [[seven-day week]], the [[lunisolar]] [[Intercalation (timekeeping)|intercalary adjustment]] and the names of the months. Until the [[Tannaitic]] period (approximately 10&ndash;220 CE) the calendar employed a new [[Lunar phase|crescent moon]], with an additional month normally added every two or three years to correct for the difference between twelve lunar months and the solar year. When to add it was based on observation of natural agriculture-related events.<ref>Specifically, the ripening of the [[barley]] crop; the age of the kids, lambs, and doves; the ripeness of the fruit trees; and the relation of the date to the ''[[tekufah]]'' (seasons). See the Talmud, [[Sanhedrin (tractate)|Sanhedrin]] 11b</ref> Through the [[Amoraic]] period (200&ndash;500 CE) and into the [[Geonic]] period, this system was gradually displaced by the mathematical rules used today. The principles and rules were fully codified by [[Maimonides]]  in the ''[[Mishneh Torah]]'' in the 12th century. Maimonides' work also replaced counting "years since the destruction of the Temple" with the modern creation-era ''[[Anno Mundi]].''
 
Because of the roughly eleven-day difference between twelve [[lunar month]]s and one [[solar year]], the length of the Hebrew calendar year varies in the repeating 19-year [[Metonic cycle]] of 235 lunar months, with the [[Intercalation (timekeeping)|intercalary]] month added according to defined rules every two or three years, for a total of seven times per 19 years. Even with this intercalation, the average Hebrew calendar year is longer by about 6 minutes and 25+<sup>25</sup>/<sub>57</sub> seconds than the current mean [[Tropical year|solar year]], so that every 224 years, the Hebrew calendar will fall a day behind the current mean solar year; and about every 231 years it will fall a day behind the Gregorian calendar year.
 
The era used since the [[middle ages]] is the ''[[Anno Mundi]]'' [[epoch (reference date)|epoch]] ([[Latin]] for "in the year of the world"; [[Hebrew language|Hebrew]]:&nbsp;{{hebrew|לבריאת העולם}}, "from the creation of the world"). As with ''[[Anno Domini]]'' (''A.D.'' or ''AD''), the words or abbreviation for ''Anno Mundi'' (''A.M.'' or ''AM'') for the era should properly ''precede'' the date rather than follow it, although this is no longer always followed. AM 5773 began at sunset on 16 September 2012 and ended on 4 September 2013. AM 5774 began at sunset on 4 September 2013 and will end on 24 September 2014. AM 5775 will begin at sunset on 24 September 2014 and end on 13 September 2015.<ref>[http://www.chabad.org/calendar/view/month.asp?tdate=9/5/2013&mode=j "Tishrei, 5774"]. Chabad.org. Retrieved September 3, 2013.</ref>
 
==Components==
 
===Day and hours===
{{further|Zmanim}}
The Jewish day is of no fixed length. The Jewish day is modeled on the reference to "...there was evening and there was morning..."<ref>{{bibleverse||Gen|1:5|HE}}, {{bibleverse||Gen|1:8|HE}}, {{bibleverse||Gen|1:13|HE}}, {{bibleverse||Gen|1:19|HE}}, {{bibleverse||Gen|1:23|HE}}, {{bibleverse||Gen|1:31|HE}} and {{bibleverse||Gen|2.2|HE}}.</ref> in the [[Genesis creation narrative|Creation]] account in the first chapter of [[Book of Genesis|Genesis]]. Based on the classic Rabbinic interpretation of this text, a day in the Rabbinic Hebrew calendar runs from sunset (start of "the evening") to the next sunset. One complicating factor is that there is no clear cut sunrise or sunset time at the extreme latitudes during certain seasons. At higher latitudes in summer, when the sun does not sink below the horizon, a day is counted from midday to midday, and in the winter, when the sun does not rise above the horizon, from midnight to midnight.<ref name="urlCALENDAR - JewishEncyclopedia.com">{{cite web |url=http://www.jewishencyclopedia.com/articles/3921-calendar |title=CALENDAR - JewishEncyclopedia.com |format= |work= |accessdate=2012-04-24}}</ref>
 
There is no clock in the Jewish scheme, so that a civil clock is used. Though the civil clock, including the one in use in Israel, incorporates local adoptions of various conventions such as [[time zone]]s, [[standard time]]s and [[daylight saving]], these have no place in the Jewish scheme. The civil clock is used only as a reference point - in expressions such as: "Shabbat starts at ...". The steady progression of sunset around the world and seasonal changes results in gradual civil time changes from one day to the next based on observable astronomical phenomena (the sunset) and not on man-made laws and conventions.
 
Instead of the [[international date line]] convention, there are varying opinions as to where the day changes. One opinion uses the [[antimeridian]] of [[Jerusalem]]. (Jerusalem is 35°13’ east of the [[prime meridian]], so the antimeridian is at 144°47' W, passing through eastern [[Alaska]].) Other opinions exist as well.<ref>See Willie Roth's essay [http://koltorah.org/ravj/The%20International%20Date%20Line%20and%20Halacha.htm The International Date Line and ''Halacha''].</ref><ref>"Appendix II: Baal HaMaor's Interpretation of 20b and its Relevance to the Dateline" in ''Talmud Bavli'', Schottenstein Edition, Tractate ''Rosh HaShanah'', Mesorah Publications Ltd. ("ArtScroll") 1999, where "20b" refers to the 20th page 2nd folio of the tractate.</ref>
 
Every hour is [[Biblical and Talmudic units of measurement#Day|divided]] into 1080 ''halakim'' (singular: ''[[helek]]'') or parts. A part is 3⅓ seconds or <sup>1</sup>/<sub>18</sub> minute. The ultimate ancestor of the helek was a small Babylonian time period called a ''barleycorn'', itself equal to <sup>1</sup>/<sub>72</sub> of a Babylonian ''time degree'' (1° of celestial rotation).<ref name=Neugebauer1>Otto Neugebauer, "The astronomy of Maimonides and its sources", ''Hebrew Union College Annual'' '''23''' (1949) 322–363.</ref> Actually, the barleycorn or ''she'' was the name applied to the smallest units of all Babylonian measurements, whether of length, area, volume, weight, angle, or time.
 
The weekdays start with Sunday (day 1, or ''Yom Rishon'') and proceed to Saturday (day 7), [[Shabbat]]. Since some calculations use division, a remainder of 0 signifies Saturday.
 
While calculations of days, months and years are based on fixed hours equal to <sup>1</sup>/<sub>24</sub> of a day, the beginning of each ''halachic'' day is based on the local time of [[sunset]]. The end of the Shabbat and other [[Jewish holiday]]s is based on nightfall (''Tzeth haKochabim'') which occurs some amount of time, typically 42 to 72 minutes, after sunset. According to Maimonides, nightfall occurs when three medium-sized stars become visible after sunset. By the 17th century this had become three second-magnitude stars. The modern definition is when the center of the sun is 7° below the geometric (airless) horizon, somewhat later than civil twilight at 6°. The beginning of the daytime portion of each day is determined both by dawn and [[sunrise]]. Most ''halachic'' times are based on some combination of these four times and vary from day to day throughout the year and also vary significantly depending on location. The daytime hours are often divided into ''Sha`oth Zemaniyoth'' or "Halachic hours" by taking the time between sunrise and sunset or between dawn and nightfall and dividing it into 12 equal hours. The nighttime hours are similarly divided into 12 equal portions, albeit a different amount of time than the "hours" of the daytime. The earliest and latest times for [[Jewish services]], the latest time to eat [[Chametz]] on the day before [[Passover]] and many other rules are based on ''Sha`oth Zemaniyoth''. For convenience, the modern day using ''Sha`oth Zemaniyoth'' is often discussed as if sunset were at 6:00pm, sunrise at 6:00am and each hour were equal to a fixed hour. For example, ''halachic'' noon may be after 1:00pm in some areas during [[daylight saving time]]. Within the [[Mishnah]], however, the numbering of the hours starts with the "first" hour after the start of the day.<ref>See, for example, [[Berakhoth (Talmud)|Berachot]] chapter 1, Mishnah 2.</ref>
 
===Weeks===
There is a weekly cycle of seven days, mirroring the [[creation week|seven-day period]] of the [[Book of Genesis]] in which the world is created. The names for the days of the week, like those in the Creation account, are simply the [[Ordinal number (linguistics)|day number]] within the week, with [[Shabbat]] being the seventh day. Each day of the week runs from sunset to the following sunset and is figured locally.
 
There are additional rules in the Hebrew calendar to prevent certain holidays from falling on certain days of the week.  (See [[#Rosh Hashanah postponement|Rosh Hashanah postponement]], below.) These rules are implemented by adding an extra day to Marcheshvan (making it 30 days long) or by removing one day from Kislev (making it 29 days long).  Accordingly, a common Hebrew calendar year can have a length of 353, 354 or 355 days, while a leap Hebrew calendar year can have a length of 383, 384 or 385 days.
 
====Names of weekdays====
[[File:Maurice Ascalon Shabbat Candle Sticks.jpg|right|thumb|A bronze Shabbat candlestick holder made in [[Mandatory Palestine|British Mandate Palestine]] in the 1940s.]]
The Hebrew calendar follows a seven-day weekly cycle, which runs concurrently but independently of the monthly and annual cycles. The names for the days of the week are simply the day number within the week.  In Hebrew, these names may be abbreviated using the [[Hebrew numerals|numerical value]] of the Hebrew letters, for example {{hebrew|יום א׳}} (''Day 1'', or Yom Rishon ({{hebrew|יום ראשון}})):
 
#Yom Rishon - {{hebrew|יום ראשון}} (abbreviated {{hebrew|יום א׳}}), meaning "first day" [corresponds to Sunday] (starting at preceding sunset of Saturday)
#Yom Sheni - {{hebrew|יום שני}} (abbr. {{hebrew|יום ב׳}}) meaning  "second day" [corresponds to Monday]
#Yom Shlishi - {{hebrew|יום שלישי}} (abbr. {{hebrew|יום ג׳}}) meaning  "third day" [corresponds to Tuesday]
#Yom Reviʻi  - {{hebrew|יום רביעי}} (abbr. {{hebrew|יום ד׳}}) meaning  "fourth day" [corresponds to Wednesday]
#Yom Chamishi - {{hebrew|יום חמישי}} (abbr. {{hebrew|יום ה׳}}) = "fifth day" [corresponds to Thursday]
#Yom Shishi - {{hebrew|יום ששי}} (abbr. {{hebrew|יום ו׳}}) meaning "sixth day" [corresponds to Friday]
#Yom Shabbat - {{hebrew|יום שבת}} (abbr. {{hebrew|יום ש׳}}), or more usually Shabbat - {{Hebrew|שבת}} = "Sabbath-rest day" [corresponds to Saturday].
 
The names of the days of the week are modeled on the seven days mentioned in the [[Genesis creation myth|Creation]] story. For example, {{bibleverse||Genesis|1:5|HE}} "... And there was evening and there was morning, one day". ''One day'' ({{hebrew|יוֹם אֶחָד}}) in Genesis 1:15 is translated in JPS as ''first day'', and in some other contexts (including KJV) as ''day one''. In subsequent verses the Hebrew refers to the days using ordinal numbers, e.g., 'second day', 'third day', and so forth, but with the sixth and seventh days the Hebrew includes the definite article ("the").<ref>See {{bibleverse||Genesis|1:8|HE}}, {{bibleverse-nb||Gen|1:13|HE}}, {{bibleverse-nb||Gen|1:19|HE}}, {{bibleverse-nb||Gen|1:23|HE}}, {{bibleverse-nb||Gen|1:31|HE}} and {{bibleverse-nb||Gen|2.2|HE}}.</ref>
 
The Jewish [[Shabbat]] has a special role in the Jewish weekly cycle. There are many special rules which relate to the Shabbat, discussed more fully in the Talmudic tractate [[Shabbat (Talmud)|Shabbat]].
 
In Hebrew, the word ''Shabbat'' ({{hebrew|שַׁבָּת}}) can also mean "(Talmudic) week",<ref>For example, according to [http://milon.morfix.co.il/default.aspx?q=שבת Morfix מילון מורפיקס, Morfix Dictionary], which is based upon Prof. [[Yaakov Choeka]]'s [[Rav Milim]] dictionary. But the word meaning a non-Talmudic week is שָׁבוּע ''(shavuʻa)'', according to the same "מילון מורפיקס".</ref> so that in ritual liturgy a phrase like "Yom Reviʻi bəShabbat" means "the fourth day in the week".<ref>For example, when referring to the daily psalm recited in the morning prayer ([[Jewish services#Shacharit: morning prayers|Shacharit]]).</ref>
 
====Days of week of holidays====
{{Main|Days of week on Hebrew calendar}}
 
The period from 1 Adar (or Adar II, in leap years) to 29 Heshvan contains all of the festivals specified in the Bible - [[Purim]] (14 Adar), [[Pesach]] (15 Nisan), [[Shavuot]] (6 Sivan), [[Rosh Hashanah]] (1 Tishrei), [[Yom Kippur]] (10 Tishrei), [[Sukkot]] (15 Tishrei), and [[Shemini Atzeret]] (22 Tishrei). This period is fixed, during which no adjustments are made.
 
{| class="wikitable"
|-style="background-color:#DDDDDD;text-align:center;"
|-
![[Purim]]
![[Passover]]<br/>(first day)
![[Shavuot]]<br/>(first day)
![[Seventeenth of Tamuz|17 Tammuz]]/<br/>[[Tisha B'Av]]
![[Rosh Hashanah]]/<br/>[[Sukkot]]/<br/>[[Shmini Atzeret]]/<br/>(first day)
![[Yom Kippur]]
![[Chanukah]]<br/>(first day)
![[Tenth of Tevet|10 Tevet]]
![[Tu Bishvat]]
|-
|Thu||Sat||Sun||Sun*||Mon||Wed
|Sun or Mon
|Sun or Tue
|Sat or Mon
|-
|Fri||Sun||Mon||Sun||Tue||Thu||Mon||Tue||Mon
|-
|Sun||Tue||Wed||Tue||Thu||Sat
|Wed or Thu
|Wed, Thu, or Fri
|Tue, Wed, or Thu
|-
|Tue||Thu||Fri||Thu||Sat||Mon
|Fri or Sat
|Fri or Sun
|Thu or Sat
|-
|colspan=3| ||colspan=2|<small>*Postponed from Shabbat</small>||colspan=6|
|}
 
===Months===
The Hebrew calendar is a [[lunisolar calendar]], meaning that months are based on [[lunar month]]s, but years are based on [[solar year]]s.<ref>In contrast, the [[Gregorian calendar]] is a pure [[solar calendar]], while the [[Islamic calendar]] is a pure [[lunar calendar]].</ref>  The calendar year features twelve lunar months of twenty-nine or thirty days, with an [[Intercalation (timekeeping)|intercalary]] lunar month added periodically to synchronize the twelve lunar cycles with the longer solar year.  (These extra months are added seven times every nineteen years.  See [[#Leap months|Leap months]], below.) The beginning of each Jewish lunar month is based on the appearance of the [[new moon]].<ref>Under the fixed, calculated calendar, this is only loosely true. Because the calculations are based on ''mean'' lunar months, not observed ones–and because of the [[#Rosh Hashanah postponement|Rosh Hashanah postponement rules]]—a given month may not begin on the same day as its astronomical conjunction. See {{cite web |url= http://www.sym454.org/hebrew/molad.htm|title=Moon and the Molad of the Hebrew Calendar|last1=Bromberg |first1=Dr. Irv|date= August 5, 2010|publisher= utoronto.ca|accessdate=December 16, 2012}}</ref> Although originally the new lunar crescent had to be observed and certified by witnesses,<ref>This practice continues to be used in [[Karaite Judaism]] as well as in the [[Islamic calendar]].</ref> the moment of the new moon is now approximated arithmetically.
 
The mean period of the lunar month (precisely, the [[Months#Synodic month|synodic month]]) is very close to 29.5 days.  Accordingly, the basic Hebrew calendar year is one of twelve lunar months alternating between 29 and 30 days: [[Tishrei]]  (30 days), [[Marcheshvan]] (29 days), [[Kislev]] (30 days), [[Tevet]] (29 days), [[Shevat]] (30 days), [[Adar]] (29 days), [[Nisan]] (30 days), [[Iyar]] (29 days), [[Sivan]] (30 days), [[Tammuz (Hebrew month)|Tammuz]] (29 days), [[Av (month)|Av]] (30 days), and [[Elul]] (29 days), for a total of 354 days.  In leap years (such as 5771) an additional month, Adar I (30 days) is added after Shevat, while the regular Adar is referred to as "Adar II."
 
The insertion of the leap month mentioned above is based on the requirement that [[Passover]]—the festival celebrating the Exodus from Egypt, which took place in the spring—always occur in the [northern hemisphere's] spring season. Since the adoption of a fixed calendar, intercalations in the Hebrew calendar have been assigned to fixed points in a 19-year cycle.  Prior to this, the intercalation was determined empirically:
 
<blockquote>The year may be intercalated on three grounds:  'aviv [i.e.the ripeness of barley], fruits of trees, and the equinox.  On two of these grounds it should be intercalated, but not on one of them alone.<ref name="Tosefta 1919, p. 31">Tosefta ''Sanhedrin'' 2.2, Herbert Danby, Trans., ''Tractate Sanhedrin Mishnah and Tosefta'', Society for Promoting Christian Knowledge, London and New York, 1919, p. 31.  Also quoted in Sacha Stern, ''Calendar and Community:  A History of the Jewish Calendar Second Century BCE-Tenth Century CE,'' Oxford University Press, 2001, p. 70.</ref></blockquote>
 
====Importance of lunar months====
From very early times, the [[Mesopotamia]]n [[lunisolar calendar]] was in wide use by the countries of the western Asia region. The structure, which was also used by the Israelites, was based on lunar months with the intercalation of an additional month to bring the cycle closer to the solar cycle.<ref name="DeVaux">''Ancient Israel: Its Life and Institutions'' (1961) by Roland De Vaux, John McHugh, Publisher: McGraw-Hill, ISBN 978-0-8028-4278-7, p.179</ref>
 
{{bibleverse||Num|10:10|HE}} stresses the importance in Israelite religious observance of the new month (Hebrew: {{hebrew|ראש חודש}}, [[Rosh Chodesh]], "beginning of the month"): "... in your new moons, ye shall blow with the trumpets over your burnt-offerings..." Similarly in {{bibleverse||Num|28:11|HE}}. "The beginning of the month" meant the appearance of a [[new moon]].
 
According to the ''[[Mishnah]]'' and [[Tosefta]], in the Maccabean, Herodian, and Mishnaic periods, new months were determined by the sighting of a new crescent, with two eye witnesses required to testify to the [[Sanhedrin]] to having seen the new lunar crescent at sunset.<ref>M. ''Rosh Hashanah'' 1.7</ref> The practice in the time of [[Gamaliel II]] (c. 100 CE) was for witnesses to select the appearance of the moon from a collection of drawings that depicted the crescent in a variety of orientations, only a few of which could be valid in any given month.<ref>M. ''Rosh Hashanah'' 2.6-8</ref>  These observations were compared against calculations.<ref>b. Rosh Hashanah 20b:  "This is what Abba the father of R. Simlai meant: 'We calculate the new moon's birth.  If it is born before midday, then certainly it will have been seen shortly before sunset.  If it was not born before midday, certainly it will not have been seen shortly before sunset.'  What is the practical value of this remark?  R. Ashi said:  Confuting the witnesses."  I. Epstein, Ed., ''The Babylonian Talmud Seder Mo'ed,'' Soncino Press, London, 1938, p. 85.</ref>
 
At first the beginning of each Jewish month was signaled to the communities of Israel and beyond by fires lit on mountaintops, but after the [[Samaritan]]s began to light false fires, messengers were sent.<ref>M. ''Rosh Hashanah'' 2.2</ref> The inability of the messengers to reach communities outside Israel before mid-month High Holy Days ([[Succot]] and [[Passover]]) led outlying communities to celebrate scriptural festivals for two days rather than one, observing the second feast-day of the [[Jewish diaspora]] because of uncertainty of whether the previous month ended after 29 or 30 days.<ref>b. ''Betzah'' 4b</ref>
 
In his work ''[[Mishneh Torah]]'' (1178), Maimonides included a chapter "Sanctification of the New Moon", in which he discusses the calendrical rules and their scriptural basis.  He notes, <blockquote>"By how much does the solar year exceed the lunar year? By approximately 11 days. Therefore, whenever this excess accumulates to about 30 days, or a little more or less, one month is added and the particular year is made to consist of 13 months, and this is the so-called embolismic (intercalated) year. For the year could not consist of twelve months plus so-and-so many days, since it is said: throughout the months of the year ({{bibleverse||Num|28:14|HE}}), which implies that we should count the year by months and not by days."<ref name = "tcjmwz">[http://webcache.googleusercontent.com/search?q=cache:o_6wrQe6ppUJ:personal.stevens.edu/~msenator/hand0.pdf+%22Sanctification+of+the+New+Moon%22+Maimonides&hl=en&ct=clnk&cd=3&gl=us&client=firefox-a Sanctification of the New Moon.] Translated from the Hebrew by Solomon Gandz; supplemented, introduced, and edited by Julian Obermann; with an astronomical commentary by Otto Neugebauer. Yale Judaica Series, Volume 11, New Haven: Yale University Press, 1956</ref></blockquote>
 
====Names of months====
Biblical references to the pre-Jewish calendar include ten months identified by number rather than by name. In parts of the [[Noach (parsha)|Torah portion ''Noach'']] ("Noah") (specifically, {{bibleverse||Gen|7:11|HE}}, {{bibleverse-nb||Gen|8:3-4|HE}}, {{bibleverse-nb||Gen|8:13-14|HE}}) it is implied that the months are thirty days long.<ref>{{bibleverse||Gen|7:11|HE}} says "... on the ''seventeenth day of the second month''—on that day all the springs of the great deep burst forth..." and {{bibleverse-nb||Gen|8:3-4|HE}} says "...At the end of the ''hundred and fifty days'' the water had gone down, (4) and on the ''seventeenth day of the seventh month'' the ark came to rest on the mountains of Ararat..." There is an interval of 5 months and 150 days, making each month 30 days long.</ref> There is also an indication that there were twelve months in the annual cycle ({{bibleverse|1|Kings|4:7|HE}}, {{bibleverse|1|Chronicles|27:1-15|HE}}).
 
Many countries in the western Asian region used the Mesopotamian calendar from very early times, though the names of months varied.<ref name="DeVaux"/> Prior to the Babylonian exile, the names of only four months are referred to in the [[Tanakh]]:
*''[[Aviv]]'' - first month - literally "spring" ({{bibleverse||Exodus|12:2|HE}}, {{bibleverse-nb||Exodus|13:4|HE}}, {{bibleverse-nb||Exodus|23:15|HE}}, {{bibleverse-nb||Exodus|34:18|HE}}, {{bibleverse||Deut.|16:1|HE}});
*''[[Iyar|Ziv]]'' - second month - literally "light" ({{bibleverse|1|Kings|6:1|HE}}, {{bibleverse-nb|1|Kings|6:37|HE}});
*''[[Ethanim]]'' - seventh month - literally "strong" in plural, perhaps referring to strong rains ({{bibleverse|1|Kings|8:2|HE}}); and
*''[[Marcheshvan|Bul]]'' - eighth month ({{bibleverse|1|Kings|6:38|HE}}).
All of these are believed to be [[Canaan]]ite names.<ref>{{cite book|last=Hachlili|first=Rachel|title=Ancient Synagogues - Archaeology and Art: New Discoveries and Current Research|year=2013|publisher=Brill|isbn=978-9004257733|page=342|url=http://books.google.co.uk/books?id=jRjhAQAAQBAJ&pg=PA342&dq=Aviv+ziv+Ethanim+Bul+Canaanite{{!}}Phoenician&hl=en&sa=X&ei=UkDAUpKGGqzY7AbfuYGIAg&ved=0CDQQ6AEwAA#v=onepage&q=Aviv%20ziv%20Ethanim%20Bul%20Canaanite|Phoenician&f=false}}</ref> These names are only mentioned in connection with the building of the [[First Temple]]. Håkan Ulfgard suggests that the use of what are rarely used Canaanite (or in the case of Ethanim perhaps Northwest-semitic) names indicates that "the author is consciously utilizing an archaizing terminology, thus giving the impression of an ancient story...".<ref>{{cite book|last=Ulfgard|first=Håkan|title=The Story of Sukkot : the Setting, Shaping and Sequel of the Biblical Feast of Tabernacles|year=1998|publisher=Mohr Siebeck|isbn=3-16-147017-6|page=99|url=http://books.google.co.uk/books?id=uxnXaYBj2wgC&pg=PA99&dq=Aviv+ziv+Ethanim+Bul+Canaanite{{!}}Phoenician&hl=en&sa=X&ei=0ErAUraSOIvQ7Aa4iYCADw&ved=0CD4Q6AEwAg#v=onepage&q=Aviv%20ziv%20Ethanim%20Bul%20Canaanite|Phoenician&f=false}}</ref>
 
At some point during the [[Babylonian exile]] or diaspora, which started in 597 BCE, Babylonian Jews commenced to use [[Babylonian calendar|Babylonian month names]], which names continue to be used today.<ref name="DeVaux"/> The [[Arabic names of calendar months#Syrian Calendar in Iraq.2C Syria.2C Lebanon.2C Palestine and Jordan|Syrian calendar]] used in the [[Levant]] region shares many of the names for months as the Hebrew calendar, such as Nisan, Iyyar, Tammuz, Ab, Elul, Tishri, and Adar, indicating a common Babylonian origin.
 
Hebrew names and romanized transliteration may somewhat differ, as they do for Marcheshvan ({{hebrew|חשוון}})  or Kislev ({{hebrew|כסלו}}): the Hebrew words shown here are those commonly indicated ''e.g.'' in newspapers.
 
{{JewishCalendar}}
 
In a regular (''kesidran'') year, Marcheshvan has 29 days and Kislev has 30 days. However, because of the Rosh Hashanah postponement rules (see below) Kislev may lose a day to have 29 days, and the year is called a short (''chaser'') year, or Marcheshvan may acquire an additional day to have 30 days, and the year is called a full (''maleh'') year. The calendar rules have been designed to ensure that Rosh Hashanah does not fall on a Sunday, Wednesday or Friday. This is to ensure that [[Yom Kippur]] does not directly precede or follow [[Shabbat]], which would create practical difficulties, and that [[Hoshana Rabbah]] is not on a Shabbat, in which case certain ceremonies would be lost for a year.
 
====Leap months====
The solar year is about eleven days longer than twelve lunar months. The Bible does not directly mention the addition of "embolismic" or [[Intercalation (timekeeping)|intercalary month]]s. However, without the insertion of embolismic months, Jewish festivals would gradually shift outside of the [[season]]s required by the Torah. This has been ruled as implying a requirement for the insertion of embolismic months to reconcile the lunar cycles to the seasons, which are integral to solar yearly cycles.
 
When the observational form of the calendar was in use, whether or not an embolismic month was announced after the "last month" ([[Adar]]) depended on 'aviv [i.e.the ripeness of barley], fruits of trees, and the equinox.  On two of these grounds it should be intercalated, but not on one of them alone.<ref name="Tosefta 1919, p. 31"/> It may be noted that in the Bible the name of the first month, ''[[Aviv]]'', literally means "spring". Thus, if Adar was over and Spring had not yet arrived, an additional month was observed.
 
Traditionally, for the [[Babylonian calendar|Babylonian]] and Hebrew [[lunisolar calendar]]s, the years 3, 6, 8, 11, 14, 17, and 19 are the long (13-month) years of the [[Metonic cycle]]. This cycle, which can be used to predict [[eclipse]]s, forms the basis of the Greek and Hebrew calendars, and is used for the [[Computus|computation of the date of Easter]] each year
 
During [[leap year]]s Adar I (or Adar [[Aleph (Hebrew)|Aleph]] &mdash; "first Adar") is added before the regular [[Adar]]. Adar I is actually considered to be the extra month, and has 30 days. Adar II (or Adar [[Bet (letter)|Bet]] &mdash; "second Adar") is the "real" Adar, and has the usual 29 days. For this reason, holidays such as [[Purim]] are observed in Adar II, not Adar I.
 
===Years===
The Hebrew calendar year conventionally begins on [[Rosh Hashanah]]. However, other dates serve as the beginning of the year for different religious purposes.
 
There are three qualities that distinguish one year from another: whether it is a leap year or a common year, on which of four permissible days of the week the year begins, and whether it is a deficient, regular, or complete year. Mathematically, there are 24 (2×4×3) possible [[combination]]s, but only 14 of them are valid. Each of these patterns is called a ''keviyah'' ([[Hebrew language|Hebrew]] קביעה for "a setting" or "an established thing"), and is encoded as a series of three Hebrew letters.
 
====Previous systems====
Before the adoption of the current AM year numbering system, other systems were in use. In early times, the years were counted from some significant historic event. (e.g. {{bibleverse|1|Kings|6:1|HE}}) During the period of the monarchy, it was the widespread practice in western Asia to use era year numbers according to the accession year of the monarch of the country involved. This practice was also followed by the united kingdom of Israel (e.g. {{bibleverse|1|Kings|14:25|HE}}), kingdom of Judah (e.g. {{bibleverse|2|Kings|18:13|HE}}), kingdom of Israel (e.g. {{bibleverse|2|Kings|17:6|HE}}), Persia (e.g. {{bibleverse||Nehemiah|2:1|HE}}) and others. Besides, the author of Kings coordinated dates in the two kingdoms by giving the accession year of a monarch in terms of the year of the monarch of the other kingdom, (e.g. {{bibleverse|2|Kings|8:16|HE}}) though some commentators note that these dates do not always synchronise.<ref name="Thiele"/> Other era dating systems have been used at other times. For example, Jewish communities in the Babylonian diaspora counted the years from the first deportation from Israel, that of [[Jehoiachin]] in 597 BCE, (e.g. {{bibleverse||Ezekiel|1:1-2|HE}}). The era year was then called "year of the captivity of Jehoiachin". (e.g. {{bibleverse|2|Kings|25:27|HE}}) During the Hellenistic Maccabean period, [[Seleucid era]] counting was used, (e.g. [http://old.usccb.org/nab/bible/1maccabees/1maccabees1.htm#v54 1 Maccabees 1:54]) at least in the Greek-influenced area of Israel. There is indication that Jews of the Rhineland in the early Middle Ages used the "years after the destruction of the Temple" (e.g., [[s:Mainz Anonymous (Wikisource)|Mainz Anonymous]]).
 
The ''[[Seder Olam Rabbah]]'' also recognized the importance of the [[Jubilee (biblical)|Jubilee]] and [[Shmita|Sabbatical]] cycles as a long-term calendrical system, and attempted at various places to fit the Sabbatical and Jubilee years into its chronological scheme.
 
====Anno Mundi (AM)====
{{further|Anno Mundi}}
[[File:Creation of Light Detail 2.png|right|thumb|The Jewish calendar's reference point is traditionally held to be about one year ''before'' the [[Genesis creation myth|Creation]] of the world.]]
Since the codification by Maimonides in 1178 CE, the Jewish calendar has used the [[Anno Mundi]] [[Epoch (reference date)|epoch]] ([[Latin]] for “in the year of the world,” abbreviated ''AM'' or ''A.M.;'' Hebrew {{hebrew|לבריאת העולם}}), sometimes referred to as the “Hebrew era”, to distinguish it from other systems based on some computation of creation, such as the [[Byzantine calendar]].
 
During the Talmudic era, from the 1st to the 10th century, the center of world Judaism was in the Middle East, primarily in the [[Talmudic Academies in Babylonia|Talmudic Academies of Iraq]] and [[Talmudic Academies in the Land of Israel|Palestine]]. Jews in these regions used [[Seleucid Era]] dating (also known as the "Anno Graecorum (AG)" or the "Era of Contracts") as the primary method for indicating a year number.<ref name=Jones>[http://books.google.co.uk/books?id=AvVPlyYjX7YC&pg=PA295 Chronology of the Old Testament, Dr. Floyd Nolen Jones] "When the center of Jewish life moved from Babylonia to Europe during the 8th and 9th centuries CE, calculations from the Seleucid era became meaningless. Over those centuries, it was replaced by that of the ''anno mundi'' era of the ''Seder Olam''. From the 11th century, ''anno mundi'' dating became dominant throughout most of the world's Jewish communities."</ref> For example, the writings of [[Josephus]] and the [[Books of the Maccabees]] used Seleucid Era dating exclusively, and the [[Avodah Zarah]] states:
<blockquote>[[Rav]] [[Aha b. Jacob]] then put this question: How do we know that our Era [of Documents] is connected with the Kingdom of Greece at all? Why not say that it is reckoned from the Exodus from Egypt, omitting the first thousand years and giving the years of the next thousand? In that case, the document is really post-dated!<br> Said [[Rav Nachman|Rav Nahman]]: In the Diaspora the Greek Era alone is used. He [the questioner] thought that Rav Nahman wanted to dispose of him anyhow, but when he went and studied it thoroughly he found that it is indeed taught [in a [[Baraita]]]: In the Diaspora the Greek Era alone is used.<ref>[http://www.come-and-hear.com/zarah/zarah_10.html Avodah Zarah, tractate 10]</ref></blockquote>
 
Occasionally in Talmudic writings, reference was made to other starting points for eras, such as Destruction Era dating,<ref>[http://www.come-and-hear.com/zarah/zarah_9.html Avodah Zarah, tractate 9] Footnote: "The Eras in use among Jews in Talmudic Times are: (a) ERA OF CONTRACTS [H] dating from the year 380 before the Destruction of the Second Temple (312&ndash;1 BCE) when, at the Battle of Gaza, Seleucus Nicator, one of the followers of Alexander the Great, gained dominion over Palestine. It is also termed Seleucid or Greek Era [H]. Its designation as Alexandrian Era connecting it with Alexander the Great (Maim. Yad, Gerushin 1, 27) is an anachronism, since Alexander died in 323 BCE—eleven years before this Era began (v. E. Mahler, Handbuch der judischen Chronologie, p. 145). This Era, which is first mentioned in Mac. I, 10, and was used by notaries or scribes for dating all civil contracts, was generally in vogue in eastern countries till the 16th cent, and was employed even in the 19th cent, among the Jews of Yemen, in South Arabia (Eben Saphir, Lyck, 1866, p. 62b). (b) THE ERA OF THE DESTRUCTION (of the Second Temple) [H] the year 1 of which corresponds to 381 of the Seleucid Era, and 69-70 of the Christian Era. This Era was mainly employed by the Rabbis and was in use in Palestine for several centuries, and even in the later Middle Ages documents were dated by it. One of the recently discovered Genizah documents bears the date 13 Tammuz 987 after the Destruction of the Temple—i.e. 917 C.E. (Op. cit. p. 152, also Marmorstein ZDMG, Vol. VI, p. 640). The difference between the two Eras as far as the tens and units are concerned is thus 20. If therefore a Tanna, say in the year 156 Era of Dest. (225 CE), while remembering, naturally, the century, is uncertain about the tens and units, he should ask the notary what year it is according to his—Seleucid—era. He will get the answer 536 (156 + 380), on adding 20 to which he would get 556, the last two figures giving him the year [1] 56 of the Era of Destruction."</ref> being the number of years since the 70 CE [[Siege of Jerusalem (70)|destruction of the Second Temple]], and the number of years since the [[dating Creation|Creation year]] based on the calculation in the [[Seder Olam Rabbah]] of Rabbi [[Jose ben Halafta]] in about  160 CE.<ref>p.107, Kantor</ref> By his calculation, based on the [[Masoretic Text]], [[Adam]] was created in 3760 BCE, later confirmed by the Muslim chronologist [[al-Biruni]] as 3448 years before the [[Seleucid era]].<ref name="ReferenceA">See ''[[The Remaining Signs of Past Centuries]]''.</ref> An example is the c. 8th century [[Baraita of Samuel]].
 
In the 8th and 9th centuries, the center of Jewish life moved from Babylonia to Europe, so that counting using the Seleucid era "became meaningless".<ref name=Jones/> In 1178 CE, [[Maimonides]] wrote in the ''[[Misheh Torah]]'', ''Sanctification of the Moon'' (11.16), that he had chosen the Epoch from which calculations of all dates should be as "the third day of Nisan in this present year ... which is the year 4938 of the creation of the world" (March 22, 1178 CE).<ref>Solomon, Gandz (1947–1948). [http://www.jstor.org/discover/10.2307/3622160?uid=3739256&uid=2&uid=4&sid=21101759510883 "Date of the Composition of Maimonides' Code"]. ''Proceedings of the American Academy for Jewish Research'', Vol. 17, pp. 1 - 7. Archived at [[JSTOR]]. Retrieved March 14, 2013.</ref> He included all the rules for the calculated calendar and their scriptural basis, including the modern epochal year in his work, and beginning formal usage of the ''anno mundi'' era. From the 11th century, ''anno mundi'' dating became dominant throughout most of the world's Jewish communities<ref name=Jones/><ref>[http://books.google.co.uk/books?id=0umDqPOf2L8C&pg=PA87 The Easter Computus and the Origins of the Christian Era, Alden A. Mosshammer]</ref> Today, the rules detailed in Maimonides' calendrical code are those generally used by Jewish communities throughout the world.
 
According to Rabbinic reckoning, the beginning of "year 1" is ''not'' [[Creation according to Genesis|Creation]], but about one year before Creation, with the new moon of its first month (Tishrei) to be called ''molad tohu'' (the mean new moon of chaos or nothing). The Jewish calendar's epoch (reference date), 1 Tishrei AM 1, is equivalent to Monday, 7 October 3761 BC/BCE in the [[proleptic Julian calendar]], the equivalent tabular date (same daylight period) and is about one year ''before'' the traditional Jewish [[Dating Creation|date of Creation]] on 25 Elul AM 1, based upon the ''[[Seder Olam Rabbah]]'' of Rabbi [[Yossi ben Halafta]], a 2nd-century sage.<ref>A minority opinion places Creation on 25 Adar AM 1, six months earlier, or six months after the modern epoch.</ref> Thus, adding 3760 before [[Rosh Hashanah]] or 3761 after to a [[Julian calendar|Julian]] (or [[proleptic Gregorian]]) year number starting from 1 CE (AD 1) will yield the Hebrew year.  For earlier years there may be a discrepancy (see: [[Missing years (Jewish calendar)]]). The year AM 5771 began on 9 September 2010 (1 Tishrei or Rosh Hashanah) and, since it was a 13-month year, ended on 28 September 2011 (29 Elul).
 
In Hebrew there are two common ways of writing the year number: with the thousands, called {{hebrew|לפרט גדול}} ("major era"), and without the thousands, called {{hebrew|לפרט קטן}} ("minor era").
 
====New year====
[[File:Liten askenasisk sjofar 5380.jpg|right|thumb|A ''[[shofar]]'' made from a ram's horn is traditionally blown in observance of [[Rosh Hashanah]], the beginning of the Jewish civic year.]]
 
{{bibleverse||Exodus|12:2|HE}} and {{bibleverse||Deut|16:1|HE}} set Aviv (now [[Nisan]]) as "the first of months":
 
:this month shall be unto you the beginning of months; it shall be the first month of the year to you.
 
Nisan 1 is referred to as the ''ecclesiastical new year''.
 
In ancient Israel, the start of the ecclesiastical new year for the counting of months and festivals (i.e. Nisan) was determined by reference to [[Passover]]. Passover is on 14 Nisan, ({{bibleverse||Leviticus|23:4-6|HE}}) which corresponds to the [[full moon]] of Nisan. As Passover is a spring festival, it should fall on a full moon day around, and normally just after, the [[vernal equinox|vernal (northward) equinox]]. If the twelfth full moon after the previous Passover is too early compared to the equinox, a leap month is inserted near the end of the previous year before the new year is set to begin. According to normative Judaism, the verses in {{bibleverse||Exodus|12:1–2|HE}} require that the months be determined by a proper court with the necessary authority to sanctify the months. Hence the court, not the astronomy, has the final decision.<ref>{{Cite book|title=Artscroll Chumash |last=Scherman |first=Nosson |year =2005}}</ref>
 
According to some Christian and Karaite sources, the tradition in ancient Israel was that 1 Nisan would not start until the barley is ripe, being the test for the onset of spring.<ref>The barley had to be "eared out" (ripe) in order to have a wave-sheaf offering of the first fruits according to the Law. {{Cite book|title=Secrets of Time |last=Jones |first=Stephen |year=1996}}</ref> If the barley was not ripe an intercalary month would be added before Nisan.
 
The day most commonly referred to as the "New Year" is 1 Tishrei, which actually begins in the seventh month of the ecclesiastical year. On that day the formal New Year for the counting of years (such as [[Shmita]] and [[Jubilee (biblical)|Yovel]]), [[Rosh Hashanah]] ("head of the year") is observed. (see {{bibleverse||Ezekiel|40:1|HE}}, which uses the phrase "beginning of the year".) This is the '''civil new year''', and the date on which the year number advances.  Certain agricultural practices are also marked from this date.<ref>See [[Maaser Rishon]], [[Maaser Sheni]], [[Maaser Ani]].</ref>
 
In the 1st century, [[Josephus]] stated that while -
 
<blockquote>Moses...appointed Nisan...as the first month for the festivals...the commencement of the year for everything relating to divine worship, but for selling and buying and other ordinary affairs he preserved the ancient order [i. e. the year beginning with Tishrei]."<ref name="Josephus, 1930">Josephus, ''Antiquities'' 1.81, Loeb Classical Library, 1930.</ref></blockquote>
 
[[Edwin Thiele]] has concluded that the ancient northern [[Kingdom of Israel (Samaria)|Kingdom of Israel]] counted years using the ecclesiastical new year starting on 1 Aviv (Nisan), while the southern [[Kingdom of Judah]] counted years using the civil new year starting on 1 Tishrei.<ref name="Thiele">Edwin Thiele, ''[[The Mysterious Numbers of the Hebrew Kings]]'', (1st ed.; New York: Macmillan, 1951;  2d ed.; Grand Rapids: Eerdmans, 1965; 3rd ed.; Grand Rapids: Zondervan/Kregel, 1983). ISBN 0-8254-3825-X, 9780825438257</ref> The practice of the Kingdom of Israel was also that of [[Babylonian calendar|Babylon]],<ref>''The Chronology of the Old Testament'', 16th ed., Floyd Nolan Jones, ISBN 978-0-89051-416-0, p. 118-123</ref> as well as other countries of the region.<ref name="DeVaux"/> The practice of Judah is still followed.
 
In fact the Jewish calendar has a multiplicity of new years for different purposes. The use of these dates has been in use for a long time. The use of multiple starting dates for a year is comparable to different starting dates for civil "calendar years", "tax or [[fiscal year]]s", "[[academic year]]s", "religious cycles", etc. By the time of the redaction of the ''[[Mishnah]]'', [[s:Mishnah/Seder Moed/Tractate Rosh Hashanah/Chapter 1/1|Rosh Hashanah 1:1]] (c. 200 CE), jurists had identified four new-year dates:
 
<blockquote>The 1st of Nisan is the new year for kings and feasts; the 1st of Elul is the new year for the tithe of cattle... the 1st of Tishri is the new year for years, of the [[Shmita|years of release]] and [[Jubilee (biblical)|jubilee years]], for the planting and for vegetables; and the 1st of Shevat is the new year for trees-so the school of Shammai; and the school of Hillel say:  On the 15th thereof.<ref>M. ''Rosh Hashanah'' 1, in Herbert Danby, trans., ''The Mishnah'', Oxford University Press, 1933, p. 188.</ref></blockquote>
 
The month of [[Elul]] is the new year for counting [[Cattle tithe|animal tithes]] (''ma'aser behemah'').  ''[[Tu Bishvat]]'' ("the 15th of [[Shevat]]")  marks the new year for trees (and agricultural tithes).
 
The table below shows the dates of the Jewish New Year.
{| style="text-align:right; background:#f0f0f0; padding: 1em;"
|-
|'''Year'''
|style="width: 10em;"|'''Date'''
|style="width: 4em;"|'''Days'''
|style="width: 6em;"|'''Year'''
|style="width: 10em;"|'''Date'''
|style="width: 4em;"|'''Days'''
|-
|5767||23 September 2006||355
|5787||12 September 2026||385*
|-
|5768||13 September 2007||383*
|5788||2 October 2027  ||355
|-
|5769||30 September 2008||354
|5789||21 September 2028||354
|-
|5770||19 September 2009||355
|5790||10 September 2029||383*
|-
|5771||9 September 2010 ||385*
|5791||28 September 2030||355
|-
|5772||29 September 2011||354
|5792||18 September 2031||354
|-
|5773||17 September 2012||353
|5793||6 September 2032 ||383*
|-
|'''5774'''||'''5 September 2013''' ||'''385*'''
|5794||24 September 2033||355
|-
|5775||25 September 2014||354
|5795||14 September 2034||385*
|-
|5776||14 September 2015||385*
|5796||4 October 2035  ||354
|-
|5777||3 October 2016  ||353
|5797||22 September 2036||353
|-
|5778||21 September 2017||354
|5798||10 September 2037||385*
|-
|5779||10 September 2018||385*
|5799||30 September 2038||354
|-
|5780||30 September 2019||355
|5800||19 September 2039||355
|-
|5781||19 September 2020||353
|5801||8 September 2040 ||383*
|-
|5782||7 September 2021 ||384*
|5802||26 September 2041||354
|-
|5783||26 September 2022||355
|5803||15 September 2042||385*
|-
|5784||16 September 2023||383*
|5804||5 October 2043  ||353
|-
|5785||3 October 2024  ||355
|5805||22 September 2044||355
|-
|5786||23 September 2025||354
|5806||12 September 2045||384*
|}
<nowiki>*</nowiki> Leap years of 13 months.
 
====Leap years====
The Jewish calendar is based on the [[Metonic cycle]] of 19 years, of which 12 are common (non-leap) years of 12 months and 7 are leap years of 13 months. To determine whether a Jewish year is a leap year, one must find its position in the 19-year Metonic cycle. This position is calculated by dividing the Jewish year number by 19 and finding the [[remainder]]. For example, the present Jewish year {{#time:xjY}} divided by 19 results in a remainder of {{#expr:{{#time:xjY}}mod 19}}, indicating that it is year {{#ifexpr:{{#time:xjY}}mod 19|{{#expr:{{#time:xjY}}mod 19}}|19}} of the Metonic cycle. Since there is no year 0, a remainder of 0 indicates that the year is year 19 of the cycle.<ref>See also [[Golden number (time)]].</ref>
 
Years 3, 6, 8, 11, 14, 17, and 19 the Metonic cycle are leap years. To assist in remembering this sequence, some people use the mnemonic Hebrew word <nowiki>GUCHADZaT</nowiki>  {{hebrew|"גוחאדז"ט"}}, where the Hebrew letters ''gimel-vav-het aleph-dalet-zayin-tet'' are used as [[Hebrew numerals]] equivalent to 3, 6, 8, 1, 4, 7, 9. The ''keviyah'' records whether the year is leap or common: פ for ''p'shutah'', meaning simple and indicating a common year, and מ indicating a leap year.<ref name="Judaism 101">{{cite web|title=The Jewish Calendar: A Closer Look|url=http://www.jewfaq.org/calendr2.htm|publisher=Judaism 101|accessdate=25 March 2011}}</ref>
 
Another memory aid notes that intervals of the [[major scale]] follow the same pattern as do Jewish leap years, with ''do'' corresponding to year 19 (or 0): a [[whole step]] in the scale corresponds to two common years between consecutive leap years, and a [[half step]] to one common year between two leap years.  This connection with the major scale is more remarkable{{editorializing|date=July 2013}} in the context of [[19 equal temperament#Connection with Hebrew calendar|19 equal temperament]].
 
To determine whether year ''n'' of the calendar is a leap year, find the remainder on dividing [(7&nbsp;×&nbsp;''n'')&nbsp;+&nbsp;1] by 19. If the remainder is 6 or less it is a leap year; if it is 7 or more it is not. For example, the {{Hebrew calendar/c|{{#time:xjY}}}} The {{Hebrew calendar/c|{{#expr:{{#time:xjY}}+1}}}}{{citation needed|date=July 2013}}
 
====Rosh Hashanah postponement====
{| class="wikitable" align="right" style="float; margin: 9px;"
! Day of week
! colspan="4" | Number of days
|-
| Monday || 353 || 355 || 383 || 385
|-
| Tuesday || 354 || || || 384
|-
| Thursday || 354 || 355 || 383 || 385
|-
| Saturday || 353 || 355 || 383 || 385
|}
 
To calculate the day on which Rosh Hashanah falls, it is necessary to first calculate the [[molad]] ([[lunar conjunction]] or [[new moon]]) of Tishrei, and then determine whether the start of the year must be postponed. The molad can be calculated by multiplying the mean length of a (synodic) lunar month (29 days, 12 hours, and 793 parts) by the elapsed time since another molad whose weekday is known. (There are 1080 "parts" in an hour, making one part equal to 3<sup>1</sup>/<sub>3</sub> seconds.) The [[#Epoch|molad tohu]] began 2 days, 5 hours, and 204 parts after the beginning of the week.
 
The rules are complicated by the fact that the months subject to adjustment, Marcheshvan and Kislev, are the eighth and ninth months of the ecclesiastical year while Tishrei is the seventh month. This means that adjustments must be made in one year in anticipation of the day of the week on which Rosh Hashanah will fall in the next year, which may itself be affected by the day on which it will fall in the third year, and so on. The process is further complicated by the need to insert leap months in accordance with their own cycle.
 
Nevertheless, only four possible adjustments are needed. These are called the Rosh Hashanah postponement rules, or ''deḥiyyot'':<ref name=Chelm.org>{{cite web|title=Chelm.org's explaination of the Jewish calendar|url=http://www.chelm.org/jewish/calendar/explain.html|date=1 August 1999|accessdate=25 March 2011}}</ref>
 
*If the molad occurs at or later than 18 hours, Rosh Hashanah is postponed a day. This is called deḥiyyah ''molad zaken'', meaning an "old conjunction."
*If the molad occurs on a Sunday, Wednesday, or Friday, Rosh Hashanah is postponed a day. If deḥiyyah molad zaken places Rosh Hashanah on one of these days, it is postponed a second day. This is called deḥiyyah ''lo ADU,'' an acronym meaning "not one, four, or six."
 
The first of these (deḥiyyah molad zaken) is thought to be a relic of when the calendar was established empirically (although there is some doubt); the second (deḥiyyah lo ADU) is applied for religious reasons.<ref name=Science&Myth>{{cite web|last=Landau|first=Remy|title=Hebrew Calendar Science and Myths|url=http://hebrewcalendar.tripod.com/|accessdate=25 March 2011}}</ref>
 
Another two rules are applied much less frequently and exist to prevent illegal year lengths. Their names are Hebrew acronyms for the way they are calculated:
 
*If the molad in a common year falls on a Tuesday after 9 hours and 204 parts, Rosh Hashanah is postponed to Thursday. This is deḥiyyah ''GaTaRaD,'' an acronym meaning "3 (Tuesday), 9, 204."
*If the molad following a leap year falls on a Monday after 15 hours and 589 parts, Rosh Hashanah is postponed to Tuesday. This is deḥiyyah ''BeTUTeKaPoT,'' and acronym for "2 (Monday), 15, 589."
 
At the innovation of the rabbis, the mathematical calendar has been arranged to ensure that [[Yom Kippur]] does not fall on a Friday or Sunday, and [[Hoshana Rabbah]] does not fall on [[Shabbat]].<ref>This is the reason given by most [[halachic]] authorities, based on the [[Talmud]], Rosh Hashanah 20b and Sukkah 43b. [[Maimonides]] ([[Mishneh Torah]], Kiddush Hachodesh 7:7), however, writes that the arrangement was made (possible days alternating with impossible ones) in order to average out the difference between the mean and true [[lunar conjunction]]s.</ref> These rules have been instituted because Shabbat restrictions also apply to Yom Kippur, so that if Yom Kippur were to fall on Friday, it would not be possible to make necessary preparations for Shabbat (such as [[Shabbat candles|candle lighting]]). Similarly, if Yom Kippur fell on a Sunday, it would not be possible to make preparations for Yom Kippur because the preceding day is Shabbat.<ref>The Talmud (Rosh Hashanah 20b) puts it differently: over two consecutive days of full Shabbat restrictions, vegetables would wilt (since they can't be cooked), and unburied corpses would putrefy.</ref> Additionally, the laws of Shabbat override those of Hoshana Rabbah, so that if Hoshana Rabbah were to fall on Shabbat certain rituals that are a part of the Hoshana Rabbah service (such as carrying willows, which is a form of work) could not be performed.<ref>Yerushalmi, ''Sukkah'' 54b.</ref>
 
To prevent Yom Kippur (10 Tishrei) from falling on a Friday or Sunday, Rosh Hashanah (1 Tishrei) cannot be a Wednesday or Friday. Likewise, to prevent Hoshana Rabbah (21 Tishrei) from falling on a Saturday, Rosh Hashanah cannot be a Sunday. This leaves only four days on which Rosh Hashanah can fall: Monday, Tuesday, Thursday, and Saturday, which are referred as the "four gates." Each day is associated with a number (its order in the week, starting with Sunday as 1), and these numbers are associated with Hebrew letters. Therefore the ''keviyah'' uses the letters ה,ג,ב and ז (representing 2, 3, 5, and 7, for Monday, Tuesday, Thursday, and Saturday) to denote the starting day of the year.
 
====Deficient, regular, and complete years====
The postponement of the year is compensated for by adding a day to the second month or removing one from the third month. A Jewish common year can only have 353, 354, or 355 days. A leap year is always 30 days longer, and so can have 383, 384, or 385 days.
 
*A ''chaserah'' year (Hebrew for "deficient" or "incomplete") is 353 or 383 days long. Both Marcheshvan and Kislev have 29 days. The Hebrew letter ח "het" is used in the ''keviyah''.
*A ''kesidrah'' year ("regular" or "in-order") is 354 or 384 days long.  Marcheshvan has 29 days while Kislev has 30 days. The Hebrew letter כ "kaf" is used in the ''keviyah''.
*A ''shlemah'' year ("complete" or "perfect") is 355 or 385 days long. Both Marcheshvan and Kislev have 30 days. The Hebrew letter ש "shin" is used in the ''keviyah''.
 
Whether a year is deficient, regular, or complete is determined by the time between two adjacent Rosh Hashanah observances and the leap year. While the ''keviyah'' is sufficient to describe a year, a variant specifies the day of the week for the first day of Pesach ([[Passover]]) in lieu of the year length.
 
A Metonic cycle equates to 235 lunar months in each 19-year cycle. This gives an average of 6939 days, 16 hours, and 595 parts for each cycle. But due to the Rosh Hashanah postponement rules (preceding section) a cycle of 19 Jewish years can be either 6939, 6940, 6941, or 6942 days in duration.  Since none of these values is evenly divisible by seven, the Jewish calendar repeats exactly only following 36,288 Metonic cycles, or 689,472 Jewish years.  There is a near-repetition every 247 years, except for an excess of 50 minutes (905 parts).
 
==History==
[[File:To the trumpeting place.jpg|right|thumb|A stone (2.43×1 m) with [[Hebrew language|Hebrew]] inscription "To the Trumpeting Place" is believed to be a part of the Second Temple.]]
 
===Mishnaic period===
The [[Tanakh]] contains several [[613 Mitzvot|commandments]] related to the keeping of the calendar and the lunar cycle, and records changes that have taken place to the Hebrew calendar.
 
It has been noted<ref name=Stern>Sacha Stern, ''Calendar and Community'', Oxford University Press, 2001, pp. 162ff.</ref> that the procedures described in the Mishnah and Tosefta are all plausible procedures for regulating an empirical lunar calendar.  Fire-signals, for example, or smoke-signals, are known from the pre-exilic Lachish ostraca.<ref>James B. Pritchard, ed., ''The Ancient Near East: An Anthology of Texts and Pictures'', Vol. 1, Princeton University Press, p. 213.</ref>  Furthermore, the Mishnah contains laws that reflect the uncertainties of an empirical calendar.  Mishnah Sanhedrin, for example, holds that when one witness holds that an event took place on a certain day of the month, and another that the same event took place on the following day, their testimony can be held to agree, since the length of the preceding month was uncertain.<ref>M. ''Sanhedrin'' 5.3:  "If one testifies, 'on the second of the month, and the other, 'on the third of the month:' their evidence is valid, for one may have been aware of the intercalation of the month and the other may not have been aware of it.  But if one says, 'on the third', and the other 'on the fifth', their evidence is invalid."</ref>  Another Mishnah takes it for granted that it cannot be known in advance whether a year's lease is for twelve or thirteen months.<ref>M. ''Baba Metzia'' 8.8.</ref>  Hence it is a reasonable conclusion that the Mishnaic calendar was actually used in the Mishnaic period.
 
The accuracy of the Mishnah's claim that the Mishnaic calendar was also used in the late [[Second Temple of Jerusalem|Second Temple]] period is less certain.  One scholar has noted<ref>Solomon Gandz, "The origin of the Two New Moon Days", ''Jewish Quarterly Review'' (New Series), v. 40, 1949-50.  Reprinted in Shlomo Sternberg, ed., ''Studies in Hebrew Astronomy and Mathematics by Solomon Gandz'', KTAV, New York, 1970, pp. 72–73.</ref> that there are no laws from Second Temple period sources that indicate any doubts about the length of a month or of a year.  This led him to propose that the priests must have had some form of computed calendar or calendrical rules that allowed them to know in advance whether a month would have 30 or 29 days, and whether a year would have 12 or 13 months.
 
===Modern calendar===
[[File:Sack of jerusalem.JPG|thumb|The [[Arch of Titus]] depicting the objects from the Temple being carried through Rome.]]
Between 70 and 1178 CE, the observation-based calendar was gradually replaced by a mathematically calculated one.<ref>Sacha Stern, ''Calendar and Community''.</ref> Except for the epoch year number, the calendar rules reached their current form by the beginning of the 9th century, as described by the [[Persia]]n [[Muslim]] astronomer [[al-Khwarizmi]] (c. 780–850 CE) in 823.<ref name=Kennedy/><ref name=Khwarizmi/>
 
One notable difference between the calendar of that era and the modern form was the date of the [[epoch (reference date)|epoch]] (the fixed reference point at the beginning of year 1), which at that time was one year later than the epoch of the modern calendar.
 
Most of the present rules of the calendar were in place by 823, according to a treatise by al-Khwarizmi. Al-Khwarizmi's study of the Jewish calendar, ''{{unicode|Risāla fi istikhrāj taʾrīkh al-yahūd}}'' "Extraction of the Jewish Era" describes the [[Metonic cycle|19-year intercalation cycle]], the rules for determining on what day of the week the first day of the month [[Tishrei|Tishrī]] shall fall, the interval between the [[Anno Mundi|Jewish era]] (creation of Adam) and the [[Seleucid era]], and the rules for determining the mean longitude of the sun and the moon using the Jewish calendar.<ref name=Kennedy>E.S. Kennedy, "Al-Khwarizmi on the Jewish calendar", ''Scripta Mathematica'' '''27''' (1964) 55–59.</ref><ref name=Khwarizmi>"al-Khwarizmi", ''Dictionary of Scientific Biography'', VII: 362, 365.</ref>
 
In 921, [[Aaron ben Meïr]] proposed changes to the calendar. Though the proposals were rejected, they indicate that all of the rules of the modern calendar (except for the epoch) were in place before that date. In 1000, the Muslim chronologist [[al-Biruni]] described all of the modern rules of the Hebrew calendar, except that he specified three different epochs used by various Jewish communities being one, two, or three years later than the modern epoch.<ref name="ReferenceA"/>
 
There is a tradition, first mentioned by [[Hai Gaon]] (died 1038 CE), that [[Hillel II|Hillel b. R. Yehuda]] "in the year 670 of the Seleucid era" (i.e., 358–359 CE) was responsible for the new calculated calendar with a fixed intercalation cycle. Later writers, such as Nachmanides, explained Hai Gaon's words to mean that the entire computed calendar was due to Hillel b. Yehuda in response to persecution of Jews.  Maimonides, in the 12th century, stated that the Mishnaic calendar was used "until the days of Abaye and Rava", who flourished c. 320–350 CE, and that the change came when "the land of Israel was destroyed, and no permanent court was left."  Taken together, these two traditions suggest that Hillel b. Yehuda (whom they identify with the mid-4th-century Jewish patriarch Ioulos, attested in a letter of the Emperor Julian,<ref>Julian, Letter 25, in John Duncombe, ''Select Works of the Emperor Julian and some Pieces of the Sophist Libanius'', Vol. 2, Cadell, London, 1784, pp. 57–62.</ref> and the Jewish patriarch Ellel, mentioned by Epiphanius<ref>Epiphanius, ''Adversus Haereses'' 30.4.1, in Frank Williams, trans., ''The Panarion of Epiphanius of Salamis Book I (Sects 1-46),'' Leiden, E. J.Brill, 1987, p. 122.</ref>) instituted the computed Hebrew Calendar because of persecution. H. Graetz <ref>H. Graetz, Popular History of the Jews, (A. B. Rhine, trans.,) Hebrew Publishing Company, New York, 1919, Vol. II, pp. 410–411. Quoted in Sacha Stern, ''Calendar and Community'', p. 216.</ref> linked the introduction of the computed calendar to a sharp repression following a failed Jewish insurrection that occurred during the rule of the Christian emperor [[Constantius II|Constantius]] and [[Constantius Gallus|Gallus]].  A later writer, S. Lieberman, argued<ref>S Lieberman, "Palestine in the 3rd and 4th Centuries", Jewish Quarterly Review, New Series 36, pp. 329–370(1946).  Quoted in Sacha Stern, ''Calendar and Community,'' pp. 216–217.</ref> instead that the introduction of the fixed calendar was due to measures taken by Christian Roman authorities to prevent the Jewish patriarch from sending calendrical messengers.
 
Both the tradition that Hillel b. Yehuda instituted the complete computed calendar, and the theory that the computed calendar was introduced due to repression or persecution, have been questioned.<ref>Sacha Stern, ''Calendar and Community: A History of the Jewish Calendar Second Century BCE-Tenth Century CE'', Oxford University Press, 2001.  In particular section 5.1.1, discussion of the "Persecution theory."</ref><ref>[[Samuel Poznanski]], "Ben Meir and the Origin of the Jewish Calendar", ''Jewish Quarterly Review'', Original Series, Vol. 10, pp. 152–161(1898).</ref><ref>"While it is not unreasonable to attribute to Hillel II the fixing of the regular order of intercalations, his full share in the present fixed calendar is doubtful."  Entry "Calendar", ''Encyclopedia Judaica'', Keter, Jerusalem, 1971.</ref> Furthermore, two Jewish dates during post-Talmudic times (specifically in 506 and 776) are impossible under the rules of the modern calendar, indicating that its arithmetic rules were developed in Babylonia during the times of the [[Geonim]] (7th to 8th centuries).<ref>[[Samuel Poznanski]], "Calendar (Jewish)", [http://www.archive.org/details/encyclopaediaofr03hastuoft ''Encyclopaedia of Religion and Ethics'', vol. 3].</ref> The Babylonian rules required the delay of the first day of Tishrei when the [[new moon]] occurred after noon.{{Citation needed|date=April 2008}}
 
The Talmuds do, however, indicate at least the beginnings of a transition from a purely empirical to a computed calendar.  According to a statement attributed to Yose, an [[Amoraim|Amora]] who lived during the second half of the 3rd century, the feast of [[Purim]], 14 Adar, could not fall on a Sabbath nor a Monday, lest 10 Tishrei ([[Yom Kippur]]) fall on a Friday or a Sunday.<ref>Yerushalmi ''Megillah'' 70b.</ref> This indicates that, by the time of the redaction of the Jerusalem Talmud (c. 400 CE), there were a fixed number of days in all months from Adar to Elul, also implying that the extra month was already a second Adar added before the regular Adar. In another passage, a sage is reported to have counseled "those who make the computations" not to set the first day of Tishrei or the Day of the Willow on the sabbath.<ref>Yerushalmi ''Sukkah'' 54b.</ref>  This indicates that there was a group who "made computations" and were in a position to control, to some extent, the day of the week on which Rosh Hashanah would fall.
 
===Usage in contemporary Israel===
Early [[Zionist]] pioneers were impressed by the fact that the calendar preserved by Jews over many centuries in far-flung diasporas, as a matter of religious ritual, was geared to the climate of their original country: the Jewish New Year marks the transition from the dry season to the rainy one, and major Jewish holidays such as [[Sukkot]], [[Passover]], and [[Shavuot]] correspond to major points of the country's agricultural year such as planting and harvest.
 
Accordingly, in the early 20th century the Hebrew calendar was re-interpreted as an agricultural rather than religious calendar. The [[Kibbutz]] movement was especially inventive in creating new rituals fitting this interpretation.
 
After the creation of the [[State of Israel]], the Hebrew calendar became one of the official calendars of Israel, along with the [[Gregorian calendar]]. Holidays and commemorations not derived from previous Jewish tradition were to be fixed according to the Hebrew calendar date. For example, the Israeli Independence Day falls on 5 [[Iyar]], Jerusalem Reunification Day on 28 Iyar, and the Holocaust Commemoration Day on 27 [[Nisan]].
 
Nevertheless, since the 1950s usage of the Hebrew calendar has steadily declined, in favor of the Gregorian calendar. At present, Israelis—except for a minority of the religiously observant—conduct their private and public life according to the Gregorian calendar, although the Hebrew calendar is still widely acknowledged, appearing in public venues such as banks (where it is legal for use on cheques and other documents, though only rarely do people make use of this option) and on the mastheads of newspapers.
 
The Jewish New Year (Rosh Hashanah) is a two-day public holiday in Israel. However, since the 1980s an increasing number of secular Israelis celebrate the Gregorian New Year (usually known as "[[Silvester]] Night"—"ליל סילבסטר") on the night between 31 December and 1 January. Prominent Rabbis have on several occasions sharply denounced this practice, but with no noticeable effect on the secularist celebrants.<ref>{{cite news |url=http://www.israelnationalnews.com/News/News.aspx/163462#.Upe6pJuA2rY |title=Rabbinate: New Year's Eve Parties 'Not Kosher' |newspaper=[[Arutz Sheva]] |author=David Lev |date=23 December 2012 |accessdate=30 November 2013}}</ref>
 
The disparity between the two calendars is especially noticeable with regard to commemoration of the assassinated Prime Minister [[Yitzchak Rabin]]. The official Day of Commemoration, instituted by a special [[Knesset]] law, is marked according to the Hebrew calendar - on 12 Marcheshvan. However, left-leaning Israelis, who revere Rabin as a martyr for the cause of peace and who are predominantly secular, hold their commemoration on 4 November. In some years the two competing Rabin Memorial Days are separated by as much as two weeks.
 
Wall calendars commonly used in Israel are hybrids. Most are organised according to Gregorian rather than Jewish months, but begin in September, when the Jewish New Year usually falls, and provide the Jewish date in small characters.
 
==Other practices==
Outside of [[Rabbinic Judaism]], evidence shows a diversity of practice.
 
===Karaite calendar===
Karaites use the lunar month and the solar year, but the Karaite calendar differs from the current Rabbinic calendar in a number of ways. The Karaite calendar is identical to the Rabbinical calendar used before the Sanhedrin changed the Rabbinic calendar from the lunar, observation based calendar, to the current mathematically based calendar used in Rabbinic Judaism today.
 
In the lunar Karaite calendar, the beginning of each month, the [[Rosh Chodesh]], can be calculated, but is confirmed by the observation in [[Israel]] of the first sightings of the new moon.<ref>[http://www.karaite-korner.org/new_moon.shtml The Karaite Korner: The New Moon in the Hebrew Bible]</ref> This may result in an occasional variation of a maximum of one day, depending on the inability to observe the new moon. The day is usually "picked up" in the next month.
 
The addition of the leap month (Adar II) is determined by observing in Israel the ripening of barley at a specific stage (defined by Karaite tradition) (called [[aviv]]),<ref>[http://www.karaite-korner.org/abib.shtml The Karaite Korner: Aviv (Barley)]</ref> rather than using the calculated and fixed calendar of [[Rabbinic Judaism]]. Occasionally this results in Karaites being one month ahead of other Jews using the calculated Rabbinic calendar. The "lost" month would be "picked up" in the next cycle when Karaites would observe a leap month while other Jews would not.
 
Furthermore, the seasonal drift of the Rabbinic calendar is avoided, resulting in the years affected by the drift starting one month earlier in the Karaite calendar.
 
Also, the four rules of postponement of the Rabbinic calendar are not applied, since they are not mentioned in the [[Tanakh]]. This can affect the dates observed for all the Jewish holidays in a particular year by one day.
 
In the Middle Ages many [[Karaite Jews]] outside Israel followed the calculated Rabbinic calendar, because it was not possible to retrieve accurate aviv barley data from the land of Israel. However, since the establishment of the [[State of Israel]], and especially since the [[Six Day War]], the Karaite Jews that have made ''[[aliyah]]'' can now again use the observational calendar.
 
===The Qumran calendar===
{{See also|Enoch calendar}}
Many of the Dead Sea (Qumran) Scrolls have references to a unique calendar, used by the people there, who are often assumed to be Essenes.
 
The year of this calendar used the ideal Mesopotamian calendar of twelve 30-day months, to which were added 4 days at the equinoxes and solstices (cardinal points), making a total of 364 days.
 
There was some ambiguity as to whether the cardinal days were at the beginning of the months or at the end, but the clearest calendar attestations give a year of four seasons, each having three months of 30, 30, and 31 days with the cardinal day the extra day at the end, for a total of 91 days, or exactly 13 weeks. Each season started on the 4th day of the week (Wednesday), every year. (Ben-Dov, ''Head of All Years'', p.&nbsp;16-17)
 
With only 364 days, it is clear that the calendar would after a few years be very noticeably different from the actual seasons, but there is nothing to indicate what was done about this problem. Various suggestions have been made by scholars. One is that nothing was done and the calendar was allowed to change with respect to the seasons. Another suggestion is that changes were made irregularly, only when the seasonal anomaly was too great to be ignored any longer. (Ben-Dov, ''Head of All Years'', p.&nbsp;19-20)
 
The writings often discuss the moon, but the calendar was not based on the movement of the moon any more than indications of the phases of the moon on a modern western calendar indicate that that is a lunar calendar.
 
===Persian civil calendar===
Calendrical evidence for the postexilic Persian period is found in [[Elephantine papyri|papyri]] from the Jewish colony at [[Elephantine]], in Egypt.  These documents show that the Jewish community of Elephantine used the [[Egyptian calendar|Egyptian]] and [[Babylonian calendar|Babylonian]] calendars.<ref>Sacha Stern, "The Babylonian Calendar at Elephantine", ''Zeitschrift für Papyrologie und Epigraphik'' 130, 159–171(2000).</ref><ref>Lester L. Grabbe, A'' History of the Jews and Judaism in the Second Temple Period, Volume 1: Yehud: A History of the Persian Province of Judah'', T&T Clark, London, 2004, p. 186.</ref>
 
The [[Sardica paschal table]] shows that the Jewish community of some eastern city, possibly [[Antioch]], used a calendrical scheme that kept Nisan 14 within the limits of the Julian month of March.<ref>Eduard Schwartz, ''Christliche und jüdische Ostertafeln,'' (Abhandlungen der königlichen Gesellschaft der Wissenschaften zu Göttingen. Philologisch-Historische Klasse. Neue Folge, Band viii, Berlin, 1905.</ref>  Some of the dates in the document are clearly corrupt, but they can be emended to make the sixteen years in the table consistent with a regular intercalation scheme. Peter, the bishop of Alexandria (early 4th century CE), mentions that the Jews of his city "hold their Passover according to the course of the moon in the month of [[Paremhat|Phamenoth]], or according to the intercalary month every third year in the month of [[Paremoude|Pharmuthi]]",<ref>Peter of Alexandria, quoted in the ''Chronicon Paschale''.  ''Corpus Scriptorum Historiae Byzantinae, Chronicon Paschale'' Vol. 1, Weber, Bonn, 1832, p. 7</ref> suggesting a fairly consistent intercalation scheme that kept Nisan 14 approximately between the Phamenoth 10 (March 6 in the 4th century CE) and Pharmuthi 10 (April 5). Jewish funerary inscriptions from Zoar, south of the Dead Sea, dated from the 3rd to the 5th century, indicate that when years were intercalated, the intercalary month was at least sometimes a repeated month of Adar.  But the inscriptions reveal no clear pattern of regular intercalations, nor do they indicate any consistent rule for determining the start of the lunar month.<ref>Sacha Stern, Calendar and Community, pp. 87–97, 146-153.</ref>
 
In 1178, [[Maimonides]] included all the rules for the calculated calendar and their scriptural basis, including the modern epochal year in his work, ''[[Mishneh Torah]]''. Today, the rules detailed in Maimonides' code are those generally used by Jewish communities throughout the world.
 
==Astronomic calculations==
 
===Synodic month - the molad interval===
A "[[new moon]]" (astronomically called a [[lunar conjunction]] and in Hebrew called a [[molad]]) is the moment at which the sun and moon are aligned horizontally with respect to a north-south line (technically, they have the same ecliptical longitude). The period between two new moons is a [[synodic month]]. The actual length of a synodic month varies from about 29 days 6 hours and 30 minutes (29.27 days) to about 29 days and 20 hours (29.83 days), a variation range of about 13 hours and 30 minutes. Accordingly, for convenience, a long-term average length called the '''mean synodic month''' (also called the molad interval) is used.  The mean synodic month is <math>\tfrac{765433}{25920}</math> days, or 29 days, 12 hours, and 793 parts (44+<sup>1</sup>/<sub>18</sub> minutes) (i.e. 29.530594 days), and is the same value determined by the Babylonians in the [[Babylonian mathematics|System B]] in about 300 BCE<ref name=Neugebauer1>Neugebauer, ''Astronomical cuneiform texts'', Vol 1, pp 271–273</ref> and was adopted by the Greek astronomer [[Hipparchus]] in the 2nd century BCE and by the Alexandrian astronomer [[Ptolemy]] in ''[[Almagest]]'' four centuries later (who cited Hipparchus as his source). Its remarkable accuracy (less than one second from the true value) is thought to have been achieved using records of lunar eclipses from the 8th to 5th centuries BCE.<ref>[[G. J. Toomer]], Hipparcus' Empirical Basis for his Lunar Mean Motions, ''Centaurus'', Vol 24, 1980, pp. 97–109</ref>
 
This value is as close to the correct value of 29.530589 days as it is possible for a value to come that is rounded off to whole parts (<sup>1</sup>/<sub>18</sub> minute). The discrepancy makes the molad interval about 0.6 seconds too long.  Put another way, if the molad is taken as the time of mean conjunction at some reference meridian, then this reference meridian is drifting slowly eastward.  If this drift of the reference meridian is traced back to the mid-4th century, the traditional date of the introduction of the fixed calendar, then it is found to correspond to a longitude midway between the [[Nile]] and the end of the [[Euphrates]]. The modern molad moments match the mean solar times of the lunar conjunction moments near the meridian of [[Kandahar]], [[Afghanistan]], more than [[longitude|30°]] east of Jerusalem.
 
Furthermore, the discrepancy between the molad interval and the mean synodic month is accumulating at an accelerating rate, since the mean synodic month is progressively shortening due to gravitational [[tide|tidal]] effects.    Measured on a strictly uniform time scale, such as that provided by an [[atomic clock]], the mean synodic month is becoming gradually longer, but since the tides slow Earth's rotation rate even more, the mean synodic month is becoming gradually shorter in terms of mean solar time.
 
===Seasonal drift===
The mean year of the current mathematically-based Hebrew calendar is more than 6 minutes and 25 seconds more than the northern hemisphere spring equinox year: the mean Hebrew year is 365 days 5 hours 55 minutes and 25+<sup>25</sup>/<sub>57</sub> seconds (365.2468 days) - computed as the molad/monthly interval of 29.530594 days × 235 months in a 19-year metonic cycle ÷ 19 years per cycle. The present-era mean northward [[Tropical year|equinoctal year]] is 365 days 5 hours 49 minutes 1 second long (365.2424 days), resulting in a "seasonal drift" of the Hebrew calendar in relation to the tropical year of about a day every 224 years. In relation to the [[Gregorian calendar]], the mean Gregorian calendar year is 365 days 5 hours 49 minutes and 12 seconds (365.2425 days), and the drift of the Hebrew calendar in relation to it is about a day every 231 years.
 
===Implications for Jewish ritual===
[[File:DetailOfMedievalHebrewCalendar.jpg|thumb||right|This figure, in a detail of a medieval Hebrew calendar, reminded Jews of the [[palm tree|palm branch]] ([[Lulav]]), the myrtle twigs, the willow branches, and the [[citron]] ([[Etrog]]) to be held in the hand and to be brought to the synagogue during the holiday of [[sukkot]], near the end of the autumn holiday season.]]
Although the molad of Tishrei is the only molad moment that is not ritually announced, it is actually the only one that is relevant to the Hebrew calendar, for it determines the provisional date of Rosh Hashanah, subject to the Rosh Hashanah postponement rules. The other monthly molad moments are announced for mystical reasons. With the moladot on average almost 100 minutes late, this means that the molad of Tishrei lands one day later than it ought to in (100 minutes) ÷ (1440 minutes per day) = 5 of 72 years or nearly 7% of years!
 
Therefore, the seemingly small drift of the moladot is already significant enough to affect the date of Rosh Hashanah, which then cascades to many other dates in the calendar year and sometimes, due to the Rosh Hashanah postponement rules, also interacts with the dates of the prior or next year. The molad drift could be corrected by using a progressively shorter molad interval that corresponds to the actual mean lunar conjunction interval at the original molad reference meridian. Furthermore, the molad interval determines the calendar mean year, so using a progressively shorter molad interval would help correct the excessive length of the Hebrew calendar mean year, as well as helping it to "hold onto" the northward equinox for the maximum duration.
 
When the 19-year intercalary cycle was finalised in the 4th century, the earliest Passover (in year 16 of the cycle) coincided with the northward equinox, which means that Passover fell near the ''first'' full moon after the northward equinox, or that the northward equinox landed within one lunation before 16 days after the ''molad'' of ''Nisan''.  This is still the case in about 80% of years, but in about 20% of years Passover is a month late by these criteria (as it was in AM 5765 and 5768, the 8th and 11th years of the 19-year cycle = Gregorian 2005 and 2008 CE). Presently this occurs after the "premature" insertion of a leap month in years 8, 11, and 19 of each 19-year cycle, which causes the northward equinox to land on exceptionally early Hebrew dates in such years. This problem will get worse over time, and so beginning in AM 5817 (2057 CE), year 3 of each 19-year cycle will also be a month late. Furthermore, the drift will accelerate in the future as perihelion approaches and then passes the northward equinox, and if the calendar is not amended then Passover will start to land on or after the summer solstice around AM 16652 (12892 CE). (The exact year when this will begin to occur depends on uncertainties in the future tidal slowing of the Earth rotation rate, and on the accuracy of predictions of precession and Earth axial tilt.)
 
The seriousness of the spring equinox drift is widely discounted on the grounds that Passover will remain in the spring season for many millennia, and the text of the Torah is generally not interpreted as having specified tight calendrical limits. On the other hand, the mean southward equinoctial year length is considerably shorter, so the Hebrew calendar has been drifting faster with respect to the autumn equinox, and at least part of the harvest festival of Sukkot is already more than a month after the equinox in years 1, 9, and 12 of each 19-year cycle; beginning in AM 5818 (2057 CE), this will also be the case in year 4. (These are the same year numbers as were mentioned for the spring season in the previous paragraph, except that they get incremented at Rosh Hashanah.) This progressively increases the probability that Sukkot will be cold and wet, making it uncomfortable or impractical to dwell in the traditional ''succah'' during Sukkot. The first winter seasonal prayer for rain is not recited until ''Shemini Atzeret'', after the end of Sukkot, yet it is becoming increasingly likely that the rainy season in Israel will start before the end of Sukkot.
 
No equinox or solstice will ever be more than a day or so away from its mean date according to the solar calendar, while nineteen Jewish years average 6939d 16h 33m 03{{fraction|1|3}}s compared to the 6939d 14h 26m 15s of nineteen mean tropical years.<ref>Weinberg, I., ''Astronomical Aspects of the Jewish Calendar'', Monthly Notes of the Astronomical Society of South Africa, Vol. 15, p. 86; available at [http://adsabs.harvard.edu/full/1956MNSSA..15...86W]</ref> This discrepancy has mounted up to six days, which is why the earliest Passover currently falls on 26 March (as in AM 5773 / 2013 CE).
 
===Worked example===
{{Abbreviations|section|date=July 2011}}
Given the length of the year, the length of each month is fixed as described above, so the real problem in determining the calendar for a year is determining the number of days in the year. In the modern calendar this is determined in the following manner.<ref>The following description is based on the article "Calendar" in Encyclopaedia Judaica (Jerusalem: Ketter, 1972). It is an explanatory description, not a procedural one, in particular explaining what is going on with the third and fourth ''deḥiyyot''</ref>
 
The day of Rosh Hashanah and the length of the year are determined by the time and the day of the week of the Tishrei ''molad'', that is, the moment of the average conjunction. Given the Tishrei ''molad'' of a certain year, the length of the year is determined as follows:
 
First, one must determine whether each year is an ordinary or leap year by its position in the 19-year Metonic cycle. Years 3, 6, 8, 11, 14, 17, and 19 are leap years.
 
Secondly, one must determine the number of days between the starting Tishrei ''molad'' (TM1) and the Tishrei ''molad'' of the next year (TM2). For calendar descriptions in general the day begins at 6 p.m., but for the purpose of determining Rosh Hashanah, a ''molad'' occurring on or after noon is treated as belonging to the next day (the second ''deḥiyyah'').<ref>So for example if the Tishrei molad is calculated as occurring from noon on Wednesday (the 18th hour of the fourth day) up until noon on Thursday, Rosh Hashanah falls on a Thursday, which of course starts Wednesday at sunset wherever one happens to be.</ref> All months are calculated as 29d, 12h, 44m, 3{{fraction|1|3}}s long (MonLen). Therefore, in an ordinary year TM2 occurs 12 × MonLen days after TM1. This is usually 354 calendar days after TM1, but if TM1 is on or after 3:11:20 a.m. and before noon, it will be 355 days. Similarly, in a leap year, TM2 occurs 13 × MonLen days after TM1. This is usually 384 days after TM1, but if TM1 is on or after noon and before 2:27:16{{fraction|2|3}} p.m., TM2 will be only 383 days after TM1. In the same way, from TM2 one calculates TM3. Thus the four natural year lengths are 354, 355, 383, and 384 days.
 
However, because of the holiday rules, Rosh Hashanah cannot fall on a Sunday, Wednesday, or Friday, so if TM2 is one of those days, Rosh Hashanah in year 2 is postponed by adding one day to year 1 (the first ''deḥiyyah''). To compensate, one day is subtracted from year 2. It is to allow these adjustments that the system allows 385-day years (long leap) and 353-day years (short ordinary) besides the four natural year lengths.
 
But how can year 1 be lengthened if it is already a long ordinary year of 355 days or year 2 be shortened if it is a short leap year of 383 days? That is why the third and fourth ''deḥiyyah''s are needed.
 
If year 1 is already a long ordinary year of 355 days, there will be a problem if TM1 is on a Tuesday,<ref>This will happen if TM1 is on or after 3:11:20 a.m. and before noon on a Tuesday. If TM1 is Monday, Thursday or Saturday, Rosh Hashanah in year 2 does not need to be postponed. If TM1 is Sunday, Wednesday or Friday, Rosh Hashanah in year 1 is postponed, so year 1 is not the maximum length.</ref> as that means TM2 falls on a Sunday and will have to be postponed, creating a 356-day year. In this case, Rosh Hashanah in year 1 is postponed from Tuesday (the third ''deḥiyyah''). As it cannot be postponed to Wednesday, it is postponed to Thursday, and year 1 ends up with 354 days.
 
On the other hand, if year 2 is already a short year of 383 days there will be a problem if TM2 is on a Wednesday.<ref>TM2 will be between noon and 2:27:16{{fraction|2|3}} p.m. on Tuesday, and TM3 will be between 9:32:43{{fraction|1|3}} and noon on Monday.</ref> because Rosh Hashanah in year 2 will have to be postponed from Wednesday to Thursday and this will cause year 2 to be only 382 days long. In this case, year 2 is extended by one day by postponing Rosh Hashanah in year 3 from Monday to Tuesday (the fourth ''deḥiyyah'' ), and year 2 will have 383 days.
 
=="Rectifying" the Hebrew calendar==
It has been argued by some {{Who|date=September 2010}} that, as the fixed arithmetic Hebrew calendar was established on the authority of [[Hillel II]], President of the [[Sanhedrin]] in AM 4119 (358 CE), only an equal authority (the modern [[Sanhedrin]]) can either amend it or reinstate the observational Hebrew calendar.{{Citation needed|date=July 2010}} The attribution of the fixed arithmetic Hebrew calendar solely to [[Hillel II]] has, however, been questioned by a few authors, such as Sasha Stern, who claim that the calendar rules developed gradually over several centuries.<ref name=Stern/>
 
Given the importance in Jewish ritual of establishing the accurate timing of monthly and annual times, some [[futurist]] writers and researchers have considered whether a "corrected" system of establishing the Hebrew date is required. The mean year of the current mathematically-based Hebrew calendar is more than 6 minutes and 25 seconds in excess of the northern hemisphere spring equinox year, and has "drifted" an average of 7–8 days late relative to the equinox relationship that it originally had. It is not possible, however, for any individual Hebrew date to be a week or more "late", because Hebrew months always begin within a day or two of the ''[[molad]]'' moment. What happens instead is that the traditional Hebrew calendar "prematurely" inserts a leap month one year before it "should have been" inserted, where "prematurely" means that the insertion causes the spring equinox to land more than 30 days before the latest acceptable moment, thus causing the calendar to run "one month late" until the time when the leap month "should have been" inserted prior to the following spring. This presently happens in 4 years out of every 19-year cycle (years 3, 8, 11, and 19), implying that the Hebrew calendar currently runs "one month late" more than 21% of the time. To a minor degree the tardiness of the calendar is also due to not correcting for the [[Laser lunar ranging|progressively shorter mean astronomical lunation interval]]—although presently this only accounts for a little over six seconds of the yearly equinox drift, it more importantly accounts for nearly two hours of ''molad'' drift relative to actual mean lunar conjunctions, which is enough to cause ''Rosh HaShanah'' to start on the "wrong" date in an appreciable number of years.
 
Dr. Irv Bromberg has proposed a 353-year cycle of 4366 months, which would include 130 leap months, along with use of a progressively shorter ''molad'' interval, which would keep an amended fixed arithmetic Hebrew calendar from drifting for more than seven millennia.<ref>Bromberg, Irv. {{Cite web|title=The Rectified Hebrew Calendar.|url=http://individual.utoronto.ca/kalendis/hebrew/rect.htm|accessdate=2011-05-13}}</ref> It takes about 3{{frac|1|2}} centuries for the spring equinox to drift an average of {{frac|1|19}}th of a ''molad'' interval earlier in the Hebrew calendar. That is a very important time unit, because it can be cancelled by simply truncating a 19-year cycle to 11 years, omitting 8 years including three leap years from the sequence. That is the essential feature of the 353-year leap cycle ({{nowrap|1= (9 × 19) + '''11''' + (9 × 19) = 353 years}}).
 
Religious questions abound about how such a system might be implemented and administered throughout the diverse aspects of the world Jewish community.<ref>[http://www.thesanhedrin.org/en/index.php/Committee_concerning_the_fixing_of_the_Calendar Committee concerning the fixing of the Calendar at TheSanhedrin.org]</ref>
 
In 2008, a calendar restoration research project by a Messianic group, whose authors claim to have restored the original ancient Hebrew creation calendar, placed a portion of their research work on the Internet. The website claims that Hebrew months and years are determined solely by the Creator through the motions of the earth, sun and moon according to Genesis 1:14, and not determined from arbitrary decisions made by men such as by calendar councils.<ref>{{Cite web|title=The Calendar Restoration Project|url=http://www.torahcalendar.com/ABOUT.asp|accessdate=2013-10-26}}</ref>
 
==See also==
{{Portal|Judaism}}
* [[Babylonian calendar]]
* [[Biblical and Talmudic units of measurement]]
* [[Chol HaMoed]], the intermediate days during Passover and Sukkot.
* [[Chronology of the Bible]]
* [[Counting of the Omer]]
* [[Gematria]], Jewish system of assigning numerical value to a word or phrase.
* [[Islamic calendar]]
* [[Hebrew numerals]]
* [[Jewish and Israeli holidays 2000–2050]]
* [[Lag BaOmer]], 33rd day of counting the ''Omer''.
* [[Notarikon]], a method of deriving a word by using each of its initial letters.
* [[Sephirot]], the 10 attributes/emanations found in Kabbalah.
* [[Significance of numbers in Judaism]]
* [[Weekly Torah portion]], division of the Torah into 54 portions.
 
==References==
{{reflist|colwidth=30em}}
 
==Bibliography==
* [[al-Biruni]]. [http://books.google.com/books?id=pFIEAAAAIAAJ&pg=PA376&lr=#PPA141,M1 The Chronology of Ancient Nations, Chapter VII]. tr. C. Edward Sachau. London, 1879.
* Ari Belenkiy. "A Unique Feature of the Jewish Calendar &mdash; ''Dehiyot''". ''Culture and Cosmos'' '''6''' (2002) 3-22.
* Jonathan Ben-Dov. ''Head of All Years: Astronomy and Calendars at Qumran in their Ancient Context''. Leiden: Brill, 2008.
* Bonnie Blackburn and Leofranc Holford-Strevens. ''The Oxford Companion to the Year: An Exploration of Calendar Customs and Time-reckoning''. Oxford University Press; USA, 2000.
* Sherrard Beaumont Burnaby. ''Elements of the Jewish and Muhammadan Calendars''. George Bell and Sons, London, 1901.
* Nathan Bushwick. ''Understanding the Jewish Calendar''. Moznaim, New York/Jerusalem, 1989. ISBN 0-940118-17-3
* William Moses Feldman. ''Rabbinical Mathematics and Astronomy'', 3rd edition, Sepher-Hermon Press, New York, 1978.
* [http://www.judaica-frankfurt.de/content/titleinfo/177450 Eduard Mahler, ''Handbuch der jüdischen Chronologie''. Buchhandlung Gustav Fock, Leipzig, 1916].
* Otto Neugebauer. ''Ethiopic astronomy and computus''. Österreichische Akademie der Wissenschaften, philosophisch-historische Klasse, Sitzungsberichte '''347'''. Vienna, 1979.
* ''The Code of Maimonides (Mishneh Torah), Book Three, Treatise Eight: Sanctification of the New Moon''. Translated by Solomon Gandz. Yale Judaica Series Volume XI, Yale University Press, New Haven, Conn., 1956.
* [[Samuel Poznanski]]. "Calendar (Jewish)". ''[[Encyclopædia of Religion and Ethics]]''. T. & T. Clark, Edinburgh, 1910, vol.&nbsp;3, pp.&nbsp;117–124.
* [[Edward M. Reingold]] and Nachum Dershowitz. ''Calendrical Calculations: The Millennium Edition''. Cambridge University Press; 2 edition (2001). ISBN 0-521-77752-6
723-730.
* Louis A. Resnikoff. "Jewish Calendar Calculations", ''[[Scripta Mathematica]]'' '''9''' (1943) 191-195, 274-277.
* Eduard Schwartz, ''Christliche und jüdische Ostertafeln'' (Abhandlungen der königlichen Gesellschaft der Wissenschaften zu Göttingen. Philologisch-Historische Klasse. Neue Folge, Band viii), Berlin, 1905.
* Arthur Spier. ''The Comprehensive Hebrew Calendar: Twentieth to the Twenty-Second Century 5660–5860/1900–2100''. Feldheim Publishers, Jerusalem/New York, 1986.
* Sacha Stern, ''Calendar and Community: A History of the Jewish Calendar 2nd Century BCE to 10th Century CE''. Oxford University Press, 2001. ISBN 9780198270348.
* Ernest Wiesenberg. "Appendix: Addenda and Corrigenda to Treatise VIII". ''The Code of Maimonides (Mishneh Torah), Book Three: The Book of Seasons''. Yale Judaica Series Volume XIV, Yale University Press, New Haven, Conn., 1961. pp.&nbsp;557–602.
* Francis Henry Woods. "Calendar (Hebrew)", ''[[Encyclopædia of Religion and Ethics]]''. T. & T. Clark, Edinburgh, 1910, vol.&nbsp;3, pp.&nbsp;108–109.
{{JewishEncyclopedia|url=http://www.jewishencyclopedia.com/view.jsp?artid=44&letter=C|article=Calendar}}<br/>
{{JewishEncyclopedia|url=http://www.jewishencyclopedia.com/view.jsp?artid=43&letter=C|article=Calendar, History of}}
 
==External links==
{{External links|date=February 2012}}
*[http://elkind.net/calendar/ Perpetual Hebrew / Civil Calendar]
*[http://www.yeshiva.co/calendar/ Jewish Calendar with Halachic times date converter and daf yomi] yeshiva.co
*[http://www.abcog.org/saadia.htm The Jewish Controversy about Calendar Postponements]
*[http://www.chabad.org/calendar/ Jewish Calendar with Zmanim - Halachic times and date converter] chabad.org
*[http://www-spof.gsfc.nasa.gov/stargaze/Sjewcale.htm Jewish calendar] scientific explanation at the [[NASA]] web site
*[http://jewishencyclopedia.com/view.jsp?artid=44&letter=C&search=Year%20of%20Creation Jewish Encyclopedia: Calendar]
*[http://www.karaite-korner.org/holiday_dates.shtml Karaite Holidays] [[Karaite Judaism|Karaite]] website
*[http://www.cgate.co.il/calendar/calendar_diaspora.asp Hebrew Calendar] Dates and Holydays (Diaspora or Israel) for both the Traditional and the Rectified calendars
*[http://www.hebcal.com/ Hebrew - Gregorian Calendar with options]
*[http://www.bethabracha.co.uk/calendar/ Bet Ha Bracha Hebrew Calendar]
{{Yeshiva site|link=http://www.yeshiva.org.il/calendar/eng/|desc=A Hebrew calendar with [[Halacha|Halachic]] times}}
 
===Date converters===
*[http://jewishholidaysonline.com Jewish Holidays Online] - List of all Jewish holidays for the current year (or any given year).
*[http://molad.palmcrust.com/ Molad] - Jewish Calendar with Zmanim and holidays for [[Mobile phone|Mobiles]].
*[http://www.tichnut.de/jewish/ Jewish Calendar for many platforms]
*[http://kaluach.org/ Kaluach - Hebrew/civil calendars]
*[http://www.hebcal.com/converter/ Hebcal Hebrew Date Converter]
*{{Wayback|url=http://www.geocities.com/DafAWeek/HebCal.html|title=Sample VB.Net and Javascript code to convert the Hebrew Date to the Gregorian Date|date=20071125180434}}
*[http://www.chabad.org/calendar/1000year.asp?AID=6225 Jewish / Civil Date Converter]
*[http://www.aish.com/literacy/reference/AishLuach_(Luach_means_-Calendar-_in_Hebrew).asp Software program that converts Hebrew dates to the civil calendar and vice versa]
*[http://www.diagnosis2012.co.uk/conv.htm Gregorian-Mayan-Julian-Islamic-Persian-Hebrew Calendar Converter]
*[http://individual.utoronto.ca/kalendis/kalendis.htm ''Kalendis'' Calendar Calculator]
*[https://addons.mozilla.org/en-US/firefox/addon/hebrew-calendar/ Firefox Add-ons. Hebrew Calendar]
*[http://www.cambridge.org/us/knowledge/isbn/item1164334/?site_locale=en_US Lisp calendar calculator] which accompanies Dershowitz & Reingold's ''Calendrical Calculations'' 3rd ed. Click "Ancillary materials" tab.
*[http://calendar-converter.com/index.php?p=jewish Hebrew/Gregorian converter], including a full Hebrew calendar.
*[http://www.jewishluach.com/default.aspx Hebrew/Gregorian Calendar converter], including a full Jewish Calendar.
*[http://www.lespenner.com/ JCAL for Windows], full Jewish/Gregorian Calendar for Windows with explanation.
<br/><!-- Spacing for aesthetic purposes: so that bottom templates don't stick to text above it -->
{{calendars}}
{{HebrewMonths}}
{{Time in religion and mythology}}
{{Chronology}}
 
 
[[Category:Hebrew calendar| ]]
[[Category:Lunisolar calendars]]
 
{{Link FA|he}}

Revision as of 00:02, 25 February 2014

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