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The Hebrew calendar () or '''Jewish calendar''' is the annual of the Second Temple in 70 CE , and based on witnesses observing the phase of the moon, and a rule-based form first fully described by Maimonides in 1178 CE, which was adopted over a transition period between 70 and 1178. The "modern" form is a fixed arithmetic Lunisolar Calendar . Because of the roughly 11 day difference between twelve lunar months and one Solar Year , the calendar repeats in a Metonic 19-year cycle of 235 lunar months, with an extra lunar month added once every two or three years, for a total of 7 times per 19 years. As the Hebrew calendar was developed in the region east of the Mediterranean Sea , references to seasons reflect the times and climate of the Northern Hemisphere . HISTORY Biblical period ( 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.]] Jews have been using a lunisolar calendar since Biblical times. The first commandment the Jewish People received as a nation was the commandment to determine the New Moon. The beginning of Exodus Chapter 12 says "This month (Nissan) is for you the first of months.". The months were originally referred to in the Bible by number rather than name. Only four pre-exilic month names appear in the '' (first; literally "Spring", but originally probably meant the ripening of barley), ''Ziv'' (second; literally "Light"), ''Ethanim'' (seventh; literally "Strong" in plural, perhaps referring to strong rains), and ''Bul'' (eighth), and all are Canaan ite names, and at least two are Phoenicia n (Northern Canaanite). It is possible that all of the months were initially identifiable by native Jewish numbers or foreign Canaanite/Phoenician names, but other names do not appear in the Bible. Furthermore, because solar years cannot be divided evenly into lunar months, an extra ''embolismic'' or Intercalary Month must be added to prevent the starting date of the lunar cycles from "drifting" away from the Spring, although there is no direct mention of this in the Bible. There are hints, however, that the first month (today's Nissan) had always started only following the ripening of barley; according to some traditions, in case the barley had not ripened yet, a second-last month would have been inserted. Only much later was a systematic method for inserting a second-last month, today's Adar I, adopted. Babylonian exile During the Babylonian Exile , immediately after 586 BCE, Jews adopted Babylon ian names for the months, and some sects, such as the Essenes , used a solar calendar during the last two centuries BCE . The Babylonian Calendar was the direct descendant of the Sumerian Calendar . Names and lengths of the monthsIn this table below, Hebrew names and romanized transliteration may somewhat differ, as they do for כסלו / Kislev or חשוון / ''Mar''heshvan: the Hebrew words shown here are those indicated e.g. in the newspapers. During leap years Adar I (or Adar Aleph — "first Adar") is considered to be the extra month, and has 30 days. Adar II (or Adar Bet — "second Adar") is the "real" Adar, and has 29 days as usual. For example, in a leap year, the holiday of Purim is in Adar II, not Adar I. Names of the weekdays The Hebrew calendar follows the common seven-day weekly cycle. The Hebrew names for the weekdays are simply the day number within the week, in Hebrew, sometimes (noticeably in the newspapers) abbreviated as יום א׳ (''Day 1'' = Sunday) and so on, using the Numerical Value of the Hebrew letters: Yom Rishon ( Hebrew : יום ראשון), abbreviated יום א׳ = "first day" = Sunday Yom Sheni (יום שני), abbr. יום ב׳ = "second day" = Monday Yom Shlishi (יום שלישי), abbr. יום ג׳ = "third day" = Tuesday Yom Reviʻi (יום רבעי), abbr. יום ד׳ = "fourth day" = Wednesday Yom Ḥamishi (יום חמישי), abbr. יום ה׳ = "fifth day" = Thursday Yom Shishi (יום ששי), abbr. יום ו׳ = "sixth day" = Friday Yom Shabbat (יום שבת or more usually שבת - Shabbat), abbr. יום ז׳ = "seventh day or Sabbath day (Rest day)" = Saturday In Hebrew, the word "Shabbat" (שַׁבָּת) can also mean "(Talmudic) week",For example, according to 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". so that in ritual liturgy a phrase like "Yom Reviʻi bəShabbat" means "the fourth day in the week".For example, when referring to the daily psalm recited in the morning prayer ([[Jewish services The lengths are described in the section Names And Lengths Of The Months . In leap years, a 30 day month called Adar I is inserted immediately after the month of Shevat, and the regular 29 day month of Adar is called Adar II. This is done to ensure that the months of the Jewish calendar always fall in roughly the same seasons of the solar year, and in particular that Nisan is always in spring. Whether either Chesvan or Kislev both have 29 days, or both have 30 days, or one has 29 days and the other 30 days depends upon the number of days needed in each year. Thus a leap year of 13 months has an average length of 383½ days, so for this reason alone sometimes a leap year needs 383 and sometimes 384 days. Additionally, adjustments are needed to ensure certain holy days and festivals do or do not fall on certain days of the week in the coming year. For example, Yom Kippur, on which no work can be done, can never fall on Friday (the day prior to the Sabbath ), to avoid having two consecutive days on which no work can be done. Thus some flexibility has been built in. The 265 days from the first day of the 29 day month of Adar (i.e. the twelfth month, but the thirteenth month, Adar II, in leap years) and ending with the 29th day of Heshvan forms a fixed length period that has all of the festivals specified in the Bible, such as Pesach (Nisan 15), Shavuot (Sivan 6), Rosh Hashana (Tishri 1), Yom Kippur (Tishri 10), Sukkot (Tishri 15), and Shemini Atzeret (Tishri 22). The festival period from Pesach up to and including Shemini Atzeret is exactly 185 days long. The time from the traditional day of the ''vernal Equinox '' up to and including the traditional day of the ''autumnal equinox'' is also exactly 185 days long. This has caused some unfounded speculation that Pesach should be March 21 , and Shemini Atzeret should be September 21 , which are the traditional days for the equinoxes. Just as the Hebrew day starts at sunset, the Hebrew year starts in the Autumn (Rosh Hashanah), although the mismatch of solar and lunar years will eventually move it to another season if the modern fixed calendar isn't moved back to its original form of being judged by the Sanhedrin (which requires the Beit Hamikdash ) Karaite interpretation Karaites use the lunar month and the solar year, but the Karaite calendar differs from the Rabbinical calendar in a few ways: Determination of the first month of the year - (called Aviv ), which is the month Passover falls out and determination of the first day of each month ( Rosh Chodesh ). The 4 rules of postponement are not applied, as they are not found in the Tanakh . It is determined when to add a 13th month by observing the ripening of Barley (called Abib ) in Israel , rather than the calculated and fixed calendar of Rabbinic Judaism . This puts Karaites in sync with the Written Torah , while other Jews are often a month later. The beginning of each month is determined by the Rosh Chodesh - which can be calculated, but is confirmed by observation of the first sightings of the new moon in Israel . For several centuries, many Karaites, especially those outside Israel, have just followed the calculated dates of the Oral Law (the Mishnah and the Talmud ) with other Jews for the sake of simplicity. However, in recent years most Karaites have chosen to again follow the Written Torah practice. ACCURACY The molad interval is currently about 0.6 seconds too long, and the discrepancy is accumulating at an accelerating rate as the mean lunation interval is getting progressively shorter, due to Earth-Moon gravitational tidal effects. The accumulated "error" since the era of Hillel II is such that the molad moments are now almost 1 hour and 40 minutes late, relative to the mean lunar conjunctions at the original reference meridian that was midway between the Nile River and the end of the Euphrates River. Today the molad moments match the mean lunar conjunction moments in terms of the mean solar time near the meridian of Qandahar, Afghanistan, more than 30° east of Jerusalem! 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. If the intention of the calendar is that Passover should fall near the ''first'' full moon after the northward equinox, or that the northward equinox should land within one lunation before 16 days after the ''molad'' of ''Nisan'', then 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 Hebrew year 5765, an 8th year of the 19-year cycle = Gregorian 2005 AD). Presently this occurs after the "premature" insertion of a leap month in years 8, 19, and 11 of each 19-year cycle, which causes the northward equinox to land at exceptionally early moments in such years. This problem will get worse over time, and so beginning in Hebrew year 5817 the 3rd year 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 Hebrew year 16652, or about 10885 years from the present. (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 9, 1, 12 and 4 of each 19-year cycle (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''. As the 19-year cycle (and indeed all aspects of the calendar) is part of codified Jewish law, it would only be possible to amend it if a Sanhedrin could be convened. It is traditionally assumed that this will take place upon the coming of the Messiah , which will mark the beginning of the Era Of Redemption according to Jewish belief. paragraph is in conflict with the historical gradual evolution of the calendar rules that was outlined above. If the calendar development was indeed gradual and did not reach its final form until Maimonides, who published the first complete and unambiguous codification of both the observational and fixed-arithmetic Hebrew calendars, then a Sanhedrin is not required to change it. If the calendar rules were set by the Sanhedrin of Hillel II, then the gradual history outlined above is wrong and only the present or future Sanhedrin can change them. An excellent solution would be to replace the 19-year cycle with a 353-year cycle of 4366 lunations, including 130 leap months. It is predicted that this cycle, together with use of a progressively shorter molad interval, will keep the amended calendar from drifting for more than 7 millennia (deduct 3 millennia if the traditional molad interval is retained). The calendar arithmetic to do this is straightforward and is documented in the public domain (see the external link to the Rectified Hebrew Calendar). Another possibility would be to calculate the astronomical moment of the actual northward equinox and declare a leap year if and only if Pesach would otherwise start before the equinox. Similar ideas are used in the Chinese Calendar and some Indian Calendar s. This would be very accurate, but would require a central authority to be responsible for the official calculations, because there are small differences between astronomical algorithms, depending on the methods employed. Adopting an astronomical calendar would require more explicit definition of the calendar rules. Should the calculated equinox moment be the actual astronomical equinox, or the mean astronomical equinox, and which meridian of longitude should the moment be referred to? (The traditional equinox moments of Tekufat Shmuel drift at the same rate as the Julian calendar, and those of Tekufat Adda drift at the same rate as the fixed arithmetic Hebrew calendar, so neither can be used.) Should the leap month be inserted if the equinox would otherwise land after the end of the first day of Passover (as Maimonides suggested), or should the cutoff be the moment of the Korban Pesach sacrifice 30 minutes after noon on the 14th of Nissan (most compatible with the Torah command in Deuteronomy 16:1), or should the average equinox moment align with the average moment when the month of Nissan starts (calendrically most sensible)? Should a progressive molad be used, or the actual lunar conjunction, or a prediction of new lunar crescent visibility (a reliable way to do that still doesn't exist), and which meridian of longitude should the moment be referred to? Should month lengths vary such that any month can have 29 or 30 days, or should the present rules for fixed month lengths be continued? (In particular, should the length of Elul be fixed at 29 days, which was mentioned in many places in the Talmud?) Should there be any offset between the "molad" moment (however determined) and the start of months (one day yields good agreement with the performance of the fixed arithmetic calendar)? Should Rosh HaShanah postponement rules be continued, or advance/postpone used instead (arithmetically much simpler)? The compatibility of the selected astronomical rules with the dates of High Holy Days and other events, and with the weekly Torah portions, needs to be evaluated and confirmed as acceptable. PROGRAMMERS' GUIDE The audience for this summary of the mechanics of the Hebrew calendar presumably is composed of computer programmers who wish to design software that accurately computes dates in the Hebrew calendar. The following details may prove useful for validating such software. Note, however, that published Hebrew calendar algorithms are much simpler than the details listed below, and there is no need to employ tables in computer implemention of Hebrew calendar arithmetic. As usual, tables are useful shortcuts for humans carrying out the calculations manually. # The Hebrew calendar is computed by lunations. One mean lunation is reckoned at 29 days, 12 hours, 44 minutes, 3⅓ seconds, or equivalently 765433 parts = 29 days, 13753 parts, where 1 minute = 18 parts (''halakim'' plural, ''helek'' singular). # A common year must be either 353, 354, or 355 days; a leap year must be 383, 384, or 385 days. A 353 or 383 day year is called ''haserah''. A 354 or 384 day year is ''kesidrah''. A 355 or 385 day year is ''shlemah''. # Leap years follow a 19 year schedule in which years 3, 6, 8, 11, 14, 17, and 19 are leap years. The Hebrew year 5758 (which starts in Gregorian year 1997) is the first year of a cycle. # 19 years is the same as 235 lunations. # The months are Tishri, Cheshvan, Kislev, Tevet, Shevat, Adar, Nisan, Iyar, Sivan, Tammuz, Av, and Elul. In a leap year, Adar is replaced by Adar II (also called Adar Sheni or Veadar) and an extra month, Adar I (also called Adar Rishon), is inserted before Adar II. # Each month has either 29 or 30 days. A 30 day month is full (מלא pronounced: ''maleh'', ''maley'', or ''malei''), whereas a 29 day month is defective (חסר pronounced: ''ħaser'' or ''khaser'').
# Tishri 1 (Rosh Hashana) is the day during which a '' Molad '' (instant of the mean lunar conjunction) occurs unless that conflicts with certain postponements (''dehiyyot'' plural; ''dehiyyah'' singular). Note that for calendar computations, the Jewish date begins at 6 pm or six fixed hours before midnight when the date changes in the Gregorian calendar, ''not'' at nightfall or sunset when the observed Hebrew date begins.
# Postponements are implemented by adding a day to Kislev of the preceding year, making it full. If Kislev is already full, the day is added to Cheshvan of the preceding year, making it full also. If a delay of two days is called for, both Cheshvan and Kislev of the preceding year become full. # A reference epoch in modern times is molad Tishri for Hebrew year 5758, which is at 22:07:10 on Wednesday, begins at noon, it can be reckoned twelve hours earlier for programming purposes, which is what is meant here by the phrase, "midnight-referenced." Calculation by use of partial weeks There are a number or approaches that can be taken in calculating Hebrew dates. One that is widely documented uses partial weeks and a table of limits. This method relies on all postponements being defined in terms of a seven-day week. That means that whole weeks between the epoch and the Molad of the current year can be eliminated, leaving only a partial week with a few days, hours and parts. :A nineteen-year cycle has 235 months of 29d 12h 793p each or 6939d 16h 595p. Eliminating 991 weeks leaves a partial week of 2d 16h 595p or 69715p. :A common year has 12 months of 29d 12h 793p each or 354d 8h 876p. Eliminating 50 weeks leaves a partial week of 4d 8h 876p or 113196p. :A leap year has 13 months of 29d 12h 793p or 383d 21h 589p. Eliminating 54 weeks leaves a partial week of 5d 21h 589p or 152869p. Postponement B requiring a delay until the next day (beginning at 6 pm) if a molad occurs at or after noon effectively means that the week begins at noon Saturday for computational purposes. Calculate the partial week between the molad of the desired Hebrew year and the preceding noon Saturday considering the partial week before molad Tishri of AM 1 (or the first year of a more recent nineteen-year cycle) and the partial weeks from the intervening cycles and years within the current cycle, eliminating whole weeks via mod 181440, the number of parts in one week. Thus molad Tishri AM 1, which is 1d 5h 204p after 6 pm Saturday, is increased by 6 hours to 1d 11h 204p or 38004p. This is 5h 204p after the beginning (6 pm) of the second day of the week. In Western terms, this is 23:11:20 on Sunday (because it is before midnight), 6 October 3761 BCE in the Proleptic Julian Calendar . This date is midnight-referenced Julian day number 347997. Consulting the Table of Limits below, 1 Tishri is the second day of the week, equivalent to the tabular Western day of Monday (same daylight period as the Hebrew day), which is 7 October 3761 BCE . This means no postponement was needed (both the molad Tishri and 1 Tishri were on the second day of the week). Alternatively, the molad of a more recent Hebrew year may be selected as the epoch if it is the first year of a nineteen-year cycle, such as 5758 (used in rule 9), which is 303 nineteen-year cycles after molad Tishri AM 1. Thus molad Tishri 5758 is (38004 + 303×69715) mod 181440 = 114609 parts after noon Saturday, or 4d 10h 129p, which is 4h 129p after the beginning (6 pm) of the fifth day of the week. In Western terms, this is before midnight, which yields the date and time indicated in rule 9. Consulting the Table of Limits, 1 Tishri is the fifth day of the week, or tabular Thursday 2 October 1997 (Gregorian), again no postponement was needed. By applying the postponements to the moladot Tishri at the beginning and end of any Hebrew year, a table of four gates ( (892–942). In the following table, the years of a nineteen-year cycle are listed in the top row, organized into four groups: a common year after a leap year but before a common year (LCC, 1 4 9 12 15), a common year between two leap years (LCL, 7 18), a common year after a common year but before a leap year (CCL, 2 5 10 13 16), or a leap year between two common years (C'''L'''C, 3 6 8 11 14 17 19). The week since noon Saturday on the left is partitioned by a set of limits between which the molad Tishri of the Hebrew year can be found. The resulting type of year in the body of the table indicates the day of the Hebrew week of 1 Tishri (2, 3, 5, or 7), the four gates, and whether the year is deficient (−1), regular (0), or abundant (+1). NOTES REFERENCES
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