Lessons on the Hebrew Calendar at the Intersection of
&
Chanukah Thanksgiving Donald J. Cymrot
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Cover Design by Ken Falk
Lessons on the Hebrew Calendar at the Intersection of Chanukah and Thanksgiving Many have observed that in the year 2013, coinciding to the Hebrew year of 5774, the first day of Chanukah, that is the 25th of Kislev, will fall on national holiday of Thanksgiving, currently the fourth Thursday in November. This intersection between the first day of Chanukah and Thanksgiving has been incorrectly described as a “once in an eternity”1 phenomena, and given rise to such expressions as “Thanksgivukkah” or latke‐turkey mashups. Although the overlap is quite rare, it is not unique. Nonetheless, the rarity of the coincidence of these two days provides an opportunity to learn more about Hebrew calendar in explaining not what will happen but why the event is so rare. Lesson 1: A Brief History of Thanksgiving The first Thanksgiving in the new world was celebrated by the Pilgrims in Plymouth Colony in the year 1621. Some argue that the Pilgrims modeled this celebration after the Jewish festival of Sukkot, but there are several reasons to doubt this connection. First, unlike Sukkot, Thanksgiving did not immediately become an annual event. It gradually captured the popular imagination first spreading across New England and then to the other colonies. Second, the Pilgrims did not build live in sukkah‐ like structures to live in during the holiday. Third, even though the Pilgrims were conversant is the Hebrew Bible and they did retain the observance of the Sabbath and some other commandments, they did not accept ceremonial or temporal commandments such as the observance of Sukkot.2 The Continental Congress proclaimed the first national Thanksgiving in 1777.3 President George Washington proclaimed the first post‐revolutionary war Thanksgiving on Thursday November 26, 1789. Presidents Adams and Monroe also proclaimed national Thanksgivings, but the custom fell out of use by 1815, after which the celebration of the holiday was limited to individual state observances. By the 1850s, almost every state and territory celebrated Thanksgiving, but it was not a national holiday. In 1863, President Lincoln revived the custom of Presidential proclamations in the hope that it might serve to unite the war‐torn nation. He actually declared Thanksgiving on August 6 celebrating the victory at Gettysburg and on the last Thursday in November. Lincoln was influenced in this decision by Sarah Josepha Hale, the influential editor of the popular women’s magazine Godey’s Lady’s Book who had been campaigning for a national Thanksgiving since 1827. Even after 1863, the national Thanksgiving was not a fixed annual event. Rather, each President still had to proclaim Thanksgiving each year, and the last Thursday in November became the customary date. In 1939, President Roosevelt decided to lengthen the Christmas shopping season by declaring Thanksgiving for the next‐to‐the‐last Thursday in November. Although controversial at the time, two 1
See, for example, https://sites.google.com/site/mizrahijonathan/home/ThanksgivingAndHanukkah See http://dir.groups.yahoo.com/neo/groups/Happy_Thanksgiving/conversations/topics/360 for arguments both for and against the proposition that Thanksgiving is based on Sukkot. 3 See http://www.plimoth.org/learn/MRL/read/thanksgiving‐history 2
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years later, in 1941, Congress permanently established the holiday as the fourth Thursday in the month. As it is now practiced, Thanksgiving cycles from year to year between the 22nd and 28th of November. Both the Lincoln proclamation in 1863 and the Roosevelt shift in 1939 turn out to be important qualifiers for those claiming that this year is unique. Lesson 2: The Origin and Structure of the Hebrew Calendar The Hebrew calendar is based on a 19‐year cycle that includes 12 regular (i.e., 12‐month years) and 7 leap years (i.e., 13‐month years). In the times of the Temple in Jerusalem, the Sanhedrin would determine the beginning of each month based on witnesses’ testimony as described in the Talmud. The transition to a fixed calendar is often attributed to Rabbi Hillel II during the fourth century of the Common Era. However, some modern historians argue that the fixed calendar evolved over several centuries probably culminating in the eighth Century.4 Nonetheless, Hillel II may have established the pattern for leap years shown in the table below. Table 1: Number of Months in Each Year of the 19‐Year Cycle 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19
1 Year Months 12 12 13 12 12 13 12 13 12 12 13 12 12 13 12 12 13 12 13 The Hebrew calendar is similar to the calendar developed by the Greek astronomer Meton in the 5th century BCE, which in turn may have been based on the work of earlier Babylonian astronomers. The Rambam speculates that the Hebrew calendar may have been developed independently by the Tribe of Issachar, the tribe of the scholars, but the book describing the Hebrew calendar has been lost.5 Like the Metonic cycle, the Hebrew calendar lasts 19 years and includes 235 months per cycle. But, the Hebrew calendar is a religious concept; it makes adjustments not included in the Metonic cycle to account for religious needs. As a result, the Hebrew calendar has a mechanism to postpone (or dehiyyah) the start of Rosh Hashanah under a set of circumstances. Specifically, Rosh Hashanah is postponed so that it does not begin on three days of the week, Sunday, Wednesday and Friday. Using Hebrew letters to represent the days of the week, this constraint is known as אדו לא (transliterated to Lo ADU or not ADU). The א represents Sunday. If the year begins on a Sunday, the sixth day of Sukkos, known as Hoshanah Rabbah, would fall on the Sabbath. One of the observances on Hoshanah Rabbah is to beat the willow branch (aravot) from lulav on the ground. A problem arises because this beating violates one of the prohibitions of the Sabbath and so it must be avoided. The ד 4
See http://en.wikipedia.org/wiki/Hillel_II. Yes, this citation is from Wikapedia, but this entry is based on a citation of a book by Sacha Stern entitled Calendar and Community published by Oxford University Press in 2001 5 Solomon Gandz, Julian Obermann, and Otto Neugebauer, The Code of Maimonides, Book Three Treatise Eight Sanctification of the New Moon, Yale University Press, New Haven, 1956, page 73. This idea of the role of the tribe of Issachar likely comes from a verse 3318 in Devarim, “Of Zebulun he said: Rejoice O Zebulun, in your excursions and Issachar in your tents.” The Rabbinic interpretation of this verse is that these two tribes were partners with Zebulun conducting business and earning money to support the scholarship of Issachar.
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represents Wednesday. If the year began on Wednesday, Yom Kippur would fall on Friday and there would be no time to prepare for the Sabbath. The ו represents Friday and is the converse of the previous case. If the year begins on Friday, Yom Kippur would fall on Sunday and preparations for Yom Kippur would have to take place on the Sabbath, also a prohibition. Because of the leap years and the אדו postponements, the Hebrew year can take on six different lengths. In non‐leap years, the year can be 353, 354 or 355 days, and the leap years can be 383, 384, 385 days. Table 2 shows the length of each month in each one of these six configurations. The basic pattern is alternating months of 30 and 29 days as shown in a 354 day year. The difference between the leap years and the non‐leap years is the 30 day month of Adar ()א (which is inserted between the months of Shevat and the normal month of Adar). The other changes that can occur are adjustments in the number of days in the months of Cheshvan and Kislev. In a 353 or 383 day year, the month of Kislev is shortened to 29 days. In a 355 or 385 day year, the month of Cheshvan is lengthened to 30 days. The changes in the basic pattern are shown in the shaded boxes in the table. Table 2: Days in Each Month by Days in a Year Month 353 354 355 383 384 385 Tishrei 30 30 30 30 30 30 Cheshvan 29 29 30 29 29 30 Kislev 29 30 30 29 30 30 Tevet 29 29 29 29 29 29 Shevat 30 30 30 30 30 30 Adar ()א 30 30 30 Adar ()ב 29 29 29 29 29 29 Nisan 30 30 30 30 30 30 Iyar 29 29 29 29 29 29 Sivan 30 30 30 30 30 30 Tammuz 29 29 29 29 29 29 Ab 30 30 30 30 30 30 Elul 29 29 29 29 29 29 The constraints on the first day of Rosh Hashanah imply that there are also constraints on the day of the week the Chanukah begins. From the first day of Rosh Hashanah to the first day of Chanukah is 84 or 85 days depending on whether Cheshvan has 29 or 30 days. If the gap between Rosh Hashanah and Chanukah is 84 days (that is 12 full weeks), Chanukah starts on the day of the week before Rosh Hashanah. In this case, one might suppose that Chanukah could start on Sunday, Monday, Wednesday and Friday. If Cheshvan is 30 days it falls on the same day of the week as Rosh Hashanah
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so in this case Chanukah could fall on a Monday, Tuesday, Thursday and Saturday. It appears that Chanukah could fall on any day of the week. Lesson 3: Not All Combinations of Year Length and Start Dates are Possible However, there is a further constraint on the Hebrew calendar. There are only a limited number of combinations (14) of year start dates and year lengths, known as keviyyot. These keviyyot exist because the end of each year must ensure that the next year does not fall on one of the אדו days. Thus, a regular year that begins on a Monday can be 353 or 355 days because the following year would begin on a Thursday or Saturday respectively. But, if the year had 354 days, the following year would begin on Friday violating the אדו constraint. Table 3 shows the allowable and unallowable combinations of first day of Rosh Hashanah and days in the year. The unallowable combinations are shaded. In 13 of the 14 cases, the shaded cells contain one of the ADU day. The explanation for the shading of a 385 day starting on Tuesday is not at all straightforward and is not particularly relevant for the current discussion (see Appendix B). Table 3: The Keviyyot of the Hebrew Calendar
Length of Year in Days
1st Day of Rosh Hashanah
Mon
Tue
Thu
Sat
353 354 355 383 384 385
Thu Fri Sat Sat Sun Mon
Fri Sat Sun
Sun Mon Tue
Sun Mon Tue*
Tue Wed Thu
Tue Wed Thu Thu Fri Sat
So are there any days of the week that Chanukah cannot begin on? The answer is Tuesday. A year, whether regular or leap, beginning on Tuesday does not include a 30th of Cheshvan. In a regular year, a Tuesday Rosh Hashanah must be 354 days, which means the following year begins on Saturday. In a leap year, a Tuesday Rosh Hashanah will be 384 days, which will start the following year on Monday. So in any year beginning on Tuesday, Chanukah will fall on Monday. One conclusion from this analysis is that Chanukah can begin on a Thursday. So we have demonstrated that the relationship between Chanukah and Thanksgiving in terms of the day of the week, but what about the 4th Thursday in November. Although there is a fixed pattern of leap years, the length of any given year or the pattern from cycle to cycle of when a day falls on the Hebrew calendar and the secular calendar is not fixed. 4
Lesson 4: Not all 19‐year cycles have the same number of days The table below illustrates one of the sources of variation in the 19‐year cycle that in turn makes the intersection of Chanukah and Thanksgiving less common. Although the place of the regular years and leap years is the same in every cycle, the number of days in each year varies from one cycle to the next. The table below illustrates this point by comparing the current cycle (i.e., 5758 to 5776) to the next (i.e., 5777 to 5795). The table shows the day of the week of the first day of Rosh Hashanah and the number (#) of days in the year. This year, 5774, is the 17th year of the current cycle. Rosh Hashanah is on Thursday in both this year and next. Since the 17th year of the cycle is a leap year, the number of days in the year (from Thursday to Thursday) must be 385 days. There are two important things to notice in this table. First the length of the year is different between this cycle and next in all but four of the 19 years. Sometimes the current cycle’s year is longer and something the next cycle’s year is longer. Second, the imbalances are not equal. The current cycle is one day longer than the next cycle. Table A: Day of the Week for the First Day of Rosh Hashanah and Number of Days in the Year: 5758 to 5776 and 5777 to 5795 Cycle First # of First # of Year Day Days Day Days Difference 1 Thu 354 Mon 353 1 2 Mon 355 Thu 354 1 3 Sat 385 Mon 385 0 4 Sat 353 Mon 355 ‐2 5 Tue 354 Sat 353 1 6 Sat 385 Tue 384 1 7 Sat 355 Mon 355 0 8 Thu 383 Sat 383 0 9 Tue 354 Thu 355 ‐1 10 Sat 355 Tue 354 1 11 Thu 383 Sat 385 ‐2 12 Tue 354 Sat 355 ‐1 13 Sat 355 Thu 354 1 14 Thu 385 Mon 383 2 15 Thu 354 Sat 355 ‐1 16 Mon 353 Thu 354 ‐1 17 Thu 385 Mon 383 2 18 Thu 354 Sat 355 ‐1 19 Mon 385 Thu 385 0 Total Days 6941 6940 1
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In this table we have demonstrated that not all cycles are identical either the day of the week each year starts and the total number of days in the cycle (even though all cycles have 235 months.) Lesson 5: Leap Years Start Early Across the 19‐year cycle of the Hebrew calendar, some things stay the same and some things vary. The foundation of the 19‐year cycle is the fixed pattern of leap years, which always occur in years 3, 6, 8, 11, 14, 17 and 19. As noted above, in each of these leap years, a 30‐day month is inserted between Shevat and Adar. This pattern of leap years has implications for the timing of the start of each year relative to the secular calendar. Some years fall earlier on the secular calendar than others. The yearly pattern is illustrated in the figure below using the first day of Chanukah (Kislev 25) as the marker. The figure plots the first day of Chanukah for the current cycle, which started in 1997 and the next cycle which will start in 2016. There are several things worth noting about the pattern. First, the pattern over the two cycles though similar is not identical. Each 19‐year cycle is different from the next even though the leap years fall in the same sequence. Second, the local trough of each cycle occurs in a leap year—that is, Chanukah starts earlier in leap years than in the non‐leap years on either side of it. This finding is a little counter‐intuitive because leap years have more days than non‐ leap years. But, recall that the extra days for leap years are inserted after Chanukah. Finally, the 17th year is the earliest in the full cycle.
Figure 1: Kislev 25 by Year in the 19‐Year Cycle 29‐Dec 26‐Dec 23‐Dec 20‐Dec 17‐Dec Leap Year
14‐Dec
Current cycle 11‐Dec
Next cycle
8‐Dec 5‐Dec 2‐Dec 29‐Nov 26‐Nov 1
2
3
4
5
6
7
8
9
10 11 12 13 14 15 16 17 18 19
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The year 5774 is the 17th year of the current cycle and that’s why it is the earliest Chanukah in recent memory. The appendix provides a more detailed illustration and explanation of the relative start dates of each year in the cycle based on the principle of the dominance of recent months. Lesson 6: Chanukah has fallen on a Thursday in November before, but… The intersection of Chanukah and Thanksgiving actually depends on the overlap of two cycles. The figure below illustrates this point. The red line in the figure below shows the same cyclical pattern as above. The blue line shows the cyclical pattern of Thanksgiving. Between 1990 and 2021, Thanksgiving falls on November 28th five times and Chanukah begins on November 28th in both 1994 and 2013. But, these cycles only overlap in 2013 because in 1994 Thanksgiving falls on November 24th. 1‐Jan
Figure 2: The Chanukah and Thanksgiving Cycles
22‐Dec
12‐Dec
2‐Dec
22‐Nov
12‐Nov
Thanksgiving Day
Chanukah 1st Day
1990 1991 1992 1993 1994 1995 1996 1997 1998 1999 2000 2001 2002 2003 2004 2005 2006 2007 2008 2009 2010 2011 2012 2013 2014 2015 2016 2017 2018 2019 2020 2021
2‐Nov
The table below shows the first day of Chanukah in the 17th year of the calendar cycle starting in 5527 (1766 on the secular calendar) to 5983 (2222). The starting point is shortly after the adoption by most colonies of the Gregorian calendar, which is the secular calendar we use today. The end point is the last 17th year before the Hebrew year of 6000 by which time we are expecting the Messiah to fix our calendar problems as well as a few other things. In years in which Chanukah falls on November 29th 7
or later, the lines are greyed out because Chanukah would fall on the 5th Thursday in November, which will be the week after the current celebration of Thanksgiving. Table 4: The First Day of Chanukah on the Secular Calendar in Select Years Secular Hebrew Day of Year Month Day Year Week 5983 Nov 30 2222 * 5964 Dec 1 2203 * 5945 Nov 29 2184 * 5926 Nov 29 2165 * 5907 Nov 28 2146 Mon 5888 Nov 30 2127 * 5869 Nov 29 2108 * 5850 Nov 28 2089 Mon 5831 Nov 28 2070 Fri 5812 Nov 28 2051 Tue 5793 Nov 29 2032 * 5774 Nov 28 2013 Thu 5755 Nov 28 1994 Mon 5736 Nov 28 1975 Fri 5717 Nov 29 1956 Thu* 5698 Nov 29 1937 Mon 5679 Nov 29 1918 Fri 5660 Nov 29 1899 Wed 5641 Nov 27 1880 Sat 5622 Nov 28 1861 Thu 5603 Nov 28 1842 Mon 5584 Nov 28 1823 Fri 5565 Nov 28 1804 Wed 5546 Nov 27 1785 Sun 5527 Nov 27 1766 Thu * but, Thanksgiving falls a week earlier Notice that the table demonstrates a phenomenon known as calendar drift. Starting in the middle of the next century, the first day of Chanukah will always fall after the 4th Thursday in November and in the cycle including 5964, the earliest Chanukah will not come until December. Calendar drift is the tendency for the Hebrew calendar to shift to later in the secular calendar year. Calendar drift occurs because the average length of a Hebrew year is longer than the average length of a secular year. On average, the Hebrew calendar is drifting four days relative to the secular calendar per millennia.
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The final column of the table shows the day of the week that Chanukah starts in each of these years. Over the approximately 450‐year6 period, the first day of Chanukah fell on a Thursday three times. Two of those instances (1766 and 1861) occurred prior to President Lincoln’s declaration of a national Thanksgiving holiday. Lesson 7: We need to look beyond the 17th year of the cycle Although the 17th year is the earliest year of the cycle, as Figure 1 shows the 6th year is generally only one day behind. Before concluding that 2013 is the only time in history that the national holiday of Thanksgiving interests with the beginning of Chanukah, we should check year 6s. Table 5 is the same as Table 4 except for the 6th years in the Hebrew calendar cycle. In the secular year of 1888, Chanukah starts on the November 29th, the last Thursday of November. After 1888 and into the future, Chanukah starts too late to fall on Thanksgiving. Before President Roosevelt changed the day of Thanksgiving, Chanukah started in December, and subsequent to that change Chanukah never again will start on or before the 28th of November or earlier. Table 5: The First Day of Chanukah on the Secular Calendar in the 6th Year of the Cycle Secular Hebrew Day of Year Month Day Year Week 5706 Nov 30 1945 * 5687 Dec 1 1926 5668 Dec 1 1907 5649 Nov 29 1888 Thu 5630 Nov 30 1869 Tue 5611 Nov 30 1850 Sat 5592 Nov 29 1831 Wed 5573 Nov 29 1812 Sun 5554 Nov 28 1793 Fri 5535 Nov 28 1774 Mon 5516 Nov 29 1755 Sat * Thanksgiving fell a week earlier So, the statement that this year is unique in history has now acquired two limitations. First, the national holiday of Thanksgiving, and second the 17th year of the calendar cycle. 6
The table starts with 1766 because that year roughly corresponds to the adoption of the Gregorian calendar in the British colonies in America. Colonies controlled by Spain and France adopted the Gregorian calendar in different years. See http://www.webexhibits.org/calendars/year‐countries.html.
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Lesson 8: Doesn’t the Jewish day start at sunset Chanukah this year will begin on Wednesday evening November 26th but Thanksgiving isn’t until Thursday November 27th so the whole analysis has been based on a false starting point because this year we will like two Chanukah candles on Thanksgiving. However, the calendar lessons described in this paper does allow us to consider a true intersection between Chanukah and Thanksgiving—that is, one in which Chanukah begins on a Thursday evening. We have learned that there are 84 days between the first day of Rosh Hashanah and the first day of Chanukah except in years in which we insert a 30th day of Cheshvan. In years with Rosh Hashanah starting on Saturday without a Cheshvan 30, Chanukah will begin on a Friday or more precisely on Thursday evening. According to our keviyyot table, a leap year can start on a Saturday and include 383 days, which would mean no Cheshvan 30. The rest of our analysis shows that such a leap year would have to occur in the 17th year of the cycle, which is the earliest start for a year in each cycle. This real intersection of Chanukah and Thanksgiving has occurred several times in history, in the years 1823 and 1975 and it will occur again in 2070. In 1918, the first day of Chanukah (Friday November 29th) fell on Thanksgiving because President Roosevelt did not change the day from the last to the fourth Thursday in November until 1941. Some Final Thoughts The intersection of Chanukah and Thanksgiving is a rare enough phenomenon as to draw the attention of the general (Jewish) population to questions about the calendar. Although this paper reviews the facts of this intersection in the past, present and future, my goal is to introduce causal observers to some of the underlying mechanisms that have created this intersection. In other words, not what is happening but why? This paper represents only a small beginning to the opportunity for much more detailed study. I leave it to the reader to seize this opportunity.
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Appendix A Why some years start earlier: The recency principle Although the starting date on the secular pattern for each year of the 19‐year cycle can vary from cycle to cycle, the order of the start dates does not generally change. The 17th year of the cycle is always the earliest, and the 9th year is always the latest. Because of slight variations in the number of days in each cycle, occasionally two years within a cycle will start on the same secular calendar date. However, the order of the starting dates (from earliest to latest) is determined by the pattern of the regular and leap years. The purpose of this section is to provide some insights into both the pattern and the causes of the pattern, which we call the recency principle. During a regular year, the Hebrew calendar loses about 11 days to the secular calendar, and in a leap year, the Hebrew calendar gains about 19 days on the secular calendar. As a result, when a Hebrew year is preceded by two regular years, it will tend to fall earlier in the secular year than one that is preceded by a leap year. As we showed in the Figure 1 in the main text, leap years tend to start earlier than regular years because leap years are always preceded by a regular year. Recall that the leap month (Adar )א that generates the relative movement forward of the Hebrew calendar always falls in the late winter so leap years affect the start of the next year and not the leap year itself. So why is the 17th year of the cycle the earliest? Prior to the 17th year, four out of five most recent years are regular and stretching back even further six of eight most recent years are regular. The heavy concentration of regular years pushes the start of the 17th year earlier in the secular year. The 6th year, which is the next earliest, is preceded by four out of five regular years, but only five out of eight regular years. The table below illustrates the difference between Years 17 and 6 of the cycle in terms of the preceding years. The only differences between these two years in the cycle occur eight and nine years prior to the year of the cycle. In Year 17 the eighth preceding year is 12 months and the ninth preceding year is 13 months. In Year 6 this order is reversed. The result of this small difference is that Year 17 starts one day earlier in the secular year than Year 6.
Yr Length of Preceding Years in Order 17 12 12 13 12 12 13 12 12 13 12 13 12 12 13 12 12 13 12 13 6 12 12 13 12 12 13 12 13 12 12 13 12 12 13 12 12 13 12 13 9 13 12 13 12 12 13 12 12 13 12 13 12 12 13 12 12 13 12 12
In contrast the 9th year, the latest in the cycle is preceded by three of six leap years. The table below shows a retrospective view of the most recent years in each of the 19 years in the cycle. The first column shows the number of months in the preceding year. The second column shows the sum of the months in the prior two years and the third column shows the prior three years, and 11
so on. As an example, year 1 in the cycle is preceded by year 19 of the previous cycle when there were 13 months in the year. Two years prior to year 1 (year 18 in the previous cycle) was a regular year of 12 months so the total of the two preceding years is 25 (13+12). Three years prior (i.e., year 17 of the previous cycle) was a leap year thereby increasing the total to 38 (13+12+13). The cumulative total for each year of the cycle is 235, but the path from the start is different for each year. In each column of the table (shown at the bottom of the table), there is one of two numbers (i.e., 12 or 13 in the first column and 24 or 25 in the second column). In each column, some of the cells are shaded and some are not. The shading in a cell means that the number in the cell is the lower of the two numbers in that column. For example in the fifth column, the numbers are 61 or 62. The cells with 61 are shaded and the cells with 62 are not. The final column of the table shows the total number of shaded cells in each row. For example, the row for year 5 has 11 shaded cells and the row for year 12 has 3 shaded cells. This final column shows the order of the start of the year from the latest (year 9) to the earliest (year 17).
Year 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19
Table A1: Determining the order of the start of year for each year of the 19‐year cycle Cumulative months prior to current year Order 13 25 38 50 62 75 87 99 112 124 136 149 161 174 186 198 211 223 235 2 12 25 37 50 62 74 87 99 111 124 136 148 161 173 186 198 210 223 235 9 12 24 37 49 62 74 86 99 111 123 136 148 160 173 185 198 210 222 235 16 13 25 37 50 62 75 87 99 112 124 136 149 161 173 186 198 211 223 235 4 12 25 37 49 62 74 87 99 111 124 136 148 161 173 185 198 210 223 235 11 12 24 37 49 61 74 86 99 111 123 136 148 160 173 185 197 210 222 235 18 13 25 37 50 62 74 87 99 112 124 136 149 161 173 186 198 210 223 235 6 12 25 37 49 62 74 86 99 111 124 136 148 161 173 185 198 210 222 235 13 13 25 38 50 62 75 87 99 112 124 137 149 161 174 186 198 211 223 235 1 12 25 37 50 62 74 87 99 111 124 136 149 161 173 186 198 210 223 235 8 12 24 37 49 62 74 86 99 111 123 136 148 161 173 185 198 210 222 235 15 13 25 37 50 62 75 87 99 112 124 136 149 161 174 186 198 211 223 235 3 12 25 37 49 62 74 87 99 111 124 136 148 161 173 186 198 210 223 235 10 12 24 37 49 61 74 86 99 111 123 136 148 160 173 185 198 210 222 235 17 13 25 37 50 62 74 87 99 112 124 136 149 161 173 186 198 211 223 235 5 12 25 37 49 62 74 86 99 111 124 136 148 161 173 185 198 210 223 235 12 12 24 37 49 61 74 86 98 111 123 136 148 160 173 185 197 210 222 235 19 13 25 37 50 62 74 87 99 111 124 136 149 161 173 186 198 210 223 235 7 12 25 37 49 62 74 86 99 111 123 136 148 161 173 185 198 210 222 235 14 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 Column Number
This table illustrates the order of the years but does not explain why. Although the count of months for each year of the 19‐year cycle starts at 0 and ends at 235, each year follows a slightly different path. In year 17, the cumulative count starts off relatively slowly because of the high concentration of 12
regular years just preceding that year, but in the more distant years (i.e., later in the count) the pace of the count picks up because of the relatively high concentration of leap years. During the period of the slow start, the Hebrew calendar is moving earlier on the secular calendar. The pattern for year 9 is just the reverse—that is, a fast start and a slow ending. The figure below illustrates the recency principle by showing the average cumulative months for each row in the table above. Even though all rows start at zero and end at 235 the averages are not the same. Because the number of the first column is included in the cumulative total of each subsequent column, any row that starts with a 12 will have a lower average than any row that starts with a 13. Then any row with a 24 in the second column will have a lower average than any row with a 25 in the second column. In other words, the years just proceeding a particular year has a stronger influence on the start of the year relative to the secular calendar than the years just succeeding that year.
Figure B1: Average Number of Months in Each Year of the 19‐Year Cycle 124.4
124.2
124.0
123.8
123.6
123.4
123.2
123.0 1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
Month in the 19‐Year Cycle
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Appendix B What is the molad, why does it matter, and another interesting fact The molad is the Hebrew term for the birth of the new moon. The Rabbis estimated that the time between new moons is 29 days 12 hours 44 minutes and about 3.33 seconds. Actually the Rabbis divided an hour into 1080 parts or chalakim. In terms of chalakim the molad occurs every 29 days 12 hours and 793 chalkim. In most shuls, the Gabbai announces the time of the coming molad on the Shabbas before Rosh Hodesh. The molad has two functions. The molad for Tishrei determines whether there is a postponement of Rosh Hashanah. If molad falls before halachic mid‐day7 on a lo‐ADU day, Rosh Hashanah starts on that day. If it falls after mid‐day, Rosh Hashanah is postponed until the next allowable day. The molad also determines when the start of the period for reciting the Kiddish Levanah prayer. Kiddish Levanah is generally recited after the Sabbath at least 72 hours after the molad.8 We can use the timing of the molad to explain why a leap year on Tuesday cannot be 385 days. The elapsed time of 13 moladim is 383 days, 21 hours and 589 chalakim.9 If the first Rosh Hashanah is on Tuesday, the molad must have fallen mid‐day or earlier. If it occurs exactly at mid‐day, the next molad of Tishrei has to fall about 2 hours before mid‐day on a Monday the following year. In this case, the following Rosh Hashanah would fall on Monday, 384 days later. In order for the molad of Tishrei in the second year to fall after mid‐day on Monday, the previous molad Tishrei would have occurred after mid‐day on Tuesday. In this case, Rosh Hashanah would have been delayed until Thursday. Thus, a leap year starting on a Tuesday cannot be 385 days. A common misconception about the molad is that it determines the start of each month. Actually, the molad does not necessarily fall on Rosh Hodesh or even the day before Rosh Hodesh. As noted above, the molad occurs every 29 days 12 hours and 793 parts or approximately 12 ¾ hours. In a 29‐day month, the molad falls about 12 ¾ hours into the next month. In a 30‐day month, the molad falls about 11 ¼ hours short of the full month. In this year of 5774, there will be five 25‐day months and eight 30‐day months. Cumulatively, the sum of the 13 molad cycles will be approximately 33 ¾ hours shorter than the months so the molad will fall more than a day short of 13 full months. During the year the gap between the cumulative months and the cumulative moladim will be even larger. From the beginning of the year through Adar ()א, four of the five10 months will be 30 days and only one 7
Halachic mid‐day is the midpoint between sunrise and sunset. If, for example, the sun rises at 7 AM and sets at 6 PM, mid‐day would be at 12:30 PM. 8 In many congregations, Kiddish Levanah is delayed in Tishrei and Ab until after Yom Kippur and Tisha B’Ab respectively. 9 12 moladim span 354 days 8 hours and 876 parts. 10 The number of Rosh Hodeshes is five instead of six because Tishrei is different from other Rosh Hodeshes. Rosh Hodesh Tishrei starts on the 1st of Tishrei and lasts two. In all other cases of a 30 day month, the 1st day of Rosh Hodesh falls on the 30th day of the previous month.
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month will be 29 days. Over this period, the cumulative months will be 33 hours longer than the moladim. Table B‐1 illustrates the difference in the molad and the start of Rosh Hodesh for the Year 5774 (i.e., the current year). The molad for Tishri falls in the morning of Thursday September 5th, but the beginning of Rosh Hodesh is at sundown on Wednesday September 4th (i.e., the same day on the Hebrew calendar. Table B‐1: The Gap Between the Molad and the Start of Rosh Hodesh Month Molad Days/ Approx. Start of Rosh Gap in Month Hodesh Hours Tishrei 9/5/13 10:46 AM 30 9/4/13 6:00 PM 16.8 Cheshvan 10/4/13 11:30 PM 30 10/4/13 6:00 PM 5.5 Kislev 11/3/13 12:15 PM 30 11/3/13 6:00 PM ‐5.7 Tevet 12/3/13 1:00 AM 29 12/2/13 6:00 PM 7.0 Shevat 1/1/14 1:44 PM 30 1/1/14 6:00 PM ‐4.3 Adar א 1/31/14 2:29 AM 30 1/31/14 6:00 PM ‐15.5 Adar ב 3/1/14 3:13 PM 29 3/1/14 6:00 PM ‐2.8 Nisan 3/31/14 3:58 AM 30 3/31/14 6:00 PM ‐14.0 Iyar 4/29/14 4:43 PM 29 4/29/14 6:00 PM ‐1.3 Sivan 5/29/14 5:27 AM 30 5/29/14 6:00 PM ‐12.5 Tammuz 6/27/14 6:12 PM 29 6/27/14 6:00 PM 0.2 Ab 7/27/14 6:57 AM 30 7/27/14 6:00 PM ‐11.0 Elul 8/25/14 7:41 PM 29 8/25/14 6:00 PM 1.7 Since Cheshvan is a 30‐day month this year, Rosh Hodesh is on Saturday October 4th. The molad for Cheshvan is at 11:30 PM on the same day so the gap has fallen from about 16.8 hours to 5.5 hours. By Rosh Hodesh Kislev, another‐30 day month this year, the molad occurs before the start of Rosh Hodesh by about 5.7 hours. Tevet, the next month is only 29 days, so period between Rosh Hodeshes is shorter by about 12 ¾ hours than the period between moladim. In this case, the molad Shevat once again falls on Rosh Hodesh. The next two months are both 30 days, so in total the molad occurs about a day sooner relative to Rosh Hodesh Shevat or by about 15 ½ hours before Rosh Hodesh Adar ב. This month represents the peak difference between the molad and Rosh Hodesh. The rest of the year alternatives between 29‐ and 30‐day months and so the gap between the molad and Rosh Hodesh tends to narrow. If Rosh Hodesh Tishrei had fallen closer to sundown on September 4th the gap between the molad and Rosh Hodesh would have grown to over a day. The figure below shows a notional representation of the diversion between Rosh Hodesh and the molad in this case. Figure B‐1: A notional 385 day year Months Molad
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The molads advancing at a steady pace reach 13 full cycles faster than the cycle of Rosh Hodeshes because of the preponderance of 30 day months. Another factor than can cause a separation between the molad and Rosh Hodesh is the postponement of Rosh Hashanah. For example, in the year 5768, the molad for Tishrei took place on Wednesday at 4:26 AM of 20 plus hours before the beginning of Rosh Hashanah. That year also started on Thursday but it was only 383 days long, which means that both Cheshvan and Kislev were only 29 days. Nonetheless, the molad for Kislev fell on Shabbos at 5:54 AM and two chalokim still a day and a half before the start of Rosh Hodesh on Sunday evening. A 385‐day year represents one end of the spectrum in terms of the molad and Rosh Hodesh. The other end of the spectrum is a 353‐day year represents the other end of the spectrum. In such a year, there are seven 29‐months and five 30‐day months, so the Rosh Hodeshes are occurring relatively faster than the moladim. In this case, the molad can fall later and later during the day of Rosh Hodesh and in some rare cases can even fall after Rosh Hodesh. The figure below shows a notional representation of this case.
Figure B‐2: A notional 353 day year Months Molad
The molads advancing at a steady pace take a longer time to complete the 12 months than the cycle of Rosh Hodeshes.
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