Babylonian, Jewish, Muslim, Luni-Solar, Indian, Iranian Calendars

The Months of the Babylonian Calendar

1. Nisannu 30 7. Tashritu 30

2. Aiyaru 29 8. Arakhsamna 29

3. Simannu 30 9. Kislimu 30

4. Du'uzu 29 10. D.abitu 29

5. Abu 30 11. Sabad.u 30

6. Ululu I 29 12. Addaru I 29

6. Ululu II 29 12. Addaru II 30

The Babylonian Calendar

after R.A. Parker & W.H. Dubberstein, Babylonian Chronology[Providence, Rhode Island, 1956]

The beginning of the month in the Babylonian calendar was determined by the direct observation by priests of the young crescent moon at sunset after theastronomical New Moon. This custom is remembered in Judaism and Islâm with the principle that the new calendar day begins at sunset. In Islâm, monthswhose commencement is of religious significance, like the month after the Fast of Ramadân, still depend on the actual observation of the crescent moon by a

respected religious authority. If weather prevented the observation of the crescent, the Babylonianswould begin the new month anyway after 30 days. In the Jewish and Islâmic calendars, eachmonth is given a conventional length, alternating 30 days and 29 days. For convenience, the tableat left applies that device for the Babylonian months, which will enable us to construct a workingmodel of the Babylonian calendar without the priests of Marduk.

With the actual observation of the crescent by the Babylonians, eventually a pattern emerged, andthis began to suggest a cycle. This was the 19 Year Cycle, discussed below. The cycle settleddown into its classic form in the 19 year period beginning in 424 BC [R.A. Parker & W.H.Dubberstein, Babylonian Chronology, Providence, R.I., 1956]. A fairly complete record ofintercalations is available from about 623. The distribution of intercalary months is evident fromabout 500, while the 424 cycle is noteworthy in that a second Ululu becomes standard in the 17th

year. As it happens, the 17th year is the one in which Nisannu occurs the earliest.

The Babylonian New Year was,astronomically, the first New Moon (actuallythe first visible crescent) after the Vernal

Equinox. Modern dates on the Gregorian calendar for the Babylonian New Year may be chosen fromthe following table. In this table, the "uncorrected" dates use the 19 year lunar cycle, just as it wasestablished in the 5th century BC, continued straight down to the present. The earliest New Year ismarked with "<" and the latest with ">." Note that in the "uncorrected early" column the earliest date isonly 3/31 and the latest is all the way to 4/28. The 19 year cycle adjusts lunar months to the solar year;

Babylonian, Jewish, Muslim, Luni-Solar, Indian, Iranian Calendars http://www.friesian.com/calendar.htm

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Uncorrected Corrected

AD/AN AD/AN early: late: early: late:

1990/2737 2009/2756 01- 4/26 01- 4/27 01* 3/27 01* 3/28

1991/2738 2010/2757 02- 4/15 02- 4/16 02- 4/15 02- 4/16

1992/2739 2011/2758 03* 4/4 03* 4/5 03- 4/4 03- 4/5

1993/2740 2012/2759 04- 4/23 04- 4/24 04* 3/24 04* 3/25

1994/2741 2013/2760 05- 4/12 05- 4/13 05- 4/12 05- 4/13

1995/2742 2014/2761 06* 4/1 06* 4/2 06- 4/1 06- 4/2

1996/2743 2015/2762 07- 4/20 07- 4/21 07* 3/21 07* 3/22

1997/2744 2016/2763 08* 4/9 08* 4/10 08- 4/9 08- 4/10

1998/2745 2017/2764 09- 4/28> 09- 4/29> 09* 3/29 09* 3/30

1999/2746 2018/2765 10- 4/17 10- 4/18 10- 4/17> 10- 4/18>

2000/2747 2019/2766 11* 4/6 11* 4/7 11- 4/6 11- 4/7

2001/2748 2020/2767 12- 4/25 12- 4/26 12* 3/26 12* 3/27

2002/2749 2021/2768 13- 4/14 13- 4/15 13- 4/14 13- 4/15

2003/2750 2022/2769 14* 4/3 14* 4/4 14- 4/3 14- 4/4

but if the Babylonian New Year was supposed to be the first New Moon after the Vernal Equinox, thenthe system has been running slow and the cycle is much in need of correction. There are no priests ofMarduk any more to do that. The correction, however, can be accomplished simply by delaying everysingle intercalation a whole year. Hence the "corrected" columns, where earliest and latest dates are3/20 & 4/17 (or 3/21 & 4/18).

"Early" and "late" refer to the best day to see the new crescent (meaning theprevious evening of the calendar date, however, since by Babylonian reckoning, aswith the Jewish and Moslem calendars today, the day begins at sunset). This is theother problem that such a calendar must deal with, to adjust the length of the lunarmonth to whole days. This was not even attempted by the Babylonians, so thetable just provides a range (early vs. late), that we can compare with other lunarand luni-solar calendars. On the Moslem calendar the first day of the month isusually the second day after the astronomical New Moon (so that the crescent canbe observed). The "late" columns fit that pretty well. On the Jewish calendar, thefirst day of the month can be the New Moon itself, or it can be delayed as much ason the Moslem calendar. In 1992, for instance, both the Jewish and the Moslemmonths (Niisân & Shawwaal) corresponding to the Babylonian New Year happento begin on 4/4, only a day after the astronomical New Moon, so the "early" datewould be preferable for the 1992 Babylonian New Year, lest 1 Nisannu be lonelyon 4/5.

The "AN" years are the Era of Nabonassar, Anno Nabonassari, dating from thereign of the Babylonian King Nabûnâs.iru in 747 BC. Any AN year can beobtained simply by adding 747 to the year of the AD era. Note that 747 BC isequivalent to -746 AD (1 BC=0 AD). The appropriate Seleucid year (AnnoSeleucidarum), named after Seleucus I, one of Alexander the Great's generals,who obtained the eastern part of Alexander's Empire, can be calculated by adding311 to the AD era -- e.g. 1992 AD = 2739 AN = 2303 Anno Seleucidarum -- butthe Greek reckoning of 2303 begins the previous fall. The Era of Nabonassarworks excellently for the Babylonian calendar, since dividing any AN year by 19gives the year of the 19 year cycle as the remainder; e.g. 2739/19 = 144 rem 3.Although the 19 year cycle was not regularized until the 4th century, theastronomical records handed down from the Babylonian Priests Kidunnu and


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2004/2751 2023/2770 15- 4/22 15- 4/23 15* 3/23 15* 3/24

2005/2752 2024/2771 16- 4/11 16- 4/12 16- 4/11 16- 4/12

2006/2753 2025/2772 17§ 3/31< 17§ 4/1< 17- 3/31 17- 4/1

2007/2754 2026/2773 18- 4/18 18- 4/19 18§ 3/20< 18§ 3/21<

2008/2755 2027/2774 19* 4/7 19* 4/8 19- 4/7 19- 4/8

Berossos through the Greco-Roman astronomer Claudius Ptolemy begin withNabonassar. It was Ptolemy who thus formulated the Era of Nabonassar for hisastronomical reckoning. The Era was never used by the Babylonians themselves.

A further complication was that the Era of Nabonassar was only used by Ptolemyin conjunction with the Egyptian calendar, which had a year that was exactly 365days long (no leap years) and so ran fast: That "Era of Nabonassar" was already upto 2741 in 1992. The Seleucid Era was used with the Babylonian calendar, butdivision by 19 inconveniently does not work with it. The Era of Nabonassar

doesn't cover much of Mesopotamian history, but it does cover the history of the calendar that we know about; and Ptolemy's "Canon of Kings," a list ofrulers from Nabonassar to the Roman Emperor Antoninus Pius, was absolutely fundamental for ancient chronology -- as recounted in E.J. Bickerman'sChronology of the Ancient World [Cornell, 1982].

The tables above are not constructed from astronomical data (except indirectly) but are schematically determined using a trick borrowed from theconstruction of the Gregorian Easter tables: the corresponding New Moon for the following year is determined simply by subtracting 11 from the given year'sdate; e.g. a 4/26 New Year one year means that the next year it will be 4/15. In an intercalary year (marked with "*"), 30 days are added; e.g. 4/4 -11 +30 =4/23. This works out quite well, except that it comes out a day off after 19 years. The Gregorian Easter reckoning simply ignores that extra day. With theBabylonian calendar, something else is possible: once every 19 years a second month of Ululu is added as the intercalary month instead of a second Addaru.Originally that was in the 17th year (marked "§"). If Ululu II is added as 29 days instead of 30, that makes the whole cycle come out even, which is what isdone in the table. Year 17 also happens to be the one with the earliest New Year, so we could adopt the rule that the year with the earliest New Year, whichwill always be an intercalary year, is also the one with an extra Ululu instead of an extra Addaru. Hopefully, the priests of Marduk would have approved. Inthe "corrected" calendar, the year with Ululu II turns out to be year 18 anyway, which isn't very different from the traditional year.

Using Gregorian dates as above, we end up off by a day against the moon about every 235 years. Thus, as time goes on, a day must occasionally be added tothe given dates. Right now we happen to be in a bit of a cusp: the "late" tables above will become increasingly accurate and will remain so for a couple ofcenturies, longer than we now need to worry about. Or we can simply construct a complete modern system for the Babylonian calendar, as follows.

Adding 7 months every 19 years approximates the solar year with 235 lunar months. That is mathematically (bycontinued fractions) the most accurate convenient cycle for a luni-solar calendar and would give, using the mean valueof the synodic month (29.530588 days), a year of 365.2467463 days long. This may be called the "Metonic" year, afterthe Greek astronomer who described the cycle, although the Babylonians discovered it first. The mean solar (tropical)year is 365.24219878 days long. The calendar thus has two problems: (1) This is more accurate than the Julian Calendar(365.25) but less accurate than the Gregorian (365.2425) and must in the long run make provision for correction -- it isoff a day every 219 years against the sun. (2) The calendar cannot be corrected for the sun by subtracting a day every219 years or so, because this would then put it out of synchronization with the moon. A luni-solar calendar must regulate


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its lunar side with days and its solar side by its addition of months. The solar side thus must be corrected by modifyingthe 19 year cycle, most conveniently by delaying an intercalation every 342 years (18 cycles). By such delays, thecalendar would lose an entire month after 6498 years, which reduces the Metonic year to 365.2422018 days, accurate to a day in 336,700 years.

For the moon, days may be added just as days are added to the Julian, Gregorian, and Moslem calendars. The Julian pattern, a day every four years, isconveniently accurate, more accurate than in the Julian calendar itself: 365.25 days is off a day in 307 years against the Metonic year but off a day in only128 years against the solar year [note that the Gregorian year, 365.2525, is less accurate against the Metonic year, off a day in 235 years]. A Gregorian-likecorrection on the Julian year may thus be imposed against the Metonic year: skipping a day every 300 years; 365 + 1/4 - 1/300 = 365.2466666. Thatapproximates the Metonic year to within a day every 12,555 years. Quite accurate enough for the moon. With the 6498 year cycle of intercalations, 365 +1/4- 1/300 - 29/6498, this produces a solar year of 365.2422038 days. That is not quite as accurate as the pure intercalation cycle: it is now off a day in 201,005years. That is practically perfect, however; the orbits of the earth and the moon are liable to vary enough in that period of time, and the rotation of the earth toslow down enough, to render greater "accuracy" meaningless.

Babylonian Numbers and Measure

The Jewish and Moslem Calendars with the Era of Nabonassar

A Modern Luni-Solar Calendar

Philosophy of Science, Calendars

Philosophy of Science

Philosophy of History, Calendars

Philosophy of History

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The Jewish and Moslem Calendars


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JewishMonths

Christian Months in Arabic

1. Tishrii 3010.

Tishriinu l'awwaal

October

2. Xeshwân 29/3011.

Tishriinu ttaanii

November

3. Kislêw 30/2912.

Kaanuunu l'awwaalDecember

4. T.êbêt 291.

Kaanuunu ttaanii

January

5. Shebât. 302.

Shubaat.February

6. 'Adâr 293.

'AadaarMarch

6. 'Adâr Shênii 30 No intercalations

7. Niisân 304.

NiisaanApril

and the Era of Nabonassar

The Jewish calendar retains not only the Babylonian Month names (e.g. Nisan for Nisannu) butalso the Babylonian 19 year cycle. The adoption of the cycle is evidently the reform effected bythe Patriarch Hillel II in the 4th century, but the cycle as presently constituted dates from the 9thor 10th centuries, when the complete calendar system was apparently formulated. The 19 yearcycle is the only true cycle in the Jewish calendar, since the method of adding days depends onthe mean value of the synodic month and does not produce a repetition of dates within anysignificant length of time. The dates of Rô'sh Hashshânâh, however, roughly repeat after 247years (13 cycles).

The names of the Babylonian months are retained not only in the Jewish calendar (see themwritten in Hebrew below) but in the Gregorian calendar used by Christians in the Levant andIraq. The Arabic versions of these names are given in the table at right. There have been some

alterations, with three of the ancient names dropped, a new one -- , Kânûn -- introduced,

and two of the names used twice. I have not seen an explanation for these alterations. In Egyptwe see Arabic versions of the familiar names from Latin.

The Moslem calendar consists of years of 12 lunar months. A reform effected by the ProphetMuh.ammad dispenses with attempts at intercalation. The Moslem year is therefore short, only354 or 355 days, and the calendar runs fast. The Era for the calendar begins on the evening ofthe Prophet's Flight from Mecca to Medina. That occurred at the time of the first visiblecrescent of the New Moon, on the first day of the month of Muh.arram, or 16 July 622 AD(Julian reckoning). The "Flight" in Arabic is the H.ijrah, so the Era of the Moslem calendar iscalled that of the H.ijrah or, in English, the Hegira -- "AH," the Anno Hegirae.

The problem of the Moslem clalendar is then simply to add days to keep it accurate with themoon. This is accomplished with a calendar cycle that adds 11 days every 30 years -- in years 2,5, 7, 10, 13, 16, 18, 21, 24, 26, and 29. The extra day comes at the end of the calendar year,making the month of Dhuu lH.ijjah 30 days long instead of 29. There are 360 months in thecycle, and 354 days in a common year. The gives 10620 + 11 = 10631 days for the cycle, or anaverage of 29.53055556 days for the month. That will be off a day against the mean synodic


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8. 'Iyyâr 295.

'Ayyaar

May

9. Siiwân 306.

H.aziiraanJune

10. Tammuuz 297.

TammuuzJuly

11. 'Âb 308.

'AabAugust

12. 'Eluul 299.

'AyluulSeptember

The Months of the Moslem Calendar

1. alMuh.arram 30 7. Rajab 30

2. Shafar 29 8. Sha'baan 29

3. Rabii'u l'awwal 30 9. Ramad.aan 30

4. Rabii'u ttaanii 29 10. Shawwaal 29

5. Jumaadaa l'uulaa 30 11. Duu lQa'dah 30

6. Jumaadaa l'aaxirah 29 12. Duu lH.ijjah 29/30

235 m x 72

= 16920 m47x 5 x 6 x 4 x 3

x 30 yx 12 m

1410 y

month (29.530588) every 2568.5(Moslem) years, or just slightly lessaccurate for the moon than the Gregoriancalendar is for the sun (off a day in 3320years).

Since the Jewish calendar adds a monthevery two or three years, thecorrespondence between Jewish andMoslem months shifts at those times.Muh.arram of year 1 of the Hegira Eracorresponded to Abh in the Jewishcalendar. Muh.arram moves entirely

around through the seasons and returns to being Abh in 32 or 33 years. If we ask how long itwould take for the 19 year Jewish cycle and the 30 year Moslem cycle to commensurate, thisturns out to be 1368 solar (Jewish) or 1410 Moslem years. The following table shows how thesenumbers break down into prime (or small multiples of prime) factors.

The number of months in a 19 year cycle is 235, which is simply 47 times 5. 47 is then the smallest number ofMoslem 30 year cycles (360 months) that is commensurate with an integer number of 19 year cycles (72). 47 30-yearcycles is 16920 months, or 1410 Moslem years. 16920 months is 72 19-year cycles, or 1368 (72 times 19) Jewishyears. In Iran a "solar" Hegira Era is also used, so 1410 lunar Moslem years would equal 1368 solar Iranian Moslem

years (at least on the approximation of the 19 year cycle).

1368 is a number that turns out to have a curious property. 1368 years before 622 ADputs us in 747 BC, the first year of the Era of Nabonassar, which was used by ClaudiusPtolemy for his system of chronology. An interesting coincidence. The year 1 AH is thus the year 1369 AN. The fullJewish/Moslem cycle brings us from 622 AD down into our own time: 622 plus 1368 is 1990. The year 1990 thus corresponds to

1411 AH and to 2737 (1368 x 2 + 1) AN. This may be of no practical importance, but it is a curiosity of history that the Era of a Babylonian King, as used bya Greco-Roman astronomer with the Egyptian calendar, fits in with the Era of the Moslem calendar on the basis of a cycle generated by the interaction of theIslâmic calendar 30 year cycle and the Babylonian 19 year cycle as used by the Jewish calendar. Since the chronology of ancient history is based on the Eraof Nabonassar in Ptolemy's Canon of Kings anyway, it makes one wonder if the Era of Nabonassar should be used as the proper, neutral Common Erabetween the religions of Judaism, Christianity, and Islam.


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The Babylonian Calendar

The Jewish Calendar

Islâmic Dates with Julian Day Numbers


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Philosophy of Religion



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The Jewish Calendar

Information about the origin of the modern Jewish calendar is not always historically accurate. It is often said that the calendar was formulated by PatriarchHillel II in 358/359 AD/CE. However, it appears likely that the calendar reform at this point was simply to introduce the Babylonian 19 year cycle, whichmeant that lunar intercalations did not need to be announced year by year. We can estimate the date for the present full mechanism of the calendar from theamount of error that has accumulated. The benchmark for the New Moon is now accurate for a meridian in Afghanistan. If we runthings back to when it would have been accurate for a meridian through Jerusalem or Babylon, the centers of Jewish life andcalendar studies, we just get back to around the 9th or 10th centuries. As it happens, we know that there were controversies aboutthe calendar in that era. Saddiah Goan (882-942), who wrote works on the calendar, participated in a dispute about whether thePalestinian or Babylonian communities would rule on calendar issues. He represented the Babylonian community (which by thencentered more in Baghdad, where recourse was sometimes needed to rulings by the Caliph, than in Babylon), which won thedispute. It seems beyond coincidence that was the period for which the new Moon benchmark would have been accurate, and it implies a Babylonian


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247 Year Cycles

y AD y AM JD d p

-3761 0 347,610 60,095

--

933 4693 2061,714 42,900

1180 4940 2151,930 41,995

1427 5187 2242,146 41,090

1674 5434 2332,362 40,185

1921 5681 2422,578 39,280

meridian.

The following technique for analyzing the Jewish calendar is based on that of Charles Kluepfel, known from personal correspondence, with definitionsparaphrased from Arthur Spier, The Comprehensive Hebrew Calendar (Feldheim Publishers, 1986).

The date of Rô'sh Hashshânâh is determined by the occurrence of the actual mean New Moon, the , Môlâd ("birth"), associated with the first month

of the year, Tishrii. Calculated to an accuracy of 3/10 of a minute, the length of the synodic month is expressed in special units (at 18/minute or 1080/hour)called , Xalâqîm (singular , xêleq), "parts" (p). The synodic month (m) is thus 765433p long. The day is considered to begin at mean sunset

or 6 PM. Noon is therefore reckoned to occur at 18h, not 12h. The Môlâd Tishrii is calculated by an absolute counting of months from a Benchmark of 5h204p on Monday 7 October 3761 BC/BCE (the Môlâd Tishrii of year 1 Annô Mundi).

If the reckoning of days is always kept to whole weeks following an original Shabbât, the remaining excess of parts places the Môlâd Tishrii in a clearrelation to the week. In the following tables for the determination of , Rô'sh Hashshânâh (the "Head of the Year"), only the excess of parts

need be stated. However, for the determination of an absolute date in relation to other calendars, a count of whole weeks and excess parts may be made forconvenience from a 0 AM year benchmark (3762 BC or -3761 AD) of Julian Date 347,610d, with an excess of 60,095p. The four dehiyyôt orpostponements modify the way in which the Môlâd Tishrii determines Rô'sh Hashshânâh. Note that since a zero year benchmark is used, Rô'sh Hashshânâhfor the year 1 AM must be calculated with additions and subtractions just as for other years.

For absolute dates of the Jewish calendar in Julian Day Numbers, we begin with three tables. The 19 Year Cycle familiarfrom the Babylonian Calendar gives us a sum of 6937d 69,715p for 19 years. Thirteen of these cycles give us 247 years,which has a sum of 90,209d 180,535p. This is only 905 parts, or 50m 17s, short of an even 12,888 weeks, which is asclose as the calendar comes, in a reasonable length of time, to repeating itself. After 247 years, then, the sequence ofRô'sh Hashshânâh roughly repeats itself. It is convenient, therefore, to treat the calendar in 247 year segments.


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2168 5928 2512,794 38,375 247 Year Cycle

y d p

0 0 0

19 6,937 69,715

38 13,874 139,430

57 20,818 27,705

76 27,755 97,420

95 34,692 167,135

114 41,636 55,410

133 48,573 125,125

152 55,517 13,400

171 62,454 83,115

190 69,391 152,830

209 76,335 41,105

228 83,272 110,820

247 90,209 180,535

The 19 Year Cycle

y d p type

0* 0 0 L

1 378 152,869 CF

2 735 84,625 C

3* 1092 16,381 L

4 1470 169,250 CF

5 1827 101,006 C

6* 2184 32,762 L

7 2569 4,191 CB

8* 2919 117,387 L

9 3304 88,816 CF

10 3661 20,572 C

11* 4011 133,768 L

12 4396 105,197 CF

13 4753 36,953 C

14* 5103 150,149 L

w p d

2 362,880 14

1 181,440 7

The table at left lists a zero year Annô Mundi benchmark and then gives the value in days andparts for 247 year cycles going back to the period of Saddiah Goan. If we wish to calculate the

Day Number for, say 1 Tishrii 5771 AM, we begin by substracting the most recent cyclical year, 5681 AM (1921 AD), from thisyear: 5771 - 5691 = 90y. We note the days and parts for the 5681 cycle: 2422,578d 39,280p.

Next we move on to the table, at right, that breaks down the 247 year cycle. 90 years is larger than76, so we substract 76 from 90: 90 - 76 = 14y, and add the corresponding days and parts to ourprevious values: 2422,578 + 27,755 = 2450,333d and 39,280 + 97,420 = 136,700p. These numbersactually will not change so long as we are in the same 19 year cycle.

If our sum of parts ends up being larger than the number of parts in a week, we must substract181,440p from the total and add 7d to the sum of days. If the sum of parts is still larger than a week,we must repeat the procedure. However, in this case, for 5771 AM, our sum of parts is below181,440p and this procedure is unncessary.

Now we must locate ourselves within the 19 year cycle, which is displayed on the table at left. Theremainder of years above was 14y, so we are in the 14th year of the 19 year cycle. We see from thetable that this is a Leap Year (L). This of significance below. Meanwhile, we must add the days andparts for year 14 to our running sums: 2450,333d + 5103 = 2455,436d and 136,700 + 150,149 =286,849p.

In this case, our sum of parts is larger than one week but smaller than two, so wemust make the proper modifications: 2455,436 + 7 = 2455,443d and 286,849 -181,440 = 105,409p.


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15 5488 121,578 CF

16 5845 53,334 C

17* 6195 166,530 L

18 6580 137,959 CB

19* 6937 69,715 L

The First Dehiyyâh

Before d p After d p

Sunday 1 0 0

Monday 2 25,920 Monday 2

Tuesday 3 51,840 Tuesday 3 51,840

Wednesday 4 77,760 77,760

Thursday 5 103,680 Thursday 5

Friday 6 129,600 129,600

Shabbât 7 155,520 Shabbât 7

Sunday 8 181,440 181,440

Monday 9 Monday 9

The FirstDehiyyâh,Closed Up

d p

Monday 2 0

Tuesday 3 51,840

Thursday 5 77,760

Shabbât 7 129,600

Monday 9 181,440

The Second Dehiyyâh

We now have reduced the year count to zero and have the obtained values 2455,443d 105,409p for the year 5771 AM. Sincethis is for day zero of 5771 AM, we would actually need to add 1d to get the Julian Day Number for Rô'sh Hashshânâh. But itis not going to be that simple. For four reasons Rô'sh Hashshânâh can be delayed. These are the , dexiyyôt,

"postponements" (singular , dexiyyâh), and our calculation of the Day Number must be postponed until the effects of

the dehiyyôt are examined. Note in the following tables, however, that the number of the day of the week (e.g. 1 for Sunday)will be a number that we add to the total for days, as well as the day of the month (e.g. 1 for 1 Tishrii). The number of parts inour sum places us in the week of Rô'sh Hashshânâh. The number of parts in our sum is not subsequently altered.

The First Dehiyyâh

When the Môlâd Tishrii occurs on a Sunday, Wednesday, or Friday -- using the thresholds inrelation to our sum of parts -- Rô'sh Hashshânâh is postponed to the following day. This is doneto prevent Yôm Kippûr from occurring on the day before or the day after the Shabbât or HôshanâRabbâ from occurring on the Shabbât.

To construct the table, we add 25,920p (1080p x 24h) for each day; strike out disallowed daysand irrelevant thresholds. Sunday and Monday of the following week are included in this tablefor reasons that will be apparent in the second dehiyyâh.

The Second Dehiyyâh

When the Môlâd Tishrii occurs at noon (18h) or later, Rô'sh Hashshânâh is postponed to the next day -- or if this day is a Sunday, Wednesday, or Friday, to

Monday, Thursday, or the Shabbât, respectively, because of the first dehiyyâh. This is done to prevent Rô'sh Hashshânâh from occurring before the NewMoon, since the reckoning of the Môlâd is based on the mean New Moon, which may occur several hoursbefore the apparent New Moon.


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Before d p After d p

Monday 2 0 Monday 2 0

Tuesday 3 51,840 Tuesday 3 45,360

Thursday 5 77,760 Thursday 5 71,280

Shabbât 7 129,600 Shabbât 7 123,120

Monday 9 181,440 Monday 9 174,960

Common Years (C) (see below for common years following leap years)

Before Third Dehiyyâh After Third Dehiyyâh (C)

2/353/5 0 + 113,196 = 113,196 2/353/5 0 + 113,196 = 113,196

2/355/7 9,924 = 123,120 - 113,196 2/355/7 9,924 = 123,120 - 113,196

3/354/7 45,360 + 113,196 = 158,556 3/354/7 45,360 + 113,196 = 158,556

3/356/2 61,764 = 174,960 - 113,196 61,764 = 174,960 - 113,196

5/354/2 71,280 + 113,196 = 3,036 5/354/2

5/355/3 113,604 = 45,360 - 113,196 5/355/3 113,604 = 45,360 - 113,196

7/353/3 123,120 + 113,196 = 54,876 7/353/3 123,120 + 113,196 = 54,876

7/355/5 139,524 = 71,280 - 113,196 7/355/5 139,524 = 71,280 - 113,196

9/353/5 174,960 + 113,196 = 106,446 9/353/5 174,960 + 113,196 = 106,446

To construct the table, subtract 6480p (=6h) from each threshold. We now notice that the threshold for thefollowing Monday is within the range of our current week (181,440p).

Format Note

In the tables below, on the left is found a notation such as "2/353/5," wherein "2" signifies the day uponwhich the year begins, i.e. a Monday, "353" the length of the year, and "5" the day upon which thefollowing year begins, i.e. a Thursday. The equation to its right demonstrates how the length of the yearand the day upon which the following year begins are calculated. A common year (C = 12m) containsexactly 50w 113,196p, and a leap year (L = 13m) exactly 54w 152,869p. The sequence of common andleap years is shown in the table above. The excess of parts for each kind of year need only be added to the

excess of parts for the current year to determine the placement of the Môlâd Tishrii for the following year and, as a consequence and with the addition of theweeks, the length of the current year. Determining the threshold for a change in the length of years starting on the same day simply involves reckoningbackwards from the thresholds of the following years, as is shown by the use of subtraction rather than addition in the equations on the right.

The Third Dehiyyâh

When the Môlâd Tishrii of a common year falls on Tuesday, 204 parts after3 A.M. (3d 9h 204p or 61,764p) or later, Rô'sh Hashshânâh is postponed toWednesday, and, because of the first dehiyyâh, further postponed toThursday (5/354/2). This is done to eliminate a common year that is 356dlong, making for only seven kinds of common year. Drop the year 3/356/2and the irrelevant old threshold for Thursday. Now there is a singlethreshold for the change from Tuesday to Thursday for the current year andfrom Saturday to Monday for the following year.


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Leap Years (L)

Before Fourth Dehiyyâh After Fourth Dehiyyâh (L)

2/383/7 0 + 152,869 = 152,869 2/383/7 0 + 152,869 = 152,869

2/385/2 22,091 = 174,960 - 152,869 2/385/2 22,091 = 174,960 - 152,869

3/384/2 45,360 + 152,869 = 16,789 3/384/2 45,360 + 152,869 = 16,789

5/382/2 71,280 + 152,869 = 42,709 71,280 + 152,869 = 42,709

5/383/3 73,931 = 45,360 - 152,869 5/383/3

5/385/5 90,335 = 61,764 - 152,869 5/385/5 90,335 = 61,764 - 152,869

7/383/5 123,120 + 152,869 = 94,549 7/383/5 123,120 + 152,869 = 94,549

7/385/7 151,691 = 123,120 - 152,869 7/385/7 151,691 = 123,120 - 152,869

9/383/7 174,960 + 152,869 = 146,389 9/383/7 174,960 + 152,869 = 146,389

The Fourth Dehiyyâh

When, in a common year succeeding a leap year, the Môlâd Tishrii occurs

on Monday, 589 parts after 9 A.M. (2d 15h 589p or 42,709p) or later, Rô'shHashshânâh is postponed to Tuesday. This is done to eliminate a leap yearthat is 382d long , making for only seven kinds of leap year. Drop the year5/382/2 and the irrelevant old threshold for Tuesday of the following year.


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Common Years between leap years (CB)

Before Fourth Dehiyyâh (C) After Fourth Dehiyyâh (CB)

2/353/5 0 + 113,196 = 113,196 2/353/5 0 + 113,196 = 113,196

2/355/7 9,924 = 123,120 - 113,196 2/355/7 9,924 = 123,120 - 113,196

3/354/7 45,360 + 113,196 = 158,556 3/354/7 42,709 + 113,196 = 155,905

5/354/2 61,764 + 113,196 = 174,960 5/354/2 61,764 + 113,196 = 174,960

5/355/3 113,604 = 45,360 - 113,196 5/355/3 113,604 = 45,360 - 113,196

7/353/3 123,120 + 113,196 = 54,876 7/353/3 123,120 + 113,196 = 54,876

7/355/5 139,524 = 71,280 - 113,196 7/355/5 139,524 = 71,280 - 113,196

9/353/5 174,960 + 113,196 = 106,446 9/353/5 174,960 + 113,196 = 106,446

Common Years following but not between leap years (CF)

Before Fourth Dehiyyâh (C) After Fourth Dehiyyâh (CF)

2/353/5 0 + 113,196 = 113,196 2/353/5 0 + 113,196 = 113,196

2/355/7 9,924 = 123,120 - 113,196 2/355/7 9,924 = 123,120 - 113,196

3/354/7 45,360 + 113,196 = 158,556 3/354/7 42,709 + 113,196 = 155,905

5/354/2 61,764 + 113,196 = 174,960 5/354/2 61,764 + 113,196 = 174,960

5/355/3 113,604 = 45,360 - 113,196 5/355/3 113,604 = 45,360 - 113,196

7/353/3 123,120 + 113,196 = 54,876 7/353/3 123,120 + 113,196 = 54,876

7/355/5 139,524 = 71,280 - 113,196 7/355/5 130,008 = 61,764 - 113,196

9/353/5 174,960 + 113,196 = 106,446 9/353/5 174,960 + 113,196 = 106,446

Now there is a single threshold for the change from Tuesday to Thursdayfor the current year and from Monday to Tuesday for the following year.Note new following year Thursday threshold from the third dehiyyâh. Thefourth dehiyyâh results in three different tables for common years, withthe original C table holding only for common years that follow commonyears.

Note that there is a new following year Thursday threshold from the thirddehiyyâh.

This may all seem fearfully confusing. Traditionally it has been theprinciple matter of concern for the calculation of Rô'sh Hashshânâh. Here,however, the results may be simplified for our purposes.


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Results of all the Dehiyyôt

L p d d/y CF p CB p C p d d/y

0 2 383 0 0 0 2 353

22,091 2 385 9,924 9,924 9,924 2 355

45,360 3 384 42,709 42,709 45,360 3 354

71,280 5 383 61,764 61,764 61,764 5 354

90,335 5 385 113,604 113,604 113,604 5 355

123,120 7 383 123,120 123,120 123,120 7 353

151,691 7 385 130,008 139,524 139,524 7 355

174,960 9 383 174,960 174,960 174,960 9 353

JewishMonths

Common Years Leap Years

353 354 355 383 384 385

1. , Tishrii 30 0 0 0 0 0 0

2. ( ),

(Mar)Xeshwân29/30 30 30 30 30 30 30

The outcome of all the dexiyyôt can be summarized in the table at right. Recalling our sums for5771 AM, 2455,443d 105,409p. Since 5771 is a Leap year, we need only concern ourselves withthe column at left. 105,409p is larger than 90,335p but smaller than 123,120p. Therefore, wehave the type of year listed on the 90,335p row: 5771 AM is a year that begins on Thursday(5d) and is 385 days long. From the table above, we see that the following year will also begin ona Thursday -- 5/385/5. We add the day of the week to our sum of days, and 1 for the day of themonth, so the full Julian Day Number for Rô'sh Hashshânâh is 2455,443 + 5 + 1 = 2455,449d.This is 9 September 2010, reckoned, of course, from sunset of the previous day, 8 September.

The process of converting from Julian Day Numbers to Julian or Gregorian dates is examined

elsewhere. Or the Gregorian date may be read from an almanac, for instance The AstronomicalAlmanac for the Year 2010 [U.S. Government Printing Office, Washington, and Her Majesty'sStationery Office, London, 2008]. There on page B18, we find the "Julian Date" for 9 Septembergiven as "5448.5." This is the number in "myriads," i.e. four integers before the decimal, leavingout the "245" of the full count. Also, the "Julian Date" is for the day count at Midnight of 9September. The proper Julian Day Number, 2454,449d, is for the following Noon, which is thebeginning of the Julian Day, as before 1925 Noon was the beginning of the Nautical andAstronomical days.

For Common years, the process of using the table works the same way, except that we must select the appropriate column for the three different kinds ofcommon years, i.e. following or between leap years, or neither. For instance, we can examine the calculation for last year, 5770 AM. The day sum looks likethis: 2422,578 + 27,755 + 4753 = 2455,086d and 39,280 + 97,420 + 36,953 = 173,653p. 5770 AM is year 13 in the 19 year cycle, a Common (C) year. Thepart sum exceeds the threshold (139,524) for a Common year 7/355 (7/355/5, which gives us the day of the week for Rô'sh Hashshânâh of 5771). The daysum this thus 2455,086 + 7 + 1 = 2455,094d, which is Saturday, 19 September 2009.

The table at right gives us the information we need to produce Day Numbers for Jewishdates during the year after Tishrii. (Sometimes Niisân is counted as the first month of thecalendar, which is the Babylonian counting but is inconsistent with the practice of theJewish calendar.) In Tishrii itself, of course, all we need to do is add the day of themonth instead of just 1 for Rô'sh Hashshânâh. To use the table we need to know thelength of the year. The Third and Fourth Dehiyyôt limit the possible lengths of years tosix (rather than eight). We have the feature here that days are not added at the end of theyear for the leap or "excessive" years, whose last digit is 5. We also have the curiousfeature of "defective" years, who last digit is 3 and so which are a day shorter than the


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3. , Kislêw 30/29 59 59 60 59 59 60

4. , T.êbêt 29 88 89 90 88 89 90

5. , Shebât. 30 117 118 119 117 118 119

6. , 'Adâr 29 147 148 149 147 148 149

6. ,

'Adâr Shênii30 -- 177 178 179

7. , Niisân 30 176 177 178 206 207 208

8. , 'Iyyâr 29 206 207 208 236 237 238

9. , Siiwân 30 235 236 237 265 266 267

10. , Tammuuz 29 265 266 267 295 296 297

11. , 'Âb 30 294 295 296 324 325 326

12. , 'Eluul 29 324 325 326 354 355 356

common or "regular" years of 354 and 384 days. For "excessive" years, the month ofXeshwân, which is ordinarily 29 days long, contains insetad 30 days. For "defective"years, the month of Kislêw, which is ordinarily 30 days long, is cut down to 29 days.

For 5771 AM, what we do then is the addition 2455,443 + 5 + [month of 385d year] +[day of month] = [Julian Day Number].

Lost in all our calcuations may be a characteristic of the Annô Mundi date. If we dividethe Annô Mundi year by 19, the remainder gives us the position of the year in the 19thyear cycle. Thus, 5771/19 = 303 remainder 14. This works like the years of the Era ofNabonassar for the Babylonian calendar. 5771 AM corresponds to 2758 AN -- 2758/19= 145 remainder 3.

There may be grounds for some confusion here, since 2758 AN does not begin untilApril 2011. However, the years of the Era that was actually used with the Babyloniancalendar, the Seleucid Era, where 2758 AN is 2322 Annô Seleucidae, was reckoned bythe Greeks from the previous Autumn. So 2322 ASel clearly corresponds to 5771 AM,and that is the basis of matching it with 2758 AN, even though the latter begins byBabylonian reckoning six months later.

The same year in the Jewish and Babylonian calendars is at different places in the 19year cycle because the two cycles are out of phase. This happened because of the errorthat had built up over the centuries in the Babylonian calendar. The Jewish calendar ofthe time of Saddiah Goan has corrected the intercalation of months. The pattern ofBabylonian intercalations is preserved by starting the cycle at a different point. Ofcourse, since then, error has built up in the Jewish calendar. The 8th and 19th year leap years, at least, should be delayed one year. This would requirechanging the traditional pattern of intercalations, which has never been done. The existence of a center of Jewish life and religious authority, in Israel,however, does mean that the calendar could be authoritatively reformed, even if the priests of the Sanhedrîn, who originally governed the calendar, do notexist. The chief Rabbis of the Sephardic and Ashkenazic communities could easily assume that responsibility.

The calculation for AM 5772 begins with the same numbers for the benchmark (5681y 2422,578d 39,280p) and the 247 year cycle (76y 27,755d 97,420p).Now however, we are in the 15th year of the 19 year cycle (15y 5488d 121,578p). This will be a Common Year following a Leap Year (CF). Adding thenumbers gives a total of 2455 821d 258 278p. The number of parts exceeds a week, so we subtract 181 440p and add 7d: 2455 828d 76 838p. When weexamine the table for the excess of parts, we are over the threshold at 61,764p, which gives us a year 5/354/2, a year that begins on a Thursday, is 354 days


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long, and will be followed by a year (5773) that begins on a Monday. Thus, for the final Julian Day Number, we add 5d for Thursday and 1d for 1 Tishrii toour total of days: JD 2455 834d. This turns out to be 29 September 2011.

Like 5772, the calculation for AM 5773 begins with the same numbers for the benchmark (5681y 2422,578d 39,280p) and the 247 year cycle (76y 27,755d97,420p). Now we are in the 16th year of the 19 year cycle (16y 5845d 53,334p). This will be a Common Year (C). Adding the numbers gives a total of 2456178d 190 034p. The number of parts exceeds a week, so we subtract 181 440p and add 7d: 2456 185d 8 594p. When we examine the table for the excess ofparts, we are not over the threshold at 9,924p, which gives us a year 2/353/5, a year that begins on a Monday, is 353 days long, and will be followed by a year(5774) that begins on a Thursday. Thus, for the final Julian Day Number, we add 2d for Monday and 1d for 1 Tishrii to our total of days: JD 2456 188d.This turns out to be 17 September 2012.

The Jewish Eras of the World


The Days of the Week




Kings of Israel and Judah

Judaea of the Maccabees and Herodians

The State of Israel, 1948-present



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Copyright (c) 1996, 1997, 1998, 1999, 2001, 2002, 2004, 2009, 2010, 2011, 2012 Kelley L. Ross, Ph.D. All Rights Reserved


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Byzantine Era, as of 988 AD 5509 BC

Maximus the Confessor (c.580- 662) 5493 BC

William Hales (1747-1831), A NewAnalysis of Chronology

5411 BC

Scaliger's Julian Period 4713 BC

Seder Olam,Small Chronicle of the World, 1121 AD

4359 BC

Eastern Jews, according to Abu-lFarangi 4220 BC

Western Jews, according to Riccioli 4184 BC

Chinese Jews, according to Brotier 4079 BC

Moses Maimonides, Universal History 4058 BC

Bishop James Ussher (1581-1656) 4004 BC

Sir Isaac Newton (1643-1727)c.4000BC

Johannes Kepler (1571-1630) 3992 BC

The Venerable Bede (c.672-735) 3952 BC

The Jewish Eras of the World

Before modern geology, the only estimates of the age of the world were religious. In India, we have vast cycles of times in an essentially eternal universe. Inthe West, estimates for a temporally finite universe were based on revelation. Judaism and Christianity had substantial material to work with in thechronology and counts of generations in the Bible. This material, however, was ambiguous, and we end up with a wide spread of estimates, over a range ofalmost two thousand years.

In the Christian context, the most famous estimate of Creation is certainly that of the Irish ArchbishopJames Ussher, who thought that the first day of the World was 23 October 4004 BC on the JulianProleptic Calendar, a day reckoned, however, to have begun (in the Babylonian, Jewish, and Islamicfashion) the previous sunset. Since this date was used in many English editions of the Bible in the 19thcentury, many people, like William Jennings Bryan (1860-1925), were left with the impression thatthis was the universally agreed result of Biblical research. Thus, Byran would reference it in hisCreationist prosecution in the Scopes "Monkey Trial" of 1925. However, there were many Biblicalestimates of the age of the world in Ussher's own 17th century, and the ones that had been used thelongest originated with Byzantine historians as far back as the beginning of the 7th century.

When I was in High School, I used to ask Jewish friends what it is that theera of the Jewish Calendar actually dated. They did not know. I had to readIsaac Asimov to discover that it was the Creation. The era was an AnnôMundi (AM), an "in the year of the world," date. The famliar Jewish Era

goes back to 3760 BC, but, as in Christianity, this has not been the onlyestimate of the age of the world in the history of Judaism. My source on

the variety of Jewish dates of Creation was a book I found while digging through the main library atthe University of Texas: Modern Judaism: or a brief account of the opinions, traditions, rites, andceremonies of the Jews in modern times, by John Allen (1771-1843) [2nd Edition, R.B. Seeley and W.Burnside, London, 1830, pp.366-367]. Since this was a book published in 1830, the "Modern" in thetitle now looks a little incongruous. But it is nice to see this list from a relatively naive source, i.e. one

unaware of the subsequent history of geology and Darwinism. Allen was unaware of any certainsource of the era, from 3760 BC, that had actually already become customary with the Jewishcalendar. The "Universal History" referenced by Allen may be An Universal History: From the


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Joseph Justus Scaliger (1540-1609) 3949 BC

John Lightfoot (1602-1675) 3929 BC

David Ganz, Chronology 3761 BC

accepted Jewish Anno Mundi 3760 BC

Rabbi Gersom, Playfair 3754 BC

Seder Olam Rabba,Great Chronicle of the World, 130 AD

3751 BC

Rabbi Habsom, Universal History 3740 BC

Rabbi Nosen, Universal History 3734 BC

Rabbi Hillel, circa 358 AD 3700 BC

Rabbi Zachuth, Universal History 3671 BC

Rabbi Lipman, Universal History 3616 BC

Earliest Accounts to the Present Time, by George Sale, George Psalmanazar, Archibald Bower, GeorgeShelvocke, John Campbell, John Swinton [C. Bathurst, London, 1759].

The Days of the Week







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There seems little call to have a modern luni-solar calendar, which keeps track of both the seasons and the Moon. Surviving luni-solar calendars, the Jewishand the Chinese, are now used mainly for ritual purposes. On the other hand, the tides are strongly affected by the phases of the moon, and sailors andfishermen may keep in mind that the tides are the strongest at the New and Full Moons. At the same time, as ancient people were certainly aware, the

lunar month matched up closely with the menses of women. The sort of feminists who wish to valorize the femininecertainly highlight the affinity of the feminine to the Moon; but I have never met any women who actually paid anyattention to lunar calendar months -- although female calendar buffs cannot fail but be aware of them.

For the future, there is at least one conceivable reason why a luni-solar calendar might eventually be desired: Whenthere are human colonies on the Moon, it will be of rather more practical concern than it is on Earth what phase theMoon is in, since that determines whether it is day or night outside. For lunar inhabitants, this may or may not turn outto be of importance in their lives (since the surface conditions may not be of that much significance, except for thoserequired to go outside), but they might like an intuitive way of keeping track of it anyway.

Since the rules for determining the actual date are complicated in both the Jewish and Chinese calendars, something simpler might be in order. The problem

of any luni-solar calendar is its dual purpose. Keeping track of the Moon requires adjustment of days. Keeping track of the Sun requires adjustment ofmonths. Adding or subtracting days, as the Julian or Gregorian calendars do, to adjust the seasons will not work, sincethis will ruin correspondence to the Moon. The best convenient rule for the Sun is thus still the Babylonian 19 yearcycle. The continued fraction for the number of synodic months per year (12.368267058) can be seen at right. Adding


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123 months every 334 years would be very cumbersome to keep track of. Another virtue of the 19 year cycle is that iscan be used to keep track of the Moon also. There are 235 months per 19 year cycle, and this averages out to365.2467463 days/year. This means that the number of days per year in our calendar will track the Moon if itapproximates the length of this "Metonic" year -- i.e. fitting the 235 lunar months rather than the actual 19 solar(tropical, i.e. tracking the seasons) years.

The basic day pattern for the year can be borrowed from the practice of the Jewish and Islâmic calendars, i.e. analternation of 30 and 29 day months. The 19 year cycle then adds 7 months every 19 years. As considered for the Babylonian calendar above, if six of thosemonths are 30 days each, and the 7th (the Ululu II that occurs only once every 19 years) is 29 days, this averages out to exactly 365 days per year: (19 x ((6x 30) + (6 x 29)) + (6 x 30) + 29)/19 = 365. Intercalary days must then be added to this to approximate the Metonic year.

The easiest rule for adding days to a year is the Julian intercalation, i.e. an extra day every 4 years. This is familiar and very easy to keep track of. It is alsomore accurate for the Metonic year than for the tropical year -- off a day in 307 years rather than the day in 128 years that the Julian calendar errs against theseasons. This also gives us the simplest correction to use for the Julian intercalation: Century years evenly divisible by 300 would not be leap years for ourluni-solar calendar = 365 +1/4 -1/300. This gives a year of 365.246 days [where "6" is a repeating decimal]. Against the Metonic year, that is only off a dayin 12,555 years, at least four times as accurate as the Gregorian calendar, and even more accurate for the Moon than the purely lunar Islâmic calendar.

That takes care of the Moon. The remaining problem, however, is that the Metonic year is not accurate enough for the Sun. It is off a day in 219 years -- moreaccurate than the Julian calendar (off a day in 128 years), but not by much. The 365 +1/4 -1/300 day year is off a day in 224 years. Retaining the 19 yearcycle means that it must occasionally be adjusted. It runs slow, and so the dates fall later in the year over time. The way to adjust it is to periodically delayone of the intercalations of months.

In a 19 year cycle, one year starts the latest. This will follow the intercalary year that itself starts the latest. When the latest year is starting too late, theintercalation in the previous year can be delayed into the following year, which means that the year starting the latest suddenly becomes the year starting theearliest. As it happens this can be conveniently done after exactly 18 of the 19 year cycles, i.e. every 342 years. After every delay has been done 19 times,i.e. once for every year in the cycle, we get a larger cycle in which the pattern of delays will occur again -- 342 x 19 = 6498 years. After a complete 6498year cycle, what ends up happening is that one of the 29 day months disappears; it has in effect been delayed out of existence. Now, 365 +1/4 -1/300-29/6498 gives us an average solar year of 365.2422038 days. This only off a day against the tropical year in over 200,000 years -- accurate far beyond thelimits of certainty, just as the 6498 year cycle itself is longer than human history -- making it comparable to the Eras of the World contemplated in Judaismand Christianity.

Such a calendar serves the purpose. Four things have to be kept track of: (1) the leap day every 4 years, (2) the loss of a leap day every 300 years, (3) ourposition in the 19 year cycle, and (4) the delay of the latest intercalation in the 19 year cycle every 342 years. The rest takes care of itself -- i.e. we don't haveto worry where we are in the 6498 year cycle.

Another way to do this calendar, however, is set aside the Julian intercalation and the 300 year correction and to piggyback our reckoning onto the Gregorian


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AN, Era of Nabonassar

1 229 343 457 685 913 1027 1141

BC AD

747 519 405 291 63 166 280 394

0 3/27* 3/28* 3/28* 3/29* 3/30* 3/31* 3/31 4/1

1 4/15 4/16 4/16 4/17 4/18> 4/19> 3/20<§ 3/21<§

2 4/4 4/5 4/5 4/6 4/7 4/8 4/7 4/8

3 3/24* 3/25* 3/25* 3/26* 3/27* 3/28* 3/27* 3/28*

4 4/12 4/13 4/13 4/14 4/15 4/16 4/15 4/16

5 4/1 4/2 4/2 4/3 4/4 4/5 4/4 4/5

calendar. This makes it easier to determine actual dates, Gregorian dates, for luni-solar reckoning. The Gregorian year is 365 +1/4 -3/400 = 365.2425 days.This is off one day in 3320 years against the seasons and one day in 220 years against the Metonic year. Exactly 12 of the 19 year cycles equals 228 years. Ifwe figure a day correction after that span we get, 365 +1/4 -3/400 +1/228 = 365.246886. This is off just a day in 7161 years against the Metonic year. This isquite accurate enough for our purposes, indeed more than twice as accurate as the Gregorian year is for the Sun. If we figure in the 342 year corrections ofthe 19 year cycle, we get 365 +1/4 -3/400 +1/228 -29/6498 = 365.2424231. This is off a day against the Sun in 4459 years, more accurate than the Gregoriancalendar itself, but in the same order of magnitude.

A 228 year cycle also turns out to be quite convenient when we realize that three of them are equal to two 342 year cycles: 3 x 228 = 2 x 342 = 684 years.This is also, by a nice coincidence, actually half of the 1368 years that has been noted as the period in which the cycles of the Jewish and Islâmic calendarsare commensurable -- 1368 years also being the span between the beginning of the Era of Nabonassar (747 BC) and the beginning of the Islâmic Hegira Era(622 AD). A further 1368 years brings us down to our time, to 1990 AD.

In constructing the Gregorian dates for our luni-solar calendar, we operate on the principle that the year, using the Babylonian New Year, should start on orafter the Vernal Equinox. This is defined as March 21st for the Gregorian calendar, but it usually occurs on March 20th (Universal Time). As it happens, thecalendar can be conveniently designed so that the earliest New Year in each 19 year cycle just ranges from March 20th to March 22nd. The latest New Yearthen ranges from April 17th to April 19th. Actual dates can then be constructed using a simple rule from the Gregorian Easter reckoning: Each year, the lunardates occur 11 days earlier. Thus, a New Year one year on 4/15 will occur on 4/4 the next year. When a month is intercalated, this adds 30 days, unless, of

course, it is the Ululu II, when only 29 days are added. After 19 years, thisreturns to the original date. We don't worry about the Julian intercalation or itscorrections because the Gregorian calendar takes care of that for us. We justapply the 228 year day correction against the Gregorian calendar; and the 342year month correction against the 19 year cycle.


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6 3/21<§ 3/22<§ 3/22* 3/23* 3/24* 3/25* 3/24* 3/25*

7 4/8 4/9 4/10 4/11 4/12 4/13 4/12 4/13

8 3/28* 3/29* 3/30* 3/31* 4/1 4/2 4/1 4/2

9 4/16 4/17 4/18> 4/19> 3/21<§ 3/22<§ 3/21* 3/22*

10 4/5 4/6 4/7 4/8 4/8 4/9 4/9 4/10

11 3/25* 3/26* 3/27* 3/28* 3/28* 3/29* 3/29* 3/30*

12 4/13 4/14 4/15 4/16 4/16 4/17 4/17> 4/18>

13 4/2 4/3 4/4 4/5 4/5 4/6 4/6 4/7

14 3/22* 3/23* 3/24* 3/25* 3/25* 3/26* 3/26* 3/27*

15 4/10 4/11 4/12 4/13 4/13 4/14 4/14 4/15

16 3/30* 3/31* 4/1 4/2 4/2 4/3 4/3 4/4

17 4/18> 4/19> 3/21<§ 3/22<§ 3/22* 3/23* 3/23* 3/24*

18 4/7 4/8 4/8 4/9 4/10 4/11 4/11 4/12

19 3/27* 3/28* 3/28* 3/29* 3/30* 3/31* 3/31 4/1

AN

1369 1597 1711 1825 2053 2281 2395 2509

AH, Hejira Era

1 229 343 457 685 913 1027 1141

AD

622 850 964 1078 1306 1534 1648 1762

In the table at left, which covers the first 1368 years of the Era of Nabonassar,"<" marks the year with the earliest New Year, ">" marks the year with thelatest New Year, "*" marks ordinary intercalary years, and "§" marks theintercalation of the 29 day Ululu II. The later, it will be observed, alwaysoccurs in the year with the earliest New Year. The column with the darkershade of purple background, beginning in 405 BC (or 343 AN), is the one inwhich the classic Babylonian 19 year cycle was fixed, where the intercalationsare in the 3rd, 6th, 8th, 11th, 14th, 17th, and 19th years, with the Ululu II in the17th year. The 9th year is the one with the latest New Year. The intercalation inthe 8th year is the one that is next delayed, in 63 BC (or 685 AN).

The Hegira Era here, of course, has to be the solar Hegira, as is used in Irân --which conveniently also happens to be reckoned from the Vernal Equinox(Nou Rûz, "New Day," in Persian), unlike the standard Islâmic New Year,which moves through the seasons.

Also important to note is that the zero year in the tables, although thebenchmark, is prior to the actual first year of the calendar cycle. 622 AD, thenis year 1, not year 0, in the cycle; and its luni-solar New Year will be on 3/22.

In each of these 1368 periods, there are four intercalation delays, the first at


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0 4/2 4/3 4/3 4/4 4/5 4/6 4/6 4/7

1 3/22* 3/23* 3/23* 3/24* 3/25* 3/26* 3/26* 3/27*

2 4/10 4/11 4/11 4/12 4/13 4/14 4/14 4/15

3 3/30* 3/31* 3/31 4/1 4/2 4/3 4/3 4/4

4 4/18> 4/19> 3/20<§ 3/21<§ 3/22* 3/23* 3/23* 3/24*

5 4/7 4/8 4/7 4/8 4/10 4/11 4/11 4/12

6 3/27* 3/28* 3/27* 3/28* 3/30* 3/31* 3/31 4/1

7 4/15 4/16 4/15 4/16 4/18> 4/19> 3/20<§ 3/21<§

8 4/4 4/5 4/4 4/5 4/7 4/8 4/7 4/8

9 3/24* 3/25* 3/24* 3/25* 3/27* 3/28* 3/27* 3/28*

10 4/12 4/13 4/12 4/13 4/15 4/16 4/15 4/16

11 4/1 4/2 4/1 4/2 4/4 4/5 4/4 4/5

12 3/21<§ 3/22<§ 3/21* 3/22* 3/24* 3/25* 3/24* 3/25*

13 4/8 4/9 4/9 4/10 4/12 4/13 4/12 4/13

14 3/28* 3/29* 3/29* 3/30* 4/1 4/2 4/1 4/2

15 4/16 4/17 4/17> 4/18> 3/21<§ 3/22<§ 3/21* 3/22*

16 4/5 4/6 4/6 4/7 4/9 4/9 4/9 4/10

17 3/25* 3/26* 3/26* 3/27* 3/28* 3/29* 3/29* 3/30*

18 4/13 4/14 4/14 4/15 4/16 4/17 4/17> 4/18>

19 4/2 4/3 4/3 4/4 4/5 4/6 4/6 4/7

the beginning. There are six day corrections. The delay and the day correctionoccur at the same time twice in the period, at the beginning and at the 684 yearpoint. This coincidence frequently result in a two day change, rather than justone. Where this occurs, we sometimes have the phenomenon of the extra daybeing taken back later. Thus, in the 11th year of the cycles in the Hegira Eratable, we go from 4/2 to 4/4 to 4/5 but then back to 4/4 again. Thiscounterintuitive sort of retrograde movement occurs because of the way our 29day leap month jumps around from one period to another. A similar oddityturns up in the Gregorian Easter tables.


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AN

2737 2965

AH

1369 1597

AD

1990 2218

0 4/8 4/9

1 3/28* 3/29*

2 4/16 4/17

3 4/5 4/6

4 3/25* 3/26*

5 4/13 4/14

6 4/2 4/3

7 3/22* 3/23*

8 4/10 4/11

9 3/30* 3/31*

10 4/18> 4/19>

11 4/7 4/8

12 3/27* 3/28*

13 4/15 4/16

corrected uncorrected

0 2736/2755 4/8 1989/2008 4/7*

1 2737/2756 3/28* 1990/2009 4/26

2 2738/2757 4/16 1991/2010 4/15

3 2739/2758 4/5 1992/2011 4/4*

4 2740/2759 3/25* 1993/2012 4/23

5 2741/2760 4/13 1994/2013 4/12

6 2742/2761 4/2 1995/2014 4/1*

7 2743/2762 3/22* 1996/2015 4/20

8 2744/2763 4/10 1997/2016 4/9*

9 2745/2764 3/30* 1998/2017 4/28>

10 2746/2765 4/18> 1999/2018 4/17

11 2747/2766 4/7 2000/2019 4/6*

12 2748/2767 3/27* 2001/2020 4/25

13 2749/2768 4/15 2002/2021 4/14

14 2750/2769 4/4 2003/2022 4/3*

15 2751/2770 3/24* 2004/2023 4/22

16 2752/2771 4/12 2005/2024 4/11

17 2753/2772 4/1 2006/2025 3/31§<

18 2754/2773 3/21§< 2007/2026 4/18

The table at left brings the calendar into the first two cycles of the current 1368 year period. The table at right compares the dates inthe current corrected cycle to what they would be if we stuck to the originalBabylonian 19 year cycle without the correction of delaying the intercalations. Thisis given with the benchmark date a day earlier. Given variations in the actual dates ofthe New Moons, the concern in the corrected calendar, since Ululu II might occurearly in the cycle and subtract a day from subsequent years, is to keep the NewYear's date from occuring too early. In the uncorrected cycle, since Ululu II occurslate, this is of less concern.

Comparing the corrected and uncorrected cycles, it can be noted that all sevenintercalations have by this point been delayed to the next year. The last one to bedelayed, from the 17th year, was the earliest (or, on the proposed system, the new)intercalation back in the foundational cycle in 405 BC. There is a nice symmetry inthis, and another nice coincidence with our place in the Era of Nabonassar.

All of these dates are based on the Babylonian rule for the beginning of the Month: Not the New Moon, but the first day on which the Young Moon, a crescent, can beseen right after sunset. This is usually the second calendar day after the New Moon,though it must then be remembered that the Babylonian day (like the Jewish andIslâmic) begins at sunset of the day before. The Jewish month can begin with theNew Moon, but usually it is delayed for ritual or other reasons into the range of thevisible crescent. The Islâmic month, like the Babylonian, is supposed to begin withthe crescent. If we want a luni-solar calendar based on the New Moon, all these datesmust be advanced by a couple of days.


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14 4/4 4/5

15 3/24* 3/25*

16 4/12 4/13

17 4/1 4/2

18 3/21§< 3/22§<

19 4/8 4/9

19 2755/2774 4/8 2008/2027 4/7*Without using the tables, the character of a year within the 6498 year cycle can bedetermined mathematically. If the remainder of the formula ((Y x 2393) +1025)/6498, where Y is the year of the Era of Nabonassar (AN), runs from 0 to 2051, the year is a leap year with a 30 day leap month(*). If the remainder runs from 2052 to 2392, the year is a leap year with a 29 day leap month (§). Other remainders are for commonyears. 2393 is the number of leap years in the 6498 year cycle. This is one less than 7 times the number of 19 year cycles (342 x 7 =2394). It can be determined that the 19 year period from 5130 to 5148 (counting 0-18 in the 19 year cycle) contains only 6intercalations, and no 29 day month. By one reckoning (starting with 0 rather than 1), this is where the 2394th leap month disappears.


Philosophy of Science, Calendars

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The Calendar in India

There is a completely separate Indian calendrical tradition. In the "Book of the Cattle Raid," in the Book of Virât.a, in the Mahâbhârata, Duryodhana claimsthat the Pân.d.avas have failed to keep their agreement to stay in exile for twelve years and in hiding for one. Bhis.ma reckons (47.1-5) that they have keptthe agreement, and he mentions that the calendar adds an extra month every five years. A.L. Basham, in The Wonder that was India [1954, 1967, Rupa &Company, Calcutta, etc., 1981, 1989], states the calendar rule as adding an extra month every thirty months (p. 494). Sixty months is five years (5x12). Thatmeans two months in five years. Basham also says that this was done "as in Babylonia." But that is not true. The Babylonians added seven lunar monthsevery nineteen years, which is often called the "Metonic" cycle (after the Greek astronomer Meton) and is still used by the Jewish calendar.


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Lunar Months,now Solar Months

Caitra March 22/21-April 20

Vaishâkha April 21-May 21

Jyais.t.ha May 22-June 21

Âs.âd.ha June 22-July 22

The economist Amartya Sen has a discussion of Indian calendars in his recent The Argumentative Indian, Writings on Indian History, Culture and Identity[Allen Lane, Penguin, 2005]. His essay, "India through its Calendars" [pp.317-333], however, is almost entirely about the Eras used in different calendars,not about the calendars themselves. One might be left not realizing that the same calendar can use different Eras, or that the same Era can be used bydifferent calendars. The only actual calendar rule he mentions is that of the Mahâbhârata, though its meaning is clarified: "each year consists of twelvemonths of thirty days, with a thirteenth (leap) month added every five years" [p.325]. The use of thirty day months makes it plain that we are dealing withapproximations to the solar year, but this rule produces a formidably poor approximation. If a thirty day month is added every five years, this averages out toa 366 day year, which would be off no less than three days in that period. Thus, a shorter intercalation would be needed, either 26 or 27 days, depending onone's estimation of the true length of the tropical year. Sen does mention that the mathematician Varâhamihra, in the sixth century AD, gave the length ofthe year as 365.25875 days [p.329]. This is significantly too long (over the 365.24220 days of the tropical year) and would be off a day in only 60 years.Such a value would be a discouraging glimpse into Indian astronomy, in that the Greeks had much better values much earlier, except that Varâhamihra's valuewas probably for the sidereal rather than the tropical year. Sen does mention the sidereal year (365.25636, or 365.25636042, days), the movement of the sunagainst to the stars rather than relative to the equinoxes, but he also doesn't say why he gives it. Taking Varâhamihra's value to be for the sidereal year, it isaccurate to a day in 418 years.

Sen does not discuss how calendars were regulated given inaccurate rules like that of the Mahâbhârata or values for the sidereal year, which is otherwise notused for civil calendars. I was left with the impression that the calendars may actually have been regulated "as in Babylonia" in its historically earlier sense,i.e. with months inserted as needed, without any prior rule or calculation being applied. All this required was some established political or priestly authoritywith the recognized function of doing so. Since the moment of the Vernal Equinox can easily be observed from the kinds of observatories that were built inmediaeval India, the authorities need merely have inserted the extra month when the year otherwise would have begun before the Equinox.

A satisfactory treatment of the Indian calendar can now be found in The Oxford Companion to the Year, An exploration of calendar customs andtime-reckoning [Bonnie Blackburn & Leofranc Holford-Strevens, Oxford U Press, 1999, 2003, pp.715-721]. The original calendar, as we might suspect, wasluni-solar, with an intercalation of months. The month names are given at right. The rule of the Mahâbhârata, so poor for a solar year, may have beenintended, as in Basham's reading, to mean two lunar months in five years. For a lunar calendar adjusting to thesolar year, the best approximations (by continued fractions) to the difference between twelve synodic monthsand the tropical year would be to add one month every three years, three every eight, four every eleven, sevenevery nineteen, or 123 every 334. The last is not very practical. Some Greek cities used three every eight. Thatalready is a lot more accurate than two every five -- if Balsam (or the Mahâbhârata) was talking about lunarmonths. Three months in every eight years results in an error of a month in 149 years, while two in every fiveresults in an error of a month in only 32 years. That is better than one in every three, which is off a month in 29years, but otherwise looks pretty miserable. Four months every eleven years results in an error of a month in216 years; and seven every nineteen results in an error of a month in 6494 years. For all practical purposes, ofcourse, 6494 years is eternity. That does not mean that the Babylonian (or Jewish) calendar is just fine for thatlong. Those calendars can be adjusted before an error of an entire month builds up. But Indian calendars usingthe 2/5 rule are going to be wildly inaccurate before the passage of much time at all. Of course, one problem


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Shrâvan.a July 23-August 22

Bhâdrapada,Praus.t.hapada

August 23-September 22

Âshvina,Âshvayuja

September 23-October 22

KârttikaOctober 23-November 21

Mârgashîrs.a,Âgrahâyan.a

November 22-December 21

Paus.a,Tais.a

December 22-January 20

MâghaJanuary 21-February 19

PhâlgunaFebruary 20-March 21/20

Solar/Zodiacal Monthor Rasi

Mes.a Aries

Vr.s.abha Taurus

Mithuna Gemini

with sources like Balsam and Sen is that they don't seem very aware of differences between lunar and solarcalendars. Both were used in India. But while the Mahâbhârata rule (at least as stated by Sen) looks tailoredfor a solar calendar, a luni-solar calendar, with lunar months and intercalations, looks to be older and moreindigenous.

The names of the lunar months are given with dates of the Gregorian year. This represents the adaptation of thecalendar to the tropical year as formulated in an official Indian Government calendar reform in 1957. With thiscalendar now pegged to the Gregorian, any mysteries and peculiarities about its use disappear. Two dates aregiven in March because the year begins on March 21 in Gregorian leap years, March 22 otherwise. Thesemonths now correspond to the signs of the Zodiac (with the Vernal Equinox in Aries), unlike the traditionalcalendar, which used the actual constellations of the Zodiac (where the Vernal Equinox is now in Pisces,moving into Aquarius).

Part of the calendar reform was the official adoption of the Saka Era. The Astronomical Almanac [U.S.Government Printing Office, Washington, and Her Majesty's Stationery Office, London] always gives the Eraof the Indian calendar thus, with its New Year as specified in the table. The Almanac for 2001, for instance,cites the New Year on March 22 and the year as 1923 [p.B2]. Amartya Sen mentions that the use of the SakaEra is first attested in an inscription from 543 AD (Saka year 465), at the very end of the Gupta period [p.326].

The Los Angeles Times of November 17, 2001, says that the Indian New Year occurred the previous day,November 16, and that it began the year 2058 -- signifying an Era benchmarked at 57 BC. This would be theVikrama Era, a historical alternative to the Saka and other Indian eras, with a New Year reckoned from thelunar month of Kârttika; but the Times article contains no discussion of what the Era is or about possible alternates. The Times article and the New Yearcelebration at the cited Hindu temple in Los Angeles, thus raised more questions than they answered. Probably the temple was using one of the traditional,regional Indian calendars, of which there are many, covered by Indian publications but not even by the The Oxford Companion to the Year.

In historic India, from Gupta times onward, the lunar calendar was pegged to a solar year. This is where the sidereal value of theyear comes in, since the movement of the sun was traced, not relative to the equinoxes, but against the stars. The "stars" meantthe constellations of the Zodiac, with names that are translations of the names of the signs of the Zodiac in Greco-Romanastronomy. Basham, who discusses this [p.495], doesn't mention how this calendar was governed. The Oxford Companion to theYear says [p.718] that the moon was considered to be in the month of Caitra when the sun was in the constellation Aries. Whenthe lunar month began depended on the convention. In the North of India, the month began with the day after the Full Moon. Inthe South of India, and in Indian astronomy, the month began with the day after the New Moon. If two months would beginwhile the sun is in the same Zodiacal constellation, the first is intercalary, with the same name as the second. If in the shortZodiacal periods of the winter (when the sun, near perihelion, moves quickly), a lunar month should entirely encompass the


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Karkat.a Cancer

Sim.ha Leo

Kanyâ Virgo

Tulâ Libra

Vr.shcika Scorpio

Dhanus Sagittarius

Makara Capricorn

Kumbha Aquarius

Mîna Pisces

Days of the Week

Ravivâra Sunday

Somavâra Monday

Man.galavâra Tuesday

Budhavâra Wednesday

Br.haspativâra Thursday

Shukravâra Friday

Shanivâra Saturday

sun's passage through a constellation, with the next month due to begin two Zodiacal periods after it began, then the name for themonth associated with the intervening period is passed over. This is the calendar apparently developed by Gupta era astronomersmentioned by Amartya Sen, like the mathematician and astronomer Âryabhat.a (in 499 AD). Sen is aware that it drifted againstthe tropical year but does not seem to realize that this is an artifact of its direct use of the stars, which implies a sidereal ratherthan tropical standard. Also, since it is based on the direct use of the stars, there is no general calendar rule for it, and itdepended, like the Chinese calendar, on direct astronomical observations, or at leastsophisticated calculations, by the responsible authorities. It is noteworthy that thereformed calendar is adjusted to Gregorian calendar dates relative to the signs, not theconstellations, of the Zodiac -- where the Vernal Equinox, no longer in Aries, is now inPisces, entering Aquarius. The calendar is thus detached in every way from a siderealreference.

The seven days of the week were also imported, named, as in Latin, after the planets, inthe same sequence used there.

Amartya Sen's examination of calendars includes the Vikrama and Saka Eras but also theKollam and Bengali San Eras, which are benchmarked at 824 AD and 593 ADrespectively -- i.e. subtract those numbers from the AD year for the appropriate calendaryear. The oldest Eras he gives are for the Buddha Nirvân.a calendar, benchmarked at 544BC (add to the AD year), and the Kaliyurga calendar, benchmarked at 4001 BC.

Although Sen is aware that the Kaliyurga Era does not date any historical event, he does not explain all the differentversions of the calendar cycles, and the system into which the Kaliyurga, as a cyclical period, is embedded. That is all treated here in a footnote to the pageon the devotionalistic Gods of Hinduism. Also, we have the anomaly that the beginning of the Kaliyurga period, cited by Sen from Whitaker's Almanack, wasa thousand years later as attested by the Arab historian al-Bîrûnî (973-1048). This is perplexing. Sen is aware of the problem, citing [p.323] Âryabhat.a thatthe Kaliyurga benchmark was more like 3101 BC (probably al-Bîrûnî's own source). Sen says that the older benchmark is "quite widely used" but does not orcannot account for the origin of the convention. Sen's Buddhist Era (from Whitaker's Almanack again) also seems to differ by a year from the Era ofBuddhism used in Thailand, benchmarked at 543 BC. As it happens, The Oxford Companion to the Year also has the Era of Buddhism beginning in 543, soperhaps some small confusion accounts for the difference -- the Oxford Companion itself says that the Era is "elapsed" years since 544, which may leavereaders not realizing that 544 would be year 0, with year 1 delayed until 543.

Cycles of Time in Hinduism and Buddhism



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AvestanMiddle Persian,

PahlaviModern Persian days

Fravashinâm Fravardîno Farvardin 31

Ashahê Vahistahê Ardavahist Ordi Behesht 31

Haurvatâto Horvadad Khordâd 31

Philosophy of Religion, Hinduism



Sangoku Index



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Iranian Calendars

While modern Irân has become a fiercely Islâmic country, it retains some elements to remind us of its previous religion, Zoroastrianism. Thus, a verycommon male given name is Mehrdâd, which actually means "given by Mithra," Mithra being a god even of pre-Zoroastrian Irân (Mitra in the Vedas).There are even versions of the same name in Greek and Latin: Mithradates

Of great interest is the continuation in modern Irân of the ancient Zoroastrian calendar. While the religious Islâmic calendar is of course used in Irân, theancient solar calendar also continues to be used as a civil calendar. The table containsthe names of the Zoroastrian months as they occur in Avestan, the ancient sacredlanguage of Zoroastrianism, in Middle Persian, or Pahlavi ("Parthian"), the languageof the Sassanid Empire, and in Modern Persian (Fârsi), as used today. Many of theAvestan names are identifiable as relating to what have been called the ZoroastrianArchangels, and to some familar, pre-Zoroastrian gods (Mithra again). The spellingfor Modern Persian indicates the Persian vowel quality, not, as is common, the vowelsas they would be read in Arabic.


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Tistryêhe Tîr Tir 31

Amerotâto Amerôdad Mordâd 31

Khshathrahê Vairyêhe Shatvaîrô Shahrivar 31

Mitrahê Mitrô Mehr 30

Apâm Âvân Âbân 30

Âthrô Âtarô Âzar 30

Dathushô Dînô Dei 30

Vanheus Mananho Vohumân Bahman 30

Spentayâo Armatôis Spendarmad Esfand 29/30

Month Length Date

Bahâ 19 March 21

Jalâl 19 April 9

Jamâl 19 April 28

'Az.amat 19 May 17

Nûr 19 June 5

Rah.mat 19 June 24

Kalimât 19 July 13

The Irânian year begins with the Vernal Equinox, March 20 or 21. This Persian NewYear, Noruz (literally, "New Day"), is often celebrated by Irânian expatriates as theirdistinctively national holiday. The assignment of the lengths of the months reflects thefact that spring and summer in the northern hemisphere are longer than fall and winter.The Persian months are thus actually zodiacal months, comparable to the ChineseSolar Terms. The twelfth month is 29 days in common years, 30 days in leap years.My source (A.K.S. Lambton, Persian Grammar, Cambridge University Press, 1967,p.255-256) does not specify in what year the extra day is added or whether theintercalation scheme is merely Julian or if the Gregorian or some other correction isnow applied.

The Era used with this solar calendar is still the Islâmic H.ijrah Era, but it is countedin full solar (365 day) rather than in the short lunar (354 day) years of the Islâmiccalendar proper. This means that the Persian year beginning on March 21 can bedetermined just by subtracting 621 from the AD Era year. Thus, the Persian New Yearin 1999 began the solar Hegira year 1378. As discussed elsewhere, this solar Hegiraera is equivalent to the year of the Era of Nabonassar (747 BC) minus 1368. Since, astronomically, the Babylonian year also began at the Vernal Equinox, theBabylonian year of the Era of Nabonassar can always be obtained just by adding 1368 to the Irânian solar Hegira year -- 1999 is 1378 + 1368 = 2746 AnnoNabonassari.

Another Irânian calendar also begins with the Vernal Equinox. That is the sacred calendar for the Bahâ'i Faith. The founder of the Faith, the prophetBahâ'ullâh, was exiled from Irân and imprisoned by Turkey in Haifa. There he was buried after his death in 1892,and there the international headquarters of the Faith is located, while the city itself has passed from Turkey toBritish Palestine and now to the State of Israel.

The Bahâ'i calendar has the unique structure of being divided into 19 months of 19 days each. This only falls 4days short of a 365 day year, which is filled in with intercalary days. The names of the months are given with theirArabic vowel quality, since they are all Arabic words. The intercalary period has been located so that, if the datesgiven in the table are observed, an intercalation by the Gregorian calendar on February 29 will automaticallyproduce a Bahâ'i intercalary period of 5 rather than 4 days.

The Bahâ'i Faith, although owing much to Islâm, and especially to Irânian Islâm, sees itself as a separate religionthat is the successor to Islâm, as Christianity saw itself as the successor to Judaism -- without, however, rejectingthe legitimacy of the earlier religions. Unfortunately, to the Irânian authorities, especially after the advent of the"Revolutionary" Irânian theocracy, this meant that Bahâ'is were actually apostates from Islâm, a crime punishable


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Kamâl 19 August 1

Asmâ' 19 August 20

'Izzat 19 September 8

Mashîyyat 19 September 27

'Ilm 19 October 16

Qudrat 19 November 4

Qawl 19 November 23

Masâ'il 19 December 12

Sharaf 19 December 31

Sult.ân 19 January 19

Mulk 19 February 7

[intercalation] 4/5 February 26

'Alâ' 19 March 2

by death under Islâmic Law. Thus, after 1979, all the Bahâ'i holy places in Irân were systematically destroyed andan intense persecution of members of the Faith begun. Many, consequently, fled the country as quickly as possible.

The Faith had long seen itself, however, as an international religion, and communities had long been established allover the world. A local Bahâ'i community had been founded in Hawai'i, for instance, while it was still anindependent country. Persecution in Irân, therefore, is liable to be of little significance for the growth of thereligion. Indeed, air travelers approaching O'Hare International Airport, in Chicago, are often curious what theunusual large building is on the shore of Lake Michigan. It is the Bahâ'i Temple, in Wilmette, Illinois, which hasexisted since the early days of the century.

Irânian calendars thus present us with intriguing combinations of pre-Islâmic, Islâmic, and post-Islâmic features,even as Irânian nationalism struggles violently with its own identity and its own religious heritage. In the Persiannational epic, the Shâh Nâmah of the poet Firdawsî (c.940-c.1020), one of the first bookswritten in New (i.e. Islâmic) Persian, there is a striking image from a dream: Four menpulling hard on the corners of a square white cloth, but the cloth does not tear. The men areinterpreted to be Moses, Jesus, Muh.ammad, and Zoroaster -- Zara u tra in Avestan,with the /z/ as in English, the in as English "thin," and as English "sh"; Zarto t, Zardot, Zardoha t, Zarâdo t, etc. in Modern Persian -- and the cloth the Religion of God. The

inclusion of Zoroaster with the other principal Founders of Monotheism is the distinctivelyIrânian touch, as Irân itself could be the cloth, pulled fiercely by both internal and externalreligious influences -- though ironically the word for "religion" in Arabic itself, dîn, appears to be borrowed fromMiddle Persian (dên).

Iranian Index



Zoroastrianism under the Achaemenids

The Zoroastrian Immortals and Elements

Zoroastrianism under the Sassanids


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Babylonian, Jewish, Muslim, Luni-Solar, Indian, Iranian Calendars

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Transcript of Babylonian, Jewish, Muslim, Luni-Solar, Indian, Iranian Calendars