The origins of the 247-year calendar cycle

The origins of the 247-year calendar cycle Abstract Many medieval and early modern Jewish calendars were based on the assumption that the calendar repeats itself exactly after 247 years. Although this cycle – famously referred to as the ʿIggul of R. Naḥshon Gaon – is discussed in many sources from medieval to modern, its origins are still a mystery. The present article attempts to shed light on the early history of reiterative Jewish calendar by looking at the oldest 247-year cycles identified to date. The sources, discovered in the Cairo Genizah, demonstrate that the 247-year cycle originated in Babylonia in the middle of the 10th century and was put together by Josiah b. Mevorakh (ibn) al-ʿĀqūlī, previously known from Judaeo-Persian calendar treatises. In contrast, a large body of manuscript evidence shows that the attribution of the cycle to R. Naḥshon Gaon (874–882 CE) is not attested before the 12th century and may be unhistorical. The 247-year cycle may have been proposed as an alternative Jewish calendar that would eliminate the need for calculation and prevent calendar divergence. But at least from the early 12th century the cycle was seen as a means of setting the standard calendar, even though it is not fully compatible with the latter. Many medieval and early modern Jewish calendars were based on the assumption that the calendar repeats itself exactly after 247 years. This cycle – best known under the title ʿIggul of R. Naḥshon Gaon – is not fully compatible with the standard Jewish calendar but diverges in a small number of years every century. A convenient if imprecise method of calendation, the 247-year cycle spread to all corners of the Jewish world, however, its first beginnings are virtually unknown.1 In this article I attempt to shed light on the history of the reiterative Jewish calendar by examining the earliest 247-year calendar cycles identified to date. A calendar is considered reiterative or cyclical if it repeats itself exactly after a certain number of years, i.e. any two dates that many years apart fall on the same day of the week. The standard Jewish calendar in use today takes just under seven 1. On the 247-year cycle see Sacha Stern, Calendar and Community. A History of the Jewish Calendar, 2nd cent. BCE – 10th cent. CE (Oxford: Oxford University Press, 2001), p. 193; Raḥamim Sar-Shalom, Gates to the Hebrew Calendar (Netanyah: R. Sar-Shalom, 1984) (Hebrew), p. 51; Yosef Tobi, The Jews of Yemen. Studies in Their History and Culture (Leiden: Brill, 1999), pp. 211-226; Hayyim Yehiel Bornstein, ‫ חלק א׳‬,‫דברי ימי־העבור האחרונים‬ (“The Later History of Calendar,” part 1), Ha-Tequfah 14–15 (1934, 3rd edition): 321–372, on pp. 354-358; Hayyim Yehiel Bornstein, ‫( מחלקת רב סעדיה גאון ובן מאיר‬The Dispute of Rav Saadia Gaon and Ben Meir) (Warsaw, 1904), pp. 141–144; Eran Raviv, Mathematical Studies in the Hebrew Calendar (unpublished PhD thesis, Bar Ilan University, 2015), pp. 53–111. -1- hundred thousand years to repeat exactly.2 This cycle is obviously impractical as it is too long to be used in calendar reckoning. Of more practical significance is the period of 247 years after which the standard calendar largely repeats itself, except for two to seventeen years which differ from corresponding years 247 years before.3 The non-cyclical nature of the Jewish calendar means that it cannot be set once and for all but must be calculated on a regular basis. The reckoning is based on the 19year cycle of intercalations, the calculation of the astronomical new moon (molad), and a set of additional rules.4 On this basis three variables must be derived. Firstly, the day of the week of the New Year must be established. It generally corresponds to the day of the week of the molad of Tišri, but is postponed should the calculated molad fall on the forbidden days of Sunday, Wednesday and Friday. The New Year is also postponed should molad Tišri occur later than 18 hours of the 24-hour day beginning at 6pm (this rule is known as molad zaqen). Secondly, the length of the variable months Marḥešvan and Kislev must be calculated. In the Jewish calendar months have a fixed length of either 29 or 30 days, whereby 30-day months alternate with those of 29 days. Only two months, Marḥešvan and Kislev, are variable and can have 30 days in some years and 29 days in others. Marḥešvan and Kislev occur is three combinations: ‫ חסרים‬defective – both 29 days, ‫ כסדרן‬orderly – Marḥešvan 29 and Kislev 30 days long, or ‫ שלמים‬full – both 30 days. Thirdly, the presence or absence of an additional 30-day intercalary month Adar I must be deduced from the 19-year cycle of intercalations, wherein twelve years are plain and consist of twelve months and seven years are intercalated and thirteen months long. A combination of these three data determines the course of the entire year. Due to various religious constraints only fourteen such combinations are allowed, and to set a calendar for a particular year ultimately means to establish to which of the fourteen types (also called characters) the year in question will belong. The type of a year can be represented by a sign so that a Jewish calendar for any number of years can be formulated as a sequence of signs expressing their characters. The signs indicate the day of the week of the New Year, the length of Marḥešvan and Kislev and the day of the week of Passover, which latter is deducible from the day of the week of the New Year, the length of the variable months and the year’s being plain or intercalated. An example of such sign is ‫ בחג‬where the first letter represents the day of the week of the New Year (here ‫ב‬, Monday), the second – the length of the 2. The recurrence period of the Jewish calendar is 689, 472 years. (see, e.g., Sar-Shalom, Gates to the Hebrew Calendar, p. 52). 3. On the accuracy of the 247-year cycle see Raviv, Mathematical Studies, pp. 57-62. 4. For a detailed explanation of the workings of the Jewish calendar see Sar-Shalom, Gates to the Hebrew Calendar, esp. pp. 52, 131-140; for the history of the calculated Jewish calendar see Stern, Calendar and Community, pp. 155-275. -2- months (here ‫ ח‬for ‫ חסרים‬defective), and the third – the day of the week of Passover (here ‫ג‬, Tuesday). The middle letter of the sign can be ‫ ח‬for ‫ חסרים‬when Marḥešvan and Kislev are 29 days long, ‫ כ‬for ‫ כסדרן‬when Marḥešvan is 29 days and Kislev is 30, and ‫ ש‬for ‫ שלמים‬when both are 30 days long. In Oriental manuscripts the letter ‫ מ‬for ‫ מעוברת‬is added to indicate intercalated years. For example, ‫ גכמז‬describes a year that begins on a Tuesday (‫ ג‬for day three), is orderly (‫ כ‬for ‫)כסדרן‬, is intercalated (‫מ‬ for ‫ )מעוברת‬and has Passover on Saturday (‫ ז‬for day seven). In manuscripts from other geo-cultural areas the sign is more likely to be ‫גכז‬. Reiterative calendars based on the 247-year cycle claim that the character of a year is always the same as that of a year 247 years before or after it so that once a correct sequence of 247 symbols is established, it can be used indefinitely without any changes. As is mentioned above, this claim holds only approximately in the framework of the standard Jewish calendar. If a sequence of 247 year types compatible with the standard calendar is re-used for the following 247 years, it will deviate from a calendar calculated for these next 247 years in five to fifteen signs. Such deviations always come in clusters of two to three years, which is conditioned by the above-mentioned New Year postponements and the allowed length combinations of Marḥešvan and Kislev . Depending on their provenance reiterative Jewish calendars are written down as sequences of 247 year type signs laid out in different ways. In a substantial group of manuscripts the cycle is referred to as the ʿIggul of R. Naḥshon Gaon (gaon of Sura from 874 CE to 882 CE) and formatted as a table of nineteen columns over thirteen rows. In this table each column represents a year in the 19-year cycle of intercalations, and each row – one such 19-year cycle (247 years are thirteen cycles of nineteen years). Each cell of the table is filled with a sign determining the calendrical type of the relevant year. It is in this form and under this title that the 247-year cycle is best known in the secondary literature on the subject, where R. Naḥshon Gaon’s connection to the cycle is generally taken as historically valid, whereupon the cycle is dated to the 9th century.5 However, such early origins of the 247-year cycle are not confirmed by any other known textual evidence. Indeed, the 247-year cycle is not mentioned in the correspondence relating to the Saadia–Ben Meir dispute (921–924 CE),6 and is equally absent from al-Bīrūnī’s comprehensive and well-informed section on the Jewish calendar in his work The Chronology of the 5. For references, see footnote 1. Raviv, Mathematical Studies is a notable exception, see footnote 10. 6. Personal communication from Sacha Stern and Marina Rustow, who are currently in the process of compiling and editing the entire corpus of texts related to the dispute. On this project see Marina Rustow, Sacha Stern, “The Jewish Calendar Controversy of 921–22: Reconstructing the Manuscripts and their Transmission History,” in Time, Astronomy, and Calendars in the Jewish Tradition, eds Sacha Stern, Charles Burnett (Leiden: Brill, 2014), pp. 79–95. On the Saadia–Ben Meir calendar dispute see also Stern, Calendar and Community, pp. 256–275 and Bornstein, ‫מחלקת רב סעדיה גאון ובן מאיר‬. -3- Ancient Nations completed in 1000 CE.7 An examination of over two hundred sources shows that the earliest manuscript to explicitly mention R. Naḥshon Gaon in association with the 247-year cycle refers to a calendar starting in 1198/9 CE (Oxford, Bodl. Canon. Or. 1, fol. 81r). The earliest unattributed calendar that has the shape usually associated with the ʿIggul of R. Naḥshon Gaon (i.e. a table of nineteen columns over thirteen rows) covers the period between 1123/4–1369/70 CE (Moscow State Library, Guenzburg 481, fol. 102r)8 and the earliest such calendar implied by the sources must have started in 1104/5 CE.9 Moreover, contrary to what might be expected of a cycle put together in the 9th century, ʿIggulim, so-called of R. Naḥshon Gaon, do not carry calendrical information that predates 1006/7 CE.10 Taken together this evidence clearly calls for a re-evaluation of the current thinking on the origins and history of the reiterative Jewish calendar. I propose to approach this goal by looking at a group of manuscripts in which the 247-year cycle is not attributed to R. Naḥshon Gaon and is not given the shape of a table. The method of creating a reiterative calendar that will be discussed here was previously known from only a handful of Judaeo-Persian treatises on the Jewish calendar.11 It is attributed to Josiah b. Mevorakh al-ʿĀqūlī (or ibn al-ʿĀqūlī) and is dubbed in Judaeo-Persian sources dūlābī, “waterwheel-like” – a reflection of its ever repeating nature. Recently I was fortunate to find a number of Cairo Genizah fragments related to Josiah b. Mevorakh’s calendar, including actual calendars, statements of the system’s use and а critique of the 247-year cycle. Unlike previously known calendars of Josiah b. Mevorakh, this new material is in Judaeo-Arabic. In addition, Josiah b. Mevorakh’s cycle has been discovered in a Byzantine manuscript on the Jewish calendar, this time in Hebrew. These largely unstudied sources furnish 7. See Abū Rayḥān al-Bīrūnī, The Chronology of Ancient Nations 7; trans. C. Edward Sachau (London: published for the Oriental Translation Fund of Great Britain & Ireland by W.H. Allen & Co., 1879), pp. 141-175. A new annotated translation of The Chronology of Ancient Nations is in preparation by François de Blois, whom I thank for drawing my attention to al-Bīrūnī’s silence on the 247-year cycle. 8. The earliest fragmentary table of a similar format (Manchester, Rylands B 4471), which may or may not have covered the entire 247 years, takes 1048/9 CE as its starting point. 9. This is inferred from a marginal note in Munich, Cod. Hebr. 128, fol. 28r that speaks of 19-year cycle 270 as the beginning of a next iteration of the 247-year cycle, indicating that its previous iteration started thirteen cycles earlier in the beginning of the 19-year cycle 257, i.e. 1104/5 CE. 10. In a similar vein, Raviv, Mathematical Studies, pp. 55–56 and p. 86 concludes that the attribution of the 247-cycle to R. Naḥshon Gaon is anachronistic, and the cycle was not in use before the second half of the 11th– the beginning of the 12th century. 11. Elkan N. Adler, “The Persian Jews: Their Books and Their Ritual,” The Jewish Quarterly Review 10/4 (1898): 584–625, p. 623; Tobi, The Jews of Yemen, pp. 215–216; Tobi, “The Dispute over the 247-year Cycle in Yemen,” in Studies in Judaism and Islam presented to Shelomo Dov Goitein on the occasion of his eightieth birthday by his students, colleagues and friends, eds Shelomo Morag, Issachar Ben-Ami and Norman A. Stillman (Jerusalem: Magnes Press, 1981) (Hebrew), pp. 193–228, esp. 196–198, 206–207. Raviv, Mathematical Studies, pp. 88-102 analyses Judaeo-Persian 247-year calendars but also comments on one Genizah fragment related to R. Josiah b. Mevorakh’s cycle. -4- important evidence on the creation, spread and practical use of the 247-year calendar cycle. The structure of Josiah b. Mevorakh al-ʿĀqūlī’s calendar Josiah b. Mevorakh al-ʿĀqūlī’s work on calendar consists of an introduction followed by fourteen chapters, each dedicated to one of the fourteen possible types of the Jewish year. To make it clear how this calendar works I edit here the introduction with the beginning of a chapter on the year type ‫ בחג‬as found in T-S 10K20.2. ‫רח‬ ֗ ‫בש‬ ֗ ‫רצי‬ ֗ ‫קאל יאשיהו בן מבורך בן אלעאקולי‬ ‫אללה ענה אדא ארדת תערף רווס אל‬ ‫שהור ואלאעיאד פכד סני אלאסכנדר‬ ‫מע אלמטלובה ואסקט מנהא אלף סנה‬ ‫ומא יתבקי אסקטה ֗ר ֗מז֗ ֗ר ֗מז֗ ואלדי‬ ‫יבקי מע]ך[ בעד דלך אטלבה עלי הדה‬ ‫אלאלואח אלת]י[ בין ]י[דיך אדא וגדתה תקרא‬ ‫תגד אלשהור ואלאעיאד צחיחה‬ ֗ ‫תחת אללוח‬ ‫כמא תשתהי אן שא אללה תעאלי‬ ‫ ֗מ ֗ב ֗ס ֗ט ֗פו֗ ֗צ ֗ג ֗קי֗ ֗ג ֗ק ֗כ ֗ק ֗מ‬12 ֗‫֗טו‬ ‫֗ק ֗ס ֗ד ֗ק ֗צ ֗א ֗ק ֗פ ֗ד ֗רי֗ ֗א ֗רי֗ ֗ח ֗ר ֗ל ֗ח‬ ֗‫חסרין פשוטה סימן ֗ב ֗ח ֗ג ֗טו‬ ‫אלד כפורים‬ ֗ ‫תשרי סוכה ושמיני ֗ב צום גדליה‬ .... ‫֗ד ערבה ֗א מרחשון ֗ג ֗ד כסלו ֗ה‬ In the name of God Said Josiah b. Mevorakh b. al-ʿĀqūlī, may God be pleased with him: if you want to know the beginnings of months and the festivals, take the years of Alexander including the required (year), 12. -5- T-S 10K20.2v deduct from them 1000 years, and cast out 247s from what remains. What is left after this, look it up in the tables that you have before you, and when you find it, read what is under the table and you will find the correct months and festivals as you wanted, so God will. 15, 42, 69, 86, 93, 113, 120, 140, 164, 191, 184,13 211, 218, 238 defective, plain, sign ‫בחג‬, 1514 Tišri, Sukkot and Šemini (ʿAṣeret): Monday; fast of Gedaliah: Wednesday; (day of) Atonement: Wednesday; (day of the) Willow:15 Sunday; Marḥešvan: Tuesday and Wednesday; Kislev: Thursday ... As can be glimpsed from this excerpt, each chapter of Josiah b. Mevorakh al-ʿĀqūlī’s calendar is made up of three elements: 1) a set of numbers, 2) the character of the year described in that chapter, and 3) a fuller description of the calendar, including the beginning of months, festivals and fasts. The list of numbers at the beginning of each chapter identifies which years will have the character described in the chapter. They do so not by giving the years’ dates but by referring to their positions within the 247-year cycle. This position is calculated as the remainder from subtracting 1000 from the Seleucid date (SE) and casting out 247s (for the purposes of this calendar if the SE date minus 1000 is a multiple of 247, the remainder is not 0 but 247). In order to use Josiah b. Mevorakh al-ʿĀqūlī’s calendar in any given year, one must take that year’s SE date and determine its remainder by following the algorithm described above. One must then look for it within the sets of numbers given in each of the fourteen chapters. The chapter that lists the sought remainder will describe the correct course of the year for that date. Take, for example, year 1262 SE. Its remainder in Josiah b. Mevorakh al-ʿĀqūlī’s algorithm can be calculated as (1262-1000) modulo 247 and equals 15. The number 15 can be found on the list of remainders for a defective and plain year with the character ‫( בחג‬see the edited text above). This means that in 1262 SE the month of Tišri will start on a Monday, the first day of Sukkot as well as Šemini ʿAṣeret will fall on a Monday, the fast of Gedaliah will be on a Wednesday, the day of Atonement will be on a Wednesday, 13. This number is out of order here and in other related manuscripts. 14. This number is intended to represent the count of numbers above, and should be 14. 15. I.e. the 7th day of Sukkot. -6- and so on. Manuscripts of Josiah b. Mevorakh al-ʿĀqūlī’s calendar and related texts 1) Genizah fragments16 Cambridge, T-S 6K2.1: two leaves; a critique of the 247-year cycle in the hand of Joseph b. Jacob ha-Bavli, a scholar active in Egypt in the late 12th–early 13th century;17 cf. Cambridge, T-S NS 98.40, T-S Misc.25.29, T-S AS 144.164 and Cambridge, T-S AS 144.111. Cambridge, T-S 10K20.2 and T-S K19.12: three non-consecutive leaves (one folio and one bifolio), paleographically datable to the 13th–14th century, that contain an introduction and a description of five year types. Mentions R. Saadia Gaon with reference to the division of weekly portions. Cambridge, T-S K2.8: fourteen bifolios containing an introduction and a description of thirteen out of the fourteen year types. The arrangement of lists of remainders suggests that the fragment was written in the end of the 13th century, around 1296/7 CE. Cambridge, T-S K2.41: eight bifolios containing a description of eight year types, tentatively paleographically datable to the 13th–14th century. T-S K2.41 is clearly related to JTS ENA 3329 and ENA 1640.5 (see below) as is shown by numerous common features of the fragments, such as irregularities in the ordering of remainders, scribal mistakes, writing 15 as ‫ הי‬as opposed to ‫ טו‬in other copies, etc. Cambridge, T-S Ar.2.12: one folio with writing in different directions and by two different hands hand 1: remainder lists for the last two year types, without fuller descriptions of the course of the year; probably, the original text of this fragment. hand 2: a draft of an introduction to a work on calendar describing among other things how remainders for each year type were established. Additional passages copied here in the same hand include a calendar for years 1492–1494 SE (1180/1– 1182/3 CE). Cambridge, T-S NS 98.2 and T-S AS 144.118: three folios (one folio and one noncontinuous bifolio) beautifully written in square script and paleographically datable to the 13th–14th century. The author describes the history of the Jewish calendar 16. I thank Dr. Amir Ashur of Tel–Aviv University for helping me assess the handwriting of Genizah documents. 17. See Alexander Scheiber, “Materialien zur Wirksamkeit des Joseph ben Jakob Habavli als Schriftsteller und Kopist”, Acta Orientalia Academiae Scientiarum Hungaricae 23 (1970): 115–130. -7- and testifies to the popularity of Josiah b. Mevorakh al-ʿĀqūlī’s scheme. Cambridge, T-S NS 98.40, T-S Misc.25.29, and T-S AS 144.164: four non-consecutive leaves (two folios and one bifolio), paleographically datable to the 2nd half of the 12th–1st half of the 13th century. The fragments contain a description of three year types and a critique of the 247-year cycle; cf. Cambridge, T-S 6K2.1 and Cambridge, T-S AS 144.111. Cambridge, T-S NS 98.95: one badly rubbed folio containing a description of one year type. Cambridge, T-S NS 312.94: one folio with holes, paleographically datable to the 13th–14th century; contains an introduction to Josiah b. Mevorakh al-ʿĀqūlī’s calendar. Cambridge, T-S AS 144.32: one bifolio, rubbed and badly stained, partially illegible. It is tentatively paleographically datable to the 13th century and contains a description of two year types. Cambridge, T-S AS 144.46, T-S AS 144.166: two leaves containing descriptions of four year types; paleographically datable to the 12th–14th century. Cambridge, T-S AS 144.111: one leaf that contains a description of three year types, a critique of the 247-year cycle and a note in a secondary hand establishing remainders for some of the years in the 19-year cycle 258 (1123/4–1142/3 CE); cf. Cambridge, T-S NS 98.40, T-S Misc.25.29, T-S AS 144.164 and Cambridge, T-S 6K2.1. Cambridge, T-S AS 144.228, T-S AS 144.286 and T-S AS 203.216: all three fragments join to form one folio. They carry an introduction to Josiah b. Mevorakh’s calendar, an explanation of the algorithm using 1443 SE (1131/2 CE) as an example and a description of two year types. Manchester, Rylands B 3390 and Rylands B 5508: remains of three badly torn leaves (one folio and one bifolio) containing a partial description of two year types, paleographically datable to the 11th–13th century. New York, JTS ENA 1640.5 and ENA 3329: fourteen leaves containing a description of all fourteen year types but not the introduction, paleographically datable to the 13th–14th century. This copy is clearly related to T-S K2.41 (see above). 2) Judaeo-Persian manuscripts London, BL Or. 2451: a Bible in a Persian hand copied in Qum by Samuel b. Aaron b. Yehosef and dated in colophon 1482/3 CE. Fols 363v–375v carry Josiah b. Mevorakh al-ʿĀqūlī’s calendar. The arrangement of remainders in this manuscript indicates that at least its calendar part was copied from a Vorlage penned around -8- 1330/31 CE.18 The calendar of remainders in London, BL Or. 2451 is identical (including the scribal mistakes) to that in Oxford, Bodl. Heb. e.60, also copied in Qum by Samuel b. Aaron b. Yehosef. London, BL Or. 9884: a Bible in a Persian hand copied in 1468/9 CE. Fols 308r–314r contain Josiah b. Mevorakh al-ʿĀqūlī’s calendar. London, BL Or. 10576: a prayer-book for the whole year according to the Persian rite copied in the 16th–17th century. Fols 153r–158v contain the 247-year cycle attributed to Josiah b. Mevorakh al-ʿĀqūlī. The calendar is said to start after 1494 SE (1182/3 CE) and must have been copied from an earlier Vorlage. The cycle has an unusual shape in that it is presented not as lists of remainders pertaining to each year type but as a numbered sequence of 247 year types. Compare London, BL Or. 10702. London, BL Or. 10702: a fragmentarily preserved prayer-book for the whole year according to the Persian rite copied in the 15th century. On fol. 30r there are remains of Josiah b. Mevorakh al-ʿĀqūlī’s calendar in the form of a continuous sequence of 247 year types, of which only numbers 218–241 have survived. Compare London, BL Or. 10576. Oxford, Bodl. Heb. e.60: a Bible in a Persian script copied in Qum by Samuel b. Aaron b. Yehosef and dated 1484/5 CE. Josiah b. Mevorakh al-ʿĀqūlī’s cycle is on fols 450r–461v. The calendar of remainders in Oxford, Bodl. Heb. e.60 is identical to that in London, BL Or. 2451 and was probably copied from the same Vorlage. 3) Manuscripts from other geo-cultural areas Oxford, Bodl. Poc. 368: a 15th century astronomical–calendrical miscellany copied in a number of Byzantine hands. Fol. 219r presents a calendar scheme identical to Josiah b. Mevorakh’s cycle but not attributed to any authority. The origins of Josiah b. Mevorakh al-ʿĀqūlī’s system The instructions provided in the introduction to Josiah b. Mevorakh al-ʿĀqūlī’s cycle of remainders explain how this calendar should be used but do not say anything on how the calendar was put together. We do not possess a description of the working process by Josiah b. Mevorakh himself, but a later scholar claiming to have taken 18. For an explication of this date see section on the distribution and use of Josiah b. Mevorakh’s calendar below. -9- the same course of action as Josiah b. Mevorakh, by then deceased,19 describes his working process as follows:20 I looked in each of them at the days of the week on which (New Year) is set, which are Monday, Tuesday, Thursday and Saturday. There are fourteen (types of) years, not .... These are ‫בשה‬, ‫בשמז‬, ‫בחמה‬, ‫בחג‬, ‫גכה‬, ‫גכמז‬, ‫השא‬, ‫השמג‬, ‫הכז‬, ‫החמא‬, ‫זשג‬, ‫זשמג‬,21 ‫זחא‬, and ‫זחמג‬. I counted how many times each of these fourteen signs occurs in each 19-year cycle, added them up, and itemized them. Thus, in thirteen 19-year cycles there are twenty-nine years of the type ‫בשה‬, I made for it twenty-nine (symbols). That is, for each year I looked at its Seleucid date, removed 1000 from the total and 247s from what remained, and that what was left over I made into a symbol. The process is then a straightforward one: amass calendrical data for thirteen 19year cycles, group together years with the same year type and for each group note down ordinal numbers of years that comprise it, counting in 247-year cycles with an epoch in 1001 SE. A question arises how the initial set of calendrical data for 247 years was compiled: was it based on the standard molad calculation or on some other set of rules not involving the molad? Fixed, non-empirical, calendars that do not depend on the calculation of the molad have been recently discovered in the Cairo Genizah.22 These schemes operate with Rabbinic calendrical concepts but follow their own rules for determining the character of a year. Importantly, sequences of year types produced by these rules do not form cycles of 247 years but much shorter cycles, which differ crucially from the standard Jewish calendar. On the contrary, the sequence of characters generated by Josiah b. Mevorakh al-ʿĀqūlī’s remainders is very close to the standard calendar. This is unlikely a coincidence since the standard Jewish calendar is not in any obvious way reducible to a combination of shorter sequences and is thus not easy to reproduce following structural considerations alone. For this reason it is most likely that the sequence of 247 year types underlying Josiah b. 19. T-S Ar.2.12: ‫וקד סלכת פי אל]מ[גמוע מא סלכה פיה ז֗ ֗ל‬. The fragment, which appears to be an autograph draft, contains calendrical information for 1180/1–1182/3 CE and was most probably written around these dates. 20. T-S Ar. 2.12r: ‫איאם‬ ‫ונטרת מנהם יום‬ ֗ ‫֗ה ֗ש ֗א ֗ה ֗ש ֗מ ֗ג ֗ה ֗כז֗ ֗ה ֗ח ֗מ ֗א ז֗ ֗ש ֗ג ז֗ ֗ש ֗מ ֗ג ז֗ ֗ח ֗א ז֗ ֗ח ֗מ ֗ג פעדדת כם פי כל מחזור מן הדה אלי֗ ֗ד עלאמה וגמעתהם ופצלתהם פכאן פי‬ ‫נטרת כל סנה מא תאריכהא ללשטרות אסקטת אלף גמלה‬ ֗ ‫אלי֗ ֗ג מחזור מא עלאמתה ֗ב ֗ש ֗ה כט סנה עמלת להא ֗כ ֗ט ודלך אנני‬ ‫פצל געלתה סימן‬ ֗ ‫ואלבקיה ֗ר ֗מז֗ ֗ר ֗מז֗ ומא‬ 21. This is a mistake, the expected sign is ‫זשמה‬. [ ֗‫אר? והם ֗ב ֗ש ֗ה ֗ב ֗ש ֗מז֗ ֗ב ֗ ֗ח ֗מ ֗ה ֗ב ֗ח ֗ג ֗ג ֗כ ֗ה ֗ג ֗כ ֗מ]ז‬...‫ שי‬...‫אלקביעה ]א[לדי הם ֗ב] ֗ג ֗ה?[ז֗ והם י֗ ֗ד סנה לא תצי‬ 22. See Sacha Stern, “A Primitive Rabbinic Calendar from the Cairo Genizah,” forthcoming. - 10 - Mevorakh’s cycle was initially based on the standard molad calculation.23 Operating with relative positions of years within a 247-year cycle instead of their SE or AM dates means that Josiah b. Mevorakh’s calendar applies not to a particular 247-year interval24 but to any stretch of 247 consecutive years from 1001 SE onwards. The resultant lack of dates in copies of Josiah b. Mevorakh al-ʿĀqūlī’s calendar creates difficulties for dating this system. The epoch of 1001 SE (689/90 CE), determined as the first year when the algorithm described in the introduction becomes usable, is not helpful in dating the system as it is clearly too early. Indeed, the above considerations show that the 247-year cycle cannot pre-date the molad calculation, which in all likelihood has been known since the 9th century but not before.25 Instead, this epoch was probably chosen in order to simplify calculations, since for a thousand years the operation of taking away 1000 produced a number that can be more easily cast out by 247 than the full SE date. The downside of choosing such an epoch is that 247-year cycles calculated from it are not synchronised with 19-year cycles of intercalation. Instead they start in year four of the 19-year cycle if counted from the year of Creation as was the rule in Palestine and as is common today or in year three of the 19-year cycle if counted from Adam’s epoch as was common in Babylonia. Indeed, using the count from Creation, 1001 SE is 4450 AM, 19-year cycle 235, year four. Earlier attempts to date the cycle of remainders proved inconclusive. In Lon. BL Or. 10576, one of the Judaeo-Persian manuscripts, Josiah b. Mevorakh al-ʿĀqūlī’s calendar is said to start after 1494 SE (1182/3 CE). This starting point, together with the honorific “of blessed memory” added to Josiah’s name, led Tobi to deduce that Josiah b. Mevorakh lived in the first half of the 12th century or earlier.26 A terminus post quem of 1000 CE was inferred by Adler from the fact that “this chronologist is unknown to Albīrūnī,”27 an opinion challenged by Steinschneider for whom “the ignorance of Albiruni is no proof for the time of Joschia!”28 New evidence from the Cairo Genizah allows dating this sage and his calendar with far more precision. 23. It is particularly telling that pairs of consecutive year types precluded in the standard calendar by the molad calculation alone never appear in the 247-year cycle. For examples of such prohibited sequences see Sherrard Beaumont Burnaby, Elements of the Jewish and Muhammadan Calendars with Rules and Tables and Explanatory Notes on the Julian and Gregorian Calendars (London: George Bell and Sons, 1901), pp. 108, 115. 24. As is the case with the ʿIggul of R. Naḥshon which, although it is said to repeat itself exactly, is always formulated for a particular thirteen cycles of nineteen years, e.g., 19-year cycles 258–270. 25. It is first attested in al-Khwārizmī’s treatise on the Jewish calendar of 823/4 CE. See Stern, Calendar and Community, pp. 200-210. 26. Tobi, The Jews of Yemen, p. 215. Raviv, Mathematical Studies, p. 89 accepts this dating. 27. Adler, “The Persian Jews,” p. 623. 28. Moritz Steinschneider, “An Introduction to the Arabic Literature of the Jews. I,” Jewish Quarterly Review 12/2 (1900): 195–212, p. 201. - 11 - The methodology for dating a cycle of remainders depends on the 247-year cycle not being a true cycle from the point of view of the standard calendar. Because the sequence of year types does not recur exactly, for any given sequence it is possible to establish one and only one 247-year period during which this sequence will correspond to the standard calendar. In the next (or previous) iteration of the cycle most remainders will produce correct results but some will deviate from the molad calculation. By analysing all preserved cycles of remainders and establishing the 247-year interval to which each calendar pertains it may be possible to establish the original sequence as it was fixed by Josiah b. Mevorakh al-ʿĀqūlī, on the assumption that it was based on the molad calculation. The period covered by the original sequence can help us date the system and its author. Starting from 1001 SE, the earliest date when the described algorithm is applicable, the first four iterations of the 247-year cycle are: first iteration: 1001 SE–1247 SE (689/90–935/6 CE) second iteration: 1248–1494 SE (936/7–1182/3 CE) third iteration: 1495–1741 SE (1183/4–1429/30 CE) fourth iteration: 1742–1988 SE (1430/31–1676/7 CE) This takes us to the second half of the 17th century which, according to the catalogues, is an adequate terminus ad quem for the latest known manuscript containing the cycle of remainders. As mentioned above, two consecutive 247-year sequences differ from one another in ca. two to seventeen years. Table 1 lists all years in which the four above-mentioned iterations of the 247-year cycle are not identical. Cells with a grey background indicate deviations from the first iteration of 1001–1247 SE. Table 1 remaind 1st iteration er SE date year type 2nd iteration 3rd iteration 4th iteration SE date year type SE date year type SE date year type 6 1006 ‫זשג‬ 1253 ‫זשג‬ 1500 ‫זשג‬ 1747 ‫זחא‬ 7 1007 ‫הכז‬ 1254 ‫הכז‬ 1501 ‫הכז‬ 1748 ‫גכה‬ 8 1008 ‫בחה‬ 1255 ‫בחה‬ 1502 ‫בחה‬ 1749 ‫זשה‬ 49 1049 ‫זשה‬ 1296 ‫זחג‬ 1543 ‫זחג‬ 1790 ‫זחג‬ 50 1050 ‫זחא‬ 1297 ‫השא‬ 1544 ‫השא‬ 1791 ‫השא‬ - 12 - ‫זחא‬ ‫‪1794‬‬ ‫זחא‬ ‫‪1547‬‬ ‫זחא‬ ‫‪1300‬‬ ‫זשג‬ ‫‪1053‬‬ ‫‪53‬‬ ‫גכז‬ ‫‪1795‬‬ ‫גכז‬ ‫‪1548‬‬ ‫גכז‬ ‫‪1301‬‬ ‫החא‬ ‫‪1054‬‬ ‫‪54‬‬ ‫בשה‬ ‫‪1796‬‬ ‫בשה‬ ‫‪1549‬‬ ‫בשה‬ ‫‪1302‬‬ ‫גכה‬ ‫‪1055‬‬ ‫‪55‬‬ ‫בחה‬ ‫‪1806‬‬ ‫בחה‬ ‫‪1559‬‬ ‫בשז‬ ‫‪1312‬‬ ‫בשז‬ ‫‪1065‬‬ ‫‪65‬‬ ‫זשג‬ ‫‪1807‬‬ ‫זשג‬ ‫‪1560‬‬ ‫בחג‬ ‫‪1313‬‬ ‫בחג‬ ‫‪1066‬‬ ‫‪66‬‬ ‫בחג‬ ‫‪1810‬‬ ‫בחג‬ ‫‪1563‬‬ ‫בשה‬ ‫‪1316‬‬ ‫בשה‬ ‫‪1069‬‬ ‫‪69‬‬ ‫השא‬ ‫‪1811‬‬ ‫השא‬ ‫‪1564‬‬ ‫זחא‬ ‫‪1317‬‬ ‫זחא‬ ‫‪1070‬‬ ‫‪70‬‬ ‫הכז‬ ‫‪1835‬‬ ‫הכז‬ ‫‪1588‬‬ ‫הכז‬ ‫‪1341‬‬ ‫השא‬ ‫‪1094‬‬ ‫‪94‬‬ ‫בשז‬ ‫‪1836‬‬ ‫בשז‬ ‫‪1589‬‬ ‫בשז‬ ‫‪1342‬‬ ‫גכז‬ ‫‪1095‬‬ ‫‪95‬‬ ‫זחג‬ ‫‪1888‬‬ ‫זשה‬ ‫‪1641‬‬ ‫זשה‬ ‫‪1394‬‬ ‫זשה‬ ‫‪1147‬‬ ‫‪147‬‬ ‫השא‬ ‫‪1889‬‬ ‫זחא‬ ‫‪1642‬‬ ‫זחא‬ ‫‪1395‬‬ ‫זחא‬ ‫‪1148‬‬ ‫‪148‬‬ ‫זחא‬ ‫‪1892‬‬ ‫זשג‬ ‫‪1645‬‬ ‫זשג‬ ‫‪1398‬‬ ‫זשג‬ ‫‪1151‬‬ ‫‪151‬‬ ‫גכז‬ ‫‪1893‬‬ ‫החא‬ ‫‪1646‬‬ ‫החא‬ ‫‪1399‬‬ ‫החא‬ ‫‪1152‬‬ ‫‪152‬‬ ‫בשה‬ ‫‪1894‬‬ ‫גכה‬ ‫‪1647‬‬ ‫גכה‬ ‫‪1400‬‬ ‫גכה‬ ‫‪1153‬‬ ‫‪153‬‬ ‫הכז‬ ‫‪1913‬‬ ‫הכז‬ ‫‪1666‬‬ ‫השא‬ ‫‪1419‬‬ ‫השא‬ ‫‪1172‬‬ ‫‪172‬‬ ‫בשה‬ ‫‪1914‬‬ ‫בשה‬ ‫‪1667‬‬ ‫גכה‬ ‫‪1420‬‬ ‫גכה‬ ‫‪1173‬‬ ‫‪173‬‬ ‫הכז‬ ‫‪1933‬‬ ‫השא‬ ‫‪1686‬‬ ‫השא‬ ‫‪1439‬‬ ‫השא‬ ‫‪1192‬‬ ‫‪192‬‬ ‫בשז‬ ‫‪1934‬‬ ‫גכז‬ ‫‪1687‬‬ ‫גכז‬ ‫‪1440‬‬ ‫גכז‬ ‫‪1193‬‬ ‫‪193‬‬ ‫החא‬ ‫‪1974‬‬ ‫החא‬ ‫‪1727‬‬ ‫החא‬ ‫‪1480‬‬ ‫השג‬ ‫‪1233‬‬ ‫‪233‬‬ ‫גכה‬ ‫‪1975‬‬ ‫גכה‬ ‫‪1728‬‬ ‫גכה‬ ‫‪1481‬‬ ‫הכז‬ ‫‪1234‬‬ ‫‪234‬‬ ‫זשג‬ ‫‪1976‬‬ ‫זשג‬ ‫‪1729‬‬ ‫זשג‬ ‫‪1482‬‬ ‫בחג‬ ‫‪1235‬‬ ‫‪235‬‬ ‫בחג‬ ‫‪1979‬‬ ‫בחג‬ ‫‪1732‬‬ ‫בחג‬ ‫‪1485‬‬ ‫בשה‬ ‫‪1238‬‬ ‫‪238‬‬ ‫השג‬ ‫‪1980‬‬ ‫השג‬ ‫‪1733‬‬ ‫השג‬ ‫‪1486‬‬ ‫זחג‬ ‫‪1239‬‬ ‫‪239‬‬ ‫‪- 13 -‬‬ Table 2 presents data for the same years of possible calendar divergence as it is found in various manuscripts of Josiah b. Mevorakh al-ʿĀqūlī’s calendar. Not all preserved copies of this calendar are complete, and some have description of only one or two year types. The following notation is used in Table 2: a) Data year type: remainder is on the list for this given year type. {year type}: remainder is not on the list for this given year type even though the relevant year type is represented in the manuscript. The absence of a remainder so marked is not due to a scribal error or a hole in the manuscript and is therefore significant (the difference between scribal errors and significant variations is explained below). This notation is used for incomplete manuscripts where not all year types have been preserved, which makes it necessary to draw conclusions from silence. empty cell: a) in incomplete manuscripts data for a remainder are missing because the relevant year type has not survived; b) in complete manuscripts a remainder is not assigned to any year type due to a scribal mistake; c) lacuna in the manuscript. Each year type is marked by numbers 1 to 4 to indicate in which iterations of the 247-year cycle it is correct. For year types given in curly brackets it indicates iterations in which it is correct for the remainder to be missing from the list, e.g.: ‘remainder 8: ‫ בחה‬1–3’ means that in iterations 1–3 it is correct for remainder 8 to be on the list of remainders for the year type ‫;בחה‬ ‘remainder 65: {‫ }בחה‬1-2’ means that in iterations 1–2 it is correct for remainder 65 to be missing from the list of remainders in the year type ‫בחה‬. b) Manuscripts classmark A+classmark B: Genizah fragments join and are part of the same copy Related manuscripts that contain identical or very similar lists of remainders are grouped together and are represented by one column. Lon. BL Or. 10702 is excluded from the table for being too fragmentary and inconclusive. - 14 - remain T-S NS der 98.40 +T-S Misc.25 .29+TS AS 144.16 429 T-S AS T-S AS T-S AS 203.21 144.11 144.32 32 6+T-S 131 AS 144.22 8+T-S AS 144.28 630 6 T-S AS 144.46 +T-S AS 144.16 633 T-S Ar.2.12 , T-S NS 98.9534 Ryland sB 5508+ Ryland sB 399035 {‫}זחא‬ 1-3 7 ‫ הכז‬1-3 29. Three year types are preserved: ‫בחה‬, ‫ בחג‬and ‫החא‬. 30. Two year types are preserved: ‫ בשה‬and ‫( זשג‬the latter is extremely fragmentary). 31. Three year types are preserved: ‫השא‬, ‫ גכז‬and ‫זחא‬. 32. Two year types are preserved: ‫ הכז‬and ‫בחג‬. 33. Four year types are preserved: ‫בחה‬, ‫בשז‬, ‫ בחג‬and ‫השג‬. ENA 3329+ ENA 1640.5, T-S K2.4136 T-S T-S 10K20. K2.838 2+T-S K19.12 Ox. Bodl. Poc. 368 37 Lon. BL Lon. BL Lon. BL Or. Or. Or 10576 2451, 988439 Ox. Bodl. Heb. e.60 ‫ זשג‬1-3 {‫}זחא‬ 1-3 ‫ זשג‬1-3 ‫ זשג‬1-3 ‫ זחא‬4 ‫הכז‬40 1-3 ‫ הכז‬1-3 ‫ הכז‬1-3 ‫ גכה‬4 ‫ הכז‬1-3 ‫הכז‬41 1-3 34. T-S Ar.2.12 preserves remainders for the year types ‫( זחא‬only some remainders survive) and ‫ זחג‬and T-S NS 98.95 for the year type ‫ זחג‬only. Unlike other manuscripts grouped together in one column, these two cannot be shown to be related, and are only placed together for considerations of space. 35. Two year types are partially preserved: ‫ זחג‬and ‫בשז‬. 36. ENA 3329+ENA 1640.5 is complete. In T-S K2.41 only eight year types are preserved; missing are: ‫גכז‬, ‫השא‬, ‫זשג‬, ‫זשה‬, ‫גכה‬, ‫זחא‬. 37. Five year types are preserved: ‫בחג‬, ‫זשה‬, ‫השג‬, ‫זחא‬, ‫הכז‬. 38. The year type ‫ זשג‬is missing. 39. Remainders for ‫ זחג‬are corrupt in the manuscript and are given as identical to those of ‫ זחא‬apart from two years. 40. In ENA 3329+ENA 1640.5 remainder 7 is also given in ‫גכה‬, where it is found severely out of place (cf. T-S K2.8). 41. Remainder 7 is also given in ‫( גכה‬cf. ENA 3329+ENA 1640.5). 8 ‫ בחה‬1-3 ‫ בחה‬1-3 49 ‫ זחג‬2-4 ‫ ?זחג‬2-4 ‫ זחג‬2-4 {‫}זשה‬ 2-4 50 ‫ זחא‬1 53 54 ‫ בחה‬1-3 {‫}זשה‬ 1-3 ‫ ?זשג‬1 ‫ החא‬1 55 {‫}זחא‬ 2-4 {‫}בחה‬ 1-2 66 ‫ בחג‬1-2 69 {‫}בחג‬ 1-2 ‫השא‬ 2-4 ‫השא‬ 2-4 ‫השא‬ 2-4 ‫השא‬ 2-4 ‫השא‬ 2-4 ‫ זחא‬2-4 ‫ זחא‬2-4 ‫ זחא‬2-4 ‫ זחא‬2-4 ‫ זחא‬2-4 ‫ זחא‬2-4 ‫ זחא‬2-4 {‫ }גכז‬1 ‫ גכז‬2-4 ‫ גכז‬2-4 ‫ גכז‬2-4 ‫ גכז‬2-4 ‫ גכז‬2-4 ‫ גכז‬2-4 ‫בשה‬42 2-4 ‫בשה‬43 2-4 ‫בשה‬ 2-4 ‫ בשז‬1-2 ‫בחג‬44 3-4 ‫בחה‬45 3-4 ‫ בחה‬3-4 ‫ בחה‬3-4 ‫ בחה‬3-4 ‫ בחה‬3-4 ‫ בשז‬1-2 ‫בשה‬ 1-2 ‫ זחג‬2-4 ‫ זחג‬2-4 ‫ זחג‬2-4 ‫ זחג‬2-4 {‫ }זחא‬1 {‫}בשה‬ 1 65 ‫ בחה‬1-3 ‫ בחה‬1-3 ‫ בחה‬1-3 ‫ בחה‬1-3 ‫ זשה‬4 ‫בשה‬ 2-4 ‫בשה‬ 2-4 ‫בשה‬ 2-4 ‫ בחג‬1-2 ‫ בחג‬1-2 ‫ זשג‬3-4 {‫}בחג‬ 3-4 {‫}בחג‬ 1-2 ‫ בחג‬3-4 ‫ בחג‬3-4 ‫ בחג‬3-4 ‫ בחג‬3-4 ‫ בחג‬3-4 ‫ בחג‬3-4 ‫ בחג‬3-4 {‫}בחג‬ 1-2 ‫ זשג‬3-4 ‫ זשג‬3-4 ‫ זשג‬3-4 ‫ זשג‬3-4 42. In both fragments the remainder given in ‫ בשה‬is 58, and 55 is not assigned to any year type. This is a clear scribal mistake based on the similarity of the Hebrew numerals ‫ נח‬and ‫נה‬. The same is also the case in T-S K2.8. 43. By scribal error the remainder given in ‫ בשה‬is 58, and 55 is not assigned to any year type. Cf. ENA 3329+ENA 1640.5 and T-S K2.41. 44. Both fragments give here ‫בחג‬, the symbol for a plain defective year beginning on Monday, whereas what is expected is ‫ – בחה‬a symbol for an intercalated year. 45. The remainder given in ‫ בחה‬is 68, and 65 is not assigned to any year type. This is a clear scribal mistake based on the similarity of the Hebrew numerals ‫ סח‬and ‫סה‬. Cf. remainder 55 in this manuscript as well as in ENA 3329+ENA 1640.5 and T-S K2.41. 70 ‫ זחא‬1-2 94 ‫ השא‬1 95 ‫ גכז‬1 ‫השא‬ 3-4 ‫ הכז‬2-4 ‫השא‬ 3-4 ‫השא‬ 3-4 ‫השא‬ 3-4 ‫השא‬ 3-4 ‫השא‬46 3-4 ‫ הכז‬2-4 ‫ הכז‬2-4 ‫ הכז‬2-4 ‫ הכז‬2-4 ‫ הכז‬2-4 ‫ הכז‬2-4 ‫ הכז‬2-4 {‫ }בשז‬1 147 {‫}זחא‬ 3-4 ‫ בשז‬2-4 ‫ בשז‬2-4 {‫}זחג‬ 1-3 ‫ בשז‬2-4 ‫ בשז‬2-4 ‫ בשז‬2-4 ‫ בשז‬2-4 ‫ בשז‬2-4 ‫ זשה‬1-3 ‫ זשה‬1-3 ‫ זשה‬1-3 ‫זשה‬47 1-3 ‫ זשה‬1-3 ‫ זשה‬1-3 ‫ זשה‬1-3 148 ‫ זחא‬1-3 ‫ זחא‬1-3 ‫ זחא‬1-3 ‫ זחא‬1-3 ‫ זחא‬1-3 ‫ זחא‬1-3 ‫ זחא‬1-3 ‫ זחא‬1-3 151 {‫}זחא‬ 1-3 ‫ זשג‬1-3 {‫}זחא‬ 1-3 {‫}גכז‬ 1-3 ‫ החא‬1-3 152 ‫ החא‬1-3 153 {‫}בשה‬ 1-3 172 ‫ החא‬1-3 ‫ החא‬1-3 ‫ החא‬1-3 ‫ החא‬1-3 ‫ החא‬1-3 ‫ גכה‬1-3 ‫השא‬ 1-2 {‫}הכז‬ 1-2 173 ‫השא‬ 1-2 {‫}הכז‬ 1-2 ‫ גכה‬1-2 192 ‫ זשג‬1-3 ‫ זשג‬1-3 ‫ זשג‬1-3 ‫ זשג‬1-3 ‫השא‬ 1-3 {‫}הכז‬ 1-3 ‫השא‬ 1-3 {‫}הכז‬ 1-3 ‫השא‬ 1-2 ‫גכה‬48 1-3 ‫ גכה‬1-3 ‫ גכה‬1-3 ‫ גכה‬1-3 ‫השא‬ 1-2 ‫ הכז‬3-4 ‫השא‬ 1-2 ‫ הכז‬3-4 ‫ גכה‬1-2 ‫ גכה‬1-2 ‫בשה‬ 3-4 ‫בשה‬ 3-4 ‫בשה‬ 3-4 ‫השא‬ 1-3 ‫השא‬ 1-3 ‫השא‬ 1-3 ‫השא‬ 1-3 ‫השא‬ 1-3 46. Remainder 70 is also given in ‫זחג‬, but the list of remainders for this year type is corrupt in the manuscript. 47. The remainder given in ‫ זשה‬is 146, and remainder 147 is not assigned to any year type. This is a scribal mistake based on the graphic similarity of the Hebrew numerals ‫ קמו‬and ‫קמז‬. The remainder given in ‫ גכה‬is 123, and remainder 153 is not assigned to any year type. This is a scribal mistake based on the graphic similarity of the Hebrew numerals ‫ קכג‬and ‫קנג‬. Similar confusion occurred in this manuscript between Hebrew numerals ‫ כח‬and ‫ נח‬and ‫ קכו‬and ‫קנו‬. 48. 193 233 ‫ גכז‬1-3 {‫}החא‬ 1 238 239 {‫}בשז‬ 1-3 ‫ השג‬1 234 235 {‫}בשז‬ 1-3 ‫ הכז‬1 ‫ בחג‬1 ‫ בחג‬1 ‫ בשה‬1 {‫}בחג‬ 2-4 ‫ בחג‬2-4 ‫ בחג‬2-4 ‫ השג‬2-4 {‫}זחג‬ 2-4 ‫ גכז‬1-3 ‫ גכז‬1-3 ‫ גכז‬1-3 ‫גכז‬49 1-3 ‫ החא‬2-4 {‫}השג‬ 2-4 ‫ החא‬2-4 ‫ החא‬2-4 ‫ החא‬2-4 ‫ החא‬2-4 ‫ החא‬2-4 ‫ גכה‬2-4 {‫}הכז‬ 2-4 ‫ גכה‬2-4 ‫ גכה‬2-4 ‫ גכה‬2-4 ‫ גכה‬2-4 ‫ גכה‬2-4 {‫}בחג‬ 2-4 ‫ זשג‬2-4 ‫ זשג‬2-4 ‫ זשג‬2-4 ‫ זשג‬2-4 ‫ גכז‬1-3 ‫ גכז‬1-3 ‫ בחג‬2-4 ‫ בחג‬2-4 ‫ בחג‬2-4 ‫ בחג‬2-4 ‫ בחג‬2-4 ‫ בחג‬2-4 ‫ בחג‬2-4 {‫}זחג‬ 2-4 ‫ השג‬2-4 ‫ השג‬2-4 ‫ השג‬2-4 ‫ השג‬2-4 ‫ השג‬2-4 ‫ השג‬2-4 ‫ השג‬2-4 49. Lon. BL Or. 10576, fol. 155r reads here ‫גכמה‬, where ‫ מ‬stands for ‫מעוברת‬, intercalated. This is a clear scribal mistake, since the character of an orderly intercalated year starting on Tuesday is ‫גכז‬, not ‫גכה‬. Other mistakes in the day of the week of Passover are found in this manuscript. A scrutiny of Table 2 against Table 1 reveals that lists of remainders presented in different manuscripts show significant differences that cannot be written off as mere scribal mistakes. Admittedly, most copies of this calendar are ridden with scribal errors because copying sets of numbers is an arduous task in which the copyist is not aided by the context. However, scribal mistakes can in most cases be distinguished from significant variations. Indeed, mistakes usually apply to single years and generate random results assigning remainders to year types that are incorrect in any iteration of the 247-year cycle. On the contrary, iteration related deviations show up in groups of two to three consecutive years50 and produce remainders that are incorrect in one iteration of the cycle but correct in another. Three fragmentarily preserved copies of the calendar contain a version of Josiah b. Mevorakh’s cycle that is particularly early. These are T-S NS 98.40+T-S Misc.25.29+T-S AS 144.164, T-S AS 203.216+T-S AS 144.228+T-S AS 144.286, and T-S AS 144.111. The following remainders are decisive for dating the version: remaind T-S NS 98.40+T-S er Misc.25.29+T-S AS 144.164: ‫בחה‬, ‫ בחג‬and ‫החא‬ T-S AS 203.216+T-S T-S AS 144.111: AS 144.228+T-S AS ‫השא‬, ‫ גכז‬and ‫זחא‬ 144.286: ‫ בשה‬and ‫זשג‬ 50 ‫ זחא‬1 53 54 ‫ ?זשג‬1 ‫ החא‬1 55 {‫ }זחא‬1 {‫ }גכז‬1 {‫ }בשה‬1 94 ‫ השא‬1 95 ‫ גכז‬1 233 {‫ }החא‬1 235 ‫ בחג‬1 238 ‫ בשה‬1 It is immediately obvious that remainders in these copies refer to the first iteration of Josiah b. Mevorakh’s calendar, i.e., to years 1001–1247 SE (689/90–935/6 CE). As I argued above, Josiah b. Mevorakh’s cycle of remainders must have been 50. As was mentioned above this follows from the rules of postponements and the allowed lengths of the variable months Marḥešvan and Kislev. - 19 - originally put together using the standard molad calculation, which makes a construction date in the 7th century very unlikely.51 More probable is that it was constructed around the end of this 247-year period or the beginning of the next one using calendrical records for the near past in combination with data calculated retrojectively for more remote years, or by retrojective calculation alone.52 The most likely terminus post quem for the creation of Josiah b. Mevorakh’s calendar is the Saadia–Ben Meir dispute of 921–924 CE, when methods of calendation were discussed in fine detail but the 247-year cycle was not mentioned.53 It can be conjectured that Josiah b. Mevorakh’s calendar of remainders was devised in the aftermath of the dispute as a means of preventing future calendar dissidence by eliminating the need for calculation, an alternative to using the so-called Four Gates table advocated by the protagonists of the dispute. The decade of 980s may be suggested as the cycle’s terminus ante quem. Inasmuch as the second iteration of Josiah b. Mevorakh’s cycle becomes different from the first in 984/5–985/6 CE and then in 988/9–990/1 CE (cf. remainders 49–50 and 53–55 in Table 1), in this decade calendrical data for the previous 247 years would be found deviant from the standard calendar and would unlikely be used as a basis for a calendar cycle. Taken together the two termini indicate that the calendar of remainders was conceived in the middle of the 10th century. This dating fits well with the scheme’s not being mentioned by al-Bīrūnī54 as news of the method may not have reached him in Transoxania by the time his book was being completed in 1000 CE. Josiah b. Mevorakh al-ʿĀqūlī: a tentative identification Josiah b. Mevorakh al-ʿĀqūlī (or ibn al-ʿĀqūlī) must have been a scholar of Babylonian descent.55 His nisba al-ʿĀqūlī may refer to ʿĀqūlā, a pre-islamic (Syriac) 51. Stern, Calendar and Community, pp. 200-210. 52. Raviv, Mathematical Studies, pp. 88 and 102 maintains that R. Josiah b. Mevorakh calculated a calendar for 247 years starting from 1494 SE (1182/3 CE) and recycled it back twice to 1001 SE. This conclusion is based on a limited corpus consisting of Lon. BL Or. 10576, Ox. Bodl. Heb. e.60, Lon. BL Or 9884 and T-S 10K20.2, all of which reflect the third iteration of the 247-year cycle of remainders (see Table 2). In view of Genizah fragments that carry earlier iterations of the 247-year cycle Raviv’s conclusions are untenable. Additional evidence against Raviv’s analysis is provided by the blessing of the dead (raḍiya Allāhu ʿanhu or z”l) attached to R. Josiah b. Mevorakh’s name in all surviving copies of his cycle, in which the name has been preserved, including T-S AS 144.111 datable to ca. 1123/4 CE. 53. See footnote 6 above. 54. See footnote 7 above. 55. See also Tobi, The Jews of Yemen, p. 215. - 20 - name of Kūfa56 or to Dayr al-ʿĀqūl, a town on the Tigris southeast of Baghdad.57 His Babylonian allegiance is brought out in his calendar that fixes year 923 CE, one of the years of the calendar dispute, as ‫ בחג‬in line with the Babylonians and contrary to the Palestinians who fixed it ‫זשג‬. Josiah b. Mevorakh (ibn) al-ʿĀqūlī is not a known personality but he may be mentioned in manuscripts other than copies of his calendar. A Genizah fragment T-S Ar.1b.5 contains a translation and commentary on Song of Songs and Lamentations by “shaykh Abū ʿAlī R. Josiah ben R. Mevorakh ben R. Isaac known as ibn al-ʿĀqūlī al-Kātib, may God prolong his existence,” copied in the year 400 of the Arabs (1009 CE).58 A list of books in Mosseri I,106.1 mentions a commentary on haʾazinu by Ben al-ʿĀqūlī (recto, line 25). A 13th century copy of Maimonides’ Guide of the Perplexed in Oxford, Bodl. Hunt. 162 preserves a textual variant where ibn al-ʿĀqūlī is mentioned together with 10th–early 11th century authorities who are said to have written against the eternity of the world, namely R. Hayye Gaon (gaon of Pumbedita, d. 1038 CE), Aharon ibn Sarjado (gaon of Pumbedita in 942–960 CE), Ibn Janaḥ (ca. 990–1050 CE), Ibn al-ʿĀqūlī, Ben Ḥofnī ha-Kohen (gaon of Sura, d. 1013 CE), R. Dosa (gaon of Sura, ca. 935–1017 CE) and his father R. Saadia Gaon (gaon of Sura, 882-942 CE).59 Judging by his name, the author of the commentary in T-S Ar.1b.5 is likely to be the 56. Moshe Gil, In the Kingdom of Ishmael: Studies in Jewish History in Islamic Lands in the Early Middle Ages; Texts from the Cairo Genizah: Letters of Jewish Merchants (Tel-Aviv: Tel-Aviv University, 1997) (Hebrew), vol. 1, pp. 507-508. 57. In his monumental dictionary of Islamic traditionists entitled al-Ansāb and arranged by the scholars’ nisbas ʿAbd al-Karīm ibn Muḥammad al-Samʿānī (1113–1166 CE) derives the nisba al-ʿĀqūlī from Dayr al-ʿĀqūl only. See ʿAbd al-Karīm ibn Muḥammad al-Samʿānī, al-Ansāb no. 1662 and no. 2652 (Hyderabad: Osmania Oriental Publications Bureau, 1978), vol. 5, pp. 441-442, vol. 9, pp. 149-150. On Dayr al-ʿĀqūl see A. A. Dari, “Dayr alʿĀḳūl,” in The Encyclopaedia of Islam2 (Leiden: Brill, 1965), vol. 2, p. 196. 58. T-S Ar.1b.5r: ‫ והו תפסיר איכה מ]מא[ פ]ס[רה ותרגמה ונתרה‬.‫באלנטם ואלשרח ואלתרתיב‬ ֗ .‫לישועתך קויתי ייי כתא]ב[ אלרזיה ואלנחיב‬ ‫אלכבתאאב אטאל אללה בקאה‬ ַ ‫ונטמה אלשיך אבו עלי ֗מרב יאשיה בן ֗מרב מבורך בן ֗מרב יצחק אלמשהור באבן אלעאקולי‬ ֗ ‫אשהרה סנה ת׳ לתאריך אלערב‬ 59. Oxford, Bodl. Hunt. 162, fol. 66v, a marginal note in the hand of the main scribe that gives an alternative version of the final phrase of part I of the Guide, to be inserted after the words ‫אלכ׳וץ מע‬ ֗ ‫ארגע אלי‬ ֗ ‫ובעד דלך‬ ‫אלפלאספה פי מא יקולונה מן קדם אלעאלם‬: ‫סרגאדו‬ ֗ ‫איצא מתל רבנו האיי ואהרן בן‬ ֗ ‫תגרדת ללרד עליהם בל קבלי‬ ֗ ‫וארד עליהם ולסת אזעם אנני וחדי מן דון ג׳ירי‬ ّ ‫נ״א‬ ... ‫ור דוסא וואלדה רבנו סעדיה גאון זכרם כולם לברכה‬ ֗ ‫ואבן ֗גנאח ואבן אלעאקולי ובן חפני הכהן‬ The note was first published by Salomon Munk, Notice sur Rabbi Saadia Gaon et sa version Arabe d’Isaie (Paris: Imprimerie de Cosson, 1858), p. 13. Munk erroneously cites the manuscript as Uri 359 (now Oxford, Bodl. Hunt. 267), whereas the correct number in the catalogue Uri is 309 (now Oxford, Bodl. Hunt. 162). The note was discussed or republished by M. Steinschneider, S. Poznanski, and A. Harkavy, in all cases on the basis of Munk’s original publication and citing the erroneous catalogue number (see Moritz Steinschneider, Die Arabische Literatur der Juden (Frankfurt a. M.: Kauffmann, 1902), pp. 269-270; Samuel Poznanski, ‫רב דוסא ברב סעדיה גאון‬ (R. Dosa be-Rav Saadia Gaon) (Berditchev: ‪Scheftel, 1906‬), p. 25; Abraham Harkavy, .‫זכרון לראשונים וגם לאחרונים‬ ‫ זכרון הגאון רב שמואל בן חפני וספריו‬:‫ מחברת שלישית‬.‫ זכרון לראשונים‬:‫( חלק ראשון‬On the Rishonim and the Aḥaromim. Part I: On the Rishonim. Vol. III: On R. Samuel ben Ḥofni Gaon and his books) (St. Petersburg, 1880), p. 17). I thank Rahel Fronda from the Bodleian Library, Oxford for her help with the manuscripts. - 21 - same person who composed the calendar of remainders, which means that Josiah b. Mevorakh was still alive in 1009 CE. If this identification is correct, it supports dating the calendar of remainders to the middle of the 10th century. Critique and modifications of the system Most manuscripts of the earliest possible version of Josiah b. Mevorakh al-ʿĀqūlī’s treatise include the calendar of remainders as part of a critique of the 247-year cycle. These are manuscripts T-S NS 98.40+T-S Misc.25.29+T-S AS 144.164 and TS AS 144.111. The same critique also survived in T-S 6K2.1, where it was copied without the calendar. It was composed by Joseph bar Āraḥ, a personality known from early 12th-century business letters,60 who set out to explain why Josiah b. Mevorakh’s reiterative scheme fails to correspond to the standard calendar calculation in certain years. Joseph bar Āraḥ’s argument is as follows. For a calendar cycle to work molad Tišri must recur exactly at the end of its cyclicity period, i.e., the surplus of a cycle must be seven days sharp, which taken modulo seven is equivalent to zero. Inasmuch as the surplus of 247 years is not seven days but 6 days 23 hours and 175 parts, molad Tišri of year N+247 will not equal that of year N but be 905 parts smaller.61 This has implications for moladot in the vicinity of various calendrical limits, such as those approaching the limit of molad zaqen (i.e. 18 hours if counted from 6pm, or 6 hours of the day if counted from 6am). If molad of year N exceeds the limit of molad zaqen, this year will be postponed. If, however, the excess is less than 905 parts, molad of year N+247 being 905 parts less will fall below the limit of molad zaqen, the year will not be postponed, and the type of year N+247 will not be the same as that of year N. Thus, a year with molad Tišri on Saturday, 18 hours and 904 parts must be fixed ‫ בח‬plain (i.e., not intercalated), but the type of a year 247 years later will be ‫ זש‬plain, because its molad Tišri will be Saturday, 17 hours and 1079 parts, which is below the 18-hour limit of molad zaqen.62 On the other hand, if molad Tišri of year N exceeds the limit of molad zaqen by greater than or equal to 905 parts, molad Tišri of year N+247 will also exceed the limit of molad zaqen and both years will be fixed the same. For example, a year with molad Tišri on Saturday, 18 hours and 905 parts will remain ‫ בח‬plain in the next cycle because the molad in this cycle will be Saturday, 18 hours. And in the following cycle it will become ‫ זש‬plain, because the molad will be Saturday, 17 60. T-S 13J20.8 and T-S 12.329. 61. T-S NS 98.40, fol. 1: ‫וכ ֗ג סאעה וקעה חלקים פאדא אצפתהא אלי מולד אי סנה שית מן‬ ֗ ‫ופצלתהא ו֗ א]יא[ם‬ ֗ ‫אן ֗ר ֗מז֗ סנה הו י֗ ֗ג מחזור קמרי שמסיה‬ [‫אלר ֗מז֗ אלתאני לה ויכון מולד אלתאניה אנקץ פי אלעדד מן מולד אלאולה פי איא]ם‬ ֗ ‫אי ֗ר ֗מז֗ שית וצלת אלי מולד מתלה מן‬ ‫בץ ֗ה חלקים וה]ו[ נקץ אלפצלה ען אלאסבוע אלתאם חתי לו אנה אסבוע תאם וצלת אלי מתל אלמולד סוא בלא‬ ֗ ‫אלאסבוע‬ 62. ‫זיאדה ולא נקצאן וכאן יתם לה ז֗ ֗ל מא צדר בה וקאלה‬ T-S NS 98.40, fol. 1v: ‫ומתאלה מתל י֗ ז֗ ו֗ ֗ץ ֗ד פאנה ינתקל מן פבח אלי פזש אד יכון אלמו֗ י֗ ז֗ ֗ה ֗ת ֗ת ֗ר ֗ע ֗ט‬ - 22 - hours and 175 parts.63 Joseph bar Āraḥ’s exposition makes it clear that in order to continue using Josiah b. Mevorakh’s cycle beyond its first iteration without deviating from the standard calendar one has to update the remainders. To underpin his argument Joseph bar Āraḥ presents a copy of Josiah b. Mevorakh’s calendar in which all necessary emendations have been made to update it to the second iteration (1248–1494 SE, 936/7–1182/3 CE). In order to draw attention to the required changes, Joseph bar Āraḥ does not simply replace old numbers with new ones but keeps the calendar in its original form and graphically marks out remainders that are outdated, adding the new ones outside of the main text. In T-S AS 144.111 remainders 50 in ‫זחא‬, 94 in ‫ השא‬and 95 in ‫ גכז‬are enclosed in a rectangle, and remainder 54 is introduced at the end of the list in ‫ גכז‬with a special insertion sign.64 In T-S NS 98.40+T-S Misc.25.29+T-S AS 144.164 remainders 235 in ‫ בחג‬and 54 in ‫ החא‬are enclosed in a rectangle, and new remainders are noted below the main list: 238 in ‫ בחג‬and 233 in ‫החא‬.65 Very similarly looking corrections are also found in T-S AS 203.216+T-S AS 144.228+T-S AS 144.286, which may or may not have belonged to a copy of Joseph bar Āraḥ’s critique: remainder 238 in ‫ בשה‬and remainder 53 in ‫ זשג‬are encircled, but updated numbers have not survived due to the poor state of preservation of the fragment. It is interesting that corrections in Joseph bar Āraḥ’s work cover the entire 247 years of the cycle, including years that were long past when the critique was composed in the beginning of the 12th century. This gives a clear indication that the purpose in amending the cycle was not to extend its usability but to demonstrate that it is not properly reiterative within the framework of the standard molad calculation. Copies of Josiah b. Mevorakh’s cycle included in the critique have in common a number of conspicuous features of wording and layout, in addition to the graphic way in which calendar was updated. Firstly, in all of them chapters concerning the different year types are listed following the same order in which they occur at the beginning of an iteration, i.e. ‫ בשה‬is described first because it corresponds to remainder 1, followed by ‫ זשג‬which is the year type for remainder 2, etc. The majority of other manuscripts group year types by day of the week of the New Year starting with all year types that begin on a Monday, followed by all types that begin on a Tuesday, then by all those that begin on a Thursday and closing with all types that begin on a Saturday. Secondly, all copies refer to the last day of Passover with 63. T-S NS 98.40, fol. 1v: ‫והו מתלא י֗ ז֗ ו֗ ֗ץ ֗ה פאנה יתבת עלי פבח פי אלדור אלאכר איצא אד יכון אלמולד פיה י֗ ז֗ ו֗ ופי‬ ‫מ]א[ בעדה פזש אד יצי]ר[ ]א[למולד י֗ ז֗ ֗ה ֗ק ֗ע ֗ה‬ 64. Remainder 50 was probably added to the list of ‫ השא‬but only the insertion sign survives. Remainder 53 may have been added in ‫ זחא‬but the area where this amendment would have been made is badly stained. 65. For a summary of year types expected in various iterations of the 247-year cycle see table 1. - 23 - an uncommon Judaeo-Arabic term ‫‘ ֗כס‬diminishing.’66 Two more manuscripts of the cycle exhibit the same features and are clearly related to Joseph bar Āraḥ’s update, namely, T-S AS 144.32 and T-S AS 144.46+T-S AS 144.166. In these manuscripts marginal corrections made by Joseph bar Āraḥ are integrated into the main text but outdated remainders are not always successfully removed. Thus, in T-S AS 144.32 an enframed remainder 234 (1st iteration) appears on the main list in ‫ הכז‬alongside remainder 94 (2nd–4th iterations) and both 235 (1st iteration) and 238 (2nd–4th iterations) are given in ‫בחג‬, whereas in T-S AS 144.46+T-S AS 144.166 both 233 (1st iteration) and 239 (2nd–4th iterations) are listed in ‫השג‬. These two manuscripts represent a shift of perspective: from this point on the updated cycle is no longer copied to prove its faultiness but rather in order to be used. Notably, it is only at this stage that the cycle appears to have become popular: we do not possess a single pre-critique (before the first half of the 12th century) copy of Josiah b. Mevorakh’s calendar, whereas post-critique versions penned in the 13th–14th century abound. As is was used, the reiterative calendar was brought in tune with the standard calendar. Joseph bar Āraḥ’s scientific method of checking and correcting a full iteration from remainder 1 to remainder 247 did not strike root, and a pattern of updating remainder lists in some years only is evident across manuscripts of Josiah b. Mevorakh’s calendar that do not belong to the critique. ENA 3329+ENA 1640.5, T-S K2.41, T-S 10K20.2+T-S K19.12, and T-S K2.8 update remainders for the third iteration (1183/4–1429/30 CE) but stop before remainders 172–173, which are left the same as in previous iterations. London, BL Or. 9884 corrects remainders 6–8 to the fourth iteration (1430/31–1676/7 CE), but fails to do so for remainders 147– 148, 151–153 and 192–193. In fact, of all preserved manuscripts of Josiah b. Mevorakh’s calendar only London, BL Or. 10576 contains remainders that pertain to one and the same iteration of the 247-year cycle. It refers to the third iteration (1183/4–1429/30 CE), but it is difficult to say whether it was freshly calculated, or simply updated as far as 1354/5–1355/6 CE (remainders 172–173) – the last update necessary in the 3rd iteration, but not in 1435/6–1437/8 CE (remainders 6–8) – the first update of the 4th iteration.67 This gradual modification of the scheme probably indicates that whoever copied and corrected the cycle of remainders did not think of it in terms of 247-year long iterations but used it as a convenient tool to determine the calendar for the next 66. The same term is also used by Saadia Gaon in his prayer book (see Israel Davidson, Simcha Assaf, B. Issachar Joel, Siddur Rav Saadia Gaon, 2nd edition (Jerusalem: Mekize Nirdamim, 1963), p. 58 and p. 135, line 17). 67. Rylands B 5508+Rylands B 3990 may have been another such copy but it is mutilated and not a reliable witness. All preserved data in this copy refer to the second iteration of the cycle. - 24 - years, at best a few coming decades. It may be conjectured that corrections were made in a haphazard manner by users of the calendar who checked and if necessary, corrected in their copy only those years that were relatively close to their time.68 When such corrected versions were copied again, user corrections were integrated into the main text and became part of the updated lists of remainders, much in the same way as was done in T-S AS 144.32 and T-S AS 144.46+T-S AS 144.166 with respect to corrections introduced by Joseph bar Āraḥ. The process of updating the cycle of remainders started no later than the beginning of the 12th century and continued at least until the middle of the 15th century: the latest attested corrections to the scheme, incorporated in the main text of London, BL Or. 9984, pertain to years 1435/6–1437/8 CE (iteration 4, remainders 6–8). That the next lot of corrections necessary for 1576/7–1577/8 CE (iteration 4, remainders 147–148) are not attested may be conditioned by the preserved sources, the bulk of which were copied before the 16th century. Both Joseph bar Āraḥ’s critique that highlights the 247-year cycle’s divergence from the standard calendar, and the corrections made to remedy this clearly indicate that Josiah b. Mevorakh’s scheme was not seen by its users as an alternative calendar. Instead it was perceived as an easy means of reckoning the standard calendar and was thus not permitted (at least in theory) to differ from it. Notably neither the critique nor the necessary corrections dissuaded everybody from relying on Josiah b. Mevorakh’s cycle. Thus, the author of T-S Ar.2.12 expects one to “find it correct without a shadow of a doubt,”69 whereas T-S Ar.29.31+T-S Ar.29.3v presents calculations to support an argument that although the 247-year cycle is not a true cycle, mistakes produced by it are few and in many cases will happen in such distant future (not until some 10,000 years later) that it remains a perfectly usable calendar. The distribution and use of Josiah b. Mevorakh al-ʿĀqūlī’s calendar The relatively high number of Oriental manuscripts of Josiah b. Mevorakh’s calendar, and the gradual updating of the cycle by its users signal out the popularity of this method of calendation. The same is confirmed by a contemporary witness whose voice is preserved in T-S NS 98.2:70 68. A 14th-century source from Yemen reports that 247-year cycles in circulation at that time were checked in 1647 SE (1335/6 CE) for at least as far as 1667 SE (1355/6 CE) (Tobi, The Jews of Yemen, pp. 215–216; Tobi, “The Dispute over the 247-year Cycle,” p. 211). 69. T-S Ar.2.12: ‫יגדה צחיח בלא שךּ ולא ריב‬. 70. T-S NS 98.2, fol. 2: ‫ונצרנא כתרה אעתמאד אלנאס עלי עבור לרבינו יאשיהו בן מבורך ז֗ ֗ל לאנה סהל קריב אלמאכד פעמדנא קאבלנא מנה נסך‬ ֗ ‫כתירה פוג]ד[נאהא מכתלפה כלף עטים וליס מנה צחיח‬ - 25 - We saw that people often rely on the calendar of R. Josiah b. Mevorakh of blessed memory because it is simple and easy to grasp. We intentionally collated many versions of it and found them significantly different and there is not among them a correct one. The manuscripts themselves furnish evidence of having been used in practice. T-S K19.12v contains corrections in a second hand to the description of a year type. A hand different from that of the main scribe left a comment on year type ‫ הכז‬in T-S K2.41: “this is our blessed year.”71 T-S AS 144.111 contains an added note intended to make using the cycle even more straightforward by establishing remainders for some of the years in the 19-year cycle 258 (1123/4–1142/3 CE). But most revealing is a marginal note in London, BL Or. 2451 that reads: “I calculated using this cycle as it is written [here] year 5495 is cycle 58.”72 Then in thicker characters it continues: “year 5503 is cycle 66.”73 This note correctly determines that years 5495 AM (1734/5 CE) and 5503 AM (1742/3 CE) correspond to remainders 58 and 66 in the cycle of Josiah b. Mevorakh. It must be noted that the cycle of remainders does not differ from the standard calculation in any of these years. In addition, 15th-century manuscripts London, BL Or. 2451 and Oxford, Bodl. Heb. e.60 inherited from their common Vorlage74 an arrangement that shows active engagement with the calendar of remainders in order to make it more straightforward to use. In these manuscripts remainders for a number of year types are given not from low to high but start between 148 and 175, going full circle from this starting point. These remainders most probably reflect the period when the author of the Vorlage was writing, and were moved to the top of the lists to make it easier to see them. The relevant calendar sections are ordered so as to allow using the treatise as a continuous text, even if only for a small number of years. Take for example, remainders 151, 152 and 153. In iterations 1–3 remainder 151 belongs to the year type ‫זשג‬, remainder 152 belongs to the year type ‫החא‬, and remainder 153 to the year type ‫גכה‬. In most copies of Josiah b. Mevorakh’s cycle sections on ‫זשג‬, ‫ החא‬and ‫ גכה‬are found in different parts of the calendar because year types are ordered by day of the week of the New Year. On the contrary, in London, BL Or. 2451 and Oxford, Bodl. Heb. e.60 the section on ‫ זשג‬is directly followed by that on ‫ החא‬and then by that on ‫גכה‬. In this way a user having once established that his year corresponds to remainder 151 could find the relevant section, i.e., ‫זשג‬, bookmark it in the manuscript, live through that year following the directions on ‫זשג‬, and by the end of the year arrive exactly at the place in the manuscript where a description of 71. T-S K2.41, plate 3r: ‫הדה סנתנא אלמבארכה‬. 72. London, BL Or. 2451, fol. 369v: ‫בזה מחזור חשבתי כמו שכתוב שנת התצה מחזור נח הוא‬. The term ‘cycle’ ‫ מחזור‬is used here to indicate a remainder. 73. London, BL Or. 2451, fol. 369v: ֗‫שנת התקג מחזור ֗סו‬. 74. On the relation between these two manuscripts see description of manuscripts above. - 26 - his next year (remainder 152, year type ‫ )החא‬begins.75 This arrangement does not work equally well in all iterations of the 247-year cycle and fits best years 1642– 1669 SE (1330/31–1357/8 CE), implying that it was elaborated sometime around 1330 CE. Knowledge of Josiah b. Mevorakh’s calendar of remainders or at least the association of Josiah b. Mevorakh’s name with the 247-year cycle appears to have been geographically wide-spread. Oriental manuscripts containing the scheme and its critique come from Egypt and Persia. In addition, 14th-century Yemenite sources attribute the 247-year cycle to Josiah b. Mevorakh and claim that the Jews of Yemen rely heavily on Josiah b. Mevorakh’s calendar.76 It is, however, not entirely clear if the 247-year cycle actually circulated in Yemen as a cycle of remainders. To the best of my knowledge, no Yemenite manuscripts preserve a cycle of remainders, and Josiah b. Mevorakh is always mentioned together with other authorities, such as R. Naḥshon Gaon, or R. Samuel b. Joseph ha-Kohen,77 which is not the case in cycles of remainders preserved in Genizah fragments or in Judaeo-Persian manuscripts. It is not impossible that Josiah b. Mevorakh was known to have composed a calendar treatise based on the 247-year cycle so that his name became associated with the idea of such a cycle, whatever the actual form. Outside the Oriental geo-cultural area two Ashkenazi manuscripts mention R. Josiah as one of the authorities for the 247-year cycle:78 R. Hayye and his father R. Sherira Gaon, and the geonim R. Naḥshon and R. Josiah understood the principle regarding the end of this calculation and said 75. A similar arrangement is found in copies of Joseph bar Āraḥ’s critique, where year types are listed in the same order as they occur at the beginning of an iteration. 76. See, e.g., an anonymous ʿIbbur ha-Šanim, composed in 1329 CE, as edited in Tobi, “The Dispute over the 247-year Cycle,” p. 207 on the basis of ms 1236 in Ben-Zvi Institute, Jerusalem: ‫ והו עגול דר׳‬,‫ והו מנסוב לר׳ יאשיה בר מבורך‬,‫ והו י׳׳ג מחזור מן מחאזיר אלעיבור אלד׳י כל מחזור י׳׳ט סנה‬,‫ומחזור גדול‬ ‫נחשון‬ A statement to the same effect is found in ʿIbbur ha-Šanim by R. Maʿūḍa b. Solomon al-Lidānī, as edited in Tobi, “The Dispute over the 247-year Cycle,” p. 210 on the basis of New York, JTS 4463, fol. 98r-100r: ‫וכאן אכת׳ר אעתמאד אלנאס עלי עיבור יאשיה בירב מבורך ועלי עבור שמואל בר יוסף כהן לאנהא עיבורות סהלה וליס‬ ‫יד׳כר פיהא מולד ולא דחייה בל קד הי מוצ׳ועה ברבאטאת מערופה מת׳ל בש׳׳ה בח׳׳ג זש׳׳ג זח׳׳א הכ׳׳ז גכ׳׳ה ומת׳ל בשמ׳׳ז‬ ‫החמ׳׳א גכמ׳׳ז פי אלמעוברות‬ 77. It is not clear who R. Samuel b. Joseph ha-Kohen was and in what way he was associated with the 247year cycle. Tobi, The Jews of Yemen, p. 219 suggests that the reference may be to a 10th century Palestinian gaon of the same name (on R. Samuel b. Joseph ha-Kohen Gaon see Moshe Gil, Palestine during the First Muslim Period (Tel-Aviv: Tel-Aviv University, 1983) (Hebrew), vol. 1, p. 542). 78. These are Oxford, Bodl. Opp. 614, a 14th century Ashkenazi miscellany and Cincinnati, HUC 436, a 15th century Ashkenazi prayer book for the whole year. The text, nearly identical in both manuscripts, is cited here according Oxford, Bodl. Opp. 614, fol. 50v: ‫ גאונים עמדו על עיקר סוף זה החשבון והם אמרו כי לסוף ֗ר ֗מז֗ שנים כמו‬.‫ור יאשיה‬ ֗ .‫רב האיי ורב שרירא גאון אביו ורב נחשון‬ ‫שהן מצוינין לי֗ ֗ג מחזו׳ שהן של י֗ ֗ט שנים חוזר החשבון חלילה בחסירין ובשלימין וכסדרן ובקביעות המועדים כבראשונה בלי‬ ‫חסירות ויתרות וסדר כל זה סימן לכל עדת ישראל‬ - 27 - that at the end of 247 years, which are written down as thirteen cycles of nineteen years, the calculation will always return to what it was in the beginning without any addition or deficit with regard to defective, full and orderly (years) and the fixing of festivals. The arrangement of all this is a sign for the whole congregation of Israel. At present, there is no evidence to connect R. Hayye Gaon and R. Sherira Gaon with the 247-year cycle, and their names may have been adduced here to make the statement more authoritative. R. Naḥshon is the standard authority for this cycle, although the history of this attribution is yet to be studied. R. Josiah is said here to be one of the geonim, and indeed, Josiah b. Aharon Gaon was a Palestinian gaon between ca. 1011–1025 CE.79 However, considering that Josiah b. Aharon Gaon is not known to have supported the 247 cycle, whereas a work on this cycle by Josiah b. Mevorakh al-ʿĀqūlī was in circulation at least in the Orient, the latter must be intended. Josiah b. Mevorakh’s cycle of remainders makes another non-Oriental appearance in a 15th century manuscript copied in a number of Byzantine hands, which contains Isaac Israeli’s magnum opus on calendar Yesod ʿOlam and a number of other astronomical and calendrical treatises (Oxford, Bodl. Poc. 368). Among them is a short, one page section on reiterative calendar written in Hebrew and introduced as follows:80 To know the character of the year with ease, count the years of Alexander up to the year that you are in, including your year, and discard the thousand. Cast out 247s from what is left and look for the number that remains among the 247 numbers in the fourteen tables, and you will find what you need with God’s help. For example, the year 5202 from Creation is year [1]753 of Alexander. Remove the thousand and what remains is 753. Cast out 247s from 753, and what remains is 12. We searched for 12 in the fourteen gates and found it in the gate ‫זשג‬. Do the same with all of them. Then follow fourteen tables of remainders for the fourteen types of the Jewish year, but the longer descriptions of the course of the year are lacking. Although the name of Josiah b. Mevorakh does not appear in this text, it is obvious that the described 79. See Gil, Palestine, vol. 1, pp. 543-5. 80. Ox. Poc. 368, fol. 219r: ֗‫לדעת קביעות השנה בנקל חשוב שנות אלסכנדר עד השנה אשר אתה בה ובשנתך והשלך מהם האלף והנותר השליכם ֗ר ֗מו‬ ‫ המשל שנת ֗ה ֗ר ֗ב ליצירה היא שנת ֗ת ֗שנ֗ ֗ג‬.‫הר ֗מו֗ בי֗ ֗ד שערים ותמצא חפצך בעה‬ ֗ ‫֗ר ֗מו֗ והמנין אשר ישאר לך תכנס בו במספר‬ ‫הת ֗שנ֗ ֗ג ֗ר ֗מו֗ ֗ר ֗מו֗ ישארו ֗י֗ב בקשנו ֗י֗ב בי֗ ֗ד שערי׳ מצאנוה בשער ז֗ ֗ש ֗ג וכן תעשה‬ ֗ ‫הת ֗שנ֗ ֗ג השלך‬ ֗ ‫לאלסכנדר השלך האלף ישארו‬ ‫לכלם‬ Note that ‫ רמו‬is written where ‫ רמז‬is expected. The mistake of writing a vav in place of a zayin runs through the entire passage under consideration. Additional examples include ‫ לו‬for ‫לז‬, ‫ קמו‬for ‫קמז‬, ‫ קצו‬for ‫( קצז‬compare footnote 47). - 28 - method is based on his composition. Firstly, this 15th century Byzantine calendar instructs one to start with the year from Creation and to convert it to a Seleucid date, the era used in Josiah b. Mevorakh’s calendar. Secondly, it applies the same algorithm to work out the remainders, with the same epoch of 1001 SE. The presented remainders are identical to those in Josiah b. Mevorakh’s work (give or take scribal mistakes) and reflect the stage in the development of the cycle when remainders are updated for the third iteration up to but not including remainders 172–173 (1354/5–1355/6 CE), which are left the same as in the previous iteration. The same situation is found in ENA 3329+ENA 1640.5, T-S K2.41, T-S 10K20.2+TS K19.12, and T-S K2.8. Examples illustrating the method in Oxford, Bodl. Poc. 368 are for years 5202 AM (1441/2 CE, fourth iteration, remainder 12) and 5224 AM (1463/4 CE, fourth iteration, remainder 34), meaning that the remainders were outdated at the time of copying but would not produce any mistakes until 1576/7 CE (fourth iteration, remainder 147) when the first aberration was due to occur more than 100 years after the date of the last given example. A final comment on the spread of Josiah b. Mevorakh’s cycle of remainders must concern an Italian version of the reiterative 247-year calendar. Prayer-books of the Italian rite frequently contain a calendar for thirteen 19-year cycles that does not refer to any dates but operates with cycles numbered 1–13 and years numbered 1– 247. The calendar is formatted as a sequence of 247 year types, and users are provided with an algorithm for determining their place within the sequence that, depending on the version, has an epoch of either 4998 AM (1237/8 CE) or 5017 AM (1256/7 CE). For example,81 He who wants to know for each year how to fix the New Moons, the festivals, the fasts, the reading of the weekly portions and their divisions, shall count the years above 5000, and add to them three years. He shall add them all up and cast out 247s. That what he retains is the number (of the year) in which he is in, and he shall find it in the thirteen cycles before us. This procedure is undeniably reminiscent of the Oriental algorithm by Josiah b. Mevorakh. The Italian “thirteen cycles” are not attributed to any authority, operate with a different era and epoch and are formatted differently from most copies of Josiah b. Mevorakh’s cycle, and yet the Italian and the Oriental methods of creating a perpetual calendar independent of dates are so similar that it is hard to imagine the younger Italian cycle being devised independently of its Oriental predecessor. 81. JNUL ‪Heb. 38°4281‬, fol. 298r: ‫הרוצה לידע קביעות ראשי חדשים ומועדים וצומות וקריאת פרשיות והפסקות שלכל שנה ושנה יחשוב שנות הפרט שעל‬ ‫חמשת אלפים שנה ויוסיף עליהן ֗ג שנים ויכללם יחד ויוציאם ֗ר ֗מז֗ ֗ר ֗מז֗ והנמצא בידו הוא החשבון שעומד בו וימצאהו באילו י֗ ֗ג‬ ‫מחזורים שלפנינו‬ - 29 - Concluding remarks In this article I have identified and examined the oldest traceable reiterative Jewish calendars. Evidence from the Cairo Genizah shows that the original 247-year cycle was conceptualised as a cycle of remainders and was put together in the middle of the 10th century. It predates the earliest cycles that are structured as tables of nineteen columns over thirteen rows, commonly entitled ʿIggul of R. Naḥshon Gaon, by more than 100 years. The attribution of the 247-year cycle of remainders to a Babylonian scholar Josiah b. Mevorakh (ibn) al-ʿĀqūlī appears to be historical since, being contemporary with the earliest cycle and not a high ranking authority, this scholar would not add weight to the scheme and would be an unlikely pseudoauthor. The cycle of remainders may have been proposed in the aftermath of the Saadia–Ben Meir dispute of 921–924 CE as an alternative for the standard calendar that was capable of preventing future calendar dissidence caused by differences in the calendar calculation procedures practiced in Babylonia and Palestine. However, users of the 247-year cycle clearly regarded it as a means of reckoning the standard calendar and strove to keep the cycle in line with the standard calculation by updating the remainders. The reiterative method was subjected to rigorous criticism in the early 12th century, but continued to be widely used in the Orient at least until the middle of the 18th century, knowledge of it spreading to other geo-cultural areas including Byzantium, Italy and Ashkenaz. Focusing on the origins of the 247-year cycle, this article leaves open a number of important questions related to Jewish calendar cycles in medieval manuscripts, which will be dealt with in forthcoming research. These include a study of 19x13 calendar tables known as the ʿIggul of R. Naḥshon Gaon and of the Italian “thirteen cycles” as well as of their relationship to the early cycles of remainders; the history of the cycle’s attribution to R. Naḥshon Gaon; the extent to which 247-year cycles were used in practice; and the 16th century controversy surrounding the inclusion of the 247-year cycle in printed editions of the Arbaʿah Turim of Jacob b. Asher, one of the most influential rabbinic codes of law ever to have been produced. - 30 -