- CALENDAR (Heb. לוּחַ, lu'aḥ). The present Jewish calendar is lunisolar, the months being reckoned according to the moon and the years according to the sun. A month is the period of time between one conjunction of the moon with the sun and the next. The conjunction of the moon with the sun is the point in time at which the moon is directly between the earth and the sun (but not on the same plane) and is thus invisible. This is known as the מוֹלָד, molad ("birth," from the root ילד). The mean synodic month (or lunation) is 29 days, 12 hours, 44 minutes, and 3⅓ seconds (793 parts (ḥalakim); in the Jewish system the hour is divided into 1,080 parts each of which is 3⅓ seconds). The solar year is 365 days, 48 minutes, and 46 seconds, which means that a solar year exceeds a lunar one (12 months) by about 11 days. The cycles of 12 lunar months must therefore be adjusted to the solar year, because although the Jewish festivals are fixed according to dates in months, they must also be in specific (agricultural) seasons of the year which depend on the tropical solar year. Without any adjustment the festivals would "wander" through the seasons and the "spring" festival (Passover), for example, would be celebrated eventually in winter, and later in summer. The required adjustment is realized by the addition of an extra month (Adar II) in each of seven out of the 19 years that constitute the small (or lunar) cycle of the moon (maḥazor katan or maḥazor ha-levanah). In 19 years the solar cycle exceeds the lunar by about 209 days, which are approximately 7 months. In Temple times this intercalation was decided upon in the individual years according to agricultural conditions (Tosef., Sanh. 2:2; Sanh. 11b); later, however, it was fixed to be in the years 3, 6, 8, 11, 14, 17, and 19 of the cycle (see below). In the calendar month only complete days are reckoned, the full (מָלֵא, male) months containing 30, and the defective (חָסֵר, ḥaser) months 29 days. The months Nisan, Sivan, Av, Tishri, Shevat and (in a leap year) Adar I are always male; Iyyar, Tammuz, Elul, Tevet, and Adar (Adar II in a leap year) always ḥaser, while Ḥeshvan and Kislev vary. Hence, the common year contains 353, 354, or 355 days and the leap year 383, 384, or 385 days. For ritual purposes, e.g., in reckoning the times fixed for prayers or the commencement and termination of the Sabbath, the day is deemed to begin at sunset or at the end of twilight , and its 24 hours (12 in the day and 12 in the night) are "temporary" hours varying in length with the respective length of the periods of light and darkness. But in the reckonings of the molad the day is the equatorial day of 24 hours of unvarying length and is deemed to commence at 6 P.M., probably in terms of local Jerusalem time. -Fixing Rosh ha-Shanah (New Year's Day) The year begins on Tishri 1, which is rarely the day of the molad, as there are four obstacles or considerations, called deḥiyyot, in fixing the first day of the month (rosh ḥodesh). Each deḥiyyah defers Rosh Ha-Shanah by a day, and combined deḥiyyot may cause a postponement of two days: (1) mainly in order to prevent the Day of Atonement (Tishri 10. from falling on Friday or Sunday, and Hoshana Rabba (the seventh day of Sukkot; Tishri 21) from falling on Saturday, but in part also serving an astronomical purpose (see below). Rosh Ha-Shanah never falls on Sunday, Wednesday, or Friday (according to the mnemonic לא אד"ו ראש known as the postponement addu – probably first vocalized iddo; cf. Ezra 8:17). (2) Entirely for an astronomical reason, if the molad is at noon or later (מוֹלָד זָקֵן or מוֹלָד יח) Rosh Ha-Shanah is delayed by one day or, if this would cause it to fall as above, two days. These two deḥiyyot, owing to the mentioned limits on the number of days in the year, entail another two. (3) The third deḥiyyah is as follows: If the molad in an "ordinary" (not leap) year falls at ג"טר"ד, that is the third day (Tuesday), at 9 hours, 204 ḥalakim, that is, 3:11 A.M. and 20 secs. – Rosh Ha-Shanah is put off two days. A postponement to Wednesday is not permitted (as in (1), so that it is deferred to Thursday. The object is as follows: If the molad of Tishri occurs at that hour, the outcome would be a year which is one day too long. The following table of moladot will illustrate this: calendar Tishri Tuesday 3:11.20 secs. A.M. Ḥeshvan Wednesday 3:55.23 secs. P.M. Kislev Friday 4:39.27 secs. A.M. Tevet Saturday 5:23.30 secs. P.M. Shevat Monday 6:07.33 secs. A.M. Adar Tuesday 6:51.37 secs. P.M. Nisan Thursday 7:35.40 secs. A.M. Iyyar Friday 8:19.43 secs. P.M. Sivan Sunday 9:03.47 secs. A.M. Tammuz Monday 9:47.50 secs. P.M. Av Wednesday 10:31.53 secs. A.M. Elul Thursday 11:15.57 secs. P.M. Tishri Saturday 12:00.00 secs. (noon) The last figure (Tishri) constitutes a molad zaken as described in (2), and this would, therefore, lead to a deferment of a day, thus making Rosh Ha-Shanah fall on Sunday, which again is not permitted, so that the festival will be moved one further day, to Monday. The interval between Rosh Ha-Shanah and the next one would then be 356 days which is a day longer than the maximum ordinary year. Rosh Ha-Shanah is therefore delayed from Tuesday to Thursday (as Wednesday is ineligible), and the result is a year of 354 days which, as distinct from the minimal year of 353 and the full one of 355 days, is called "regular" or "common." (4) This deḥiyyah is very infrequent. It is known as בט"ו תקפ"ט אחר עבור שנה, that is when the molad of Tishri, following immediately after a leap year, occurs on the second day (Monday) at 15 hours, 589 ḥalakim, which means Monday, 9:32 A.M. and 43⅓ secs. If the reckoning is made backward by subtracting 13 moladot, the Tishri of the preceding year would have had its molad on Tuesday at 12 noon. Having occurred at that time, Rosh Ha-Shanah of the previous year would have been on Thursday since Tuesday's molad was "zaken," and two days deferment must take place as Wednesday is impermissible. If Rosh Ha-Shanah then commenced on Thursday in the previous year, that year would have consisted of 382 days only which is too short for a leap year. By deferring Rosh Ha-Shanah of the current year from Monday to Tuesday, the year, retroactively, lasts for 383 days, which is a minimal leap year. -The Year The "character" of the year, named kevi'ah (from קבע, kava; lit., "to fix"), is indicated by two or three Hebrew letters: the first, used as a numeral, gives the day of the week on which Rosh Ha-Shanah occurs; the second is the initial of the Hebrew word for defective, regular, or complete (ḥaser, ke-sidrah, or shalem); while in some calendric works a third letter, again used as a numeral, indicates the day of the week on which Passover begins. For an arithmetical reason inherent in the system, there are not 24 deḥiyyot – 4 × 3 × 2 for the four "permitted" days and the three types of both the common and the leap year – but only 14, i.e., seven for the common and seven for the leap year. For the common year, they are (זש(ג) ,זח(א) ,הש(א) ,הכ(ז) ,גכ(ה) ,בש(ה) ,בח(ג and for the leap year (זש(ה) ,זח(ג) ,הש(ג) ,הח(א) ,גכ(ז) ,בח(ה) ,בש(ז. Any particular year's sequence of the feasts and fasts and of the lectionary, in Israel and in the Diaspora, is determined by its kevi'ah. Tables of the 14 types of years, of the data necessary for the calculation of both the kevi'ah of every year and of the molad of every month, as well as tables of corresponding dates in the Jewish and in the secular calendar, are attached to a great many old and new treatises on the Jewish calendar. THE TRUE AND THE MEAN MOLAD Owing to inequalities in the rate of both the solar and the lunar motion in longitude, the mean conjunction may precede or be preceded by the true conjunction. The absolute maximum interval between them, arising from the combined effect of the maximum quotas of the solar and the lunar anomaly, is approximately 14 hours. In Tishri – never far from the time of the maximum effect of the decrease in solar velocity, the solar apogee being about July 1 – approximately 14 hours is the maximum interval from the true conjunction to the mean conjunction, whereas the maximum interval from the mean conjunction to the true conjunction will not exceed six to seven hours; in Nisan – never far from the time of the maximum effect of the increase in solar velocity, the solar perigee being about December 31 – approximately 14 hours is the maximum interval from the mean conjunction to the true conjunction and only six-seven hours from the true conjunction to the mean conjunction; with varying seasonal maxima and minima in the other months of the year. THE PHASIS Leaving out of account the unpredictable factor of atmospheric conditions, the length of the interval from the true conjunction to the first sighting of the new crescent, the phasis is determined by four predictable astronomical factors: the interval from the true conjunction to the ensuing sunset(s), the season of the year, the lunar latitude, and the geographical longitude and latitude of the place of observation. In the region of Jerusalem – observations at which may well be presupposed in the calculation of the astronomical basis of the Jewish calendar – shortly before the autumnal equinox the minimum interval from the true conjunction to the phasis is approximately 20 hours, while the maximum is close to 72 hours, with the minimum of approximately 18 hours shortly before the vernal equinox and the various respective maxima and minima throughout the year. The phasis necessarily occurs a short time of varying length after sunset, before or after the appearance of the stars. Hence, the day of the phasis may be the day commencing a short while before the moment of the phasis or the day ending a short while after the moment of the phasis. Rosh Ha-Shanah may commence nearly 18 hours before the moment of the molad, i.e., with the molad at 17 hours 1079 ḥalakim on one of the four "permitted" days (excepting the deḥiyyot (4) and (3) on Monday and Tuesday, respectively), or more than 38 hours after the moment of the molad, i.e., with the molad in any common year on Tuesday at 9 hours 204 ḥalakim, and Rosh Ha-Shanah postponed to Thursday (deḥiyyah (3), ג"טר"ד בִּפְשׁוּטָה), with the consequence of variations, mutatis mutandis, in the commencement of New Moons of months other than Tishri. The period of this calendric vacillation does not correspond with the periods of astronomical vacillations in the mentioned respective intervals between the true and mean conjunctions, from the true conjunction to the moment of the phasis and between the moment of the phasis and the commencement of the day of the phasis. This notwithstanding, it results from the mentioned four vacillations – one calendric and three astronomical – that in the vast majority of cases the four deḥiyyot, including deḥiyyah (1) לא אד"ו ראש, do not delay Rosh Ha-Shanah until after the day of the phasis, but merely bring the former nearer to the latter or make the two coincide, an astronomical reason underlying all the deḥiyyot noted by Maimonides. Rosh Ha-Shanah does, of course, occasionally occur before the day of the phasis begins or, in some extremely rare cases, on the day immediately after the phasis (never later), with a rather wider range of the occurrence of the New Moon before and after the day of the phasis in other months; such oscillation is inherent in a system, like the present Jewish calendar, based on mean values. The mentioned reckoning of the lunation at 29d. 12h. 44 min. 3⅓ sec. slightly exceeds the present astronomically correct value (29d. 12h. 44 min. 2.841 secs.). The discrepancy is constantly increasing by a very small figure, owing to the secular acceleration of the mean lunar motion, but the cumulative effect of this is so small that it will remain negligible for hundreds of millennia. Nor can it be ascertained when, if ever, the moment of the molad was identical with the moment of the mean conjunction since, because of the great many inequalities in the moon's movement in longitude, it is practically impossible to fix the mean position of the moon at any time. Moreover, it is no more than an assumption (no less difficult to prove than to disprove) that the occurrences of the molad are expressed in the terms of local Jerusalem time. -Tekufot As stated, the four seasons in the Jewish year are called tekufot. More accurately, it is the beginning of each of the four seasons – according to the common view, the mean beginning – that is named tekufah (literally "circuit," from קוף related to נקף, "to go round"), the tekufah of Nisan denoting the mean sun at the vernal equinoctial point, that of Tammuz denoting it at the summer solstitial point, that of Tishri, at the autumnal equinoctial point, and that of Tevet, at the winter solstitial point. The mean length of the seasons, each exactly one quarter of the year, was reckoned by Mar Samuel (c. 165–254, head of the academy at nehardea in Babylon) at 91d. 7½ h. Hence, with his solar year of 365d. 6h., or 52 weeks and 1¼ days – identical in length with the Julian year – the tekufot move forward in the week, year after year, by 1¼ days. Accordingly, after 28 years the tekufah of Nisan reverts to the same hour on the same day of the week (Tuesday 6 P.M.) as at the beginning: this 28-year cycle is named the great, or solar, cycle (maḥazor gadol, or maḥazor ḥammah). This length of the solar year is important in respect of two minor rituals only: (1) the date of She'elah, the commencement in the Diaspora of the petition for rain inserted in the benediction Birkat ha-Shanim in the Amidah, on December 5 or 6 in the twentieth century; (2) the Blessing of the Sun on the day of the tekufah of Nisan at the beginning of the 28-year cycle. The frequent occurrence, in the last centuries, of Passover (Nisan 15–21) prior to the day of Mar Samuel's tekufah of Nisan – whereas the purpose of intercalation is to avoid the tekufah of Tevet extending to Nisan 16 (RH 21a) – is held by some scholars to show that in the making of the present Jewish calendar Mar samuel 's value was deliberately departed from, and the length of the solar year was more accurately calculated at 365d. 5h. 55 min. 2527/<sub>57</sub> sec., a calculation associated with the name of Rav Adda (perhaps Rav Adda b. Ahavah, a Babylonian amora of the third century). According to other scholars, this is but the fortuitous result of dividing by 19 the 6939d. 16h. 595p. contained in 235 lunations reckoned at 29d. 12h. 793p. each, the oldest sources knowing no other value for the length of the solar year than 365¼d., arising from Mar Samuel's tekufah. Actually clues are traceable in talmudic dicta,1 as also in abraham ibn ezra 's Sefer ha-Ibbur (ed. by S.J. Halberstam, 1874, 8a) and Maimonides' Code,2 for values close to the modern estimate of the length of the tropical solar year at 365d. 5h. 48 min. 46 sec. If the average length of the solar year in the present Jewish calendar exceeds this by approximately 6⅔ min., this discrepancy was left out of account as it was assumed that its cumulative effect would remain negligible over a long period at the end of which the present system was expected to be replaced again by a system based on true values more akin to the earlier Jewish calendar in which New Moons (days of the phasis) and intercalations were proclaimed on the basis of both observation and calculation. The notable days in the present Jewish calendar are in the main the Pentateuchal festivals, with additional days in the Diaspora (see festivals ). Earlier additions include the fasts in Zechariah 7:5 and 8:19 observed on Tammuz 17, Av 9, Tishri 3, and Tevet 10, while the observance of the festive days enjoined in Megillat Ta'anit fell into desuetude, except Purim and Ḥanukkah on Adar 14–15 (in leap years, Adar II) and Kislev 25–Tevet 2 (or 3) respectively. Among later additions we note the Fast of esther on Adar 13 (or 11; or Adar II), New Year for Trees (see tu bi-shevat ) on Shevat 15, and israel independence day (Yom ha-Aḥma'ut) on Iyyar 5. -Historical According to a tradition quoted in the name of hai gaon (d. 1038), the present Jewish calendar was introduced by the patriarch hillel II in 670 Era of the Seleucids = 4119 Era of the Creation = 358/59 C.E. (500 C.E., claimed to derive from another version, seems to rest on a mistake). This possibly only refers to the present fixed order of the seven leap years in the 19-year cycle, whose introduction would have had to be more suitable at that time than earlier to achieve the main raison d'être of intercalation – to prevent the lunar Nisan 16 from occurring before the day of the tekufah of Nisan (RH 21a, see above) in the crucial 16th year in the 19-year cycle – on the presupposition that the tekufah of Nisan stands for the true, not the mean, vernal equinox. Apparent variations in the ordo intercalationis, i.e., בהז יגוח (2, 5, 7, 10, 13, 16, 18), אדוט בהז (1, 4, 6, 9, 12, 15, 17) and גבטב״ג alias גהח אדוט = גבגגגב"ג (3, 5, 8, 11, 14, 16, 19) by the side of the present order גוח אדזט (3, 6, 8, 11, 14, 17, 19), which are met with as late as the tenth century, are but variant styles of the selfsame order. These are in part also indicated by the epochal molad variously given as (דכתח = 4d. 20h. 408p.), בהרד = 2d. 5h. 204p., ויד = 6d. 14h. op. and גכבתתעו = 3d. 22h. 876p. which artificially go back to the beginning of the Era of the Creation and variously place its epoch in the autumn of 3762, −61, −60, −59 and −58 B.C.E. respectively (see chronology ). While it is not unreasonable to attribute to Hillel II the fixing of the regular order of intercalations, his full share in the present fixed calendar is doubtful. -Early Indications of Intercalation Some elements in it clearly date from earlier times, others may well have been introduced much later. The present names of the 12 months are already attested in several post-exilic biblical books, the Assuan Papyri, the Apocrypha, and Megillat Ta'anit, replacing the pre-Exilic names Abib, Ziv, Bul, and Ethanim and the designation by numbers. Intercalation is claimed to be evident from the figures in Ezekiel 1:1, 3:15, 4:4–6 and 8:1, with similar indications in I Kings 12:32–3 and II Chronicles 30:2–3; the old sectarian claim that the ancient Israelite calendar was purely solar, in vogue again because of the solar year in Enoch and Jubilees and a Qumran fragment, is militated against by the evident derivation from the moon of the terms חֹדֶשׁ (ḥodesh) and יֶרַח (yeraḥ) and by the connection between the moon and the festivals in Psalms 104:19. The New Moon (Num. 28:11, and parallels) was determined by the phasis in the preceding evening, hence the plausibility of an early biblical record (I Sam 20:18) of its prediction for "tomorrow." At a much later age, any month still consisted of either 29 or 30 days, the "sanctification" of the 30th as the New Moon being subject to witnesses' reports of the time and circumstances of their sighting of the new crescent scrutinized by a court competent to check them, and only accepted if tallying with each other and not contrary to astronomical prediction, with the further proviso of agreement by the court and formal declaration of "sanctification" before night set in. Proceedings were at times deliberately prolonged or speeded up, with the occasional choice of some observational post favorable for early sighting of the new crescent (Ein Tov), in order to avoid whenever possible a festival day, especially the Day of Atonement, falling immediately before or after the Sabbath.3 In keeping with this, the number of the full months3 varied between four and eight in the common, and between four and nine in the leap years, with 352–6 days in 12 lunar months, variations greatly in excess of those in the present calendar. Some of these variations were early eliminated. Already under the aegis of R. judah ha-nasi (c. 200) and of his pupil Ray (d. 247), Elul and Adar (in a leap year Adar II) contained invariably 29 days only. R. Yose b. Bun (c. 300) assumed the same fixed number of days in the months Adar-Elul as in the present calendar, with Rosh Ha-Shanah postponed from Wednesday and Friday but not yet from Sunday (TJ Meg. 1:2, 70b). Also the mean length of the lunation in the canon of rabban gamaliel (c. 100) at 29d. 12⅔h. 73p. tallies with 29d. 12h. 793p. in the present calendar. Attested in all the texts of Rosh Ha-Shanah 25a, and with a parallel in the Almagest of Ptolemy (c. 140), even though wrongly calculated, his ⅔h. 73p. is unlikely to be due to "late interpolation." As for 792p. arising from a dictum (Ar. 9b) of ravina (d. 420), it is an approximation only as evident from its context. -Regularization of Intervals of Intercalation The intervals of intercalation were at first irregular, intercalation being in part due to the prevailing state of various agricultural products and to social conditions. Regularity will also have been hampered by the Romans suppressing what they considered stirrings of Jewish nationalism (Tosef., Sanh. 2:2–9, and parallels). Astronomy was, however, always a powerful factor, as the state of the crops is ultimately determined by the sun's position in its annual path. Owing to the omission of intercalation over a period of some length, R. Akiva (d. 135. once intercalated three successive years as an emergency measure (ibid). The gradual regularizing of the intervals of intercalation had to be in the terms of the seven-year sabbatical cycle as none of the styles of the 19-year Metonic Cycle would have been compatible with the rule not to intercalate in sabbatical and post-sabbatical years (ibid.). R. Abbahu4 (c. 300) reckoned, in fact, with a long cycle of 1176 y. = 24 × 49 y. (= 24 jubilee cycles) = 24 × 7 × 7 y. (= 168 sabbatical cycles)=14545 lunations (= 12 × 176 for the 1176 y., +433 intercalations)= c. 61360 weeks 4 d.5 = c. 23 × 2556 w. 3½ d. (= 23 jubilee cycles with 606 lunations each, i.e., 49 × 12, + 18 intercalations) + 2560 w. 4d. (= the 24th jubilee cycle with 607 lunations, i.e, 49 × 12, + 19 intercalations), a system in which, in the first great cycle of 1176 years at any rate, Rosh Ha-Shanah (or perhaps only its molad) was to fall on Wednesday and Sunday respectively in the alternate first years of the 49-year jubilee cycles.6 This cycle, devised by David and Samuel according to R. Abbahu's homily on I Chronicles 9:22, with a remarkably early record of a similar notion in Ben Sira 47:10, is unserviceable on account of its great length, and it is unlikely that there was ever any attempt to adhere to it in practice. It is the same with the oversimplified system, at the other end of the scale, propounded by an anonymous tannaitic authority, making the common year to consist invariably of 354d. and the leap year of 383d., exceeding the integral number of weeks by four and five days respectively (Ar. 9b and parallels). This appears never to have been accepted in practice, as it just ignores the problems entailed in the lunisolar calendar (see the bold statement by R. Hananeel of Kairouan (990–1053) to Sukkah 54b (לא הוי בקי ר׳ מאיר (האחרים) בסוד העבור). It is so a fortiori with the eight-year cycle in Enoch 74:13–16 and the often quoted observation by Sextus Julius Africanus (early third century) that both the Greeks and the Jews intercalate three extra months every eight years,7 as also with the calendric data in Pirkei de-Rabbi Eliezer, chapters 6–8, marred by interpolations, and in Baraita de-Shemu'el, bristling with calendric and astronomical absurdities. Neither of the writers concerned had access to the Jews' "secret of the calendar intercalation" (sodha-ibbur) jealously guarded by its experts from outsiders, both Jewish and gentile. Convincing illustration of palpable ignorance in matters of the calendar, on the part of people otherwise highly gifted, may be seen in the famous sixth-century mosaic floor of the ancient bet alfa synagogue. It represents the 12 signs of the zodiac with the tekufah of Nisan at the beginning of Virgo, that of Tammuz at the beginning of Sagittarius, that of Tishri at the beginning of Pisces and that of Tevet at the beginning of Gemini (sic\!). -Development of the Present Order of Intercalation There is, on the other hand, unimpeachable evidence from the works of writers with expert knowledge of the calendar that the present ordo intercalationis גוח אדזט and epochal moladבהרד were not yet intrinsic parts of the calendar of Hillel II, these being seen still side by side with other styles of the ordo intercalationis and the molad as late as the 11th century. Also the four deḥiyyot developed gradually. The deḥiyyah אד"ו as has been shown, grew out of the deḥiyyah ד"ו. The general acceptance of the deḥiyyahמולד זקן in the sense of 18h., instead of 18h. 642p., as advocated by saadiah gaon 's antagonist aaron b. meir in their controversy, is not earlier than the tenth century. These are likely to have affected the remaining two deḥiyyot גטר"ד בפשוטה and בט"ו תקפ"ט אחר עבור since these are but corollaries of אד"ו and מולד זקן and the respective limits of 353–5 and 383–5 days in common and leap years. By the tenth century the Jewish calendar was exactly the same as today. A slight variation still prevails, between Israel and the Diaspora, in respect of the "secondary" days of the festivals, which lead in some years to fairly substantial differences in respect of the lectionary. -Notes 1. TJ, Yoma 4:5, 41d; TJ, Suk. 5:8, 55d = Ta'an 4:2, 68a; see The Code of Maimonides, The Book of Seasons (1961), 581. 2. Maim., Yad; interpretation of the figures there by E. Baneth (in Siebzehnter Bericht ueber die Lehranstalt fuer die Wissenschaft des Judenthums (1899), 31–42, and in Moses Ben Maimon, sein Leben, seine Werke und sein Einfluss, 2 (1914), 259) is correct; contra the strictures by O. Neugebauer, in The Code of Maimonides, Sanctification of the Moon (1956), 148; see also The Book of Seasons (1961), 581. 3. RH 2:6–8 and 3:1; Shab. 15:3; Suk. 4:2–3; Ar. 2:2, with related passages in Tosefta and the Jerusalem and Babylonian Talmuds. 4. For references see above, notes 1–2. A garbled version of this cycle is given in Kallir's piyyut for Parshat Shekalim (Baer, S., Seder, 654) where be-esrim ushenayim and u-shetei yadayim need correction and the specification of the tekufah as 911/3d. is rounded off from less than 91d. 7½ h. 5. 1176 solar years at 365d. 5h. 48m. 48s. exceed this value by 18h. 43m. 12s. and 14545 lunations at 29d. 12h. 44m. 2.8s. by 2d. 9h. 4m. 26s. This discrepancy, if considered at all, may have been thought to be partly eliminated by 434 intercalations (instead of 433) in every alternate 12th and 13th great cycle of 1176 years, reducing the discrepancy to less than 16h. in 29,400 years. Its complete elimination is, of course, impossible; the length of the day and its parts, in the terms of mean solar time, being incommensurable with either the solar year or the lunation. Kallir's obscure ששת אלפים עושים חמשה ושתי ידים מחזורות appears to be an attempt to eliminate the discrepancy by limiting the applicability of the series to the interval from the institution of the 24 priestly courses some time in David's reign (I Chron. 24:3), between 2887 and 2927 Era of the Creation (calculable from I Kings 6:1 and the traditional talmudic dating of the Exodus in c. 2450 E.C.) to 6000 E.C. 6. See below for the affinity with the Qumran calendar. 7. Transmitted in the Chronography of Georgius Synkellus (8th century). (Ephraim Jehudah Wiesenberg) -Sectarian Calendars A calendric deviation from the approved norm (see above) by Jeroboam, ruler of the Kingdom of Israel, is implied in I Kings 12:32–33, according to many modern scholars. The talmudic interpretation of II Chronicles 30:2, 13–15 also infers such a divergence (TJ, Pes. 9:1, 36c). The samaritans seem to have followed the northern calendar as distinct from that of the other Jews. In Hasmonean and Herodian times the sadducees and boethusians each had their own calendar as did – subsequently in talmudic and post-talmudic periods – the Karaites and other less well-known sects. THE 364-DAY SOLAR CALENDAR These calendars differed in a number of respects from the normative Jewish calendar, but the most radical departure appears to have been made in the solar calendar advocated in the pseudepigraphic works, Enoch and Jubilees. The "astrological" section of the (Ethiopian) Book of Enoch (chs. 72–78) describes in detail the apparent yearly movement of the sun through several points ("12 gates") of sunrise and sunset. The (basically correct) description leads to the (wrong) calculation of 364 days for the solar year – 30 days for each month and four additional days for "the signs" ("in which the sun lingers"), i.e., the solstices and equinoxes. There is also a discussion of the lunar year, with a calculation of the difference in length between it and the solar year. The tenor of these observations is that nature obeys the solar calendar, whose four quarters are the four seasons of change in climate and vegetation; that the universe moves in perfect numerical harmony; and that any other reckoning of the year is wrong. Likewise the Book of Jubilees (6:29–30) stresses that there are exactly 52 (4 × 13) weeks in the year, and condemns vehemently the sinners who use a lunar calendar, thus observing the festivals on the wrong dates. IN THE DEAD SEA SECT In the writings of the Dead Sea sect, there are several indications that the sect adopted the 364-day calendar. The Book of the Covenant of Damascus (p. 16), for instance, states that the Book of Jubilees should be followed in all matters of calendar reckoning. Again, according to the war scroll (column 2), in the future Temple there shall be 26 "courses" (i.e., "divisions") of priests and levites, i.e., a neat allocation of two weeks of service per solar year to each "course" (in direct contradiction to the biblical division into 24 courses, which does not attempt an exact division of the year (I Chron. 24:1–18). A fragment of a sectarian schedule for service in the future Temple has also been found; its evidence is, however, inconclusive (though deemed important by several scholars). THE FIXING OF THE OMER The 364-day calendar – obviously opposed to the lunisolar calendar of normative Judaism – must (like any Jewish calendar) somehow solve the problem of finding a fixed date for the Omer ceremony and for Shavuot, which follows seven weeks later. The Bible, fixing no date, commands that the Omer be offered on the "morrow of the Sabbath" (Lev. 23:11). According to the tannaim (Men. 65b) this means "on the second day of Passover" – an obviously forced interpretation, which was rejected by some sects (the Beothusians, Men. 10:3), according to tannaitic sources. It can be safely assumed that the advocates of the 364-day calendar insisted that "the morrow of the Sabbath" means "Sunday." To the problem of which Sunday was meant, a convincing solution has been suggested by A. Jaubert (in VT, 3 (1953), 250–64) as follows: The Book of Jubilees indicates that the correct date of Shavuot is the 15th of the third month. This is always a Sunday (for the obvious advantage of a 364-day calendar is that all dates fall on the same days of the week in all years). By counting back 49 days, the 26th of the first month (Nisan) is reached, i.e., the first Sunday after the week of Passover. This means that the last and first days of Passover, and the first days of Nisan and of Tishri (Rosh Ha-Shanah) are all Wednesdays, which is very logical, for the luminaries were created on Wednesday (the fourth day of the creation). INCONCLUSIVE EVIDENCE FOR USE OF CALENDAR As long as the sectarian calendar was known only from the Books of Enoch and Jubilees, there was no need to assume that anybody actually tried to put it into practice. The discovery of the writings of the Dead Sea sect introduces a thoroughly organized social body, with its own blatantly separatist way of life, which was quite capable of practicing what it preached. There is some force to S. Talmon's argument (in Scripta Hierosolymitana, 4 (1958), 162–99) that the sect's adoption of the 364-day calendar was the single most decisive factor of its separatism, for practical symbiosis of two groups using different calendars is impossible. On the other hand, the assumption that the sect actually used this calendar – despite the rather convincing evidence in its favor – remains somewhat problematical. Because the true solar year has 365¼ days, whoever uses the 364-day calendar must discover within some 30 years that it is not in accord with nature. Passover, for instance, will fall in the middle of the (Palestinian) winter. Moreover, there is reason to suppose that the sect existed for more than 30 years. An intercalary device of some kind can be conjectured, although none is indicated by our sources. It is also possible that the sect actually followed its calendar for a short period, or that it persisted with it regardless of the consequences. The evidence on the actual use of the calendar remains contradictory and inconclusive. (Jacob Licht) -BIBLIOGRAPHY: E. Mahler, Handbuch der juedischen Chronologie (1916); A.A. Akavya, Ha-Lu'aḥ ve-Shimmusho ba-Kronologyah (1956); S. Poznański, in: J. Hasting, Encyclopedia of Religion and Ethics, 3 (1910), 123, incl. bibl.; U. Cassuto, in: EJ, 9 (1932), incl. bibl.; Wiesenberg, in: HUCA, 33 (1962), 153–96; Z. Ankori, Karaites in Byzantium (1959), index; E. Kutsch, in: VT, 11 (1961), 39–47; J. Morgenstern, in: HUCA, 1 (1924), 13–78; 3 (1926), 77–107; 10 (1935), 1–148; 20 (1947), 1–136; 21 (1948), 365–496; idem, in: VT Supplement (1955), 34–76; A. Jaubert, ibid., 3 (1953), 250–64; 7 (1957), 35–61; S. Talmon, in: Scripta Hierosolymitana, 4 (1958), 162–99.
Encyclopedia Judaica. 1971.