A New Astronomically Based Chronological Model for the Egyptian Old Kingdom

In: Journal of Egyptian History
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  • 1 University of Basel
  • | 2 University of Zurich and Flinders University, Adelaide
  • | 3 University of Zurich
  • | 4 University of Marburg
  • | 5 University of Zurich
  • | 6 University of Marburg

Abstract

A recently discovered inscription on an ancient Egyptian ointment jar mentions the heliacal rising of Sirius. In the time of the early Pharaohs, this specific astronomical event marked the beginning of the Egyptian New Year and originally the annual return of the Nile flood, making it of great ritual importance. Since the Egyptian civil calendar of 365 days permanently shifted one day in four years in comparison to the stars due to the lack of intercalation, the connection of a date from the Egyptian civil calendar with the heliacal rising of Sothis is vitally important for the reconstruction of chronology. The new Sothis date from the Old Kingdom (3rd–6th Dynasties) in combination with other astronomical data and radiocarbon dating re-calibrates the chronology of ancient Egypt and consequently the dating of the Pyramids. A chronological model for Dynasties 3 to 6 constructed on the basis of calculated astronomical data and contemporaneously documented year dates of Pharaohs is presented.

Abstract

A recently discovered inscription on an ancient Egyptian ointment jar mentions the heliacal rising of Sirius. In the time of the early Pharaohs, this specific astronomical event marked the beginning of the Egyptian New Year and originally the annual return of the Nile flood, making it of great ritual importance. Since the Egyptian civil calendar of 365 days permanently shifted one day in four years in comparison to the stars due to the lack of intercalation, the connection of a date from the Egyptian civil calendar with the heliacal rising of Sothis is vitally important for the reconstruction of chronology. The new Sothis date from the Old Kingdom (3rd–6th Dynasties) in combination with other astronomical data and radiocarbon dating re-calibrates the chronology of ancient Egypt and consequently the dating of the Pyramids. A chronological model for Dynasties 3 to 6 constructed on the basis of calculated astronomical data and contemporaneously documented year dates of Pharaohs is presented.

Introduction

The Egyptian civil calendar consisted of 365 days arranged in the three seasons Akhet, Peret and Shemu, each containing four months with 30 days and at the end, five additional days (Epagomenals) were added. This civil calendar was probably introduced in the first half of the third millennium bce, starting with an assumed observation of the heliacal rising of Sirius (Sothis) on the 1st month of Akhet, 1st day. The heliacal rising of Sirius denotes its first visibility in the morning sky after a period of invisibility. Due to the lack of intercalary days, the Egyptian civil calendar permanently shifted one day in four years (tetraeteris) in comparison to the stars. As a result, the beginning of the year was moving through the civil calendar: By the end of the Old Kingdom the heliacal rising of Sothis had already shifted into the Peret season and during the Second Intermediate Period and the 18th Dynasty of the New Kingdom the New Year occurred in the Shemu season. In Ramesside times (19th Dynasty) the cycle reached the Akhet season again. This phenomenon is known as Sothis-cycle. The mentioning of a heliacal rising of Sothis combined with a date of the Egyptian calendar therefore may allow quite accurate absolute dating using astronomical charts.1 Only few Sothic dates are known from ancient Egypt, the oldest complete date so far was the el-Lahun date from the 12th Dynasty.2 Although extremely sparse, these Sothis dates are of highest importance for the chronology of ancient Egypt and ancient cultures of the Near East since the dating of the Egyptian Middle Kingdom, of the Egyptian New Kingdom, and of neighbouring regions depend on them.

The New Sothis Date

Recently a new Sothis date on an ointment jar was discovered.3 The jar mentions the “Forthcoming of Sopdet” and the date of a heliacal rising of Sirius on the beaker. For the stylistic dating of our jar several publications were used.4 Such cylindrical beakers contained perfume oil and were often given to people on special occasions and festivals—a tradition still alive in the Coptic church.5 The jar was stylistically dated into the mid to late 5th Dynasty. Inscription, palaeography and the astronomical date also point to the Old Kingdom. The inscription (Fig. 1) starting from the right column is a nominal sentence with pw:

gsw n s3-rnp.t 3bd 4 pr.t ḫft pr.t spd.t 3bd 4 3ḫt pw ḫft wp.t -rˁ

Ointment made for the protection of the year, month 4, Peret-season, for the forthcoming of Sothis, month 4, Akhet-season it is, made for the first day of the month.

The sign “wp.t -rˁ” is a cow’s horn with sun disc and can be translated as “first day of the month” but also as “beginning of the New Year,” most fitting for this festival.6 It mentions the ointment inside the jar, combined with the production date (4th month, Peret). The reason is the forthcoming of Sothis (Sirius) at the date (4th month, Akhet, 1st day). The Peret date, mentioning the protection of the year may refer to the date of production of the oil: the ointment would have been produced ca. ¾ year in advance of the heliacal rising of Sothis. This is a classic production length for the sacred oils in Egypt.7

Old Kingdom Chronology

Historical dating based on information given in king lists, radiocarbon dating, as well as various astronomical dating attempts resulted in different chronologies of the Egyptian Old Kingdom with varying degrees of disagreement.8 All these dating methods share that they are heavily influenced by the fact that the method of counting years used during Dynasties 3 to 6 is still a matter of debate. The standard theory for many years was that a regular biannual count of regnal years was employed throughout the whole Old Kingdom.9 In the framework of this hypothesis each “year of the xth cattle count” should have been followed by a “year after the xth cattle count.” It has long been noticed that the number of documents containing a “year of the count” and a “year after the count” is not about equal, as one would expect if indeed a biannual year count had been used. Instead—depending on whether graffiti of workmen are included in the statistics or not—the ratio amounts to approximately 2.8:1 and 1.85:1, respectively.10 Disregarding the graffiti results in that a “year after the count” usually occurred approximately every third year, but sometimes already every second year. Based on these numbers John Nolan proposed a connection with the original lunar calendar, namely that a “year after the count” was employed if an intercalary month was inserted into the lunar calendar at the end of the preceding year in order to keep it in line with the sidereal and solar year.11 Nolan’s hypothesis requires a reduction of the number of regnal years usually assigned to Old Kingdom Pharaohs by about 21% and hence a shortening of Old Kingdom chronology.

figure 1
figure 1

Drawing of the ointment jar with the Sothis-inscription in the archaeological collection of the University of Zurich, inv. 5821.

Citation: Journal of Egyptian History 10, 2 (2017) ; 10.1163/18741665-12340035

Copyright: Michael Habicht, digitally reworked and coloured by Patrick E. Eppenberger.

The Lunar Calendar and Intercalary Months

Nolan recently proposed that a regular nineteen-year intercalation cycle comparable to the much later well-known Metonic cycle has been used in third millennium ancient Egypt.12 Although the regular Metonic intercalation cycle may well have been known prior to its first unambiguously documented attestation one may doubt that such a cycle was used 2000 years earlier. However, this does no harm to Nolan’s basic hypothesis because the application of a regular intercalation cycle would by no means be a prerequisite for the functioning of the whole system. The so-called original lunar calendar was tied to the heliacal rising of the star Sirius.13 This event refers to the first visibility of the star Sirius in the morning sky shortly before sunrise after a period of invisibility in the night sky. A new lunar month began with the invisibility of the lunar crescent in the morning sky. A normal year consisted of twelve lunar months. Since such a lunar year with twelve months is about ten days shorter than a sidereal year an extra month has to be inserted after three years, and at times already after two years, in order to keep the lunar calendar synchronized with the sidereal year.14 The decisive astronomical phenomenon for the insertion of an additional lunar month was the heliacal rising of the star Sirius. As soon as the beginning of the first lunar month of the next year would have occurred too close to the expected date of the heliacal rising of Sirius, an intercalary month had to be inserted. Otherwise the twelfth lunar month, named after the heliacal rising of Sirius, would have ended before the name-giving event occurred. Such a lunar calendar with a simple but clever intercalation scheme can be operated without knowledge of longer intercalation cycles such as the nineteen-year cycle. Observations of the lunar crescent around new moon as well as a prediction of the date of the heliacal rising of Sirius meet all necessary requirements.

Calculations

All beginnings of lunar months and the dates of the heliacal rising of Sirius for the time span 2700 bce to 2000 bce were calculated.15 The first actual visibility of Sirius in the morning sky is highly dependent on the seeing conditions. An elevation of Sirius of 2° to 3° above the horizon was chosen with arcs of vision of 9° and 10° to account for excellent to fair observing conditions in the calculations.16 This leaves us with a time range of two to three days for the expected and observed date of the heliacal rising of Sirius. The last visibility and in consequence the first invisibility of the lunar crescent is dependent on the seeing conditions as well, but an additional factor complicates things further: due to the large uncertainty in the clock time error ΔT in the third millennium bce quite frequently it is not possible to tell unambiguously if a new lunar month started on day x or on day x-1.17 Thus, in some cases one cannot be sure whether the sequence of lunar months in two successive years was 12–13 or 13–12. Table 2 lists the Egyptian date of the beginning of the lunar month in which the heliacal rising of Sirius presumably occurred for all years between 2636 and 2280 bce, the dates of the heliacal rising of Sirius for an arc of vision of 9° to 10°, the number of lunar months in an Egyptian year as well as a minimum high chronological option for Pharaohs Khufu (conventionally dated 2589–2566 bce18 ) to Pepy ii (2278–2181 bce, see following sections).

Contemporary Sources and Astronomical Data

Contemporary documents from Dynasties 4 to 6 mentioning about 150 different years of Pharaohs are known today.19 Some of these dates are well connected to a reign of a king or implemented in a dated architectural context and are generally accepted. Other dates are uncertain in the reading of the year or attributed to several potential reigns. Of special importance are the archives from the mortuary temples of Raneferef and Neferirkare in Abusir.20 Theoretically the majority of the texts from these two archives could date to any king between Shepseskare and Pepy ii. But Paule Posener-Kriéger dated most of the documents from the Neferirkare archive into the reign of Djedkare Isesi and Unas. The same applies for the papyri from the Raneferef archive. The conventional attributions of the documents to kings were accepted (see Table 1) and a minimum High Chronology and a maximum Low Chronology from Khufu down to Pepy ii was established based on contemporary documented data and our calculations summarized in Table 2.

Several attempts have been made in the past to establish absolute dates for Djedkare Isesi and Unas based on different kinds of astronomical data and with varying results.21 On two papyri from the mortuary temple of Raneferef Wagy-feast dates are given: a Wagy date 3rd month […] day 28 in “Document iv” and a second fragmentary date in “Document iii” mentioning 1st month of Akhet day 23–29 or 29.22 The latter probably refers to the immovable Wagy-feast of Osiris fixed on the 1st month of Akhet day 18 in the civil calendar that was celebrated about a fortnight later than the beginning of the New Year on the 1st month of Akhet day 1. The former, however, relates to the moveable Wagy-feast whose feast dates were determined using the lunar calendar. Ulrich Luft derived an assumed heliacal rising of Sothis around the last days of the 2nd month of Akhet during the reign of King Raneferef based on a suggested misreading of the date in “Document iii” and an interpretation to mean 3rd month of Akhet day 23–29 instead of 1st month of Akhet.23 Leo Depuydt in using the same dates calculated an upper threshold for the heliacal rising of Sirius and reconstructed that the Wagy festival took place on 3rd month of [Akhet] day 28. Thus, since the Wagy feast was celebrated on an 18th lunar day the heliacal rising of Sirius might be dated to 3rd month of Akhet day 10 or earlier. Assuming the latest possible date as 3rd month of Akhet day 10, this event would coincide with 2506–2503 bce according to Depuydt. According to our own calculations the date iii Akhet 10 will be 2504–2491 bce.24 Rolf Krauss refrained from using such a derived Sothic date on the basis of two arguments: firstly because it is unclear how the date of the moveable Wagy feast during the Old Kingdom was established; and secondly because the resulting chronology would be a rather high one.25 We follow Krauss in neglecting a derived Sothic date, but we take into account the date 3rd month [ ] day 28 as a record for an 18th lunar day that cannot be earlier than year 1 of Niuserre and not earlier than the heliacal rising of Sirius in the respective year. Concerning the amendment of the month name both seasons—Akhet as well as Peret—were taken into account, only Shemu can be safely excluded on first sight as was already argued by Depuydt.26

Posener-Kriéger identified two further lunar dates in the Neferirkare archive that she tentatively assigned to the reign of Djedkare Isesi.27 The document in her Table 2 (Plate 3–4) allows deducing that in the 2nd month of the Shemu season day 18 was a second lunar day. The verso of this papyrus is dated to year 21 or 22 of an unnamed king. The recto was inscribed earlier, presumably about one year earlier. Due to the mentioned high number of regnal years on the verso the attribution of this date to Djedkare Isesi can be considered rather certain.28 The document in her Table 1 (Plate 5–6–7A) mentions that in the 4th month of the Shemu season days 17 and 18 were lunar days 1 and 2, respectively. The verso of this papyrus dates to the year 4 of an unnamed king, suggesting that the recto was inscribed supposedly one year earlier. This date may belong to either Djedkare Isesi or Unas.29

Recently a new Sothic date from the Old Kingdom has been published by Michael Habicht.30 Unfortunately the name of the king on the jar is missing. The given date, 4th month of Akhet, day 1 allocates the vessel somewhere between 2419–2406 bce if a reference point of Memphis is assumed. Stylistically, the jar can be attributed to the mid-5th to early 6th Dynasty.31 The stylistic dating in connection with the absolute date given by the Sothic date is in very good agreement with recent radiocarbon determinations that locate the maximum of the probability function of the accession date of Djedkare Isesi to about bce 2450 and the reign of Unas to about bce 2420.32

Counting of Regnal Years

After the death of the old Pharaoh the first partial year of his successor was counted as sema ta.wy, as year of unification of the two lands. Afterwards, theoretically a “year of” (rnp.t sp) or a “year after” (rnp.t m-ḫt sp) the cattle count could follow. To our knowledge it is not clear how the Egyptian counting worked if sema ta.wy was followed by a “year after.” Was it designated as “year after sema ta.wy,” as “year 1 after,” in another way, or was it even impossible to have a “year after” following sema ta.wy? The surviving contemporary documents show that no account of a “year after sema ta.wy” exists, but there are two different phrases that may or may not be interchangeable: rnp.t m-ḫt sp 1 and rnp.t m-ḫt sp tpy. So far, they have been treated to mean the same, namely “year 1 after” the cattle count. Years rnp.t m-ḫt sp tpy are documented for Menkaure, Shepseskaf, Djedkare or Unas, Teti and Pepy ii. Years rnp.t m-ḫt sp 1 are preserved from the reign of Userkaf, Djedkare and Merenre. We see that there exists no overlap between the list of kings with documented years rnp.t m-ḫt sp tpy and rnp.t m-ḫt sp 1 with the exception of maybe Djedkare.33 For Menkaure, one has a preserved sequence of years rnp.t m-ḫt sp tpy in the tomb of Meresankh iii, rnp.t m-ḫt sp 2 on a papyrus fragment from Gebelein and rnp.t m-ḫt sp 3 from another papyrus fragment from Gebelein. If one interprets rnp.t m-ḫt sp tpy to be a synonym for rnp.t m-ḫt sp 1 then this sequence can only be explained as a biannual counting system. In connection with a lunar calendar with regular intercalations, it is impossible to have three intercalary months within five years. One would be forced to assume some kind of extra correction for omitted earlier intercalations. If, however, one interprets rnp.t m-ḫt sp tpy to mean “year after the sema ta.wy” one is faced with a common sequence. The evidence from the reign of Menkaure as well as the fact that barely both phrases from the reign of the same king are preserved leads us to the tentative suggestion that rnp.t m-ḫt sp tpy indeed means “year after the sema ta.wy.” However, this interpretation does not significantly alter the results presented in the following section.

Resulting Chronological Models

In the first instance, the beginning of all Egyptian lunar months and the expected dates of the heliacal rising of the star Sirius at Memphis were calculated for all years between 2700 and 2000 bce. The results of these computations provide the information given in the first four rows of Table 2. In a second step the reigns of Djedkare Isesi and Unas were pinned down with the help of the lunar dates from the Neferirkare archive. The obtained data were used once in connection with the lower threshold provided by a reconstructed date of the Wagy-feast in the 3rd month of the Akhet season on day 28 (High Chronology), and once in combination with the upper threshold given in case of a Wagy-feast in the 3rd month of the Peret season on day 28 (Low Chronology). Only then the contemporary documented year dates of Djedkare Isesi and Unas were added to Table 2 and the underlying hypothesis tested that a “year after” was counted if the preceding year contained 13 lunar months. For in total 28 different documented years for these two kings only one disagreement with the calculations emerged in the case of both chronological models.34 In a fourth step the documented dates of the other kings were incorporated in Table 2 with the aim to keep their reign lengths in the chronological models as close as possible to the highest documented year number while still agreeing with the scheme of alternating “years of” and “years after” provided by the calculations. Thus, while the absolute dates of Djedkare Isesi and Unas in the chronological models can be pinned down thanks to the lunar dates and a wealth of dated documents, the absolute dates and the resulting reign lengths of all other kings summarized in Table 3 are less precise—the further away in time a king is located from Djedkare Isesi and Unas the less precise is the data.

Low Chronology

Provided that the Wagy-feast was not celebrated later than in the second month after the heliacal rising of Sirius the earliest possible chronological solution for a Wagy-feast in the 3rd month of Peret on day 28 occurs in 2242 bce.35 It would have been celebrated in the second month after the heliacal rising of Sirius in the 1st month of the Peret season on days 13–14. The Horus names of kings on preserved seals from the mortuary complex of Raneferef range down to Pepy i. In the reign of Unas the cult began to decline and it died out in the reign of Pepy i according to Posener-Kriéger and collaborators.36 Hence, the end of the reign of Pepy i cannot fall later than 2242 bce. By means of this initial threshold fits for the two lunar dates from year 20/21 of Djedkare Isesi and year 3/4 of Djedkare Isesi or Unas were sought for. One obtains reasonable fits for both possibilities and in both models we count 36 regnal years for Djedkare Isesi in total.37 Hence, we are not able to attribute the year 3 lunar date to one of the two kings with certainty. Starting from the reign of Djedkare Isesi, a Low Chronology based on the preserved documented years of kings was established. Our aim was to stay as close as possible to the highest attested years. Table 3 lists the number of years counted for each Pharaoh in our model. The Wagy-feast date in 2242 bce would fall in year 15 (corresponding to “year 9 of the cattle count”) of Pepy i. 35 of 38 different documented “years after the xth cattle count” from Khufu down to Pepy ii can be reproduced. Seven belong to years where the actual seeing conditions on the day of the theoretical heliacal rising of Sirius would have been decisive if the year consisted of 12 or 13 lunar months. In cases where the predicted heliacal rising of Sirius occurred very closely to the beginning of a new lunar month one expects that a simple scheme with a shift by one day every four years in the Egyptian calendar for the heliacal rising of Sirius was decisive instead of actual observation. Otherwise the date of the start of a new lunar calendar year would have been known in the short-term only which seems improbable. Hence, one has to count three or four of these seven occasions as disagreements too.38 Thus, in total 31 or 32 of 38 “years after the xth cattle count” (81.6% or 84.2%) can be reproduced correctly. The approx. 110 different documented “years of the xth cattle count” unfortunately does not help in testing the model. It is worth noting that it was not possible to find another fit of comparable quality of the lunar data and the documented “years after” for lower chronologies that still fulfil the criterion that the minimum distance of years to accommodate for the First Intermediate Period, Dynasty 11 and the first part of Dynasty 12 down to the Sothic date from the Middle Kingdom must be available.39 A higher “Low Chronology” is impossible if our following two basic assumptions are correct: 1) the Wagy-feast date from the mortuary temple of Raneferef cannot stem from a reign later than Pepy i, 2) it is not celebrated later than in the second month after the heliacal rising of Sirius.

High Chronology

The latest possible chronological solution for a Wagy-feast in the 3rd month of Akhet on day 28 celebrated in the first month after the heliacal rising of Sirius and not occurring earlier than the reign of Raneferef is in 2489 bce.40 Starting from this threshold one obtains a perfect fit for the lunar data in 2464 bce for “year 3” of Djedkare and in 2436 bce for “year 20 after” of Djedkare. The year 3 lunar date may also belong to Unas, in that case it would deviate by one day (month started too early) in 2428 bce and correspond to “year 2 after” of Unas. The Wagy-feast date in 2489 bce in this chronological model would fall in year 2 (corresponding to “year 1”) of Niuserre. 37 of the 38 different documented “years after the xth cattle count” can be successfully reproduced, 12 fall in years where the calculations cannot predict the sequence of years with 12 and 13 lunar months (12–13 or 13–12) with certainty.41 Thus, in total 31 of 38 “years after the xth cattle count” (81.6%) can be explained correctly with our chronological model.

Low Chronology Versus High Chronology

Our Low and High Chronologies are separated by ca. 130 years. The small amount of available astronomical data as well as the documented years of kings do not allow for a justifiable decision to favour one of the two chronological models. One has to state that our Low Chronology with the end of an assumed 54-year reign of Pepy ii in 2150 bce aligns well with the assumption about a short duration of the First Intermediate Period (30 to 60 years) if 143 years are counted for Dynasty 11 and 110–125 years for Dynasty 12 until the Sothic date in year 7 of Senwosret iii in 1866 bce or 1841 bce. However, recent radiocarbon data seem to contradict such a low chronology.42 On the other hand, the date of Khufu in our model (2504–2475 bce) coincides with the dating of this Pharaoh suggested by Kate Spence based on the alignment of his pyramid with the help of observations of simultaneous transits of two circumpolar stars (ζ Ursae Minoris and β Ursae Minoris in ca. 2478 bce).43 In the Low Chronology model the jar with a Sothic date day 1 of the 4th month of the Akhet season (2419–2406 bce) in Zurich would fall in one of the reigns of Shepseskaf, Thamphitis or Userkaf and hence in the transition between Dynasties 4 and 5. On stylistic grounds an attribution to the later 5th Dynasty would seem better.44 The presented High Chronology with the end of an assumed 54-year reign of Pepy ii in 2282 bce is only compatible with the highest estimates about the duration of the First Intermediate Period (about 150 years) and the High Chronology of the Middle Kingdom with year 7 of Senwosret iii in 1866 bce. It aligns well with recent radiocarbon data. The jar with the Old Kingdom Sothic date would stem from the reign of Unas or Teti, a dating that is in line with the stylistic dating of the vessel.

Comparison with Other Models

The relative chronology of the Old Kingdom together with discussions of the imbalance between documented “years of” and “years after” has been the subject of different studies.45 The two chronological models presented in this paper are based on the results of these studies. With the help of the few available astronomical data two absolute chronologies are established. Concerning the ratio of documented “years of” to “years after” for Dynasties 4, 5, and 6 our numbers slightly deviate from the ones given by Miroslav Verner due to our tentative assumption that rnp.t m-ḫt sp tpy and rnp.t m-ḫt sp 1 do not denote the same year.46 For Dynasty 4 the ratio of documented “years of” to “years after” amounts to 19:9 (68%:32%), for Dynasty 5 to 34:15 (69%:31%), and for Dynasty 6 to 15:13 (54%:46%).47 The calculations show an expected ratio of 64%:36% which is rather close to what the preserved documents from Dynasties 4 and 5 indicate. However, the documented year dates from Dynasty 6 are not easily reconcilable with these numbers, although it is possible to explain all but one mentioned “years after” in both chronological models.

The assumption that a regular biannual counting system was used in Dynasty 6, as presumed by Jürgen von Beckerath, would eliminate our Low Chronology: according to the highest documented years at least 50 years for Pepy i, 12 years for Merenre and 66 years for Pepy ii would have to be counted. This results in an end of reign of Pepy ii in 2128 bce at earliest. The minimum duration for the remaining kings of Dynasty 6 (3 years), of Dynasty 8 (46 years), the First Intermediate Period (30 years), Dynasty 11 (106 years) and for Dynasty 12 until the beginning of the reign of Senwosret iii totals 285 years—this would date the accession of Senwosret iii in 1843 bce at earliest which is too late according to the Middle Kingdom Sothic date from el-Lahun. However, in connection with our High Chronology a transition to a regular biannual counting system in Dynasty 6 would help to lower the number of years one has to attribute to the First Intermediate Period.

Table 4 lists the absolute dates of selected Pharaohs from our chronological models, from the handbooks of von Beckerath, Ian Shaw, and Erik Hornung et al., as well as from recent C14 measurements.48 All these chronologies are strongly dependent on the amount of years allocated to each Pharaoh.49 The two chronological models presented in this paper differ from the rest insofar as the number of calendar years counted for each king from Dynasty 4 to 6 is shortened by about 20% due to the assumption that no regular biannual counting of years was employed. However, the basic information about the reign lengths of kings in all these chronologies stems from the same sources: annals, Turin King List, Manethonian tradition and contemporary sources. The different resulting absolute dates in the models of Hornung et al., Shaw, and von Beckerath are due to varying assumptions about the duration of the First Intermediate Period and the absolute dating of the Egyptian Middle Kingdom. On the contrary, in the C14 model of Michael Dee and in our chronological models the length of the First Intermediate Period is a result of the modelling, not a basic parameter. Table 4 shows that the absolute dates of our Low Chronology are close to or up to 25 years lower than the ones given by Hornung et al. Our High Chronology dates resemble very closely the upper boundary defined by the C14 model of Dee and they are about 30 to 60 years higher than the higher dates of von Beckerath. The dates of Shaw and the lower dates of von Beckerath comprise a compromise between high and low chronologies: these are not supported by the lunar dates under our basic assumption that the Wagy-feast was not celebrated later than in the second month after the heliacal rising of Sirius.

Conclusions

Two different chronological models—a minimum High Chronology as well as a maximum Low Chronology—of Dynasties 4 to 6 are presented on the basic assumption that Nolan’s theory about the connection of the occurrence of a “year after the cattle count” with the insertion of an intercalary month in the original lunar calendar is correct. With the help of three lunar data the reigns of Djedkare Isesi and Unas were pinned down. The two chronologies differ in that in the case of the High Chronology the missing month name of the lunar Wagy-feast date was emended to 3rd month of the Akhet season and in the case of the Low Chronology to 3rd month of the Peret season. Afterwards the reigns of the kings up to Khufu and down to Pepy ii have been modelled based on the documented contemporary data and the preserved information from king lists. It was aimed at to stay as close as possible to the minimum attested year number and to account for the documented “year after the cattle count” years. It has to be stressed that the further away in time a Pharaoh is located from Djedkare Isesi the more uncertain are his modelled absolute dates. Both chronologies can explain about 82% of the documented “years after.” The Low Chronology is consistent with a short duration of the First Intermediate Period (30 to 60 years), but disagrees with recent radiocarbon determinations. On the contrary, the High Chronology is in line with the radiocarbon data but it can only be a serious solution if the First Intermediate Period lasted about 150 years.

table 1

List of all documented years of pharaohs Khufu to Pepy ii known to us, their source and possible remarks

Abbreviations used: pkvv—Posener-Kriéger, et al., Raneferef; PKdC—Posener-Kriéger and de Cenival, Abusir Papyri; bd—Baud and Dobrev, “Nouvelles Annales”; V06—Verner, et al., Raneferef Pyramid; ds—Dunham and Simpson, Mersyankh iii.

table 1table 1table 1table 1table 1table 1
table 2

List for all years between 2636 and 2280 bce with the Egyptian date of the beginning of the lunar month in which the heliacal rising of Sirius presumably occurred, the dates of the heliacal rising of Sirius for an arc of vision of 9° to 10°, the number of lunar months in an Egyptian year, the year count of pharaohs Khufu to Pepy ii according to our High Chronology as well as the documented regnal years, their source, and remarks (uncertain attributions and astronomical data)

Abbreviations used: V—Verner, “System of dating”; G—Gundacker, “Mykerinos”

table 2table 2table 2table 2table 2table 2table 2table 2table 2table 2table 2table 2table 2table 2
table 3

Absolute dates and number of counted regnal years in our Low Chronology (left) and our High Chronology (right) of the Old Kingdom.

table 3table 3
table 4

Absolute accession dates of selected pharaohs in different chronological models. From left to right: our Low Chronology; dates given in Hornung, et al., Chronology; Shaw, Oxford History; von Beckerath, “Chronologie”; the modelled 95% probability C14 accession dates of Dee, et al., “Radiocarbon-based Chronology”; and our High Chronology

table 4

Abbreviations

asaé

Annales du Service des Antiquités de l’Égypte

bifao

Bulletin de l’Institut Français d’Archéologie Orientale

bsfé

Bulletin de la Société française d’Égyptologie

gm

Göttinger Miszellen

jea

The Journal of Egyptian Archaeology

jnes

Journal of Near Eastern Studies

RdÉ

Revue d’Égyptologie

säk

Studien zur Altägyptischen Kultur

zäs

Zeitschrift für Ägyptische Sprache und Altertumskunde

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  • Bárta, M. “Radiocarbon Dates for the Old Kingdom and their Correspondences.” In Radiocarbon and the Chronologies of Ancient Egypt, A.J. Shortland and C. Bronk Ramsey, eds. 209217. Oxford: Oxbow Books, 2013.

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  • Baud, M. and V. Dobrev. “De nouvelles annals de l’Ancien Empire égyptien. Une ‘Pierre de Palerme’ pour la vie dynastie.” BIFAO 95 (1995): 2392.

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    • Export Citation
  • Beckerath, J. von. “Chronologie des Pharaonischen Ägypten.” Mainz am Rhein: Philipp von Zabern, 1997.

  • Borchardt, L. “Der zweite Papyrusfund von Kahun und die zeitliche Festlegung des mittleren Reiches der ägyptischen Geschichte.” ZÄS 37 (1899): 89103.

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  • Gautschy, R. “Der Stern Sirius im Alten Ägypten.” ZÄS 138/1 (2011): 116131.

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  • Habicht, M.E., R. Gautschy, R. Siegmann, D. Rutica, and R. Hannig. “A New Sothis Rise on a Small Cylindrical Jar from the Old Kingdom.” GM 247 (2015): 4149.

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  • Haeny, G. “Die Steinbruch- und Baumarken.” In Das Sonnenheiligtum des Königs Userkaf. Die Funde. H. Ricke, ed., 2347. Wiesbaden: Franz Steiner, 1969.

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  • Hannig, R. Grosses Handwörterbuch Deutsch—Ägyptisch: (2800–950 v. Chr.). Mainz am Rhein: Philipp von Zabern, 2000.

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  • Hornung, E., R. Krauss, and D.A. Warburton, eds. Ancient Egyptian Chronology. HdO i/83. Leiden: Brill, 2006.

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  • Krauss, R. “Lunar Dates.” In Ancient Egyptian Chronology, E. Hornung, R. Krauss, and D.A. Warburton, eds., 395431. HdO i/83. Leiden: Brill, 2006.

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1

Krauss, Sothis- und Monddaten; Gautschy, “Sirius.”

2

Krauss, Sothis- und Monddaten; Gautschy, “Sirius”; Luft, Chronologische Fixierung; Borchardt, “Kahun.”

3

Habicht, et al., “New Sothis Rise.”

4

Aston, Stone Vessels; Günther and Wellauer, Ägyptische Steingefässe.

5

Baligh, “Oil and its importance.”

6

Hannig, Handwörterbuch, 206.

7

Baligh, “Oil and its importance.”

8

See, e.g., Shaw, ed., Oxford History; Krauss, “Lunar Dates,” 429–31; Depuydt, “Sothic Chronology,” 183–84; Dee, “Radiocarbon-based Chronology,” 212–13 and 287; Bárta, “Radiocarbon Dates,” 221; Spence “Orientation of Pyramids.”

9

Gardiner, “Regnal Years.”

10

Nolan, “Cattle Counts,” 79.

11

Nolan, “Cattle Counts,” 92.

12

Nolan, “Phyle Rotations,” 340–44.

13

Parker, Calendars, 30–50.

14

A sidereal year is only slightly longer than the tropical solar year, thus a lunar calendar synchronized with a stellar event like the heliacal rising of Sirius is also synchronized with the solar year.

15

For details about the computations see Gautschy, “Sirius,” 119–20.

16

These values include refraction.

17

The clock time error ΔT is due to the fact that Earth’s rotation is not uniform, but slowing down. The slowdown rate is composed of a regular predictable part and of a fluctuating irregular contribution. The time difference between an assumed uniform rotation of the Earth and the actual one is called ΔT. It can only be determined observationally. The earliest securely dated astronomical observations that can be used to derive values of ΔT for antiquity stem from the 7th century bce. Prior to the 7th century bce the ΔT values are based on extrapolations of data from the 7th century bce onwards. In 2700 bce the uncertainty amounts to approx. ±2 hours with a ΔT of 18 hours.

18

Shaw, ed., Oxford History.

19

We used the compilations of Spalinger, “Dated Texts”; Verner, “4th and 5th Dynasty Chronology” and “System of Dating”; and of Gundacker, “Mykerinos.”

20

Posener-Kriéger, et al., Raneferef and Posener-Kriéger, Neferikare.

21

Krauss, “Lunar Dates,” 429–31; Depuydt, “Sothic Chronology”; and Luft, “Wagy.”

22

Luft, “Wagy” and Depuydt, “Sothic Chronology,” 172–74 and 183–84.

23

Luft thus assumes that the moveable Wagy-feast was celebrated in the first month after the heliacal rising of Sirius like the fixed Wagy feast although he discusses the Wagy-feast data from the Middle Kingdom Illahun temple archive where the moveable lunar Wagy-feast was demonstrably celebrated in the second month after the heliacal rising of Sirius (Luft, “Wagy,” 41; Krauss, Sothis- und Monddaten, 86–94).

24

For a reference point Memphis, Sirius 2° or 3° above horizon and an assumed arc of vision between 9° and 11°.

25

Krauss, “Wenn und aber,” 56–57 and private communication.

26

Depuydt, “Sothic Chronology,” 173.

27

Posener-Kriéger, Neferirkare, 486–88.

28

Only Pepy i and Pepy ii may be theoretically considered as alternatives.

29

Posener-Kriéger, Neferirkare, 486–88 and Krauss, “Lunar Dates,” 430–31 both finally argue for an attribution to Djedkare Isesi.

30

Habicht, et al., “New Sothis Rise.”

31

Habicht, et al., “New Sothis Rise,” 44–46.

32

Dee, “Radiocarbon-based Chronology,” 212–13 and 287.

33

Theoretically nothing speaks against a documented year rnp.t m-ḫt sp tpy and a year rnp.t m-ḫt sp 1 for the same king. Even if not identical years are meant intercalary months after already two years occur from time to time.

34

In our Low Chronology the documented “year 14 after” of Djedkare Isesi cannot be reproduced by the calculations, in our High Chronology the documented “year 4 after” of Djedkare Isesi cannot be reproduced.

35

From the archive of Illahun we know that the Wagy-feast was celebrated in the second month after the heliacal rising of Sirius (Luft, Chronologische Fixierung, 217–20). There are several possible solutions later than 2242 bce but in the following the focus will be on the highest possible Low Chronology. Finally, there is not much leeway left in combination with the lunar dates, otherwise there is not enough time available to accommodate even the shortest estimates for the duration of the First Intermediate Period (about 30 years) as well as Dynasty 11 (106 to 143 years) and the first part of Dynasty 12 (about 110 years) down to the Middle Kingdom Sothis date of Senwosret iii in 1866 bce (High Chronology) or 1841 bce (Low Chronology).

36

Posener-Kriéger, et al., Raneferef, 321–22.

37

If both lunar dates are ascribed to Djedkare Isesi the year 3 lunar date in 2328/2327 bce is deviating by one day (month started too early) and the year 20 lunar date in 2301/2300 bce perfectly fits. If the year 3 lunar date is ascribed to Unas both dates in 2301/2300 bce and 2290/2289 bce perfectly match.

38

Three out of seven can be explained with an arc of vision of 10° for the heliacal rising of Sirius, the remaining four with an arc of vision of 9°.

39

The minimum distance we defined to be 30 years for the First Intermediate Period, 106 to 143 years for Dynasty 11 and 103 to 120 years from the start of Dynasty 12 to the beginning of the reign of Senwosret iii. For the Sothic date of the Middle Kingdom see, e.g., Luft, Chronologische Fixierung, 58; Krauss “Sothic Dates,” 448–50 and Gautschy, “Sirius,” 124–25.

40

In 2489 bce the heliacal rising of Sirius fell on day 11 of the 3rd month of the Akhet season if the seeing conditions were good. The beginning of a new lunar month coincided with this day.

41

Six out of twelve can be explained with an arc of vision of 10° for the heliacal rising of Sirius, the remaining six with an arc of vision of 9°.

42

See, e.g., Dee, “Radiocarbon-based Chronology.”

43

Spence, “Orientation of Pyramids.”

44

Habicht, et al., “New Sothis Rise,” 44–46.

45

See, e.g., Spalinger, “Dated Texts”; Helck, “Teti”; Verner, “4th and 5th Dynasty Chronology” and “System of Dating”; Nolan, “Phyle Rotations.”

46

Verner, “System of Dating,” 26–38.

47

Documents for 23 out of 36 years exist for Djedkare Isesi, and for 5 out of 19 years for Unas. Taking only these two comparably well documented kings into account the ratio between “years of” and “years after” amounts to 19:9 (68%:32%).

48

Beckerath, “Chronologie,” 187–88; Shaw, ed., Oxford History, 480; Hornung, Krauss, and Warburton, eds., Chronology, 490–91; Dee, “Radiocarbon-based Chronology,” 209–17 and 287.

49

The C14 accession dates are obtained with the help of the wiggle matching method. In the modelling, information about the succession of kings as well as about their reign lengths enters the model.

  • Abu Bakr, A.M. and A.Y. Moustafa. “The Funerary Boat of Khufu.” In Aufsätze zum 70. Geburtstag von Herbert Ricke. A.M. Abu Bakr, ed., 116. Wiesbaden: Steiner, 1971.

    • Search Google Scholar
    • Export Citation
  • Anthes, R. Die Felsinschriften von Hatnub. Hildesheim: Olms, 1964.

  • Aston, B. Ancient Egyptian stone vessels: materials and forms. Heidelberg: Heidelberger Orientverlag, 1994.

  • Baligh, R. “Oil and its importance in Egypt from the oldest times.” [oral presentation] In International Congress of Egyptologists XI (2015).

    • Search Google Scholar
    • Export Citation
  • Bárta, M. “Radiocarbon Dates for the Old Kingdom and their Correspondences.” In Radiocarbon and the Chronologies of Ancient Egypt, A.J. Shortland and C. Bronk Ramsey, eds. 209217. Oxford: Oxbow Books, 2013.

    • Search Google Scholar
    • Export Citation
  • Baud, M. and V. Dobrev. “De nouvelles annals de l’Ancien Empire égyptien. Une ‘Pierre de Palerme’ pour la vie dynastie.” BIFAO 95 (1995): 2392.

    • Search Google Scholar
    • Export Citation
  • Beckerath, J. von. “Chronologie des Pharaonischen Ägypten.” Mainz am Rhein: Philipp von Zabern, 1997.

  • Borchardt, L. “Der zweite Papyrusfund von Kahun und die zeitliche Festlegung des mittleren Reiches der ägyptischen Geschichte.” ZÄS 37 (1899): 89103.

    • Search Google Scholar
    • Export Citation
  • Borchardt, L. Das Grabdenkmal des Königs Ne-user-re. Leipzig: Hinrichs, 1907.

  • Borchardt, L. Das Grabdenkmal des Königs Nefer-ir-ke-re. Leipzig: Hinrichs, 1909.

  • Borchardt, L. Das Grabdenkmal des Königs Sahure, Band 1: Der Bau. Leipzig: Hinrichs, 1910.

  • Couyat, J. and P. Montet. Les inscriptions hiéroglyphiques et hiératiques du Ouâdi Hammâmât. MIFAO 34. Cairo: IFAO, 1913.

  • Dee, M.W. “A Radiocarbon-based Chronology for the Old Kingdom.” In Radiocarbon and the Chronologies of Ancient Egypt, A.J. Shortland and C. Bronk Ramsey, eds. 209217. Oxford: Oxbow Books, 2013.

    • Search Google Scholar
    • Export Citation
  • Depuydt, L. “Sothic Chronology and the Old Kingdom.” JARCE 37 (2000): 167168.

  • Dunham, D. and W.K. Simpson. The Mastaba of Queen Mersyankh III G7530–7540. Giza Mastabas I. Boston: Museum of Fine Arts, 1974.

  • Edel, E. “Die Kalksteintäfelchen.” In Das Sonnenheiligtum des Königs Userkaf. Die Funde. H. Ricke, ed., 222. Wiesbaden: Franz Steiner, 1969.

    • Search Google Scholar
    • Export Citation
  • Eichler, E. “Untersuchungen zu den Königsbriefen des Alten Reiches.” SÄK 18 (1991): 141172.

  • Eichler, E. Untersuchungen zum Expeditionswesen des ägyptischen Alten Reiches. Wiesbaden: Harrassowitz, 1993.

  • Gardiner, A.H. “Regnal Years and Civil Calendar in Pharaonic Egypt.” JEA 31 (1945): 1128.

  • Gardiner, A.H., T.E. Peet, and J. Černý. The inscriptions of Sinai, Part I. Introduction and Plates. Oxford: Oxford University Press, 1952.

    • Search Google Scholar
    • Export Citation
  • Gauthier, H. “Quatre nouveaux fragments de la pierre de Palerme.” In Le Musée Égyptien. Recueil des Monuments et de Notices sur les Fouilles d’Égypte 3, G. Maspero, ed., 2953. Cairo: IFAO, 1915.

    • Search Google Scholar
    • Export Citation
  • Gautschy, R. “Der Stern Sirius im Alten Ägypten.” ZÄS 138/1 (2011): 116131.

  • Goedicke, H. “The Death of Pepi II.” SÄK 15 (1988): 111122.

  • Goedicke, H. “Four Hieratic Ostraca of the Old Kingdom.” JEA 54 (1968): 2330.

  • Goedicke, H. Königliche Dokumente aus dem Alten Reich. Wiesbaden: Harassowitz, 1967.

  • Goedicke, H. Die privaten Rechtsinschriften aus dem Alten Reich. Wien: Notring, 1970.

  • Gundacker, R. “Materialien zur Länge der Regierung des Mykerinos.” Sokar 21 (2010): 3043.

  • Gunn, B. “A Sixth Dynasty letter from Saqqara.” ASAÉ 25 (1925): 242255.

  • Günther, P. and R. Wellauer. Ägyptische Steingefässe der Sammlung Rudolph Schmidt (Solothurn). Ägyptologische Hefte des Orientalischen Seminars der Universität Zürich 2. Zürich: Orientalisches Seminar der Universität Zürich, 1988.

    • Search Google Scholar
    • Export Citation
  • Habicht, M.E., R. Gautschy, R. Siegmann, D. Rutica, and R. Hannig. “A New Sothis Rise on a Small Cylindrical Jar from the Old Kingdom.” GM 247 (2015): 4149.

    • Search Google Scholar
    • Export Citation
  • Haeny, G. “Die Steinbruch- und Baumarken.” In Das Sonnenheiligtum des Königs Userkaf. Die Funde. H. Ricke, ed., 2347. Wiesbaden: Franz Steiner, 1969.

    • Search Google Scholar
    • Export Citation
  • Hannig, R. Grosses Handwörterbuch Deutsch—Ägyptisch: (2800–950 v. Chr.). Mainz am Rhein: Philipp von Zabern, 2000.

  • Hassan, S. Excavations at Gîza. 1930–1931. Cairo: Government Press, 1936.

  • Helck, W. “Gedanken zum Mord an König Teti.” In Essays in Egyptology in honor of Hans Goedicke. B.M. Bryan and D. Lorton, eds., 103112. San Antonio: Van Siclen Books, 1994.

    • Search Google Scholar
    • Export Citation
  • Hornung, E., R. Krauss, and D.A. Warburton, eds. Ancient Egyptian Chronology. HdO i/83. Leiden: Brill, 2006.

  • Junker, H. Der Friedhof südlich der Cheopspyramide. Gîza x. Wien: Rohrer, 1951.

  • Junker, H. Die Mastabas der IV. Dynastie auf dem Westfriedhof. Gîza i. Wien: Hölder-Pichler-Tempsky, 1929.

  • Junker, H. Der Ostabschnitt des Westfriedhofs. Gîza viii. Wien: Rohrer, 1947.

  • Kanawati, N. “A new ḥ3t/rnpt-zp for Teti and its implication for Old Kingdom Chronology.” GM 177 (2000): 2531.

  • Krauss, R. “Egyptian Sirius/Sothic Dates and the Question of the Sothis-Based Lunar Calendar.” In Ancient Egyptian Chronology, E. Hornung, R. Krauss, and D.A. Warburton, eds., 439457. HdO i/83. Leiden: Brill, 2006.

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    Drawing of the ointment jar with the Sothis-inscription in the archaeological collection of the University of Zurich, inv. 5821.

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