« A.U.C. 709 = 45 B.C. »

The exact Julian date at which the pre-Julian calendar was replaced by the Julian calendar is determined by fixing the triennial cycle that was incorrectly used in the years before the Augustan reform of A.U.C. 746 = 8. This problem is often glossed over quickly as being trivial and obvious. However, the period has much more chronological interest and difficulty than is usually assumed, and determining the correct solution turns out to be of fundamental importance to solving Roman chronology in the years of the pre-Julian calendar.

While the Julian calendar itself began operation on Kal. Ian. A.U.C. 709 = 45, leap years were initially inserted every third year instead of every fourth, until the error was corrected by Augustus. The most detailed description of this reform is given by the fifth century author Macrobius Saturnalia 1.14.13. He states that after Caesar's death the pontiffs caused the leap day to be inserted "at the beginning of every fourth year instead of at its end" (i.e., since the Romans counted inclusively, every third year instead of every fourth), for 36 years, after which time there had been 12 leap days in a period that should have had 9. At that point, Augustus suspended intercalation for 12 years to compensate for the three extra leap days, and then resumed intercalation on the correct frequency. A similar account is given by Solinus I 40-47, and certain details are given by earlier authors; notably, Pliny, NH 18.57, states that intercalation was suspended for 12 years. The reality of the three-year cycle is proven by OGIS 458 = iPriene 105, a decree issued by the proconsul of Asia, Paullus Fabius Maximus, that explicitly synchronises the calendar of the Asian province with this cycle in a leap year.

Even knowing the date of the Augustan reform, and being assured that it did not affect the month lengths, there are several ambiguities in Macrobius' account.

Alternative models of the triennial cycle

Because of the ambiguities inherent in Macrobius, several models have been proposed for the triennial cycle. I have identified proposals by Scaliger, Kepler, Ideler and Mommsen, Matzat, Soltau and Radke.


In 1583, J. J. Scaliger, De Emendatione Temporum 159, 238 interpreted Macrobius to mean that the accumulation of quarter-days resumed in the 13th year of the reform, i.e. in A.D. 5, and that the omitted leap years were those of 5, 1, and A.D. 4, on the quadrennial cycle. He understood Macrobius' description of the pontifical error to mean that there had been 12 leap years before the reform, completing 12 triennial cycles, and assumed that the corrected calendar was intended to be synchronous with Caesar's original intention, starting Kal. Mart. 709 = 45. On this basis he deduced that the actual leap year sequence was:

42, 39, 36, 33, 30, 27, 24, 21, 18, 15, 12, 9 B.C., A.D. 8, 12......

This model is completely consistent with the literary evidence discussed above, and remains the standard modern account, subject to dispute about whether 45 B.C. itself was a leap year. It has the very attractive property that it causes the Roman calendar, after the completion of the Augustan reform, to be perfectly synchronous with the proleptic Caesarian calendar. It is almost always accepted without recognition that it is not actually given by ancient sources but is in fact a modern reconstruction. Ý


In 1614, the astronomer J. Kepler, De Vero Anno Quo Æternus Dei Filius Humanan Naturam in Utero Benedictæ Virginis Mariæ Assumpsit, Cap. V, noted that the Julian reform was actually enacted in A.U.C. 708 = 46. Kepler argued that the first Julian leap year was therefore intended to be A.U.C. 712 = 42 so that the pontifical error meant that the three year cycle must have started the year before. On this basis, but accepting Scaliger's reconstruction of the Augustan reform, he deduced that the actual leap year sequence was:

43, 40, 37, 34, 31, 28, 25, 22, 19, 16, 13, 10 B.C., A.D. 8, 12......

In his later Rodolphine Tables, however, Kepler conformed to Scaliger's model of the triennial cycle. I have been unable to locate his reason for changing his mind. In the absence of contradictory evidence, the argument seems perfectly plausible, and, while not conclusive, it at least shows that Scaliger's solution is not unique. Kepler's solution is, however, contradicted by iPriene 105, issued in a triennial leap year which must be either A.U.C. 745 = 9 or A.U.C. 746 = 8. Ý

Ideler and Mommsen

In the 19th century, Scaliger's phase of the triennial cycle was generally accepted, but it was much debated whether A.U.C. 709 = 45 itself was a leap year or not. L. Ideler, Handbuch der Chronologie II 131, published in 1824, and T. E. Mommsen, Die Römische Chronologie bis auf Caesar 282, published in 1859, argued that it was; R. Lepsius, Monatsberichte der Berliner Akademie (1858) 451, argued it was not, consistent with Scaliger's view. Thus Ideler and Mommsen argued that the actual leap year sequence was:

45, 42, 39, 36, 33, 30, 27, 24, 21, 18, 15, 12, 9 B.C., A.D. 8, 12......

Mommsen's arguments may be summarised as follows, with commentary:

And so it is. As is every fourth year before and after it. The datum is obviously proleptic, not historical, proving nothing.

Dio's text is a little unclear, but a careful reading shows that in fact Lepsius' interpretation is correct, as is usually accepted today. Mommsen's argument that Lepsius' interpretation of Dio has no apparent explanation is, of course, self-serving; if the interpretation is correct then the point is to find an explanation for it.

This argument is remarkably weak. Mommsen admitted he had no evidence to back it up, just presumption. Against it, we may note that Macrobius, Saturnalia 1.14.8-9 gives a detailed description of the care Caesar took when interpolating additional days into existing months to ensure that the reform did not affect the dates of religious festivals. It seems at least as likely that he paid equal care to ensuring that the reform would not upset the rhythms of daily life. Throwing the market cycle into disarray just to ensure that the first day of the new calendar was a market day does not seem like an auspicious start.

Mommsen's answer to the "bad luck" objection is equally weak. Dio and Macrobius may be late authors (third and fifth century, respectively), but they both drew on contemporary and reputable sources, which in the case of Macrobius are named and can be evaluated. While not every calendrical statement made by either author can be trusted, it is notable that the exceptions concern abstruse matters of calendrical theory (the precise rules of republican intercalation given in Macrobius; the exact theory of the Caesarian reform given in Dio). A simple statement of superstition does not fall into this category.

This argument is made at great length, but with no greater justification. In essence, it is an aesthetic appeal to rationalism, as seen by a 19th century German scholar. It is no different in kind to Sacrobosco's argument that the original Caesarian months must have had a more "rational" structure, as seen by a 13th century scholar, than the months in the reformed Augustan calendar.

The fundamental question is how did Caesar initialise the leap year cycle. In all solutions, there are 12 possible triennial cycles before A.U.C. 746 = 8 but 13 cycle endpoints. In principle, the first endpoint (Kal. Mart. A.U.C. 709 = 45 in Scaliger's system) could have been selected with or without an immediately preceding leap day. Macrobius only describes 12 leap days in error when 9 should have occurred. It is possible that there was no initial leap day, but it is equally possible, as Mommsen suggests, that an initialising 13th leap day, which was inherently not in error, could have occurred. Either method could serve to initialise the cycle while remaining consistent with Macrobius' account.

Scholars have waxed lyrical back and forth on this question (see e.g. A. E. Samuel, Greek and Roman Chronology 136 against the notion), but, so long as the argument is confined to determining the most "rational" way to interpret Macrobius, it is not historical but aesthetic, and hence undecidable. What is needed is evidence.

I have found two additional arguments advanced in favour of Mommsen's reconstruction.

In 1920, T. Rice Holmes, CQ 14 (1920) 46, argued that Macrobius, Saturnalia 1.14.13, said that Caesar took account of the phase of the moon when proclaiming the new calendar. He noted that a lunar conjunction occurred shortly after midnight on 2 January 45, which would be considered as having taken place on the night of 1 January 45. He supposed that this was evidence that Kal. Ian. A.U.C. 709 = 1 January 45.

The phrase in Macrobius which at the time was read "ad lunam" was reexamined by J. Willis in 1970. MS "A" reads "ad limen" which clearly shows corruption, and led Willis to conclude that the original reading was "ad limam", i.e. a reference to a calendrical revision, not to the moon. Besides, as noted by P. Brind'Amour, Le calendrier romain 360, it seems rather strange for a calendrical reform that introduced a purely solar calendar to be initiated by a lunar event.

In 1976, A. Deman, Historia 23 (1974) 271, noted that the Pompeian graffito CIL IV 4182, dated a.d. VIII Id. Feb. A.U.C. 813 = 6 February A.D. 60, was on the market day of Cumae, and that Pompeian graffito CIL IV 8863 gave a market day cycle which showed that the Roman market was two days later. Combining the two gives us that 8 February A.D. 60 was a Roman market day. He also interpreted Dio Cassius 48.33.4 as stating that Kal. Ian. A.U.C. 715 = 39 would have been a market day, following Mommsen. He noted that the distance between 1 January 45 and 8 February A.D. 60 is 38,024 = 8*4,753 days and the distance between 1 January 45 and 1 January 39 is 2,192 = 8*274 days. He therefore concluded that Mommsen was correct, and that the nundinal cycle was (re)set starting on Kal. Ian. A.U.C. 709 = 1 January 45.

Against this, Brind'Amour, Le calendrier romain 79, noted (as did Mommsen!) that we are told by Dio Cassius 60.24.7 that regularity of the nundinal cycle was interrupted in A.U.C. 797 = A.D. 44 and earlier. In her review of Brind'Amour's book, Deman's coauthor, M.-T. Raepsaet-Charlier, Phoenix 39 (1985) 292, responded that such interruptions could well have been minor perturbations, such as that of Dio Cassius 48.33.4, as she supposed it to be. That is as may be, but since we do not know the nature of the interruption, CIL IV 4182+8863 cannot be used in isolation to establish the phase of the pre-Augustan nundinal cycle. We can only use the market day of 8 February A.D. 60 to do this if we can determine what the intervening perturbations were. This issue is further discussed here.

Brind'Amour also showed, Le calendrier romain 82, that the text of Dio Cassius 48.33.4 clearly refers to Kal. Ian. A.U.C. 714 = 40 rather than Kal. Ian. A.U.C. 715 = 39, a point to which Raepsaet-Charlier did not respond.

There is no direct evidence one way or the other on whether A.U.C. 709 = 45 was a leap year. However, the following analytical argument (Brind'Amour, Le calendrier romain 45) speaks, in my view irrefutably, against it.

As noted, Dio Cassius 48.33.4 states that Kal. Ian. A.U.C. 714 = 40 would have been a market day, while Dio Cassius 40.47 states that Kal. Ian. A.U.C. 702 = 52 was also a market day. These two dates were therefore a multiple of 8 days apart. It can be shown that the intervening Republican years were all regular, i.e. 355 days each, except for A.U.C. 702 = 52 itself, which was 378 days long, and that Caesar added 90 days to A.U.C. 708 = 46, making it 445 days long. 6*355+23+445+5*365 = 4,423 = 7 mod 8 days. Therefore there was precisely one leap day between A.U.C. 709 = 45 and A.U.C. 714 = 40, not counting the extraordinary leap day of A.U.C. 713 = 41. On Scaliger's model this must be that of A.U.C. 712 = 42, but the conclusion holds for any phase of the triennial cycle. But if A.U.C. 709 = 45 had been a leap year there must have been at least one more before A.U.C. 714 = 40. Hence A.U.C. 709 = 45 cannot have been a leap year, no matter what the phase of the triennial cycle was.

This argument depends critically on the analysis of the length of the intervening years. Perhaps the weakest point is A.U.C. 708 = 46, which relies on secondary evidence, although primary evidence shows that the total intercalation of this year must have been much in excess of 67 days. Scaliger thought this year was 444 days long, which would imply two Julian leap days. This solution is only possible on Scaliger's triennial phase, in A.U.C. 709 = 45 and A.U.C. 702 = 42. However, the evidence considered here is against this phase. The MS tradition of Macrobius makes A.U.C. 708 = 46 443 (or 440) days long, which would require three Julian leap days (which is impossible) or at least one error in the analysis of the late Republican calendar (which is very unlikely). Ý


In 1883, H. Matzat, Römische Chronologie I 13-18, noted that Dio Cassius 48.33.4 records that an intercalation occurred in A.U.C. 713 = 41, against the rule, nominally in order to avoid the ill-omen of a market day on Kal. Ian. in A.U.C. 714 = 40. Dio says that this intercalation was compensated for "later", though he does not explain exactly how or when. Matzat pointed out that the three-year cycle period = 365+365+366 = 1096 = 8*137 days is a multiple of the nundinal cycle of 8 days, so the market day would have recurred on Kal. Ian. every third year after A.U.C. 714 = 40 for as long as this cycle operated, and would also have occurred on Kal. Ian. A.U.C. 711 = 43, unless the first Caesarian leap year was actually before that year. A.U.C. 709 = 45 can be eliminated by Dio's remark that the intercalation of A.U.C. 713 = 41 was against the rule. Hence A.U.C. 710 = 44 was the first Caesarian leap year. Compensation for the intercalation of A.U.C. 713 = 41 was therefore achieved by omitting the scheduled intercalation of A.U.C. 714 = 40. As a side effect of this, the nundinal letter for A.U.C. 714 = 40, and therefore of every third year before and after for as long as the triennial cycle operated, was not A but H.

On this basis, Matzat deduced that the actual leap year sequence was:

44, 41, 38, 35, 32, 29, 26, 23, 20, 17, 14, 11 B.C., A.D. 4, 8......

This argument was widely dismissed at the time, and has been generally ignored since, although it was initially accepted by L. Holzapfel at the end of an otherwise negative review of Matzat's book (Berliner philologische Wochenschrift 4:34 (1884) 1065-1069), and was also endorsed by K. Fitzler & O. Seeck, RE X (1917) 275-381, esp. 361-362. I have found the following arguments advanced against it when it first appeared:

Even if Matzat's interpretation is in error, a calendrical explanation must still be found for Dio's intercalation. The usual explanation, if the matter is noticed at all, is to suppose that it was merely a local perturbation on top of the Scaliger cycle, making A.U.C. 713 = 41 a 366-day year. While it is unclear what date was omitted to compensate, Scaliger's model requires that A.U.C. 714 = 40 (or possibly some later year) was a 364-day year in order for the total number of days be unaffected while preserving the phase of the triennial cycle. No mechanism has been identified to do this.

This all seems rather weak on the face of it, and I am surprised that Matzat's argument has not received more attention in the intervening years. His explanation for the persistence of the triennial cycle, and for the compensation of the leap day of A.U.C. 713 = 41 by omitting a planned bissextile day in the next year, are suffiicently plausible on their face that they deserve more attention than they have received. The contemporary data considered here suggests that Matzat was in fact almost entirely right. His only substantive error was to suppose that A.U.C. 746 = 8 was not a leap year, an error induced by his attempt to reconcile his reconstruction with Pliny. In any case, OGIS 458 = iPriene 105 shows that an intercalation is required after A.U.C. 713 = 41. Ý


In 1889, W. Soltau, Römische Chronologie 170ff. accepted that the nundinal data given in Dio Cassius 48.33.4 and Dio Cassius 40.47 implied that there were two leap leap days between Kal. Ian. A.U.C. 709 = 45 and Kal. Ian. A.U.C. 714 = 40, and that, from Dio Cassius 48.33.4, one of these was in A.U.C. 713 = 41. He regarded this intercalation as one of the 12 covered by Macrobius' 36 years, and so agreed with Matzat on the phase of the triennial cycle. He also agreed that the last triennial leap year was in A.U.C. 713 = 41. That leaves only the first leap day to be determined.

He noted Matzat's argument, that Dio's statement of the need to avoid market day on Kal. Ian. implied that the first leap day was in A.U.C. 710 = 44. However, he denied that it had probative value, and dismissed this date on the grounds that it was an "absurdity" to think that Caesar, having specified that leap days were to be inserted after every fourth year, would then require the second Caesarian year to be a leap year. He also dismissed A.U.C. 711 = 43 on the grounds that no-one had ever thought of a reason to propose it (apparently he overlooked Kepler). He dismissed A.U.C. 712 = 42, since the interval from 42 to 8 is less than 36 years. He argued that the 36 years must be understood to refer to the distance from the first intercalation to the starting point of the Augustan reform -- i.e., in his view, from A.U.C. 709 = 45 to A.U.C. 745 = 9 -- regardless of whether the near end was actually a leap year. Therefore the first leap day must have occurred in A.U.C. 709 = 45.

Finally, he accepted Scaliger's analysis of the 12 year suspension, measuring it from A.U.C. 745 = 9; presumably this year was chosen as the starting point since it was in phase sync with the Caesarian cycle.

Hence, in Soltau's view, the actual leap year sequence was:

45, 41, 38, 35, 32, 29, 26, 23, 20, 17, 14, 11 B.C., A.D. 8......

This reconstruction suffers from several problems:


In 1960, G. Radke, RhMP 103 (1960) 178 proposed the only new model I could locate from the 20th century. He first noted two important circumstantial problems with Scaliger's model.

The first is that M. Aemilius Lepidus, pontifex maximus after Caesar's death, was also his colleague when the reform was promulgated, and was presumably aware of Caesar's intent. Therefore it must be explained how Lepidus could have allowed the triennial leap year cycle to arise. Radke accepted Mommsen's conclusion (though not all his arguments) that A.U.C. 709 = 45. He also noted the statement of Dio Cassius 43.26 that A.U.C. 708 = 46 only had 67 days inserted into it. He therefore argued that Lepidus (like Kepler) understood A.U.C. 708 = 46 to have been the first reformed year, and he regarded it as running from Kal. Mart. to prid. Kal. Ian. A.U.C. 708, a period of 365 days. On this view, Lepidus understood Caesar to have initialised the intercalary cycle after the end of the first reformed year, rather than at the beginning of the first full reformed year. Lepidus then scheduled the next leap year to be at the end of the fourth reformed year as he understood it, i.e. in A.U.C. 712 = 42. Since these two leap days were only three years apart, the pontifical college took off from there with the triennial cycle.

Second, from Augustus, Res Gestae 10 and the Fasti Praenestini, we know that Augustus became pontifex maximus on prid. Non. Mart. A.U.C. 742 = 12. Radke noted that if the first leap day was in A.U.C. 709 = 45 then the twelfth (on a triennial cycle) was in A.U.C. 742 = 12, only a few days before Augustus became pontifex maximus. If Scaliger was right, then Augustus waited for four more years before instituting his reform, with one erroneous leap year actually occurring in his pontificate. Radke found this unbelievable, and proposed instead that Augustus cancelled the leap day scheduled for A.U.C. 745 = 9, and also omitted the Julian leap days of 5 and 1. While accepting that Sextilis was renamed "Augustus" in A.U.C. 746 = 8, he supposed, in effect, that Suetonius was in error when he dated the Augustan reform to the same year.

Radke therefore proposed that the actual leap year sequence was:

45, 42, 39, 36, 33, 30, 27, 24, 21, 18, 15, 12 B.C., A.D. 4, 8......

Against this, Brind'Amour, Le calendrier romain 358 noted the following objections:

Other objections can also be raised:

Nevertheless, the circumstantial difficulties noted by Radke are real, and an explanation is required.

The role of Lepidus can only be clarified once we have determined the correct triennial cycle, starting in A.U.C. 710 = 44. Lepidus was certainly responsible for the extraordinary intercalation in A.U.C. 713 = 41 described in Dio Cassius 48.33.4. This was intended to avoid a market day on Kal. Ian. A.U.C. 714 = 40, and no doubt Lepidus "compensated" for it by omitting the bissextile scheduled under Caesar's rule for A.U.C. 714 = 40.

Dio regards a market day on Kal. Ian. as ill-omened, and no doubt this is how the change in intercalation was officially justified. However, in this year it may also have had practical political consequences, since under the Lex Hortensia of A.U.C. 467 = 287 such a market day would have prevented comitial business occurring on that day, effectively delaying replacement of the previous year's consul L. Antonius. Since Antonius was at that time the opponent of Lepidus' ally, Octavian, in the Perusian war, it may have been seen as desirable to deprive him and his partisans of consitutional legitimacy as soon as and in as normal a fashion as possible.

There was no a priori reason such a localised political exigency should, in itself, have caused a permanent shift in the leap year cycle; the Caesarian cycle would have resumed in A.U.C. 718 = 36. However, in late summer or autumn A.U.C. 714 = 40 Lepidus took up his triumviral post in Africa. This meant that he was not in a position to prevent the college of pontiffs, taking the official justification at face value, from mechanically using the precedent of A.U.C. 713 = 41 to insert a leap day in A.U.C. 716 = 38 in order to avoid another market day on Kal. Ian. A.U.C. 717 = 37. It is this second triennial leap year that finally institutionalised the incorrect cycle.

Thus, Lepidus' role is completely explicable on Matzat's reconstruction of the triennial cycle. On this model, the triennial cycle was instituted because the pontifical college was operating outside his control. Lepidus never got the opportunity to correct the error. By A.U.C. 719 = 35 he was under house arrest, where he stayed for the rest of his life.

As far as the role of Augustus is concerned, the solution is probably connected with the fact that the first few years of his pontificate were spent, in part, constructing the Horologium Augusti in the Campus Martius. This edifice, the largest sundial ever constructed, was inaugurated in A.U.C. 745 = 9. This device would have shown up the problems in the trennial cycle very quickly, probably even before construction was finished, which may well be the immediate trigger for the Augustan reform. Ý

The correct triennial leap year cycle

For more than a century, the debate on this question has largely been restricted to the issue of whether A.U.C. 709 = 45 was a leap year or not. None of the other proposed alternatives have really gained any traction, and Scaliger's reconstruction remains the most widely accepted model.

However, in addition to the circumstantial issues and difficulties raised by Matzat and Radke, all the above models are contradicted, to greater or lesser degree, by contemporary calendrical evidence. This evidence is discussed under the entries for A.U.C. 717 = 37, A.U.C. 728 = 26, A.U.C. 730 = 24, A.U.C. 746 = 8 and A.U.C. 749 = 5. To summarize it here:

Each of these discrepancies must be resolved by ad hoc explanations if the standard model is assumed, and such explanations have been devised. Indvidually, they are more or less plausible. But the difficulties raised by pOxy 61.4175 are particularly serious: the synchronisms are completely clear and unambiguous, and are confirmed by the lunar data in the ephemeris. Efforts to reconcile this data with the standard model have so far not produced any plausible explanation.

Taking the synchronisms of pOxy 61.4175 at face value, and further noting (a) that pVindob L.1c proves that there was a 2 day discrepancy between the Roman and Egyptian calendars at some point after 8 BC, and (b) Brind'Amour's proof that there was only one leap day between Kal Ian 709 = 45 and Kal Ian 714 = 40 (in addition to the extraordinary leap day recorded for A.U.C. 713 = 41) there is a unique solution for the triennial cycle:

44, 41, 38, 35, 32, 29, 26, 23, 20, 17, 14, 11, 8 B.C., A.D. 4, 8 ....

This solution, which is adopted in the conversion table provided in these pages, matches all the data points given above without any need for ad hoc explanation. Additionally, it allows us to accept Matzat's argument that the triennial cycle permanently eliminated nundinal A market days, and his explanation for the compensation of the leap day of A.U.C. 713 = 41. It also permits us to explain why Lepidus was unable to intervene to correct the triennial error. The major proofs of this model are discussed under A.U.C. 730 = 24, A.U.C. 713 = 41 and A.U.C. 710 = 44.

To date the only inconsistency I have found with this model is that it requires that intercalation was resumed in the 12th year of the Augustan reform, rather than after 12 years, a minor discrepancy which can easily be accounted for by supposing there was at some point confusion as to whether the 12 years were accounted inclusively or exclusively, the same confusion which led to the need for the Augustan correction in the first place. It is otherwise completely consistent with the later literary sources, provided that the three omitted leap days were calculated according to the triennial cycle.

An important effect of this reconstruction for Roman chronology is that Kal. Ian. A.U.C. 709 = 31 December 46 rather than 2 January 45 as in the standard reconstruction (or 1 January 45 in Mommsen's version). This two-day difference applies to all reconstructed Roman dates in the previous decade. It has a more substantial effect on the reconstruction of late Republican chronology in the early 60s B.C. Finally, it causes a two-day phase shift in the nundinal cycle against the Julian calendar, which allows us to fix the exact dates of several years in the early second century and to reconstruct the regulatory provisions of the Lex Acilia, which governed intercalation in the pre-Julian calendar after A.U.C. 563 = 191.

Website © Chris Bennett, 2001-2011 -- All rights reserved