I've been musing about the relationship of Macedonian calendar months to Babylonian ones.
Its rather striking that Alexander's death in Daisios = Ayyaru matches the standard alignment of later times. Since the Macedonian calendar intercalated every other year while the Babylonian one intercalated on a Metonic cycle (7 in 19 years), the two should have drifted apart rather quickly. This suggests to me that the Macedonian calendar was already aligned, by Alexander himself.
In Egypt, Ptolemy II used the standard Macedonian intercalary cycle. If you project his calendar against the Babylonian/Macedonian calendar, they cross in year 6 = 281/0, which is the first year of his unchallenged rule. (At least, according to Samuel's reconstruction, I haven't checked Koenen's, which differs slightly, but it would be in the same general area. Grzybek assumes no intercalation in the early years of Ptolemy II so his model is not a comparable). There are no Egyptian/Macedonian double dates from the reign of Ptolemy I, but this intersection suggests that he regulated the calendar according to Babylonian rules and that Ptolemy II reverted to the ancestral Macedonian calendar (a big mistake).
Also, Dios was the start of the Macedonian year in Alexander's reign, as it was under the Seleucids. A while back there was some discussion on the Seleucids list about the discovery of Philip III's probable death date in the Babylonian astronomical diaries, on 27 Kislimu (= Audnaios) year 7, and how to reconcile this to the Eusebian reign length of 6 years and 4 months. One way to do it is to note that Philip III succeeded right at the end of Daisios = Ayyaru and completed 4 months to Dios = Tashritu -- this counting as his first Macedonian year. He then completed 6 years Dios-Dios, dying early in the following year.
So much for conjecture. It raises two questions:
1) What is the earliest explicit Macedonian / Babylonian double date after the death of Alexander?
2) What is the earliest evidence for Dios as the start of the Macedonian / Babylonian year after the death of Alexander?
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