Ur (modern Tell al-Muqayyar) was a Sumerian city in southern Mesopotamia established early in the Ubaid period (c. 4000 BC). The city was the primary center for the worship of the Moon god, Nanna (Sin), and is home to a magnificent ziggurat built for the purpose of his adoration. Ur was a port city for Mesopotamian trade with countries in the Persian Gulf and beyond until the 18th century BC and was probably abandoned in the 4th century BC because of a change in the course of the rivers (Roaf p101).
Tablets from pre-Sargonic (before 2334 BC) Ur give us nine month names, however their order is not known. The names are as follows:
The calender was reformed in the UrIII period by Shulgi, king of Sumer from 2094-2047 BC. Five of the pre-Sargonic month names survived the transition, and the total number of months rose from nine to twelve. The months are as follows:
The 13th month is the intercalary month.
One interesting aspect of the UrIII calendar year is that it seems to have been only 6 months long. The New Year festival was celebrated on both the 1st and 7th months. In effect, the year was broken down into two "equinox years", the beginnings of which fell on the vernal and autumnal equinox. There is both astronomical and mythological reasoning behind this, as Cohen explains:
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A Guide to Ancient Near Eastern Astronomy
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September 14, 1995