https://en.wikipedia.org/wiki/Babylonian_calendar
The Babylonian calendar was a lunisolar calendar with years consisting of 12 lunar months, each beginning when a new crescent moon was first sighted low on the western horizon at sunset, plus an intercalary month inserted as needed by decree. The calendar is based on a Sumerian (Third Dynasty of Ur) predecessor preserved in the Umma calendar of Shulgi (c. 21st century BC).