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If the months start with the new moon, wouldn't you sometimes get an 8 or 9 day week?

No, the work week was never longer than six days. At the end of each lunation, as the month transitions from the old to the new, one of two things happen: 1) either you have a seventh-day Sabbath immediately followed by New Moon; or, 2) you have the seventh-day Sabbath, followed by a work day, followed by New Moon. Anciently, the New Moons were kept as Sabbaths, so there was never more than six work days between worship days.