"And it came to pass in the time after the new moon—the second, that David's place was empty. And Saul said to his son Jonathan, "Why has the son of Jesse not come to the feast, either yesterday or today?" (1Sam. 20:27).

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in the time after : ממחרת.  This word is really two words מחרת  and מ. The preposition מ, means "in" in this case. The explanation of the sometimes extensive usage of this word lies in the term יום , which often means "time" in a general sense beyond just a literal day.  Taken to mean only "morrow" or the exact morning after the new moon, this passage is a contradiction, because we learn that it is the second day of the month in the next word.  The new moon is first seen in just after sunset at the end of the last day of the old month.  The day after it, in the literal and default usage of day is the next morning.  However, it was not the morning after the new moon.   It was the second  of the month.   A similar usage absolves Lev. 23:15 of contradiction where they are told to count seven Sabbaths "in the time after" the annual Sabbath" (torahtimes.org)

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Daniel's Literal Translation and Commentary: (http://www.torahtimes.org/translation/1sam2027.html)