"The most common ways to represent these times are, (a) to use a 24-hour clock (00:00 and 12:00, 24:00), (b) to use "12 noon" or "12 midnight", although unless the person is referring to a general time and not a specific day, "12 midnight" is still ambiguous, (c) to specify it between two successive days or dates (Midnight Saturday/Sunday or Midnight December 14/15), and (d) to use "12:01 a.m." or "11:59 p.m."" (From Wikipedia) This solves the question. Midnight belongs to neither day on either side of it, the days must be specified where that instant of time occurs. So all is good. Tuesday midnight could be between Monday/Tuesday OR between Tuesday/ Wednesday. If not specified, either may be used.