If there are three categories of days—new moon days, six work days, and Sabbath days—then the possibility of Sabbaths being fixed on the eighth, the fifteenth, the twenty-second, and the twenty-ninth of every lunar month is feasible.
But if there are only two categories of days (six work days and the seventh-day Sabbath), then the lunar Sabbath theory falls apart!
The lunar Sabbatarians say that there are three distinct categories of days. They quote Ezekiel 46:1:
Thus saith the Lord GOD; The gate of the inner court that looketh toward the east shall be shut the six working days; but on the sabbath it shall be opened, and in the day of the new moon it shall be opened.
Their argument goes like this:
What happens if new moon falls on a Tuesday (on man’s calendar)? Is the gate open or shut? There is no right answer. The solution is that the new moon never falls on a work day because it is not a work day. It is a third category of day. The gate is closed on all six work days. . . Do the math—you will discover that there are three separate categories of days in YHWH’s calendar: new moon days, work days, and Sabbaths. Since Scripture indicates that these days cannot take place at the same time, do not overlap or share the same space, then we need to rework our understanding of the calendar. (Troy Miller, Three Distinct Categories of Days, pp. 1, 2; accessed at http://www.4angelspublications.com/pdf/ThreeDistinctCategoriesDays.pdf; accesed on 10–13–13; emphasis in original)
Their argument may sound logical. If the new moon falls on Tuesday (or on any of the work days of the week) in our calendar and if we open the gate because it is new moon, then we are violating the other part of it which says the gate has to be closed on the six working days. The same is true the other way around. If we close it because Tuesday is a work day, then we are violating the other instruction to open it on new moon days.
If the new moon day is a third category of a day, the problem is solved because then it will never overlap, then the command in Ezekiel can always be obeyed, and then all the dates of the months are fixed permanently to the day of the week—the first is new moon; the eighth, the fifteenth, the twenty-second, and the twenty-ninth are Sabbaths; and the rest of the days in the month are work days.