Rabbi Et Shalom in Mikra for Shavuos speaks of the calendar used by the minim to force the chagim (and every day of the month to always be on the same day of the week.
The calendar displacement is 1.25 days a year, or 7.5 days every 6 years, which becomes 30 days every 30 years. As a result, a leap month of 28 days would be added every 22 years (6, 6, 6, 4). This actually puts the calendar ahead of the "real" time by .5 days every cycle. After 4 cycles, the calendar leads the solar time by two full days. The next leap month is after 24 years so that the calendar displacement is 30 days. The leap month of 28 days brings the calendar into "exact" adjustment with the Solar Year (28 days + the previous 2 day offset fixes the 30 day lapse after 24 years).
Among the many significant passages in the Mik'tzat Ma'aseh Torah is the Calendar of the community. Although there is much scholarly debate as to whether this calendar was ever put into practice, this solar calendar (!) is quite clearly spelled out and sheds much light on the motivation behind the Boethusian position in the debate regarding the date of the Omer offering and Shavu'ot.
The calendar (taken here from pp. 302-303 of Lawrence Schiffman's "Reclaiming the Dead Sea Scrolls", the source for much of the background information above) consisted of a 364-day year, constituting exactly 52 weeks. Each month had thirty days and, in order to keep the calendar in line with the equinoxes and solstices, a thirty-first day was added to every third month.
As a result of the exact weeks (with no remaining days) in this calendar, each Festival occurred on the same day of the week every year. [It is difficult to imagine how a calendar of this sort could ever be maintained without regular correction for the missing 30 hours every solar year; that is why, as pointed out above, many scholars claim that this calendar was never actually put into practice.]
Professor Dick Henry has suggested using this calendar for modern times. He has suggested that the calendar be implemented at the start of a leap year so that the "new" and "old" calendars could merge seamlessly and that a year when January 1 starts on a Sunday be chosen. As a result, he is trying to get his "new" calendar implemented for January 1, 2012.
The actual year used by the Gregorian Calendar gives an average calendar-year length of exactly 365.2425 days which is within one ppm of the current length of the mean tropical year (365.24219 days).Using 364.242 as the year length, the calculation shows that the calendar has fallen behind by 27.324 days after 22 years and 28.566 days after 23 years. Thus, alternating 22 and 23 years causes the calendar to be ahead of the solar year by .11 days every cycle. As a result, after five cycles of this type (5 times 45 years = 225 years), the calendar is .55 days ahead of the actual year and a leap year after 23 years instead of 22 years would drop it back by .566 days instead of pushing it ahead by .676 days. As a result, the discrepancy becomes .01 days. This discrepancy should be good enough for the calendar.
