You may have remembered seeing, years ago, the "World Calendar", a proposed calendar which would be the same every year. This would simplify planning for businesses, as well as saving a few trees. However, it had one problem.
The uniformity of the years was achieved by placing one day each year, plus a second day in leap years, outside of the week. Thus, every now and then, there would be an extra day sitting between a Saturday and a Sunday.
The trouble is that, even if the more "advanced" and "progressive" denominations go along with this idea, there are going to be a great many individuals, and churches, that will say that if God commanded them to go to church (or the synagogue, or the mosque) every Sunday (or Saturday, or Friday) He meant on the day that really is Sunday, et cetera, not whatever day we choose to call Sunday.
To me, it is quite surprising that the inventors of this scheme did not recognize that any such proposal would inevitably be a complete non-starter. (Of course, I also felt that the novel Dayworld would have been much more plausible if people were let out of the suspended animation chambers on the basis of an eight-day rotation, since eight is equal to one modulo 7. That way, everyone who wished, in any of the eight cohorts, could go to church on a subjective Sunday which is also an objective Sunday, and so on. That would, however, have messed up the title of the short story on which it was based.) However, that does not mean that it is impossible for a simplified calendar to be designed that is more respectful of religious tradition, belief, and practice.
The simple way to do so is this: let a year normally be 364 days, or exactly 52 weeks, long, and have leap years with an extra week which are 371 days long. Then, every year can start on a Sunday.
One set of calendars for a normal year and a leap year that would achieve this with a minimum of change would be the following:
January February March
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SU M TU W TH F SA SU M TU W TH F SA SU M TU W TH F SA
-------------------- -------------------- --------------------
1 2 3 4 5 6 7 1 2 3 4 1 2 3
8 9 10 11 12 13 14 5 6 7 8 9 10 11 4 5 6 7 8 9 10
15 16 17 18 19 20 21 12 13 14 15 16 17 18 11 12 13 14 15 16 17
22 23 24 25 26 27 28 19 20 21 22 23 24 25 18 19 20 21 22 23 24
29 30 31 26 27 28 29 25 26 27 28 29 30 31
April May June
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SU M TU W TH F SA SU M TU W TH F SA SU M TU W TH F SA
-------------------- -------------------- --------------------
1 2 3 4 5 6 7 1 2 3 4 5 1 2
8 9 10 11 12 13 14 6 7 8 9 10 11 12 3 4 5 6 7 8 9
15 16 17 18 19 20 21 13 14 15 16 17 18 19 10 11 12 13 14 15 16
22 23 24 25 26 27 28 20 21 22 23 24 25 26 17 18 19 20 21 22 23
29 30 27 28 29 30 31 24 25 26 27 28 29 30
July August September
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SU M TU W TH F SA SU M TU W TH F SA SU M TU W TH F SA
-------------------- -------------------- --------------------
1 2 3 4 5 6 7 1 2 3 4 5 1 2 3
8 9 10 11 12 13 14 6 7 8 9 10 11 12 4 5 6 7 8 9 10
15 16 17 18 19 20 21 13 14 15 16 17 18 19 11 12 13 14 15 16 17
22 23 24 25 26 27 28 20 21 22 23 24 25 26 18 19 20 21 22 23 24
29 30 27 28 29 30 25 26 27 28 29 30
October November December
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SU M TU W TH F SA SU M TU W TH F SA SU M TU W TH F SA
-------------------- -------------------- --------------------
1 1 2 3 4 5 1 2 3
2 3 4 5 6 7 8 6 7 8 9 10 11 12 4 5 6 7 8 9 10
9 10 11 12 13 14 15 13 14 15 16 17 18 19 11 12 13 14 15 16 17
16 17 18 19 20 21 22 20 21 22 23 24 25 26 18 19 20 21 22 23 24
23 24 25 26 27 28 29 27 28 29 30 25 26 27 28 29 30 31
30 31
July and August are each shortened to 30 days, but February is lengthened to 29 days. Thus, the changes said to have been made to the calendar to feed the vanity of ancient Roman emperors are undone. (One might even consider renaming those months Quintilis and Sextilis once again!) It might be felt preferable, however, to keep July at 31 days, and leave February at 28 days, which would reduce the amount of change needed still further.
A leap year is simple enough to construct; every month will be 31 days long, except February, which will be 30 days long.
January February March
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SU M TU W TH F SA SU M TU W TH F SA SU M TU W TH F SA
-------------------- -------------------- --------------------
1 2 3 4 5 6 7 1 2 3 4 1 2
8 9 10 11 12 13 14 5 6 7 8 9 10 11 3 4 5 6 7 8 9
15 16 17 18 19 20 21 12 13 14 15 16 17 18 10 11 12 13 14 15 16
22 23 24 25 26 27 28 19 20 21 22 23 24 25 17 18 19 20 21 22 23
29 30 31 26 27 28 29 30 24 25 26 27 28 29 30
31
April May June
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SU M TU W TH F SA SU M TU W TH F SA SU M TU W TH F SA
-------------------- -------------------- --------------------
1 2 3 4 5 6 1 2 3 1 2 3 4 5 6 7
7 8 9 10 11 12 13 4 5 6 7 8 9 10 8 9 10 11 12 13 14
14 15 16 17 18 19 20 11 12 13 14 15 16 17 15 16 17 18 19 20 21
21 22 23 24 25 26 27 18 19 20 21 22 23 24 22 23 24 25 26 27 28
28 29 30 31 25 26 27 28 29 30 31 29 30 31
July August September
==================== ==================== ====================
SU M TU W TH F SA SU M TU W TH F SA SU M TU W TH F SA
-------------------- -------------------- --------------------
1 2 3 4 1 1 2 3 4 5
5 6 7 8 9 10 11 2 3 4 5 6 7 8 6 7 8 9 10 11 12
12 13 14 15 16 17 18 9 10 11 12 13 14 15 13 14 15 16 17 18 19
19 20 21 22 23 24 25 16 17 18 19 20 21 22 20 21 22 23 24 25 26
26 27 28 29 30 31 23 24 25 26 27 28 29 27 28 29 30 31
30 31
October November December
==================== ==================== ====================
SU M TU W TH F SA SU M TU W TH F SA SU M TU W TH F SA
-------------------- -------------------- --------------------
1 2 1 2 3 4 5 6 1 2 3
3 4 5 6 7 8 9 7 8 9 10 11 12 13 4 5 6 7 8 9 10
10 11 12 13 14 15 16 14 15 16 17 18 19 20 11 12 13 14 15 16 17
17 18 19 20 21 22 23 21 22 23 24 25 26 27 18 19 20 21 22 23 24
24 25 26 27 28 29 30 28 29 30 31 25 26 27 28 29 30 31
31
There are two problems with this calendar, however. With the existing calendar, some people would have birthdays on February 29th in a leap year. Here, in a leap year, February 30th and the 31st of April, June, July, August, September, and November would all have the same problem, seven days instead of just one.
A year that is 365.242199 days long is quite closely approximated by a 365 day year with an extra day every four years. But such a year is also 52.177457 weeks long; one leap year every five years is too many, and one leap year every six years is too few.
Thus, while our current Gregorian Calendar can make exceptions to the rule of one leap year every four years only once a century (and then in only three out of every four centuries), a calendar based on adding whole weeks would have to have a rule the complications of which would be more obtrusive.
One way to handle leap years, perhaps the simplest, would be to proceed like this:
one leap year every five years 52.2 omitting a leap year every 40 years 52.175 but putting the leap year back every 400 years 52.1775
To keep the year in closer correspondence with the seasons, a gradual scheme like the following could be used:
A CYCLE is 17 years long, and consists of:
five normal years, one leap year, four normal years, one leap year, five normal years, one leap year
and is .016769 weeks short of exactly 17 years.
A NORMAL SPAN consists of seven cycles and five years as follows:
seven cycles, four normal years, one leap year
and is .004668 weeks short of exactly 124 years.
A SHORT SPAN consists of six cycles and five years as follows:
six cycles, four normal years, one leap year
and is .012101 weeks in excess of exactly 107 years.
The calendar then consists of successive rounds, where a ROUND consists of:
three normal spans, one short span, two normal spans, one short span, three normal spans, one short span, two normal spans, one short span, three normal spans, one short span
for an error of only .000179 of a week, or .001253 of a day, in 2,147 years.