Short version of this essay: I think a thirteen month calendar with a leap week is the best calendar.
What is wrong with our present Gregorian calendar is mainly that it is not aesthetic. More clearly, that it has long months and short months and some years the second month is not quite as short as other years, Sometimes the year starts on a Monday, sometimes some other day. And this is true about any other day of the year as well. It just is not very pretty (or as useful as it could be.) But this cannot be helped. The year and day and phases of the moon do not divide evenly into each other. So no matter what you do, you cannot have a perfectly symmetric, even calendar.
What I believe I have found is the best, most workable calendar that does not disturb the weekly seven day cycle. Now most "reformed calendars" feel that to make an aesthetic calendar, we have to have one week each year that has an extra day in it (and sometimes two). The reason being, of course, that 365=52x7+1 and each year we should have 365 or 366 days. There are two main problems in disturbing this seven day cycle. First that some religions would not even consider disturbing this cycle. It is of prime importance, without argument. Second is that of implementation. No governing body could start saying that next year Monday will be Sunday. There could be no transition. Some would follow the new system, some wouldn't and there would probably be chaos. (Of course, supporters of these extra days, would argue that the chaos would only last a short while, and we would be much better off for it. Possibly.)
Now a solution to this problem is to every so often add an extra week. (This solution has been around for quite a while.) So a leap year would have a whole extra week in it. This does disturb the yearly cycle, but as I noted above, we cannot have a perfectly symmetric calendar. But the cycle of leap years is very nice: we have a leap year every 5th year except for the 40th year. I.e., Leap years would be 2005, 2010, 2015, 2020, 2025, 2030, 2035, but not 2040. Anyone can follow this pattern. This pattern will prevent seasonal drift for thousands and thousands of years. However there will be seasonal drift during these five year cycles--up to about three and a half days from the average. Now I grew up on a farm, planting by the seasons, and three and a half days does not make any difference. Weather is a much more important factor. For the few people where a seasonal shift of this amount may make a difference (such as a biological study), the number of days before or after an equinox or solstice should be used. The equinoxes and solstices would not fall on the same days each year, but then they don't now.
And as long as I'm on the subject of problems, many people bring up the problem of all of the people born in this leap-week. Well, if we put the leap-week as the last week in the year, they would just celebrate on the beginning of the new year, new years day. Granted this would affect more people than the current leap-day, but it really would not be a problem.
So leap-week would be at the end of each year that is divisible by five and not forty. We've sort of accounted for the days and weeks in a year. What about months. We still have some long months and no correlation between the day of the month and the day of the week. I really feel that the way to handle this is to have 13 months.
I admit that it is hard to leave the 12 month year. Twelve is highly divisible. We can break the year into halves, quarters or thirds. But were not really doing that because the months are of unequal lengths. I understand that its not important to most people what lengths months really are, we are just looking for a timescale. I told my son yesterday that it was a month and three days til thanksgiving. Neither of us know how many days that is off-hand, though we can figure it out, but it's not important. But wouldn't it be much better to be able to say it is a month from now and know what day of the week that would be? With 13 months of 28 days each, every month would look the same. All starting on a Sunday and ending on a Saturday. (Of course, this would bias calendar makers to the mostly American system of starting the week on Sunday and away from the mostly European way of starting on Mondays. I feel bad about that.)
This idea of thirteen months has been around for a long time, Auguste Comte first devised this calendar in 1849 and was later advocated by Moses Cotsworth in the late 1800's and early 1900's, but it always seemed to be connected with having days outside of the weekly cycle and never caught on. Cotsworth thought that the extra month should be called Sol and be placed right in the middle of the year between June and July. I thing that is an excellent placement, since we could keep all the other names and they wouldn't be too far from where they are now. And the name Sol seems as good as any other (though it is somewhat ironic if you happen to live in the southern hemisphere). The middle of Sol would mark the middle of the year, which would be very nice, and the end first quarter of April would mark the end of the first quarter of the year and the end of the third quarter of the September would mark the end of the third quarter of the year. All very nice. Provided, of course, that there is not an extra week in the year. In that case, we would be not much better off then we are now. We could still use these division marks, even though they would be just approximations, or we could move them an appropriate part of a week over. That would not be hard at all. So I guess we would be quite a bit better off then we are now.
So how would this match up with the Gregorian calendar? On any given year we have to start the new year on a Sunday and that choice decides how all other years start. For me, there are two obvious ways to proceed. One is to match up some day in each calendar as close as possible, such as having on average that January first of the Gregorian calendar be January first of the new calendar. The other is to have the year start on average on an solstice or equinox. To me this second approach seems the more pleasing. On average January 1st is the winter solstice, April 7th is the vernal equinox, Sol 15th is the summer solstice, and September 23rd is the autumnal equinox. These are roughly the quarters of the year. Making this happen would start the new year in 2006 on December 25th of the Gregorian calendar.
A big advantage is that this calendar can be used side by side with the Gregorian, with only a slight difference in months and days. There would have to be a movement to use it though, and to get governments to see its value. I am not the person to pitch it, however. In fact, I see calendar reform as having approximately a zero percent chance of success, unless, as in past reforms, a large part of the world falls under the control of one person. (Calendar reform is not important enough to wish that happens.) This calendar is the best calendar that we can hope for. It is workable and any country or company could switch to it without any real problems. It just needs a good PR person or spokesperson.
For each year this calendar (.doc file) could be used. It isn't too interesting with almost every year being the same.
If you would like to compare it with the Gregorian year calendar, here are some side-by-side text files: 1900-2000 and 2000-2100.
Here are some pdf-formated yearly calendars with Gregorian references. They have an old-fashion complicated look, but have an easy explanation on the bottom of each. This is a work in progress. If you have any comments or requests, you may email me, Peter Vachuska.