A New Calendar
We have roughly 365.24 days a year, the time it takes the earth to make a complete orbit of the sun. I would like to break down the number of days in the year into equal parts. This will remove one of the inefficiencies I see with our current calendar: remembering which months have 30 days and which months have 31 days. Unfortunately, 365 doesn't break down very nicely. 365 has the very succint prime factorization of 5*73. Since, in most parts of the world, there are four distinct seasons, and I would like to represent that in my calendar somehow, the number 365 simply will not do. I'm going to work with 364.
364 breaks down into 2*2*7*13. If we want to keep something that most closely respembles our current calendar, we would have 13 months of 28 days each, with 7 day weeks. Adding in a day somewhere, along with a leap day using the current method. This has the benefit of creating months, all with the same number of days, but we have lost the ability to have an equal number of months per season, 3 for each winter, spring, summer, and autumn.
This is what I suggest: Either (1) 4 months of 91 days each, or (2) 12 months , with a 3 months pattern of 28, 28, 35 days (or 4, 4, 5 weeks). Also, the first day of the year will not be in any month, nor will it be a day of the week. It will simply be "New Years Day." Also, that night will be the winter solstice. On leap years, a day will be added exactly half of the year after New Years, which will also not be the part of any month, nor a day of the week. This may sound wonky to many, however, it comes with a very distinct advantage. Every day of the year will always be on the same day of the week. The first day of every month will always be the same day of the week. Any date in any month will always be a certain day of the week. Brilliant.