A more simple solution is to have 13 months of exactly 28 days, plus one day for new years day. That's even better because every month is exactly the same number of days which means semi-monthly and bi-weekly billing systems are the same thing. And because there's the same number of days anything billed per month can be easily prorated per day, and any billing cycle will match up with every other billing cycle... so basically everything imaginable becomes considerably easier.
The only real problem is coming up with a name for a new 13th month and where to insert it.
Well, then they can all hide indoors for the month ala the ancient Incans and the rest of us can create some sort of new sort of month long Saturnalia/Yule/Winter Solstice remix.
We could even send a Krampus to go rattle their doors and windows on the appropriate day.
OK, it breaks the assumption that quarters are a whole number of months.
12 is a handy number of months to have in the year. 12 is divisible by 2, 3, 4, and 6. Not by 5, but you can't have everything (unless we had 60 months of 6 or 7 days each... let's not go there).
13 is prime.
I think not bothering with months at all would be better than having a 13 month year.
That sounds ridiculous now but it's actually not that bad when you get used to it. Besides, people would likely still keep the month names to refer roughly (if not even exactly) to periods of the year. The real benefit would be in dropping months from the business and commerce world.
I think not bothering with months at all would be
better than having a 13 month year.
The phases of the moon are 28 days long. So a 13 month calendar also lines up with the lunar cycle. The more you think about it, you wonder how they ever came to the conclusion to use 12 months instead of 13.
(http://en.wikipedia.org/wiki/Moon and see the synodic period (quoted to a tenth of a second even though full moon to full moon can vary by about ¼ day either way).)
The only real problem is coming up with a name for a new 13th month and where to insert it.