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To name the Months
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Any system that does not have 13 months of 28 days each, plus a remainder day to keep pace with the sun, is not logical.
Having a "remainder day" is weird, but it's hard to avoid. It really sucks that 365 doesn't divide nicely into much at all. 5 and 73 are the only non-trivial answers. five 73 day months? Can't even call it a month at that point.
I guess 13x28 + 1 does indeed make most sense...
May as well embrace the weird, cuz we dont orbit in exactly 365 days anyway. So theres gonna be leap year type adjustments anyway.
1 odd day from 13x28 is the perfect excuse for a new holiday too. And avoids having to figure out is it a weekday or not. It gets to be neither, a unique special holiday not tied to religion, nationality, culture, politics, etc (though many oppose it for reasons within those topics).
speaking of leap days, I also considered using a quad-year as a unit, integrating the leap day as a standard day. 365.25x4=1461. But that only divides by 3 and 481, even worse!
And would require special handling in 3/4 of what are now centuries
There's always a remainder day, and it's not precisely 24 hours. That's why we have leap years and sometimes leap seconds. You could get rid of that by cramming all of the time into one day of varying length. This year, maybe it's 29.75 hours. Maybe next year it's 31. Astronomers and physicists could fight it out and see how closely they can match the previous year.
We need to push the Earth into a higher orbit.
The Baha'i calendar is 19 months with 19 days, and a 4 or 5 day celebration in between months 18 and 19. The year starts the day that coincides with March 21.
If no logical system can be created with missing information, very few systems are logical.