oh I hope Sam is okay with me being inadvertently nerd-sniped here. I happen to be one of the nerds who have read books such as Calendrical Calculations by Reingold & Dershowitz (and wrote them to ask for permission to re-implement their libraries in Erlang, which I swear some day I'll finish) and wrote a couple talks on calendaring and time systems!
I'm writing this off the top of my head before work so pardon the lack of strict fact-checking. Anyway here goes nothing.
Duodecimal systems make sense
When we didn't have cool fancy contraptions to count time reliably (like clocks or vibrating crystals or harnessing atoms), and even before we had the intermediary ones (water clocks, astronomical computations) we did things like count notches on sticks, and mostly observed useful natural sequences: days and nights, seasons, and the moon.
As it turns out, the lunar cycle is pretty dang regular and divides things on a good intermediary period between days and seasons (~29.5 days), it's observable by anyone (just look up dummy), and it tends to correlate with real useful shit like tides.
So if you have to tend to regular activities, you pick the lunar cycle as a good measurable period. These 29.5 days cycles line up to give you 12.38 iterations a year, which fits rather closely into duodecimal systems that were nice and convenient and behind how you even connect to days being split in 12/24 hours and hours within 60 minutes which go in 60 seconds.
Duodecimal systems suck
The problem with the lunar cycle is that it doesn't match really well with things like crops and seasons. As you drift by a week or so every year, the cyclical nature starts to mess up, and pretty much everyone ends up patching their calendars to be having leap cycles, where some year you have 13 moon cycles and some you don't, for example.
This lets you sort of align the yearly and seasonal nature of agriculture to the lunar pacing and keep things in sync. This generally works okay, but sometimes it doesn't. See this bit reported in a footnote by Calendrical Calculations, about issues in doing that in the Ottoman empire which had a strictly lunar observational calendar:
There was an interesting consequence to the strict lunar nature of the calendar in the Ottoman Empire. The Islamic calendar, as the official calendar, was used for expenditures, but revenue collecting generally followed the solar year because seasons affected income-producing activities such as agriculture, shipping, and mining. For every 32 solar years there are 33 Islamic years; thus every 33 Islamic years had one “skip” year, called a sıvıs ̧ year in Turkish, for which there was no income. Such years precipitated crises, such as in 852 a.h. (1448 c.e.) in which the troops’ pay was six months in arrears, resulting in a lack of resistance on their part when Hungarian and Serbian forces entered the Ottoman Empire. A detailed analyis of the phenomenon is given in H. Sahilliogˇlu’s article, “Sıvıs ̧ Year Crises in the Ottoman Empire,” Studies in the Economic History of the Middle East, M. A. Cook, ed., Oxford University Press, London, pp. 230−252, 1970.
In general, most calendrical systems got patched up to have "intercalary periods" (leap days, leap weeks, or leap months) and normalized the accounting of days to become arithmetic calendars rather than observational calendars, but some of them out there still rely on astronomical observations to keep in sync here and there.
Romans had 10 months
Romans had a "decimal" system. I mean they had a counting system where 10 is at least a unit (I=1, V=5, X=10, L=50, C=100, M=1000). It's not like they had a super solid base and way to write numbers that was as cool as what we got now, but they had a focus on a unit of 10 somehow.
Initially, the romans' calendar only had 10 months. Or we think so, it's so far in the past it's sort of half-mythical. But anyway, it had 10 months of 30 and 31 days, and amounted to 304 days. Which okay, you know, means you're still missing sixty-one-point-some days compared to what we now know to need.
How did they cope with that? Well the regular year was going from like March to December and neither January of February equivalents existed; they were just a big intercalary period at the end considered to be "winter" and not useful for agriculture, so why bother?
We had a cool base 10 calendar and it worked fine for everyone as a prototype, shut up.
Roman Calendar 1.0
At some point romans figured out they wanted that big intercalary period better accounted for and they did the unforgivable: they borrowed back from lunar folks. And we got 12 months again. They were roughly aligned on lunar months, but rather than mess with a good thing, the gap periods were given to January and February, each getting only 28 days or so.
February was a fucked up month, the fudge-it month where they'd sometimes chop off 5 days to re-align the years because the moon doesn't fit the sun. It was also considered the month of the dead.
Part of the reforms that followed this version also came from the Roman leaders going "these priests running time are getting real annoying" and starting to publish calendars centrally with version 1.0. This isn't a unique feature—the Chinese lunisolar calendar was a hard mess to compute and the Emperor had his own folks do it for everyone, for example—but it's a significant one in showing that it's real hard to split up observable phenomena, discipline and planning, and authority.
Julius Caesar needs a promo packet, renames calendar
Julius Caesar won power, and part of doing that came in with a reform to what we know as the Julian Calendar. He made a few changes:
- Normalized month duration to always be 30 or 31 days
- Renamed Quintilis to Iulius (July) after himself and gave it 31 days to be cool
- Renamed Sextilis to Augustus (August) after his adopted son, also gave it 31 days to be cool, and showed that nepotism sure has a place in counting time
- February actually only gets 28 days, and lots of people go "it's funny how the emperor months got 31 but Feb doesn't even get the basics" though there's like, little proof of that being the actual rationale
- The biggest change though was that every 4 years, February gets a 29th day on loaner and the intercalary period is reduced
Everyone thought that was pretty fucking cool and it became a standard in the empire (not that there was a ton of choice there). There was a small bug because as we know, the leap period doesn't line up fully every 4 years, but we had to ship to prod and there would be time to patch it up later
Patching shit, going Gregorian
Pope Gregory, calendar DevOps employee of the month in the late 16th century, was sorta mad about this legacy bug where calendar years and seasons were drifting, and knew that every 4 years is waaaay too often for intercalary periods. There was a need to a) reset the clocks a bit (which the Swedes fucked up amazingly having to roll back after trying a slow migration and having the only month of February with only 17 days in history) b) change the computation to skip 1 century out of every 4 from being a leap year:
Every year that is exactly divisible by four is a leap year, except for years that are exactly divisible by 100, but these centurial years are leap years if they are exactly divisible by 400. For example, the years 1700, 1800, and 1900 are not leap years, but the year 2000 is.
This little patch was super-noticed and not everyone agreed (the Orthodox Churches still line up on the Julian Calendar, love the stability and don't like applying patches), but this is what we've got.
All this to say: we've had the 10 month calendar in an early prototype but we've moved on since then. Please see the wiki for reasons why we are unlikely to revisit this in the near future
Late Edit: if you need further proof, please refer to the skunkwork projects around the French Republican Calendar from the French revolution, which tried to have both decimal time and months made of 3 x 10-day weeks. Even these folks required 12 months to work with, but that wasn't sufficient and never caught on. We decided not to revisit again that time.