When I first started working on a historical "persona," one thing I wanted to do was arrange it so that my persona would use a calendar that was the same as the "mundane" calendar. That is, if the calendar on my wall said, for example, that January 1st was a Saturday, in my persona's year of XXXX, January 1st was a Saturday. Now, maybe that level of "authenticity" is not for you, but I thought It would be cool. If you do too, or you're just interested in how I managed it, read on. :-)
As my article "Finding the Day of the Week" shows, it is possible to find the day of the week for any Julian/Gregorian year. So, all I needed to do was choose a year, use the day of the week method, until I found a year close to my first choice that worked. Perhaps that's enough...
One thing worried me, though; what about the next year? And the year after? Would they "line up"?
Possibly not - - - it depend on when "mundane" leap years and "persona" leap years occur. If I had started in 2017*, January 1st would have been a Monday. If I wanted something a few years before 1200, I would find that, in 1195, January 1st was a Monday. Thus, of course, all of 1195 "lines up with" 2017. But the next year, things don't work.
You see, the next year, 1196 was a leap year, but 2018 wasn't. Thus, from January 1st to February 28th, they line up. But, when 1196 has February 29th, 2018 has March 1st. Thus, ten months out of twelve don't line up. ::sigh:: What to do?
Well, there are two things you could do. One is, change your persona's year to something close, that does line up; at least for March to December. You might, however, land up having to change persona years every mundane year. The second thing to do is, go back to the start and choose a persona year in the same place in the cycle.
OK, what cycle is the cycle? It's known by two names: the Julian cycle and the Solar cycle. Problem is, both those names are used for something else, too. So, I'm going to call it "The 28-Year Cycle".
So, what is it? Well, if you had a bunch of consecutive Julian-year calendars, and recorded the day of the week of January 1st, you'd find that it went through a cycle that repeated every 28 years. That is, with seven days of the week for January 1st and four types of years---leap year, one after leap year, midway between leap years, and one before a leap year---each of the 28 combinations occurs once in every 28-year cycle.
For example 2017 started on a Monday and was one after a leap year. If I can find another with that combo near the year I want for my persona, that year, and the next, and the one after, would all line up. In fact, the two years will stay lined up until 2100 Gregorian, which is not a leap year; that spoils the 28-Year Cycle. I'll call getting this degree of lining up a "total match".
Notice that if you knew one could-be-persona-year that totally matched the mundane year, you could find all the totally matching years from 5 CE to whenever your persona's location adapted the Gregorian calendar; just add or subtract 28 or any multiple of 28. Now instead of making you struggle to find a totally matching year, and then try to remember it, or note it down and then have to remember where the note is, I'm going to make it as easy as possible.
2017 was totally matched by 1217. 2021 is totally matched by 1221. 2022 is totally matched by 1222. You'll notice the last two digits are the same; that should make it easy(-ish) to remember. Oh, and if you have an early persona, you can use 521 and 522 instead.
For instance, that "a few years before 1200" example? If I wanted to do it now, I'd take 1221 (or 1222 in a few weeks), and subtract 28. That's 1193, it's January 1st is on Friday, just like 2021. They're both "year after leap year"; both conditions are the same, so it's a total match, and I could use 1193 as a persona year this year, 1194 next year, and so on.
Actually, my interests lie much earlier. In fact, about 3 centuries earlier. Luck for me, 280 is a multiple of 28, so starting from the "remember this number" of 1221, and subtracting 280, I got 941. Still, not quite early enough. Subtracting another 28 gets 913, which works well enough. I've thought about going back another 28, to 885, but I haven't quite decided to do so or not.
As I said, this level of authenticity, aka geeking out about calendars, is not for all. But if you're interested, you might find it adds something to your characterization. Above all, have fun, and don't sweat details you don't care about.
Later note: it's now 2022, so the "key year" is 1222, and I'm using 914 as my persona's year (I decided against 886).
*I don't remember just when I first worked out all this stuff, so I'm using this as an example.