In 1 Chronicles chapter 24 David set out orders for the cohanim to serve in the Beis Hamikdash. What he established is intuitive for a 12 month year, but what was done in a 13 month year? If possible, where may I find discussion not only on what was done, but the underlying debate and justification for the decision.

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    It's a 24 week rotation, so they didn't get the same time each year anyway. – Heshy May 6 '19 at 23:00
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    @DoubleAA do you skip Pesach and Sukkot? Sukkah 5:7 talks about משמר שזמנו קבוע on Yom Tov. Anyway if it's not exactly right that shows they didn't care about it drifting through the year, however slowly. – Heshy May 6 '19 at 23:49
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    I know that Bereichos b’Cheshbon discusses this question, but I haven’t seen a copy of that Sefer in years that I could look this up. In his first piece there, he explains how the Mishmaros lined up over the course of a full calendar cycle. – DonielF May 7 '19 at 16:13
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    @KenGoss A lot of editions of Mircheves HaMishnah on the Rambam’s Mishnah Torah include it in the back. Or so I’m told - like I said, I haven’t seen a copy of Breichos b’Cheshbon in years. But you might have some better luck. – DonielF May 7 '19 at 18:48
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    His general assumption IIRC is in line with Heshy’s assumption above that each Mishmar got a week, and while everyone served on Yom Tov it was primarily one Mishmar’s week. With that said, even non-leap years get complicated really quickly. And that’s where the math kicks in. – DonielF May 7 '19 at 19:11

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