Calculating celestial events for made up calendar (super nerdy)

[Yora]

I've created a calendar with a 381 days solar year and 16 day lunar months. Working out the leap years in which there are only 23 months instead of 24 months went quite well. (Every sixth, eleventh, and sixteenth year.)

The calendar defines the beginning of a new year as "midnight, after the moment of winter solstice", and a new 16 year cycle beginning "when the moment of winter solstice had fallen on the last day of the previous calendar year". As such, the moment of full moon is always on the 8th of a month and the moment of a new moon always on the 16th.

What has turned out to be more difficult is to determine the dates for all the solstices and equinoxes for a full 16 year cycle. By definition, one winter solstice happens on the 16th day of the 24th month, every 16th year. From this reference point, the other winter solstices are simply every 381 days.
But 381 does not divide evenly through 2 or 4. In the first year of a cycle, I get the 95.25th, the 190.5th, the 285.75th, and the 381st as the equinox and solstice dates. How do I round these? Always up to the 96th, 191th, and 286th? I did that, but when I now look at my celestial events table, the patterns for the spring and fall equinoxes don't look symtrical.
The spring equinox always falls between 5th and 6th new moon. But the fall equinox only mostly falls between the 17th and 18th new moon, but sometimes (every 11th and 16th year) even before the 17th new moon.

That feels wrong.

Rounding 95.25 down to 95 also doesn't remove this effect.

My spreadsheets are pretty big, and I don't know if any of this makes sense if expressed in text. But does anyone have a hunch where I might have made a mistake?

(The reason I care is that I want to have a fixed schedule for when eclipses are happening in a fantasy campaign, which always have to happen during a new moon. Trying to actually work it out is just more fun than making something up. )

[Lord Torath]

I have not created a spreadsheet to check all of this, but I strongly suspect you have not made an error, and that's just the way things will play out.

I would round your solstices to the nearest day, and not worry too much about it. I assume your planet will have its own version of The International Date Line, which means Solstice will occur at a different time in different places anyway, and +/- 12 hours (assuming you're keeping with 24 hour days) is probably a sufficient level of precision for what you need.

I created a spreadsheet for tracking planets and moons in Spelljammer (Orbit Tracker). This may give some ideas for double-checking you equinox placements.

[Radar]

Considering that you have an odd number of days in a year, the pattern will never be symmetrical. As for rounding, then always up is the way to go: The first day of a given year starts at time "0 days" and ends with time "1 day" with anything inbetween being included. Second day of the year will thus be between "1 day" and "2 days" time. Thus n-th day falls between "n-1 days" and "n days". Thus always round up.

Also: Lord Torath has it right about solstice happening at different times at different places, but that can be fixed, since the calendar was created y specific people, so it will use their local time for defining dates.

[Rockphed]

On earth the time between equinoxes is asymmetrical. So, pick a date for one equinox and put the other equinox the same time before the solstice (so if you pick the 70th for the vernal equinox, the autumnal equinox would be on day 321). And then just propagate everything by 381 days for your 16 year cycle.

[factotum]

Can I just interject here to say that it's almost vanishingly unlikely that the year on your planet is exactly 381 days long, and if it's not, you need to thinking about leap years?