Hello fellow DMs,
I'm running a custom world that has borrowed hevily from the Dragonlance Setting. I really like the triple moons with the magical benefits they give while full. That being said, I want to tweak how often Night of the Eye (when all three moons are full and aligned) to make it happen every 360 days (once a year in my world) instead of the 504 days it takes in Krynn. I have no idea at all how to make the math work! I know that I'll have to tweak the times it takes each of the three moons to go through a cycle, but I have no clue how to figure out what the numbers need to be changed to. Here are their defalt cycles:
Solinari: Period of 36 days with 9 days per quarter
Lunitari: Period of 28 days with 7 days per quarter
Nuitari: Period of 8 days with 2 days per quarter
If someone that is good with math could tell me how to figue this out that would be great!
It doesn't have to work. You just say what happens and then boom, it happens.
Agreed. Unless you have extremely picky players, I doubt any of them are going to care too much about the math behind it. Just pick some dates and declare them as full moons, and pick one of those full moon dates to be the Night of the Eye.
bawylie wrote:
The first part is to get all 3 moons to be full at predictable intervals. I recommend taking a spreadsheet, using one colum for each moon, and start with the row for the day you want all three to be full and mark off the full moons throughout the year moving outward, making adjustments if things don't line up how you like. It's easiest if the 3 moons are full on the same numerical day every year.
As for the physical alignment, your players are very unlikely to be asking for exact position of the moons in the sky, so you can skip the math and just say they line up that one day and not mention their positioning otherwise.
Just print off a monthly calendar, mark the phases down as you see fit, and when you get to the month you want all three to align, mark that down too. Explain the deviation as a cosmic event due to external influence. Perhaps multiple other plants are in closer proximity thus speeding up or slowing down the moons orbits due to gravitational fluxes, or perhaps its divine or magical influence. Just have some explanation to describe why the moons suddenly don't adhere to their regular cycle and you're good.
Keep it simple. Use things for the "normal" months like the first Thursday, the second Tuesday, the last Friday, ect to describe when each moon is either full or new, and stick with that. Physics in your magical fantasy world don't have to play by our universes rules.
Cheers
For all three to cycle full together every 360 days the cycle needs to be evenly divisible into 360. Solinari at 36 days would be full ten times in a 360 day period, starting with a full moon then ending that way in the period. Nuitari at 8 days would be full 45 times and also at the start and end of your 360 days. However Lunitari at 28 days leaves a remander divided into 360 so it will not be full at tthe 360th day. 12.86% full. To fit exactly it needs to be 27.7 days or 30 days.
However - a full moon usually lasts for a few days. If you assume that the cycle time in days is to the highest full moon mark (and thus the middle day of the full moons days rather than the first day the moon is full) and that the moons (or at minimum Lunitari) are full for at least 3 days then every 360 days all the moons will be full together for 1 or 2 days. Just not at the peak of thier full mooness eactly at the 360 day mark.
Basically you could lay out a 360 day calander, pick which day is the three full moons and then count out the cycles forward or backward from there to see what days the moons are full on their own. There will be days when two of them are full at the same time as well. To make life easy decide on a 3 days full moon and mark the days in front and behind the "High Moon" day as full moon days as well.
Change Lunitari's "month" so the number of days is divisible into 360.
1 x 360 (fast-moving moon streaks across sky every single day)
2 x 180
3 x 120
4 x 90
5 x 72
6 x 60
8 x 45 (Nuitari)
9 x 40
10 x 36 (if you use 'tenday' instead of 'week', here is your reason) (Solitari is 36 x 10)
12 x 30
15 x 24
18 x 20
19 ^ 2 = 361 (so you have to use rounded numbers and fudge it a bit)
and of course flip each line to get fewer months with more days in each
Personally I would use:
45 months of 8 days each: Nuitari
18 months of 20 days each: Lunitari
10 months of 36 days each: Solitari
because it puts every school on a different schedule relative to each other, except for that one day per year.
WorBlade wrote:
I can't seem to convince my players that I have half a brain so I occasionally attempt toi sound erudite on forums. 
Happy gaming.