Creating a Dilunisolar Calendar Part 3: Cultural Significance

While not every calendar aligns perfectly with the seasons – certainly most on Earth do not – a world where seasons are long and brutal most certainly would. This particular culture would bring their calendar to start in spring as it is when life most commonly begins anew. There is some merit to a summer start, suggesting that the life cycle does not end in winter but rather ends just after tabula rasa, but that is a conversation for scholars born long after the development of the calendar.

Knowing the year does not start until winter has faded also lends itself to appending any additional days, such as for leap years, on to winter. The math for adding leap years is fairly simple. A miscalculation by .25 will add up to a day in four cycles. A miscalculation by .01 will add up to a day in one hundred cycles. Therefore, a miscalculation of .24 will add up to a day every four cycles excluding once each hundred years. This is roughly the metric as done on our Gregorian calendar. I chose .4147 as my rounding error for this calendar, since 41 and 47 are the hexadecimal values of my initials A and G. With a .4147 error, roughly every other year will have a leap day with the exception of once every five leap years, one out of every one hundred, twenty five out of every thousand, and 100/7 (14.2857) out every ten thousand. While once every other year might seem like a lot compared to our calendar, it’s not quite enough for what I want. Since the number is below half, the leap years will be the exception to the norm. If they were larger, we would instead subtract days for leap years (thereby leaping over a day which makes more sense to me for the term) and have each regular year be slightly longer instead.

With a culture and world so dedicated to the importance of seasons, it is not inconceivable that each season of this calendar would be constructed independently. Therefore each season would have its own rounding error. For the sake of simplicity, I will instead apply the .4147 error to each Lunar and Dilunar season rather than to just the solar year. This gives an average of 3.3176 leap days to be added to the end of winter. Why not just add this to the end of each year and be done with it? Because that is both boring and overestimates the primitive tools used to construct this calendar. Instead, every third year celebrates the addition of ten extra days with the exception of once every twenty years which only celebrates nine days except every fifth set of twenty except every twelve and a half which are instead removed twofold every twenty-five. Those numbers, of course, are from 9.9528 or the error matched every third year.

With the solar portion of the calendar completed, it is time to finalize the lunar portion. From the calendar made in the previous post, we set aside exact dates for the beginnings and endings of seasons, which was simple enough to do. That just divides the solar year by four and then separates it into a 2:1 ratio of lunar:dilunar seasons with ten months in each season. However, no calendar is ever that uniform nor should it be. We have decided two things thus far. One moon is smaller than the other and has a longer orbit. And the two moons appear to be dancing, suggesting that they often show up both independently and together.

The simplest way to accommodate the alternating cycle of lunar and dilunar months is to have each paired month track the lunar cycles rather than each month individually. Roughly one fourth of each lunar cycle has the moon mostly dark from the planetary surface. So for one moon, a 72 day on / 36 day off cycle means that the moon has a total of 108 days in its total cycle. While true that this ratio is 2:3 rather than 3:4, the absent 1/12th can be attributed to only mere slivers of the moon being visible on either side. Using this logic, the other moon would follow a 54 day cycle of 36/18. However, there is another option.

It is important to note that tracking the moon is significantly easier than tracking our position relative to the sun. It seems plausible to me that a culture in this scenario would track the absence of one moon by the completed cycle of another. The numbers are set up to do so. When the first moon goes dark, they would note the phase of the second and wait for it to repeat its phase to expect the first to return. So rather than one moon’s cycle being 108 days and the other being 54, perhaps one is 108 and the other is only 36.

To me, it only makes sense that the 108 day cycle would be on the further, smaller moon. Up until this point, that moon has been secondary but has had more days attributed to it in the calendar. To keep this consistent within the world, I have decided that the absence of the 108 cycle moon would be its apogee, or furthest point in its elliptical orbit. Not only does the angle make it difficult to see in the night sky, but so too does the actual distance. The use of apogee here also helps account for the 1/12th miscalculation as mentioned above. By doing so, this also allows there to be significant changes to the world’s behavior. In a world with two moons, tidal forces and tectonic activity are bound to be more profound in moments of lunar perigee. The secondary moon may have a longer cycle and be smaller, but she speaks louder when paired with the primary moon.  They support each other, as partners do.

In a 540/270 seasonal cycle, the 108 day cycle of the secondary moon repeats itself 7.5 times. 5 times exactly in the 540 cycle and 2.5 times in the 270 cycle. This means that each Lunar season’s months need to alternate each time. As an bonus, this 108 day cycle is exactly 12 weeks of 9 days so it will always start and end on the same day.

At this point, my calendar looks like this.

Spring | 72 / 36 / 72 / 36 / 72 / 36 / 72 / 36 / 72 / 36 | | 36 / 18 / 36 / 18 / 36 / 18 / 36 / 18 / 36 / 18 |
Summer | 36 / 72 / 36 / 72 / 36 / 72 / 36 / 72 / 36 / 72 | | 36 / 18 / 36 / 18 / 36 / 18 / 36 / 18 / 36 / 18 |
Autumn | 72 / 36 / 72 / 36 / 72 / 36 / 72 / 36 / 72 / 36 | | 36 / 18 / 36 / 18 / 36 / 18 / 36 / 18 / 36 / 18 |
Winter | 36 / 72 / 36 / 72 / 36 / 72 / 36 / 72 / 36 / 72 | | 36 / 18 / 36 / 18 / 36 / 18 / 36 / 18 / 36 / 18 |

There is some variance but not a whole lot of it. What I have noticed is that the dilunar seasons start with the same number of days in the month as the alternating lunar seasons in summer and winter. Rather than continually alternating them, I can change their order while still fitting the pattern.

Spring | 72 / 36 / 72 / 36 / 72 / 36 / 72 / 36 / 72 / 36 | | 36 / 18 / 36 / 18 / 36 / 18 / 36 / 18 / 36 / 18 |
Summer | 36 / 18 / 36 / 18 / 36 / 18 / 36 / 18 / 36 / 18 | | 36 / 72 / 36 / 72 / 36 / 72 / 36 / 72 / 36 / 72 |
Autumn | 72 / 36 / 72 / 36 / 72 / 36 / 72 / 36 / 72 / 36 | | 36 / 18 / 36 / 18 / 36 / 18 / 36 / 18 / 36 / 18 |
Winter | 36 / 18 / 36 / 18 / 36 / 18 / 36 / 18 / 36 / 18 | | 36 / 72 / 36 / 72 / 36 / 72 / 36 / 72 / 36 / 72 |

By making this change, I have coincidentally set it up such that the spring and autumnal equinoxes do not change which moon the season is dedicated to but the summer and winter solstices do. I am very happy with this change. Knowing that the larger moon’s patterns exist on a 36 day cycle rather an 54 day cycle suggest to me that the months during its seasons would not alternate as evenly. Rather, they would occasionally break down into pairs of 18 next to each other. The reason for the separation is due to the cycles of the moons not being totally in sync with the seasons as those are solar dates.

Spring | 72 / 36 / 72 / 36 / 72 / 36 / 72 / 36 / 72 / 36 | | 18 / 36 / 36 / 18 / 36 / 36 / 18 / 18 / 36 / 18 |
Summer | 36 / 18 / 18 / 36 / 36 / 18 / 36 / 18 / 36 / 18 | | 36 / 72 / 36 / 72 / 36 / 72 / 36 / 72 / 36 / 72 |
Autumn | 72 / 36 / 72 / 36 / 72 / 36 / 72 / 36 / 72 / 36 | | 18 / 36 / 36 / 18 / 36 / 36 / 18 / 18 / 36 / 18 |
Winter | 36 / 18 / 18 / 36 / 36 / 18 / 36 / 18 / 36 / 18 | | 36 / 72 / 36 / 72 / 36 / 72 / 36 / 72 / 36 / 72 |

Now we have reached a point with a consistent, but also somewhat variable pattern. All lunar seasons share the same pattern of 72/36 alternating except they alternate which order they start in. The dilunar seasons operate similarly except their numerical values are opposite of each other. Summer and Winter share the same exact pattern while spring and autumn share their pattern. Variance in lunar patterns will exist, similar to leap years in solar calendars. However, the months will remain the same for the sake of a consistent calendar as they do today. Important dates for festivals might change occasionally, being tied to the first full moon of a certain month, but will otherwise remain consistent enough.

From here, it is time to add in some cultural touches to each of the months. If there is a pantheon tied to each of the ten months or if there are other elements, determine which of them are relevant and when. I have just over 400 days to toss in to reach my goal of roughly 10 Earth years per year of this calendar. I could just add in 5 days to each month and be done with it. However, since this world is still in development and the calendar is a hobby project I will hold on to them and add them as I further develop each month individually. The last steps are to enter this calendar into the donjon calculator to see where the moons have significant positions. Any moments of identical phases, or exact opposite phases get to be marked as holidays tied to the season. Fasts, feasts, and other cultural observations can all be tied to these days.

Creating a Dilunisolar Calendar
Part 1: Design Goals
Part 2: Days, Months, Seasons, & Years
Part 3: Cultural Significance
The Calendar