Danetiska Academia

The Danetian Calendar

The Danetian calendar is a lunisolar calendar used by the Danetian people. Each month starts and ends at roughly the new moon.

The synodic period of the Moon is around 29.530 588 days. Therefore, the months of the calendar alternate between 29 and 30 days in order to keep them in sync with the phases of the Moon. If a month has 29 days, it’s called a hollow month; if it has 30, it’s called a full month.

Grouping months into years presents a challenge: If a year is defined to be 12 months, that results in 354 days, which is too short. If we instead define a year as 13 months, the result is roughly 383 days, which is too long. To get around this, some years are set to have 12 months, while others have 13, so that the average year length ends up being around 365.2421 days. Essentially, an entire leap month is inserted every two or three years in order to keep the calendar in sync with the seasons.

Calendar Calculator

Month names

The twelve months are named according to a modified version of the Chinese zodiac:

  1. Rat
  2. Ox
  3. Wolf (Tiger in the Chinese zodiac)
  4. Rabbit
  5. Eagle (Dragon in the Chinese zodiac)
  6. Snake
  7. Horse
  8. Goat
  9. Hedgehog (Monkey in the Chinese zodiac)
  10. Rooster
  11. Dog
  12. Pig
  13. Epagomenal (only in leap years)

The Danetians use these month names because they lived alongside Turkic tribes for several centuries. It was common for these Turkic tribes to use a modified version of the Chinese zodiac, with some animals replaced by local fauna.

Mathematical rules for months

Months alternate between full (30 days) and hollow (29 days) in a specified pattern in order to keep the average month length equal to 29.530 588 days. By writing this number as a continued fraction, we can see that two rational approximants arise: 1447 / 49 and 25 101 / 850. That is to say, we can approximate the synodic period of the Moon by arranging 1447 days into 49 months, or 25 101 days into 850 months for an even better approximation.

In order to accomplish this, certain months are recognized as “metallic months”. These are always full months, and are characterized by the “metallic month festivals”: the Iron Month Festival, the Silver Month Festival, and the Golden Month Festival. Certain rules are in place:

  1. After a hollow month always comes a full month, and vice-versa.
  2. After counting 17 months, the next month is recognized as an iron month. Iron months are always full months, superseding rule #1.
  3. After counting 49 months, the next month is recognized as a silver month. Silver months are always full months, superseding rule #1. Moreover, they reset the iron month count, superseding rule #2.
  4. After counting 850 months, the next month is recognized as a golden month. Golden months are always full months, superseding rule #1. Moreover, they reset both the iron month count and the silver month count, thereby superseding rules #2 and #3.

Mathematical rules for years

Years can either be short (12 months) or long (13 months; also called leap years). The average length of the month is 25 101 / 850 = 29.530 588. Thus, in order to remain in step with the tropical year of 365.2421 days, the most appropriate rational approximants to use are 235 / 19 and 4131 / 334.

The fraction 235 / 19 represents the Metonic cycle, which was already known in antiquity; it arranges 235 months into 19 years.

The calendar uses a system similar to that of metallic months, celebrating the Silver Year Festival and the Golden Year Festival. The following rules are in place:

  1. Within a cycle of 19 years, the following years are leap years: #2, #5, #7, #10, #13, #15, #18.
  2. After counting 19 years, the next year is known as a silver year, and it marks the beginning of a new Metonic cycle.
  3. After counting 334 years, the next year is known as a golden year. This resets the silver year count, superseding rule #2.

Sexagenary cycle

Another tradition inherited from the Chinese calendar is the sexagenary cycle. The twelve animals of the zodiac are combined with the five elements (wood, fire, earth, metal, water) in order to give a cycle of 60 years:

  1. wood rat
  2. wood ox
  3. fire wolf
  4. fire rabbit
  5. earth eagle
  6. earth snake
  7. metal horse
  8. metal goat
  9. water hedgehog
  10. water rooster
  11. wood dog
  12. wood pig
  13. fire rat
  14. fire ox
  15. earth wolf
  16. earth rabbit
  17. …

The current sexagenary cycle began in the year 3310, or 1984 in our calendar.

Calendar files

Here is the calendar for the current year. You may also browse any of the calendar files for other years: