What is this?

This is an attempt to render the Mayan calendar in a more familiar “monthly” calendar format.

The idea of a monthly calendar is sort of alien to the Maya, who used two cycles to track the date and a modified base-20 numbering system to track the exact date:

• The Tzolkʼin cycle, which is a 260-day cycle based on combining 20 day names with 13 numbers, used for religious and ceremonial events and for divination;
• The Haabʼ cycle, which is a 365-day cycle consisting of 18 “months” of 20 day each, plus 5 days at the end of the year known as the Wayebʼ;
• The Long Count, a modified base-20 system used to represent the number of days since the mythical date of creation, which is August 11, 3114 BCE in the proleptic Gregorian calendar or September 6, 3114 BCE in the proleptic Julian calendar. It is typically represented as five numbers separated by dots, with each number counting from 0 up to 19, except for the second last number, which counts from 0 to 17.

Since the Haabʼ is the closest equivalent to months in the Mayan system, this calendar application is based on the Haabʼ. This poses a problem, as in the Mayan system, the Long Count is used to track the absolute date and the cycles of Tzolkʼin and Haabʼ are unnumbered. To mitigate this issue, we attempt to number the Haabʼ cycles, with the date of creation in cycle 0.

How does Tzolkʼin work?

The Tzolkʼin is composed from two concurrent cycles—the number 1 to 13, and a list of 20 day names.

The day name are: Imix, Ikʼ, Akʼbʼal, Kʼan, Chikchan, Kimi, Manikʼ, Lamat, Muluk, Ok, Chuwen, Ebʼ, Bʼen, Ix, Men, Kibʼ, Kabʼan, Etzʼnabʼ, Kawak, and Ajaw.

Note that the day name and number cycles are completely independent and advance concurrently. This means that 1 Imix is followed by 2 Ikʼ and so on. There is no definite start or end to this cycle, but day names repeat every 260 days, which is the least common multiple of 13 and 20.

What's so special about this version?

Most versions of the calendar floating around doesn't use the original definition above.

Most versions uses the so-called Romme method for leap years, using the same leap year rules as the Gregorian calendar, i.e. every year divisible by four, except century years not divisible by 400. This method might make sense, except years 3, 7, and 11 were leap years under the original rules and were observed as such in real life, but the Romme method instead makes years 4, 8, 12 leap years instead.

This version uses the original rules. The JPL's DE440 and DE441 ephemerides were used to calculate the exact timings of the autumnal equinoxes between the Gregorian years 13201 BCE and 17191 CE (corresponding to the French Republican years -14991 to 15399). The times were then converted to UT1+00:09:21, the exact local time at the Paris Observatory. UT1 was chosen to keep track of the Earth's rotation without having to worry about the issues posed by leap seconds in UTC. Note that due to the uncertainty over ΔT — the difference between UT1 and Terrestrial Time (TT) used in the ephemerides — it is theoretically possible for there to be inaccuracies when the equinox occurs very close to midnight.

For more details about how I calculated this calendar, please see my blog post on the topic. This is the fourth part of a series on time-keeping, and you are highly encouraged to read the first three parts for a more complete understanding.

What are those names above the Gregorian date?

Those are the names of the days in the rural version of the calendar. This was intended to replace the Catholic Church's calendar of saints, as the French Revolution wanted to reduce the influence of the church. Every day of the year has a unique name associated with the rural economy and these names are supposed to correspond with the season.

Every quintidi is named after an animal, every décadi is named after an agricultural tool, and the remaining days are named after various plants or produce. The only exception is the winter month of Nivôse, which has the remaining days named after minerals.

What are those numbers below the Gregorian date?

The five (or more) numbers separated by dots is the corresponding Mesoamerican Long Count calendar date. This is commonly known as the “Mayan calendar.” This calendar is not available for dates before August 11, 3114 BCE (25 Thermidor -4905).

What is decimal time?

Decimal time is a time system used during the French Revolution that divided the day into 10 hours, each with 100 minutes, which contained 100 seconds each.

The result is 100,000 seconds in one day, compared to the 86,400 seconds with the normal 24-hour system. This makes it very easy to denote time as a decimal fraction of a day. For example, decimal time 5:67:72 (around 13:37:31) on January 1, 2000 can be represented as 2000-01-01.56772.

Also note that each decimal hour is 2.4 normal hours, each decimal minute is 1.44 normal minutes, and each decimal second is 0.864 normal seconds.