Calendars are such a routine part of life that we don't normally think
about how they work. However, when you're doing worldbuilding and culture
building, they can become an important part of what establishes the 'feel'
of your work.

This article discusses/describes the various types of calendars. It does
not discuss converting between calendars, nor does it actually define any
particular calendar for a particular world.

The phrase "metaphysical significance" is used as shorthand for indicating
that something has significance to a culture for reasons other than
grounded in real, measurable phenomena. As an example, the seven-day week
of most modern cultures is ultimately based on no more than the creation
legend in scripture; thus, 'seven' has metaphysical significance. On the
other hand, the year being 365 days is based on the measurable time over
which the stars progress around the sky to return to the same position;
this is not metaphysical significance.

"Day" and "Year" refer to both the calendar periods and the rotational and
revolutional periods (respectively) of the world; where it is necessary to
distinguish, a phrase such as "solar year", "calendar year", etc., will be
used.

"Week" and "month" are used to refer to multi-day periods on the calendar;
generally, the "week" is ten days or less; the "month" is 20 days or more;
periods in the gap are defined on a case-by-case basis. Where the orbital
period of a natural satellite is referenced, it will be called a LUNATION.

"Month-date dating" refers to uniquely identifying a date within the year
using subdivisions of the year ("months"), and the day within the month.
This is the "conventional" model for most calendars in current use.
"Month-date dating" may place the month and date in either order (e.g., "1
January" or "January 1"); the important feature is that both are required.
In Traveller, the Solomani, Zhodani, and K'kree calendars use this method.

"Serial dating" refers to uniquely identifying a date within the year by
simply counting days from the beginning of the year. In Traveller, the
Imperial, Vilani, Aslan, and Hiver calendars use this method. The Mayan
"Long Count" can also be considered serial dating (on a non-annular
calendar).

Types of Calendar

FIAT calendars are calendars that are established by law or edict, and do
not have any necessary connection to astronomical phenomena or metaphysical
significance on the world(s) they apply to. The Imperial calendar may be a
FIXED or SOLAR calendar for Sylea, but is a Fiat calendar for any other
world in the Imperium. Fiat calendars may have any of the structures
discussed in this article.

FIXED calendars do not change based on astronomical phenomena, and do not
have any necessary connection with them. Examples of fixed calendars are
Traveller's Imperial, Vilani, and K'kree calendars, and the Mayan Haab and
Tzolkin calendars. If based on a solar year, fixed calendars still do not
intercalate (even if a true solar calendar would). Most known fixed
calendars were intended as solar calendars, but were defined under
conditions where it was not clear that intercalation would be needed, or
was considered undesirable or inappropriate.

* HAAB-style calendars divide the year into a number of shorter periods
('months', for this article's purposes) of exactly equal numbers of days.
If this leaves a deficit as contrasted with the number of days in the year,
the remaining days are left as a period not part of any month ("Uayeb" or
"Wayeb" for the Mayan Haab calendar), or, rarely, as a "short month".
Haab-style calendars use month-date dating. The number of months in such a
calendar may, but need not, have metaphysical significance; the number of
days in the month is defined by the number of months - though the number of
months _may_ be chosen to make the length of the month close to the
lunation.

* TZOLKIN-style calendars are based on two cycles of days, whose numbers
are mutually prime. Both cycles increment daily; each day on the calendar
is a unique combination of positions in the two cycles, and a year on the
calendar consists of a number of days equal to the product of the lengths
of the two cycles. An example of how a Tzolkin-style calendar works can be
easily illustrated; assume that the two periods are five and three days
respectively. The five-day cycle names the days, "Red", "Yellow", "Orange",
"Green", and "Blue"; the three day cycle simply counts the days. A year on
such a calendar consists of the dates, in order, Red 1, Orange 2, Yellow 3,
Green 1, Blue 2, Red 3, Orange 1, Yellow 2, Green 3, Blue 1, Red 2, Orange
3, Yellow 1, Green 2, Blue 3. The lengths of the two cycles may be chosen
for their metaphysical significance, or to be as close to the length of the
solar year as possible within the mutual-primality constraint. Either or
both cycles may use names instead of numbers.

SOLAR calendars use the Solar Year as their fundamental period. The
Calendar Year is as close as possible to the Solar Year, to an integral
number of days. Intercalation will generally amount to one day every few
years, unless the calendar is modified to accommodate numbers or periods
that are significant from a social or religious perspective (which may lead
to longer intercalations at different intervals). The Gregorian calendar
commonly used today is a solar calendar (and remains one as the Solomani
calendar used in Traveller), as are the Zhodani and Aslan calendars; many
other regional calendars in use today are also solar calendars. A solar
calendar can be structured as a Haab-style calendar; in such a case,
intercalary periods, when needed, would be included in the Uayeb-equivalent
period.
LUNAR calendars use the lunation as their fundamental period. The calendar
month is as close as possible to the lunation, to an integral number of
days. Lunar calendars may be observational, with the new month beginning
when the first bit of crescent moon after the new moon is visible, at a
specified location, or they may be calculated, with the new month beginning
when the new moon would be 'observed' at a specified location under ideal
conditions, regardless of actual observation. A calendar year is some fixed
number of months, approximating the solar year, but without regard for
long-term accuracy (no intercalation, no Uayeb-equivalent period, etc.).
The Islamic calendar is an observational lunar calendar; Islamic calendars
printed in advance for planning purposes are calculated lunar calendars.

LUNISOLAR (or hybrid lunar/solar) calendars use the lunation as the
fundamental period, as the lunar calendar does, and may also be
observational or calculated. Normally, the calendar year is a fixed number
of months, but long-term accuracy is considered, and when the deficit from
the fixed number of months accumulates to the point of being equal to or
greater than an entire lunation, an additional month for that year will be
added to the calendar. The Jewish (often improperly called Hebrew) calendar
is of this type (calculated); intercalation of an additional month happens
in 7 years of each 19. The traditional Chinese calendar is also a lunisolar
calendar. The additional month may be added in a fixed location within the
calendar, as with the Jewish calendar, or in a varying location as defined
by multiple factors, as in the traditional Chinese calendar.

Tracking years

In general, a calendar counts years from a real or stipulated "epoch".
There are several ways of defining the Epoch:

1. Regnal Epochs: Dating from the beginning of a monarch's reign. This is
common in ancient documents, e.g., "In the sixth year of the reign of
Katsandogs...", and in east Asian pre-modern historical documents; it is
still practiced in Japan (other east Asian countries have abolished their
monarchies).

2. Stipulated Creation of the World: Several current calendars use this,
the best known being the Jewish calendar; no two seem to use the same date
as the epoch date. The Mayan Long Count also stipulates that 13.0.0.0.0
(corresponding to 11 August 3114 BCE in the proleptic Gregorian calendar)
was the creation date of the world.

3. Stipulated or actual date of a significant event in the life of a
significant person: The Julian and Gregorian calendars use this, dating
from the stipulated /brit milah/ of Yeshua ben Yosef of Nazareth, held to
be the Messiah in Christianity.

4. Stipulated or actual date of a significant event in the culture: The
Romans used this, dating "Ab urbe condita", 'from the founding of the city
[of Rome]'. This is also common in Science Fiction, where a local calendar
is often dated "A.L.", "After Landing", or in some older SF, "Atomic Era"
dating, usually considering the epoch to be either the first detonation of
an atomic weapon, or the activation date of the first atomic pile. The
Islamic calendar, dating from the Hejira (flight of Mohammed from Mecca to
Medina), and the short-lived French Revolutionary calendar also used this
model.

5. Mesoamerican cultures - most notably the Aztec and Maya - didn't number
their years; instead, they used the Haab and Tzolkin calendars in
conjunction. A "calendar round" was the period between two successive
occurrences of the same date pairing on the two calendars; this interval
was approximately 52 years. Within the 52-year calendar round, every
combination of a Haab date and a Tzolkin date was unique. Where greater
accuracy was required, the calendar round date would be coupled with the
Long Count for the date.

Counting Days

The most common way of counting days within a year or month is to simply
increment (generally from 1) throughout the period. The Romans, however,
used an inclusive decremental system, counting down toward one of three
significant days during the month: Kalends (the first day of the month,
sometimes 'Calends'), Ides (one day before the middle of the month), and
Nones (eight days before the Ides of the month). In an inclusive
decremental system, one counts the day itself as 'one', and counts backward
to it - so that if the Ides of the month falls on the 14th of the month,
the 12th was called "the third day before the Ides of ...". An exclusive
decremental system would make the 12th "the second day before ..."

Intercalation

Many solar calendars have origins in agrarian societies; as a result,
certain seasonal events take on an outsized importance - for example, the
ancient Egyptians were focussed on the annual flooding of the Nile River;
many cultures placed high importance on the solstices and equinoxes. Where
a solar year is not comprised of an integral number of days, the calendar
year will gradually get out of synchronization with the solar year. To
resynchronize the two, one or more days may be added to a calendar year.
These days are called INTERCALARY or EMBOLISMIC days; the process of adding
them is called INTERCALATION. The rules for where intercalary days are
added to the year will vary depending on culturally-significant factors of
many types; while the most common model is to add the additional days at
the end of a period, or between periods, there are recorded instances where
the days were inserted within and interrupting a period - for example, the
intercalation on the Gregorian calendar is sometimes called the
'bisextile'; this is because when the practice was instituted with the
Julian calendar, the intercalary day was inserted as a repeat of the sixth
day before the kalends of March (see "Counting Days", above). At one point,
when intercalation of the Roman calendar involved adding an additional
month, this month was also generally inserted between the sixth and seventh
days before the kalends of March.

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