Types of Calendar
Hermetic Systems

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The motion (or apparent motion) of the Sun and the Moon provide temporal cycles which have strongly influenced the design of most calendars, which usually attempt to accord either with the solar cycle (the cycle of the seasons) or with the lunar cycle (the cycle of the phases of the Moon) or with both. There are over forty calendars currently in use, and many others that have been used or have been invented. They thus come in many forms. They may be divided into six kinds:

1. Purely lunar calendars

Those which are based on the natural cycles of the Moon, which have months which attempt to stay as closely as possible in sync with the lunar phases, and whose years (composed of months) have no close relation with the solar cycle, for example, the Muslim Calendar.

2. Purely solar calendars

Those which are based on the cycle of the seasons, which results from the motion of the Earth around the Sun (and the fact that the Earth's axis of rotation is tilted significantly with respect to the Earth's plane of rotation about the Sun). These calendars have years which accord with the seasonal cycle and begin at or near a fixed point in that cycle (for example, the vernal equinox). Years in a purely solar calendar may be composed of months, but the months have little if any connection with the lunar cycle, for example, the Common Era Calendar (the Gregorian Calendar with years designated according to the astronomical system) commonly in use today.

3. Lunisolar calendars

These calendars aim to be both solar calendars and lunar calendars, but are more successful in tracking the seasonal cycle than the lunar cycle. Such a calendar consists of years which accord closely with the seasonal cycle and months which accord more-or-less closely with the lunar cycle. An example of a lunisolar calendar is the Liberalia Triday Calendar (which is unusual in that it has both a solar calendrical component and a lunar calendrical component, the solar component being more accurate than the lunar).

Months in the Common Era Calendar are too discrepant with the lunar cycle for this calendar to be considered a lunisolar calendar (indeed the use of the term "month" in connection with this calendar is a misnomer, since the months have practically no connection to the lunar cycles beyond the fact that they are generally a day or two longer).

4. Solilunar calendars

These calendars aim to be both solar calendars and lunar calendars, but are more successful in tracking the lunar cycle than the seasonal cycle. They consist of months which accord closely with the lunar cycle and years which accord more-or-less closely with the seasonal cycle, for example, the Chinese Calendar, the Jewish Calendar and the Meyer-Palmen Solilunar Calendar. (However there may not be much point in distinguishing solilunar calendars from lunisolar calendars; they can all be termed lunisolar calendars.)

5. Other calendars

These calendars apparently make little or no attempt to accord with the cycles of the Moon or of the Sun. For example, the Tzolkin and the Long Count in the Maya Calendar. Some of these calendars may accord with other astronomical cycles, such as that associated with the planet Venus.

One calendrical scholar (Lance Latham) has suggested that a classification of calendars should also include the category of 'luni-stellar'. According to Richard Parker the Egyptian Calendar was such a calendar, and Latham has "found references to a luni-stellar calendar in use by the Loango, a West African tribe (Sirius) and some references to another such calendar in use by Mexican coastal tribes in the early 16th century (the Pleiades)."

Calendars may also be divided into three kinds according to whether or not they depend on the times of astronomical events, and if so whether those times are observed or calculated:

1. Calendars based on rules
These calendars are specified completely in terms of rules which are independent of astronomical events, for example, how many months are in a year, how many days are in each month, etc. Once a calendar date is associated with a particular day (in common experience) then the dates of all other days before and after that day can be calculated simply be the application of the rules. Examples are the Gregorian Calendar, the Julian Calendar and the Maya Calendar.

2. Calendars based on astronomical observation

These calendars require either observation of celestial phenomena (for example, the first appearance of the crescent moon after a dark moon, the astronomical conjunction of Sun and Moon) in order to decide, for example, when a month should begin, or when an extra month should be inserted in the calendar. The Islamic Calendar is a calendar of this type.

3. Calendars based on astronomical calculation

These calendars may originally have been based on astronomical observation but, with the development of astronomical theory, calculation of the times of astronomical events has replaced observation. Examples are the Jewish Calendar and the Chinese Calendar. The latter depends on the exact times of dark moons and what are called "solar terms" (which divide the solar year into 24 parts). With refinements in astronomical knowledge the calendar may change with the introduction of different methods of calculating the exact times of astronomical events.

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