Lunisolar calendar

A lunisolar calendar is a calendar in many cultures whose date indicates both the Moon phase and the time of the solar year. If the solar year is defined as a tropical year, then a lunisolar calendar will give an indication of the season; if it is taken as a sidereal year, then the calendar will predict the constellation near which the full moon may occur. As with all calendars which divide the year into months there is an additional requirement that the year have a whole number of months. In this case ordinary years consist of twelve months but every second or third year is an embolismic year, which adds a thirteenth intercalary, embolismic, or leap month.

Their months are based on the regular cycle of the Moon's phases. So lunisolar calendars are lunar calendars with – in contrast to them – additional intercalation rules being used to bring them into a rough agreement with the solar year and thus with the seasons.

The main other type of calendar is a solar calendar.

Examples

The Hebrew, Jain, Buddhist, Hindu and Kurdish as well as the traditional Burmese, Chinese, Japanese, Tibetan, Vietnamese, Mongolian and Korean calendars (in the east Asian cultural sphere), plus the ancient Hellenic, Coligny, and Babylonian calendars are all lunisolar. Also, some of the ancient pre-Islamic calendars in south Arabia followed a lunisolar system.[1] The Chinese, Coligny and Hebrew[2] lunisolar calendars track more or less the tropical year whereas the Buddhist and Hindu lunisolar calendars track the sidereal year. Therefore, the first three give an idea of the seasons whereas the last two give an idea of the position among the constellations of the full moon. The Tibetan calendar was influenced by both the Chinese and Buddhist calendars. The Germanic peoples also used a lunisolar calendar before their conversion to Christianity.

The Islamic calendar is lunar, but not a lunisolar calendar because its date is not related to the Sun. The civil versions of the Julian and Gregorian calendars are solar, because their dates do not indicate the Moon phase – however, both the Gregorian and Julian calendars include undated lunar calendars that allow them to calculate the Christian celebration of Easter, so both are lunisolar calendars in that respect.

Determining leap months

A rough idea of the frequency of the intercalary or leap month in all lunisolar calendars can be obtained by the following calculation, using approximate lengths of months and years in days:

  • Year: 365.25, Month: 29.53
  • 365.25/(12 × 29.53) = 1.0307
  • 1/0.0307 = 32.57 common months between leap months
  • 32.57/12 = 2.7 common years between leap years

Intercalation of leap months is frequently controlled by the "epact", which is the difference between the lunar and solar years (approximately 11 days). The Metonic cycle, used in the Hebrew calendar and the Julian and Gregorian ecclesiastical calendars, adds seven months during every nineteen-year period. The classic Metonic cycle can be reproduced by assigning an initial epact value of 1 to the last year of the cycle and incrementing by 11 each year. Between the last year of one cycle and the first year of the next the increment is 12. This adjustment, the saltus lunae, causes the epacts to repeat every 19 years. When the epact goes above 29 an intercalary month is added and 30 is subtracted. The intercalary years are numbers 3, 6, 8, 11, 14, 17 and 19. Both the Hebrew calendar and the Julian calendar use this sequence.

The Buddhist and Hebrew calendars restrict the leap month to a single month of the year; the number of common months between leap months is, therefore, usually 36, but occasionally only 24 months. Because the Chinese and Hindu lunisolar calendars allow the leap month to occur after or before (respectively) any month but use the true motion of the Sun, their leap months do not usually occur within a couple of months of perihelion, when the apparent speed of the Sun along the ecliptic is fastest (now about 3 January). This increases the usual number of common months between leap months to roughly 34 months when a doublet of common years occurs, while reducing the number to about 29 months when only a common singleton occurs.

With uncounted time

An alternative way of dealing with the fact that a solar year does not contain an integer number of months is by including uncounted time in the year that does not belong to any month.[3] Some Coast Salish peoples used a calendar of this kind. For instance, the Chehalis began their count of lunar months from the arrival of spawning chinook salmon (in Gregorian calendar October), and counted 10 months, leaving an uncounted period until the next chinook salmon run.[4]

Gregorian lunisolar calendar

The Gregorian calendar has a lunisolar calendar, which is used to determine the date of Easter. The rules are in the Computus.[5]

List of lunisolar calendars

The following is a list of lunisolar calendars:

gollark: More so than some handwritten one would be, most likely.
gollark: It's very\* readable\*\*.
gollark: ```javascriptconst spaces = regex(/^ */)const whitespace = regex(/^[ \n\t]*/)const name = regex(/^[^ \n\t():]+/)const code = many(coroutine(function*() { yield spaces return yield choice([ coroutine(function*() { yield char("(") const x = yield code yield spaces yield char(")") return x }), name ])}))const program = sequenceOf([ many1(coroutine(function*() { yield whitespace const n = yield name yield whitespace yield str(":=") const c = yield code return { code: c, name: n } })), possibly(whitespace)]).map(([x, _]) => x)```parsing™
gollark: It was very elegant. I combinated™ it in a few lines of code.
gollark: It went nicely and I had a cool parser and all until it turned out that we were accidentally pushing to the wrong end of a list or something in a stupidly hard to debug way.

See also

Notes
  1. F.C. De Blois, "TAʾRĪKH": I.1.iv. "Pre-Islamic and agricultural calendars of the Arabian peninsula", The Encyclopaedia of Islam, 2nd edition, X:260.
  2. The modern Hebrew calendar, since it is based on rules rather than observations, does not exactly track the tropical year, and in fact the average Hebrew year of ~365.2468 days is intermediate between the tropical year (~365.2422 days) and the sidereal year (~365.2564 days).
  3. Nilsson, Martin P. (1920), "Calendar Regulation 1. The Intercalation", Primitive Time-Reckoning: A Study in the Origins and First Development of the Art of Counting Time among the Primitive and Early Culture Peoples, Lund: C. W. K. Gleerup, p. 240, The Lower Thompson Indians in British Columbia counted up to ten or sometimes eleven months, the remainder of the year being called the autumn or late fall. This indefinite period of unnamed months enabled them to bring the lunar and solar year into harmony.
  4. Suttles, Wayne P. Musqueam Reference Grammar, UBC Press, 2004, p. 517.
  5. Richards 2013, p. 583, 592, §15.4.

References
  • Dershowitz, Nachum; Reingold, Edward M. (2008). Calendrical Calculations. Cambridge: Cambridge University Press. ISBN 9780521885409.CS1 maint: ref=harv (link)
  • Richards, E. G. (2013). "Calendars". In Urban, Sean; Seidelmann, P. Kenneth (eds.). Explanatory Supplement to the Astronomical Almanac (3rd ed.). Mill Valley, CA: University Science Books. ISBN 978-1-891389-85-6.CS1 maint: ref=harv (link)


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