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A blue moon is an extra full moon that appears in a subdivision of a year, either the third of four full moons in a season or, recently, a second full moon in a month of the common calendar. Metaphorically, a "blue moon" is a rare event, as in the expression "once in a blue moon".
The phrase has nothing to do with the actual color of the moon, although a literal "blue moon" (the moon appearing with a tinge of blue) may occur in certain atmospheric conditions; e.g., when there are volcanic eruptions or when exceptionally large fires leave particles in the atmosphere.
The term blue moon is currently used commonly to describe a second full moon in a single solar calendar month, which happens every two to three years (seven times in the Metonic cycle of 19 years). This usage of the term "blue moon" to describe the second full moon in one calendar month results from a misinterpretation of the traditional definition of that term in the March 1946 issue of Sky & Telescope. Before then, the term was used to describe the third full moon in a season with four.
One lunation (an average lunar cycle) is 29.53 days. There are about 365.25 days in a solar year. Therefore, about 12.37 lunations (365.25 days divided by 29.53 days) occur in a solar year. In the widely used Gregorian calendar, there are 12 months (the word month is derived from moon) in a year, and normally there is one full moon each month. Each calendar year contains roughly 11 days more than the number of days in 12 lunar cycles. The extra days accumulate, so every two or three years (7 times in the 19-year Metonic cycle), there is an extra full moon. The extra moon necessarily falls in one of the four seasons, giving that season four full moons instead of the usual three, and, hence, a blue moon.
The suggestion has been made that the term "blue moon" for "intercalary month" arose by folk etymology, the "blue" replacing the no-longer-understood belewe, 'to betray'. The original meaning would then have been "betrayer moon", referring to a full moon that would "normally" (in non-intercalating years) be the full moon of spring, while in intercalating year, it was "traitorous" in the sense that people would have had to continue fasting for another month in accordance with the season of Lent.
The earliest recorded English usage of the term blue moon is found in an anti-clerical pamphlet (attacking the Roman clergy, and cardinal Thomas Wolsey in particular) by two converted Greenwich friars, William Roy and Jerome Barlow, published in 1528 under the title Rede me and be nott wrothe, for I say no thynge but trothe. The relevant passage reads:
It is not clear from the context that this refers to intercalation; the context of the passage is a dialogue between two priest's servants, spoken by the character "Jeffrey" (a brefe dialoge betwene two preste's servauntis, named Watkyn and Ieffraye). The intention may simply be that Jeffrey makes an absurd statement, "the moon is blue", to make the point that priests require laymen to believe in statements even if they are patently false. But in the above interpretation of "betrayer moon", Jeffrey may also be saying that it is up to the priests' whim to decide whether Lent is over or not, by introducing "blue moons" apparently at random.
In the 19th and early 20th centuries, the Maine Farmers' Almanac listed blue moon dates for farmers. These correspond to the third full moon in a quarter of the year when there were four full moons (normally a quarter year has three full moons). Full moon names were given to each lunation in a season. When a season has four moons the third is called the blue moon so that the last can continue to be called with the proper name for that season.
The division of the year into quarters starts with the nominal vernal equinox on or around March 21. This is close to the astronomical season but follows the Christian computus used for calculations of Easter, which places the equinox at a fixed date in the (Gregorian) calendar.
The March 1946 Sky and Telescope article "Once in a Blue Moon" by James Hugh Pruett misinterpreted the 1937 Maine Farmers' Almanac. "Seven times in 19 years there were – and still are – 13 full moons in a year. This gives 11 months with one full moon each and one with two. This second in a month, so I interpret it, was called Blue Moon." Widespread adoption of the definition of a "blue moon" as the second full moon in a month followed its use on the popular radio program StarDate on January 31, 1980.
The most literal meaning of blue moon is when the moon (not necessarily a full moon) appears to a casual observer to be unusually bluish, which is a rare event. The effect can be caused by smoke or dust particles in the atmosphere, as has happened after forest fires in Sweden and Canada in 1950 and 1951, and after the eruption of Krakatoa in 1883, which caused the moon to appear blue for nearly two years. Other less potent volcanoes have also turned the moon blue. People saw blue moons in 1983 after the eruption of the El Chichón volcano in Mexico, and there are reports of blue moons caused by Mount St. Helens in 1980 and Mount Pinatubo in 1991. In the Antarctic diary of Robert Falcon Scott for July 11, 1911 his entry says, "...the air thick with snow, and the moon a vague blue."  On that date the moon phase would have looked full.
On September 23, 1950, several muskeg fires that had been smoldering for several years in Alberta, Canada, suddenly blew up into major—and very smoky—fires. Winds carried the smoke eastward and southward with unusual speed, and the conditions of the fire produced large quantities of oily droplets of just the right size (about 1 micrometre in diameter) to scatter red and yellow light. Wherever the smoke cleared enough so that the sun was visible, it was lavender or blue. Ontario, Canada, and much of the east coast of the United States were affected by the following day, and two days later, observers in Britain reported an indigo sun in smoke-dimmed skies, followed by an equally blue moon that evening.
The key to a blue moon is having lots of particles slightly wider than the wavelength of red light (0.7 micrometer)—and no other sizes present. It is rare, but volcanoes sometimes produce such clouds, as do forest fires. Ash and dust clouds thrown into the atmosphere by fires and storms usually contain a mixture of particles with a wide range of sizes, with most smaller than 1 micrometer, and they tend to scatter blue light. This kind of cloud makes the moon turn red; thus red moons are far more common than blue moons.
The following blue moons occur between 2009 and 2021. These dates use UTC as the timezone; exact dates vary with different timezones.
Using the Maine Farmers' Almanac definition of blue moon (meaning the third full moon in a season of four full moons, and where the seasons are marked by equal 3 month intervals between solstices and equinoxes as opposed to calendar quarters), blue moons have occurred or will occur on
Unlike the astronomical seasonal definition, these dates are dependent on the Gregorian calendar and time zones.
Two full moons in one month (the second of which is a "blue moon"): 
Blue moons have been referenced in popular culture, such as: