Is the "blue" in "blue moon" a reference to betrayal?

The relationship between "blue" and "betrayer" in describing the periodic extra (thirteenth) moon in one of every three (more exactly 2.7) solar years is based on folklore and is therefore poor in documentation. It appears to be a pun and/or a case of false friends, and it's unclear how old or recent their connection is.

On the historical spellings of "blue" and "betrayer":

The modern English word "blue" has seen various spellings, including:

• "blwe" (c 1300), from the Online Etymology Dictionary.

• "blewe" (c 1150–1580), from A Concise Dictionary of Middle-English (by Mayhew & Skeat, Oxford).

The modern English word "betrayer" is a cognate of the verb "to betray".

• The infinitive was at one time in Old English spelled "belæwan" (c 5th–12th century), per the Old English Translator (compiled by a hobbyist).

• The first-person singular spelling of Old English "betray" is given above as "belæwe". This spelling matches "belewe", save for the Æ in place of the second E. Note that Æ has evolved into AE and then often simply to E in many English words.

From the above history, and knowing the non-standard history of pre-Modern English, one can see there was overlap in similar spellings of "blue" and "betray", despite their ultimate derivations being from two different PIE roots, allowing for the possibility of false-friend association and puns.

On the oft-claimed connecting word, "belewe":

The antiquated and obscure word "belewe" if often cited as a bridge between the terms "blue" and "betrayer":

• Intat.net (1993-12-03): "The blue moon was originally defined by the Maine Farmers' Almanac as the third full moon in… [Ellipses here are from the source, and no further content or citation is given there.] Some have posited that the name comes from the Old English word belewe, meaning to betray, because the blue moon betrays the usual one full moon per…"

• Unity Churchill Nursery (1999-03-15): "In calculating the dates for Lent and Easter, the Clergy identify the Lent moon. It is thought that historically when the moon's timing was too early, they named an earlier moon as a betrayer moon (belewe moon), thus the Lent moon came at its expected time. Folklore gave each moon a name according to its time of year. A moon that came too early had no folk name, and was called a blue moon, retaining the correct seasonal timings for future moons."

• Peter Geiger, Farmers' Almanac 2001 (2000-09-01): "[The beginning of this sentence is not visible in Google Books' preview] …meaning, to betray. Perhaps, then, the moon was belewe because it betrayed the usual perception of one full moon per month."

• Joe Rao, Curso Objectivo (2003-02-01): "One likely explanation has to do with the Old English word belewe, meaning to betray. The moon, this theory states, is belewe because it betrays the usual perception of one full moon per month."

• Joe Rao, Space.com via NBC News (2004-07-02): "The phrase 'once in a blue moon' was first noted in 1824 and refers to occurrences that are uncommon, perhaps even rare. … I myself once [no date or source given as to when or where exactly he means at this writing, though note he's the author of the previous quotation from a year prior] suggested that the rule might have evolved out of the fact that the word belewe came from the Old English, meaning, to betray. 'Perhaps,' I suggested, 'the second full moon is belewe because it betrays the usual perception of one full moon per month.'"

• Greg Alexander, Wikipedia (2008-02-05): "An alternative interpretation uses the other meaning of belewe (which can mean blue or betrayer)[citation here to the Farmers' Almanac website, but no quotation]. The Church was responsible for calculating … the date of Easter … the first Sunday after the [first] full moon [following spring equinox] (the egg moon). The preceding moon (Lent moon …) is also an important Christian time. In years where the Lent or egg moon would [appear] too early, the moon was a betrayer moon, [it] was not to be used to [commemorate] the death and resurrection of Christ. Thus the clergy would tell the people that it was not the Lent moon they were seeing, but a false moon—a betrayer moon."

• Farmers' Almanac Staff, Farmers' Almanac (2009-08-24): "One explanation [no citation given] connects it with the word belewe from Old English, meaning to betray. Perhaps, then, the moon was belewe because it betrayed the usual perception of one full moon per month."

• Buffalo Sunday News (2010-01-10): "Apparently the astronomical use of blue moon derives not from a color but from an earlier word, belewe, meaning betrayer. The calculation of the date of Easter and the associated Lenten period is determined by lunar cycles. In some years a reasonable date for this religious feast did not satisfy the clergy because of an extra seasonal full moon, so that moon was rejected as a betrayer—a belewe moon."

• Dave Tabler, Appalachian History (2013-01-01): "…one explanation connects it with the word belewe from Old English, meaning to betray. Perhaps, then, the moon was belewe because it betrayed the usual perception of one full moon per month. 'Yf they saye the mone is belewe, We must beleve that it is true,' says William Barlow, the Bishop of Chichester, in the Treatyse of the Buryall of the Masse, 1528. There are twelve full moons in most years, which means that three full moons occur during most seasons. One season in ten contains four full moons; hence the third moon that occurs in such a season would be the belewe, or blue, moon."

• Husna Haq, Christian Science Monitor (2015-07-29): "Some [cited with a broken link] have posited that the name comes from the Old English word belewe, meaning to betray, because the blue moon betrays the usual one full moon per month norm, by which farmers once marked the changing of seasons."

• Jon Austin, Sunday Express (2015-07-31): "…some [no citation] suggest the term blue refers to a betrayer moon from belewe in Old English."

• Gordon Johnston, NASA Science (2018-01-29): "Originally, the term blue moon referred to the third full moon in a season that has four full Moons. The earliest known reference to a blue moon in the English language is the phrase '…the mone is blewe…' from a pamphlet published in 1528. Some writers [no citation in source at to who] speculate that blue came from belewe, the phrase meant betrayer moon, and that the name referred to how an extra moon in a season confused or betrayed the dates for Lent and Easter. The newer definition of a blue moon as the second full moon in a calendar month dates from 1946."

• Jeff Parsons, Mirror (2018-02-01): "Normally, a year would have 12 moons, but when a moon appears for the 13th time—an unusual occurrence—it was referred to as a belewe moon, which means betrayer. The earliest English language reference is thought to be found in an anti-clerical pamphlet written in 1528."

From the above quotations, it's unclear whether Joe Rao originated the blue–belewe–betrayer connection, whether a different modern author drew this conclusion for Mr Rao and others to perpetuate, or whether the connection is indeed pre-modern.