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

the term "blue moon" for "intercalary month" arose by folk etymology,

the "blue" replacing the no-longer-understood belewe, 'to betray'.

I shouldn't consider myself a scholarly source of course, but it is so glaringly obvious so that it might go as common sense knowledge.

If eleven, twelve contained as is usually thought an element leven, left (two left, one left, ten,... pressumably when counting backwards), and the intercallary month was precisely those days that were left at the end of a period in calendar (just as we have to add a switch day on the 29th of february every four years, Romans at least added a month to complete the synodic year) then "belewe" cannot be any other way than related to this idiom. be- may be the common prefix.

It's conceivable that a sense "left" could also come to mean desertion, betrayal, and maybe there is a good source out there, though I suggest there were no need to look any further. I do in fact disagree with the -leven theory because it seems backwards to me, but it is trivial to source at least, and easily redcognized here in belewe.

You'd think blue "shiny" should rather mean "full moon", anyhow, no?