I wrote an article on this for OPN a while back, emphasizing the light-scattering aspect, of course, but talking about the usages of the phrase as well. I relied upon the Sky and Telescope artiicles, and the SD, and others, of course.
My thoughts:
1.) It’s not “a” Blue Moon. The original usage is to call that lunar month “Blue Moon” because it needs a name. The other moons in the Almanac each had names associated with the month – “Hunter’s Moon”, “Pink Moon”, etc. Every now and then you get four full moons in a season rather than the usual three. If you just continue to name them in order, then eventually “Harvest Moon” would start to wander through the year, being in Summer, then Spring, instead of being in the Autumn (where it belongs) all the time. So you need to throw in an eextra “named” month. The Jewish calendar has been doing this for a long time. They just repeat the name of the month, however. If the Almanac did it, they’d have, say, Hunter’s Moon followed by Hunter’s Moon.
2.) They don’t want to do this. So they call the extra month “Blue Moon”. It’s not “a” “Blue Moon”, as in a descriptive term. They call the month “Blue Moon” because that’s the standard name they use for such intercalary months.
3.) As far as I can tell, this is a Farmer’s Almanac thing. Although there are systems of naming months (The Jewish lunar calendar, the Islamic Calendar), we in greater Western Civ don’t really have a fixed set of names for the months. American Indians did, IIRC, but they don’t have a fixed set, either. The whole “Hunter’s Moon”, “Harvest Moon”, “Wolf Moon” thing sounds like it’s a piece of authentic historic lore, but it’s not. As far as I can telll, the names are the creation of Farmer’s Almanac. So when S&T got it wrong in 1946, they screwed up a magazine’s naming philosophy. They weren’t showing colossal ignorance of a cultural meme.
4.) Since they got it wronmg, a lot of people haver been using it that way, and the usage has passed into commonly received wisdom. For better or for worse, irt seems to me, “Blue moon” = “second full moon in a month” is as legit as any other mistake in the language that’s been ratified by time. There are a lot of those. Look up the history of “Item”.
5.) Those who pedantically claim that people are incorrectly using the term because that’s not what “a” Blue Moon is probably don’t properly understand the meaning of the term themselves, or they wouldn’t be using that indefinite article. See above.