Unfortunately, "Twinkle..." does not give much mnemonic aid.

Perhaps not, but, it does group the 25 letters into four musical lines that all rhyme with an "Eee" sound. And two rhyming couplets are easier to remember than 25 random abstractions, that have no meaning on their own. Though it is true that many early learners of "The ABC's" (thanks to that melody) often mistakenly think that "Elemenopee" is a single word.

Interesting about the Phoenicians; any idea when (or whether) they ever recorded their written symbols for phonemes in a particular order? I've read in several brief histories (including the introductory pages to individual letters in The American Heritage Dictionary) that the Phoenician letters started out as ideograms.

But why should Alf (Phoenician for "ox") come first? And why does Bet (Phoenician for "House") come next?

And so forth... That's the question no one seems to have an answer for.

But in any case, right now, I'm asking about when the tune that starts:

"C, C, G, G, A, A G ..." mismatched as it is, became the music with which our current version of the alphabet is taught.