I dunno. It’s close enough that I never thought about it until now.
I can’t remember ever hearing “magical.” It was always either “…the musical fruit / The more you eat, the more you toot” or “…good for your heart / The more you eat, the more you fart.”
It’s “musical” in this version (cutscene from video game “Skullmonkeys”) :
I heard the “fruit” version first, though I’m not sure if it was originally “musical” or “magical”. And the last line was “So eat your beans with every meal”.
And for the record, green beans are fruits. As are a very large number of other vegetables. “Fruit” and “vegetable” are not mutually exclusive.
He also adapted it as an opera:
The one I’m speaking. — well, it’s not quite a rhyme, but it’s pretty close.
How old is the heart-healthy version? I don’t remember children ever talking about what foods were good for your heart in the 1950’s or so.
The more pertinent question is when did “fart” become funny. The point of the heart rhyme isn’t to provide nutritional advice.
I think farts have always been funny; at least to a significant portion of the human populace. Isn’t the oldest recorded joke something about a woman farting in her husband’s lap?
Discourse’s “related threads” feature points out we did this 15 years ago. See (smell? 
) this blast from the past:
Lotta familiar names in that thread, and a few not seen nor heard from in years. And some different variations in the rhyme not mentioned here.
“musical”, and last line was “So eat some beans at every meal!”
It’s musical fruit, because “the more you eat, the more you toot” as if your butt has become a trumpet. There can be no further debate 
Also, I always appreciated the lesson in circular logic the rhyme delivers. Beans are good because they cause you to fart, and farting relieves the discomfort caused by the gas buildup due to the beans. Eh whut?
That’s the way I learned it.
“Musical” for me. Midwest circa the mid-80s.
And the last line is “So eat some beans with every meal” or “So eat your beans at every meal” - something like that.
Musical is much funnier than magical. It implies butt-trumpetry, which is hilarious to any kid.
To complicate the question, I grew up with (Wis, 1970s)
Beans beans the musical fruit
Makes a man go rooty-toot-toot
The more you eat the better you feel
So why not eat beans every meal?
It would make a nice doctoral thesis tracing the origins of this wondrous, musical, magical rhyme, and see if kids in this modern, interconnected world, all use the same rhyme now.
I think the dawn of man. Kubrick filmed Moonwatcher farting at the other tribe in 2001, but it got cut for time.
(not really)
Geroge Carlin had recorded routines talking about farts (farts are fun!) going back to the 60s, but I do not imply that is the origin. Just using it as a context in that, in the 60s, 70s, 80s, “fart” should have been in the “seven words you can’t say on TV”, because you couldn’t. No use of the word, no realistic fart sounds. Somewhere along the way the taboo got removed and now we live in the hell on earth of kid shows filled with fart jokes.
eta maybe this thread should have been names “rhyme-a-beans”
Just “musical” for me. NE US, 70s-80s.
I learned it as more like “So eat’cha beans at ev’ry meal.” I also heard ca. 1980 “musical fruit” and “good for your heart”, but never heard “magical.”
Three.
Beans, beans, they’re good for your heart.
The more you eat, he more you fart.
The more you fart, the better you feel.
So let’s have beans for every meal!
PS: Clam chowder makes 'em louder.
Turkey soup makes you poop!
And at roughly the same place along the way, the “toot” wording came to be seen as too weak and milquetoast-y to sustain what’s supposed to be a naughty playground rhyme. (Sort of a “reverse euphemism treadmill.”)
I heard the last line as
Now you’re ready for another meal of…
Beans, beans the musical fruit (etc.)
(Infinitely looping along the lines of “This is the song that doesn’t end”.)
99 pots of beans on the stove
Take one off and pass it around
…