Today the Musical, Part Eight

Today I sat down with The Great Broadway Fake Book. (I pause to tell this story: years ago--50 of them--my friend Terry turned me on to jazz. (I should also credit my sister Fay and her Ray Charles collection, and even dad's big band LP by, a band whose name I can't remember--the Elgar brothers, or something. That band was usually pitched as mellow, but they could really swing when they let it go.) Terry was into the hardest contemporary jazz--Coltrane, Ornette, later Miles and, my fav, the Jones-Lewis big band which was a powerhouse for a few years into the 70s. He was clear by the time we all finished high school that he'd be a jazz musician, which he became. And he used to talk about fake books, or fakebooks, of well-known tunes represented by only title, composer and lyricist, lyrics, melody, time signature, tempo term, and chords. Often they seemed cobbled together from different photocopiers or sheet music scores. Plastic spiral binding. 
I don't know why they're called that. Maybe because if you have the melody and the changes, you can fake the rest.)
Anyway, this afternoon I sat down, at the piano, with the fakebook of Broadway tunes and worked through four or five pages, maybe half a dozen songs, in an hour. I can read music; I know how to play chords. I'm clumsy as hell as a piano player, though. I'll have to practice before I can perform songs, accompanied by myself at the piano. 
I tell you, it's like magic. Play a Richard Rodgers tune from Allegro, you'll hear it as simple, and perhaps (lyrics by Hammerstein) sentimental, but then you're at the end of the song feeling as if you've learned from it. 
That's what I'm after: why this is so. Why I'm so moved.