I think Mapman is right, when he says, that it is impossible to quantify musicality. That is also the reason that psychology generally shies away from this problem.
Learsfool, I think, makes several excellent points, although I disagree, that "emotions are part of the music".
Humans, also higher forms of mammals have emotions. Music per se has not. It is sound, which however composers as well as their interpreters can shape cleverly, if they so chose, to arrange in such a way, that they can evoke all sorts of feelings, images and emotions in the listener. Maler and Richard Strauss were masters in this about 200 years ago, Prokofiev and Shostakovich in the last century just to mention a few. Strauss in fact was famous for saying, that if need be, he could put a glass of beer into music. There is a whole bag of tricks, as musicologists will point out, which by clevery arranging notes and the voicing and combination of instruments, by which you can evoke almost any state of mind you wish for in the listener. You might say, that music is able to manipulate us, as for example Stalin and Hitler very well knew.
However, it seems to me,that there is more to it: Bach's music is basically pure mathematics and with a bit of a jump in time also Schoenberg's. But they can and do evoke deep emotions in a listener, if he has the ear for their music.
I also fully agree with Learsfool, that what we call PraT and phrasing, are used to evoke something in the listener, who then, listening to a given piece, if he likes it would probably call "musical".
Bascially though, I think that Mapman has hit the nail on the head: As little as you can quantify what makes up a human being, you cannot quantify what makes for musicality.
You can certainly identify parts, as we try to do here, you can examine the question through musical education, historically, aesthetically, sociologically, psychologically, musicologically, but the whole is always more than all the parts and at least for me it remains a mystery.