I was just re-watching the documentary From Mao to Mozart: Isaac Stern in China the other day. There's a scene where he's teaching a master class to students in front of a packed auditorium. He was teaching a young (10-12?) girl, who had played a passage dutifully. Her playing was technically "correct" in that the notes were the ones on the page with correct spacing, and even somewhat dynamically correct in terms of relative volume. But what was missing was the connection between the notes: they sounded mechanically produced, with no breath between them.
One of my dks' favorite teachers is truly old school, very performance oriented, and an octagenarian. He encourages dancers by telling them to "sing with their bodies." This phrase is, I think, one of the most compeling descriptions of musicality. What makes it so compelling as an analogy for me is that it also allows for the full range of relationships to the music--from the tone deaf to the most extreme virtuoso; from ballads to spirituals; opera to rap; yodelling to folksongs; singing in the shower to performing for 100,000 in a huge concert space. It also allows for the diverse of ways of relating to different aspects of the music: rhythym, melody, counterpointe, amplitude, genre, context, dynamics, etc.
In front of this entire crowd, he made her sing the phrase out loud. While he could make his musical corrections clear by imitation and example, this request needed translation, and her very first reaction, before she looked mortified, was as if he had asked her to stand on her head. Very much like the story Farrell tells where Balanchine asked her to keep extending her fourth position preparation for pirouette into a virtual lunge. After taking a few seconds to gather her courage, she sang the passage, and almost miraculously, played it with the same beautiful phrasing with which she had sung it. It had life and breath. She had been given permission to use her musical imagination and apply it to the score.
His explanation was that the violin was an extension of the voice. At best, in my opinion, dancers use their bodies to sing. (As a fan of 20th century and contemporary music, I know that the singing might not always be sweet, a la Pierrot Lunaire.) That doesn't in itself mean that a dancer is musical -- many people who sing are tone deaf, and others have bad taste -- but it's a great start.