The craft in music is the art of playing. The art in music is the science of listening.
But as Ion discusses, that is not enough: the musician must be inspired, fuelled by something other than knowledge and skill. I'm talking about music but I guess this could extend: but not sure of the formulation.
If the musician is responding to other sound, then knowledge ["science"] and skill ["art"] are informative devices; with these, the musician can process what he or she is hearing with intelligence [i.e. listen]; and then act on that physically [i.e. perform].
But between those two there is something unexplained. So let's talk about inspiration, the with intelligence bit.
As Ion the rhapsode was inspired only by Homer, the improvising musician is inspired by... well, that depends on the person.
I'm going to use myself as an example to think through this.
Let's say the improvising musician is inspired by sound. The sound can be external or internal, real or imagined. Doesn't matter.
How is this inspiration from sound created?
For me, I remember listening to my parents' music [e.g. Stevie Wonder, Marvin Gaye, Luther Vandross, Diana Ross, Michael Jackson; SOS, Rose Royce; Neil Diamond, Franco, Thomas Mapfumo; Bing Crosby/Louis Armstrong, Nat King Cole]; then wrongly thinking that I'd discovered jazz on my own when I first heard Jessica Williams; and then through my college years finding out all sorts of things through live music, taping stuff off the radio, the library.
The library and Humph's BBC Radio 2 programme were the main points of inspiration for me. Because I had a love of the breadth of the music I was hearing, I began to analyse it. I wanted to understand the music and live within its skin.
I never did the same with my parents' collection of music though—I never analysed it, as I had listened to it before and it was already in me.
In a sense—and referring back to Plato, but this time The Republic—my parents' collection were the tales that were told to me as a child, and thus I accepted them without thinking. In retrospect, a lot of the music I experienced had a rich palette in terms of harmony, rhythm and melody; and in fact I was listening to jazz before I knew its name or history, so it perhaps is not surprising that I have grown into it. But my appreciation—my love of it came first.
I think I am aiming to the point of saying that the connection between the craft and the art of music is love.
Love as a word is highly emotive and suggestive, and perhaps one that people find difficult to deal with; but I think it is appropriate here. In a quest to deepen knowledge of music a musician must listen. To deepen skill of music the musician must also perform or play. But to connect that skill and knowledge the musician must love and take fuel from music—or life—itself. All of this may sound like a truism; but if you look at many music courses either virtual or physical, you will not find a discussion.
Improving music education is not simply a matter of "getting kids playing". The technique of some people now is astounding. It's now more a matter of listening—proper listening, and developing a love of listening from an early age. I'm not talking about understanding the mechanics and mathematics of music, but simply the love of it.
In exactly the same way that the written word needs readers, music and the spoken word needs listeners; and yet while time and effort is spent cultivating reading, less time is spent developing listening.
If you stop to think about it, listening is very involved. Hearing is the perception of sound. Listening is paying attention to what you hear; and exactly how, what and why you pay attention to what you hear is the reason why listening is so involved.