ARMS carve the air. A hand closes as if to pull taffy. An index finger shoots out. The torso leans in, leans back. And somehow, music pours forth — precisely coordinated and emotionally expressive — in response to this mysterious podium dance.

Concertgoers, who train their ears on the orchestra, inevitably fix their eyes on the conductor. But even the most experienced listener may not be aware of the subtle and deep connection between a conductor’s symphony of movements and the music emanating from the players.

So in an attempt to understand what is going on, we interviewed seven conductors as they passed through New York in recent seasons with an eye to breaking them down into body parts — like that poster in the butcher shop with dotted lines to show the different cuts of meat — left hand, right hand, face, eyes, lungs and, most elusive, brain.

The conductor’s fundamental goal is to bring a written score to life, through study, personality and musical formation. But he or she makes music’s meaning clear through body motion.