Between a line and a trajectory.

On a page, a function is a relationship. Give it a coordinate system and it becomes a line. Add time, gravity or a rule for collision, and the line begins to tell a different story.

A musical phrase has a similar movement. It has direction, tension and a point of arrival. A small change in timing can alter the shape of everything around it, just as a small change in an initial condition can alter a trajectory.

The analogy has limits. An equation does not describe everything that matters in a performance, and a melody is not a physics model. But moving between the two can make each easier to notice.

Building an interactive experiment is one way to test that curiosity. Instead of only reading a result, you change something and see where it goes. Sometimes the useful part is the answer. Sometimes it is the better question that appears along the way.