There’s more mathematics involved in playing the violin than I would have imagined. It’s physics, really. You get the rich, church bell sound not by pushing the bow on the strings, but by resting and gliding it. To play louder you do not necessarily change the pressure of the bow, but the speed. Speed equals volume. Location equals tone. Vibrato is in the arm, not the fingers or the wrist; and the perfect C# is a little closer to a D than you’d guess.

A mother decides to take up an instrument alongside her young daughters.