Mathematical models of flageolet harmonics on stringed instruments

Flageolet is a common technique to elicit harmonics on stringed instruments like guitars, pianos, and the violin family: the bowed or plucked string is subdivided by a slight touch of the finger. The paper discusses appropriate linear wave equations which model the flageolet phenomenon. The standard second order wave equation fails, because the resulting Dirichlet boundary condition at the finger uncouples the two parts of the string and produces tones different from the flageolet. We include and discuss fourth order corrections, due to string stiffness, as a possible source for the flageolet phenomenon.