Elementary Stability Considerations for Bowed-String Motion

cote interne IRCAM: Weinreich91a/National audienceUsing the approach first pioneered by Raman, the Helmholtz motion of a bowedstring is discussed as a special case of "two-velocity motions," in which a givenpoint (at which the bow is located ) alternates, in the course of a cycle, betweentwo constant velocities. The fact that the bow typically presents a negativeresistance to the string during the "slipping" part of the cycle is adduced as areason for the "duty cycle," that is, the fraction of the period that corresponds toslipping, to try to become as short as possible. It is shown that, for a stringwithout dissipation or stiffness, this duty cycle can be arbitrarily low for generalbow positions; data obtained with the "digital bow" illustrate this behavior. It isshown theoretically, and confirmed with computer simulations, that instabilitiesarising from the negative slipping resistance cannot be eliminated by assigning afinite positive value to the sticking resistance. The apparent stability of Helmholtzmotion observed in real playing situations remains a puzzle