The bowed string and the player

Relations between bowing parameters, i.e., force applied, bow position, and velocity, are derived in terms of load impedance presented by bridge to string, characteristic impedance, and frictional coefficients. The range between least applied force needed to couple bow to load during sticking and maximum permitting uncoupling following sticking provides the generous tolerance, variable but typically in the ratio of 1 to 10, that makes the bowed string so flexible in performance. Domains of string behavior recognized by players are related graphically to bowing parameters. An electromagnetic method for observing particle velocity in the string reveals small but significant ripples caused by forces at the bow that the idealized explanation ignores. In one very flexible string, force exerted on the bridge varied approximately inversely with frequency out to the 15th harmonic, whereas for a string equivalent to a gut G for violin force became zero near the 7th. Elastic effects are considered, and it is suggested that in strings, either solid or wound, inharmonicity of 0.1 cent per square of mode number will not perceptibly degrade bowed-string performance.