Bowing a string with a non-zero radius exerts a torque, which excitestorsional waves. In general, torsional standing waves have higher fundamentalfrequencies than do transverse standing waves, and there is generally noharmonic relationship between them. Although torsional waves have little directacoustic effect, the motion of the bow-string contact depends on the sum of thetransverse speed v of the string plus the radius times the angular velocity(rw) . Consequently, in some bowing regimes, torsional waves could introducenon-periodicity or jitter to the transverse wave. The ear is sensitive tojitter so, while quite small amounts of jitter are important in the sounds of(real) bowed strings, modest amounts of jitter can be perceived as unpleasantor unmusical. It follows that, for a well bowed string, aperiodicities producedin the transverse motion by torsional waves (and other effects) must be small.Is this because the torsional waves are of small amplitude or because of strongcoupling between the torsional and transverse waves? We measure the torsionaland transverse motion for a string bowed by an experienced player over a rangeof tunings. The peaks in (rw), which occur near the start and end of the stickphase in which the bow and string move together, are only several times smallerthan v during this phase.
展开▼
