APERIODICITY IN BOWED-STRING MOTION

Abstract

An investigation into the causes of aperiodicity in bowed-string oscillations is made using a combination of simple experiments, mathematical analysis, and computer simulation, and the status of theoretical models which idealise the behaviour as exactly periodic is thus assessed.lThree distinct sources of departure from a strictly periodic, Helmholtz type of motion are identified ( l.2,3 below).The third is the most important musically, and depends on differential slipping of the bow hairs during the nominal sticking phase of the Helmholtz cycle, a phenomenon not previously studied.I. Flyback jitter.'Flyback jitter', or cycle-by-cycle variation in the period of the sawtooth waveform of the transverse force exerted by the string on the bridge, reflects random variations in the timing of the round trip of the Helmholtz corner or propagating velocity jump.It can be measured very accurately from the zero crossings in the steep flyback in the digitized waveform.The interesting