Bifurcations in cello bowing using bow force below or above the Helmholtz regime

Abstract

Two bifurcation regimes with bowing forces above and below the thresholds for regular Helmholtz or sawtooth motion are investigated on a cello. During operation, string acceleration is measured at the bridge while bow force and speed are defined and measured on a bowing machine. High bow force causes subharmonics where the pitch depends on bowing pressure and velocity. Here sudden pitch changes were recorded at playing parameter thresholds while with slightly different parameters quasi-random scratchy sounds occurred. At very low bow forces, bifurcations appeared in the higher harmonics with two- and four-fold subdivision of periodicity, while the fundamental pitch remained stable. The reason for these bifurcations are bistable periodicities of the time series. To account for this, the sounds were analyzed using a Finite-Difference cochlea model which results in Interspike Intervals (ISI) with precise temporal resolution of these periodicities.