Bowed-string multiphonics analyzed by use of impulse response and the Poisson summation formula

Abstract

By carefully positioning the bow and a lightly touching finger on the string, the string spectrum can be conditioned to provide narrow bands of pronounced energy. This leaves the impression of multiple complex tones with the normal (Helmholtz) fundamental as the lowest pitch. The phenomenon is seen to be caused by two additional signal loops, one on each side of the finger, which through the repeating slip pattern get phase locked to the full loop of the fundamental. Within the nominal period, however, the slip pulses will not be uniform like they are during the production of a normal "harmonic" or "flageolet" but may vary considerably in shape, size, and timing. For each string, there is a large number of bow/finger combinations that bear the potential of producing such tones. There are also two classes, depending on whether the bow or the finger is situated closest to the bridge. Touching the string with the finger closest to the bridge will somewhat emphasize the (Helmholtz) fundamental. The technique is applicable to double bass and cello, while less practical on shorter-stringed instruments. Analyses based on impulse responses and the Poisson summation formula provide an explanation to the underlying system properties.