Acoustical and perceptual influence of duplex stringing in grand pianos

Abstract

This study investigates the acoustical and perceptual influence of the string parts outside the speaking length in grand pianos (front and rear duplex strings). Acoustical measurements on a grand piano in concert condition were conducted, measuring the fundamental frequencies of all main and duplex strings in the four octaves D4-C8. Considerable deviations from the nominal harmonic relations between the rear duplex and main string frequencies, as described by the manufacturer in a patent, were observed. Generally the rear duplex strings were tuned higher than the nominal harmonic relations with average and median deviations approaching +50 cent. Single keys reached +190 and -100 cent. The spread in deviation from harmonic relations within trichords was also substantial with average and median values around 25 cent, occasionally reaching 60 cent. Contributions from both front and rear duplex strings were observed in the bridge motion and sound. The audibility of the duplex strings was studied in an ABX listening test. Complete dampening of the front duplex was clearly perceptible both for an experiment group consisting of musicians and a control group with naive subjects. The contribution from the rear duplex could also be perceived, but less pronounced.

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“…Moreover, in Ref. [32], the correlogram was used to extract the fundamental frequency of the duplex strings of a piano which is not stable. The method allowed the authors to control their parameters (e.g., window length for correlation, number of periods from tone start, etc.)…”