Acoustical properties of the front-duplex system in a grand piano
Florian Pfeifle · The Journal of the Acoustical Society of America · 2016
The duplex scala, patented by Theodore Steinway in 1872, has been subject to several disputes since it found its first application in grand pianos. Not without good reason because, as was shown in the work of Öberg & Askenfeldt (2012), the physical effects explained in the patent can not be substantiated by measurements mainly because the tune of the duplex strings deviate considerably from the suggested theoretical values. Nonetheless, as published in the same work, the perceptual relevance of the rear- and more so of the front-duplex is stressed. As is shown there, even untrained musicians are able to perceive the influence of both duplex scalae. In this treatise, physical properties of front-duplex strings are considered and an explanation of the acoustical importance regarding the string vibration of the main string is given. To this end, a series of high-speed camera measurements of several duplex strings are presented. Due to the small deflection of front-duplex strings, the recorded data is processed using motion magnification methods showing the influence of different modes of vibration in different frequency bands. A physical model of a grand piano string chorus is proposed, aiding in characterizing the main influence of the front duplex string.