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Modal analysis of violoncello tailpieces – copies derived from 3 tailpieces ascribed to Stradivari.

Houssay, Anne and Fouilhé, Eric 

In previous publications, we have first identified the vibrating modes of a cello tailpiece under string tension on a dead rig (2009-2010), using hammer and accelerometer and George Stoppani's softwares and then its behaviour on a cello. We compared different measurement methods and measured the variability of wood choices on vibration modes and frequencies (2011 - 2012). The adjusted position of the tailpiece has also been explored, by varying the “after-length”, i.e. the distance of the tailpiece to the bridge which leaves a small length of vibrating string (2013). We showed that, even if it is less mentioned by luthiers and musicians, the distance of the attachment at the bottom of the instruments has more influence on the modes and on the sound than the "afterlength". Our study took a more historical path to identify the trends and theories on this “after-length” (2014). Studying a few 19th century texts mentioning its role, we showed that the "afterlenth", often discussed as an adjusting parameter of the sound, became an issue especially when the industrialization process in Markneukirchen enhanced the standardization of its length, with the consequence of a loss of experience on the violin makers' part, who stopped altogether making the tailpieces themselves. In this work, we study the changes of tailpieces at the end of the 17th century, implied by the replacement of pure gut strings (extremely thick in the lower registers) with the new wounded strings. The Musée de la musique keeps in its collection a few tailpieces of the 17th and 18th century assigned to Stradivari, who lived through his life span these important technical changes. The different choices of wood, the joints of different pieces, carved out wood, different types of inlays, ebony veneer, show the many techniques used by the makers to control the weight, to reinforce in one direction or another, to soften or harden the spring response of the piece. We aim to characterize by modal analysis these different models and compare their behaviour on the dead rig under the string tension, as well as on an instrument. We compare acoustical measurements and modal behaviour of copies of different historical tailpieces, chosen for the fact that they show the different stages in historical set up at a time of transformation of the lower register instruments of the violin family.