Effects of using scalloped shape braces on the natural frequencies of a brace-soundboard system

Many prominent musical instrument makers shape their braces into a scalloped profile. Although reasons for this are not well known scientifically, many of these instrument makers attest that scalloped braces can produce superior sounding wooden musical instruments in certain situations. The aim of this paper is to determine a possible reason behind scalloped shaped braces. A simple analytical model consisting of a soundboard section and a scalloped brace is analyzed in order to see the effects that changes in the shape of the brace have on the frequency spectrum of the brace-soundboard system. The results are used to verify the feasibility of adjusting the brace thickness in order to compensate for soundboards having different stiffness in the direction perpendicular to the wood grain. It is shown that scalloping the brace allows an instrument maker to independently control the value of two natural frequencies of a combined brace-soundboard system. This is done by adjusting the brace’s base thickness in order to modify the 1st natural frequency and by adjusting the scalloped peak heights to modify the 3rd natural frequency, both of which are considered along the length of the brace. By scalloping their braces, and thus controlling the value of certain natural frequencies, musical instrument makers can improve the acoustic consistency of their instruments.