Measurement-informed Nonlinear Modal Synthesis of 65 Classical Guitars

When a classical guitar string is plucked, vibration energy flows through the bridge into the body and is radiated as sound. Synthesising this process for a large collection of instruments requires both an efficient nonlinear string model and a robust method for extracting instrument-specific parameters from measurements. This paper addresses both issues. Starting from the publicly available dataset of Mores, which provides impulse-response measurements on 65 classical guitars, modal parameters of the bridge compliance and of the bridge-to-air radiation path are extracted for each instrument. These feed a nonlinear string model in which transverse vibration is governed by a geometrically exact elastic potential coupled at an interior bridge point to the measured body data. The nonlinear potential is quadratised via the Scalar Auxiliary Variable (SAV) method, so that the equations of motion become linear in a scalar variable and a known gradient vector, even at the continuous level. After time discretisation, the coupled system is inverted through two sequential Sherman–Morrison rank-one updates (one for the bridge coupling, one for the SAV nonlinearity), yielding an O(N) algorithm per time step. Two regularisation techniques prevent long-term drift of the auxiliary variable. The complete pipeline is demonstrated by synthesising plucked tones across all frets and strings for each of the 65 guitars.