Sound impact of simple viscoelastic damping changes due to aging and the role of the double bentside on soundboard tension in a 1755 Dulcken harpsichord

TL;DR

This paper addresses how aging-related viscoelastic damping changes affect harpsichord sound by constructing a high-resolution FDTD model of a 1755 Dulcken soundboard, calibrated with measured $T_{60}$ and thickness data. It demonstrates that reduced damping from aging generally dulls brightness, with a nonuniform, position-dependent pattern across the 8' and 4' bridges as revealed by spectral centroid analysis. A Helmholtz resonance near $f_{ ext{H}} = 37$ Hz is confirmed, and a 3D FEM stress analysis shows the double bentside configuration has negligible impact on overall soundboard tension, suggesting other factors contribute to observed brightness in historical instruments. The work highlights the need to model viscoelastic damping more precisely across frequencies to accurately predict aging effects on tonal brightness and to guide instrument restoration and preservation.

Abstract

The sound perception of wood aging is investigated on a Dulcken harpsichord of 1755 from the Museum of Applied Arts in Hamburg, Germany using a Finite-Difference Time Domain (FDTD) model of the harpsichords soundboard. The soundboard thickness was measured on the instrument at 497 positions during strings being deattached and used in the model. Impulse responses were taken on the instrument to estimate the present internal damping by calculating the T60 decay time and used as a model input. By varying the internal damping from this measured damping as a logarithmic decrement, impulse responses were simulated at 52 string positions on both, the 8' and 4' bridge. To estimate the changed sound brightness due to changed internal damping, spectral centroids were calculated from the simulated impulse responses. A dependency of brightness change due to aging on string position was found, where the lower strings have higher brightness, as expected, while the higher strings have decreased brightness. This counterintuitive finding is caused by the frequency-dependent filter effect of changed damping. Future studies need to incorporate viscoelasticity to differentiate this effect further. Furthermore, the attachment of the 8' string to the outer instead of the inner wall, a characteristic feature of Dulcken harpsichords, is investigated using a 3D Finite-Element Method (FEM) model simulation of the whole instrument. No considerable changes on the soundboard tension were found compared to an attachment of the 8' strings to the inner wall, pointing to another reason for this special construction.

Figures (8)

• Figure 1: Measured thickness distribution of the Dulcken harpsichord of 1755 from the Museum of Applied Arts in Hamburg measured using a magnetic hall effect thickness measurement device. In the treble region the soundboard is about 2.4 mm, in the bass region about 5.7 mm with continuous thinning along this way. The contour plot consists of 497 measurement points, the measurement was performed while strings were deattached. At the region of the cross bar around the soundhole the thickness is more or less constant around 4.3 mm. Larger local variations of thickness are caused by the tapering of the soundboard during a repair in 1990, or additional glue.
• Figure 2: Thickness (orange background), layout of the 8' and 4' bridges pins (white), 8' and 4' hitchpins (black), and ribs and cutoff bar (gray) of the Dulcken soundboard as input to the FDTD physical model.
• Figure 3: Difference in spectral centroid between the case of increased and decreased damped soundboard through aging of the 1755 Dulcken harpsichord FDTD model for the 8' (blue) and the 4' (yellow) string positions from bass to treble. When the damping had decreased through ages, the brightness of the sound decreases, too. The highest values of the 4' hitchpin rail are simulation artifacts and therefore omitted here.
• Figure 4: Geometry of the CAD model of the Dulcken harpsichord used for Finite-Element Method (FEM) stress analysis.
• Figure 5: String forces for the 8' (blue) and 4' (red) strings. Dark color: Forces necessary to arrive at the respective pitches the instrument is tuned in its present stage using string material (brass, iron), string thickness, and measures (diapason). Light color: Forces acting on the bridges. The highest forces are found with the 4' strings which are acting on the 4' hitchpin rail on the soundboard. The total force acting on the instrument is 3938 N, roughly corresponding to 401 kg.