Wall compliance and violin cavity modes

Violin corpus wall compliance, which has a substantial effect on cavity mode frequencies, was added to Shaw's two-degree-of-freedom (2DOF) network model for A0 ("main air") and A1 (lowest length mode included in "main wood") cavity modes. The 2DOF model predicts a V(-0.25) volume dependence for A0 for rigid violin-shaped cavities, to which a semiempirical compliance correction term, V(-x(c)) (optimization parameter x(c)) consistent with cavity acoustical compliance and violin-based scaling was added. Optimizing x(c) over A0 and A1 frequencies measured for a Hutchins-Schelleng violin octet yielded x(c) approximately 0.08. This markedly improved A0 and A1 frequency predictions to within approximately +/- 10% of experiment over a range of about 4.5:1 in length, 10:1 in f-hole area, 3:1 in top plate thickness, and 128:1 in volume. Compliance is a plausible explanation for A1 falling close to the "main wood" resonance, not increasingly higher for the larger instruments, which were scaled successively shorter compared to the violin for ergonomic and practical reasons. Similarly incorporating compliance for A2 and A4 (lowest lower-/upper-bout modes, respectively) improves frequency predictions within +/-20% over the octet.