The Violin Surface Fitting

Year: 1998 Authors: Arun K. Mitra

Core claim

Simple fitted arc models may be extended to derive an exact violin plate surface equation and study free-plate vibration.

Topics

least squares fitting, violin geometry, surface equations, vibrational properties

Domains

polynomial functions, rational functions, linear systems, music, instrument design, craft

Methods

least squares fitting, data-point interpolation, graphing

Media

violin top plate, violin back plate, rectangular coordinates

Paper text

The text below is the locally extracted OCR/Markdown version of the paper. Raw PDF files remain local and are not published here.

BRIDGES Mathematical Connections in Art, Music, and Science

The Violin Surface Fitting

Arun K. Mitra Department of Mathematics and Statistics Texas Tech University Lubbock, Texas 79409

Simple least square models for the violin arcs (for the flat boundary and the curved surface of the top and back plates) in terms of polynomials and rational functions in rectangular coordinates have been suggested. The coefficients appearing in these functions are obtained as the solutions of the associated linear system generated by fitting no more than five data points. The graphs of these equations for the central longitudinal arcs and several lateral arcs for both the top and back plates are presented. It appears that, with some modifications, one can obtain the equation of the surface of a violin plate. The aim here is to produce the exact equation, add the appropriate thickness and study the vibrational properties of free violin plates.