Comparison of Arching Profiles of Golden Age Cremonese Violins and Some Mathematically Generated Curves

R.M. Mottola

Abstract


Three mathematically generate curves are compared to the arching profiles of the plates of six golden age Cremonese violin family instruments. Generated curves include the circular arc, curtate cycloid and sinusoidal curve. Images are presented for visual comparison and a simple measure of fit is calculated for each arching profile and generated curve combination. A subjective rating of the fit of generated curves to profiles is also performed. Results indicate that the circular arc shows the closest average fit for the longitudinal arching, but the fit is only moderately close. The curtate cycloid curve shows the closest average fit for the transverse arching profiles, with very good fit shown in 27% of comparisons. Variability among the profiles sampled is too high to reliably indicate that any one of the generated curves serves as a reasonable general model for these arching profiles. The sinusoidal curve consistently under represents the transverse profiles and so is not a likely candidate as a model for an average transverse profile. The curtate cycloid curve also consistently under represents the transverse profiles at the upper and lower bout locations and so is also not a likely candidate as a model for an average profile at these locations.

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