Fitting the Mel scale

We show that there are many qualitatively different equations, each with few parameters, that fit the experimentally obtained Mel scale. We investigate the often made remark that there are two regions to the Mel scale, the first region (<~1000 Hz.) being linear and the upper region being logarithmic. We show that there is no evidence, based on the experimental data points, that there are two qualitatively different regions or that the lower region is linear and upper region logarithmetic. In fact F_M=f/(af+b) where F_M and f are the Mel and physical frequency respectively, fits better than a line in the linear region or a logarithm in the “log” region