A fundamental issue of speech is that when different individuals enunciate the same perceived sound, the corresponding spectra are different, but since we perceive them to be the same, there must have a commonality that the ear extracts to recognize the same perceived sound. In previous publications we have established this commonality and have argued that the "spectra of sounds made by different individuals and perceived to be the same can be transformed into each other by a universal warping function". We call the warping function the speech scale and in previous works we have obtained it experimentally from actual speech. In this paper we give the mathematical equation that allows one to obtain the transformation function so that the transformation results in identical warped spectra except for a translation factor.