We aim to provide tools to tackle a critical question for the linguistic community: what is the most suitable way to study the impact of tonal coarticulation in phonetics? Current methods do not fully capture the intricacies of this phenomenon. We show that we can resolve some controversy on the subject by using what is known in functional data analysis as second-order variation. Our approach treats speech frequency curves as functional observations and leverages a crucial insight: time and frequency covariance functions hold the key to understanding the finer effects of tonal coarticulation. This insight drives our two-step approach. First, we model mean functions using Generalized Additive Models. The residuals of such models are then investigated for any structure nested at covariance level using a state-the-art k-sample test for covariances. If such structure is found, we tap into it using covariance principal component analysis. We apply the method to an articulatory dataset specifically collected to study the cognitive mechanisms of tonal coarticulation.