This paper proposes new definitions of Jitter, Shimmer and HNR which do not make any periodicity nor linearity assumptions. Our approach is based on a novel algorithm for Glottal Closure Instants (GCI) detection that we have recently developed and which outperforms state-of-the-art methods, particularly in the presence of noise. The principle behind this nonlinear and multiscale algorithm is the detection of critical transitions in complex signals (such as speech). As such, the algorithm processes speech as a nonlinear dynamical system without prior hypothesis. We first use this algorithm to define "Critical Transitions Marks (CTM)" and show that they coincide with pitch marks (up to a shift constant) for normal speech. However, for pathological speech, they are completely different from the pitch marks provided by standard algorithms and correspond to real regime transitions in the speech signal. We then use these CTM as the core of new definitions of Jitter, Shimmer and HNR. We carry out experiments on the full KayElemetrics database of sustained vowels. We first show that, for normal speech, our new perturbation measures coincide with those of the MDVP and Praat softwares. We then compare the normal-vs-pathological classification performances. The results show that every new measure significantly outperforms its MDVP/Praat counterpart.