Coarticulation and invariance are two topics at the center of theorizing about speech production and speech perception. In this paper, a quantitative scale is proposed that places coarticulation and invariance at the two ends of the scale. This scale is based on physical information flow in the articulatory signal, and uses Information Theory, especially the concept of mutual information, to quantify these central concepts of speech research. Mutual Information measures the amount of physical information shared across phonological units. In the proposed quantitative scale, coarticulation corresponds to greater and invariance to lesser information sharing. The measurement scale is tested by data from three languages: German, Catalan, and English. The relation between the proposed scale and several existing theories of coarticulation is discussed, and implications for existing theories of speech production and perception are presented.