Writing systems have traditionally been classified by whether they prioritize encoding phonological information (phonographic) versus morphological or semantic information (logographic). Recent work has broached the question of how membership in these categories can be quantified. We aim to contribute to this line of research by treating a definition of logography which directly incorporates morphological identity. Our methods compare mutual information between graphic forms and phonological forms and between graphic forms and morphological identity. We report on preliminary results here for two case studies, written Sumerian and written Japanese. The results suggest that our methods present a promising means of classifying the degree to which a writing system is logographic or phonographic.