Modern and post-modern free verse poems feature a large and complex variety in their poetic prosodies that falls along a continuum from a more fluent to a more disfluent and choppy style. As the poets of modernism overcame rhyme and meter, they oriented themselves in these two opposing directions, creating a free verse spectrum that calls for new analyses of prosodic forms. We present a method, grounded in philological analysis and current research on cognitive (dis)fluency, for automatically analyzing this spectrum. We define and relate six classes of poetic styles (ranging from parlando to lettristic decomposition) by their gradual differentiation. Based on this discussion, we present a model for automatic prosodic classification of spoken free verse poetry that uses deep hierarchical attention networks to integrate the source text and audio and predict the assigned class. We evaluate our model on a large corpus of German author-read post-modern poetry and find that classes can reliably be differentiated, reaching a weighted f-measure of 0.73, when combining textual and phonetic evidence. In our further analyses, we validate the model’s decision-making process, the philologically hypothesized continuum of fluency and investigate the relative importance of various features.