Research on the music-language interface has extensively investigated similarities and differences of poetic and musical meter, but largely disregarded melody. Using a measure of melodic structure in music--autocorrelations of sound sequences consisting of discrete pitch and duration values--, we show that individual poems feature distinct and text-driven pitch and duration contours, just like songs and other pieces of music. We conceptualize these recurrent melodic contours as an additional, hitherto unnoticed dimension of parallelistic patterning. Poetic speech melodies are higher order units beyond the level of individual syntactic phrases, and also beyond the levels of individual sentences and verse lines. Importantly, auto-correlation scores for pitch and duration recurrences across stanzas are predictive of how melodious naive listeners perceive the respective poems to be, and how likely these poems were to be set to music by professional composers. Experimentally removing classical parallelistic features characteristic of prototypical poems (rhyme, meter, and others) led to decreased autocorrelation scores of pitches, independent of spoken renditions, along with reduced ratings for perceived melodiousness. This suggests that the higher order parallelistic feature of poetic melody strongly interacts with the other parallelistic patterns of poems. Our discovery of a genuine poetic speech melody has great potential for deepening the understanding of the music-language interface.