Over 30 years ago, it was suggested that difficulties in the 'auditory organization' of word forms in the mental lexicon might cause reading difficulties. It was proposed that children used parameters such as rhyme and alliteration to organize word forms in the mental lexicon by acoustic similarity, and that such organization was impaired in developmental dyslexia. This literature was based on an 'oddity' measure of children's sensitivity to rhyme (e.g. wood, book, good) and alliteration (e.g. sun, sock, rag). The 'oddity' task revealed that children with dyslexia were significantly poorer at identifying the 'odd word out' than younger children without reading difficulties. Here we apply a novel modelling approach drawn from auditory neuroscience to study the possible sensory basis of the auditory organization of rhyming and non-rhyming words by children. We utilize a novel Spectral-Amplitude Modulation Phase Hierarchy (S-AMPH) approach to analysing the spectro-temporal structure of rhyming and non-rhyming words, aiming to illuminate the potential acoustic cues used by children as a basis for phonological organization. The S-AMPH model assumes that speech encoding depends on neuronal oscillatory entrainment to the amplitude modulation (AM) hierarchy in speech. Our results suggest that phonological similarity between rhyming words in the oddity task depends crucially on slow (delta band) modulations in the speech envelope. Contrary to linguistic assumptions, therefore, auditory organization by children may not depend on phonemic information for this task. Linguistically, it is assumed that 'book' does not rhyme with 'wood' and 'good' because the final phoneme differs. However, our auditory analysis suggests that the acoustic cues to this phonological dissimilarity depend primarily on the slower amplitude modulations in the speech envelope, thought to carry prosodic information. Therefore, the oddity task may help in detecting reading difficulties because phonological similarity judgements about rhyme reflect sensitivity to slow amplitude modulation patterns. Slower amplitude modulations are known to be detected less efficiently by children with dyslexia.