Introduction Rhythm organises musical events into patterns and forms, and rhythm perception in music is usually studied by using metrical tasks. Metrical structure also plays an organisational function in the phonology of language, via speech prosody, and there is evidence for rhythmic perceptual difficulties in developmental dyslexia. Here we investigate the hypothesis that the accurate perception of musical metrical structure is related to basic auditory perception of rise time, and also to phonological and literacy development in children. Methods A battery of behavioural tasks was devised to explore relations between musical metrical perception, auditory perception of amplitude envelope structure, phonological awareness (PA) and reading in a sample of 64 typically-developing children and children with developmental dyslexia. Results We show that individual differences in the perception of amplitude envelope rise time are linked to musical metrical sensitivity, and that musical metrical sensitivity predicts PA and reading development, accounting for over 60% of variance in reading along with age and I.Q. Even the simplest metrical task, based on a duple metrical structure, was performed significantly more poorly by the children with dyslexia. Conclusions The accurate perception of metrical structure may be critical for phonological development and consequently for the development of literacy. Difficulties in metrical processing are associated with basic auditory rise time processing difficulties, suggesting a primary sensory impairment in developmental dyslexia in tracking the lower-frequency modulations in the speech envelope.