Are observed links between musicality and non-native speech sound processing due to superior sensory processing of temporal, pitch, and spectral information, which benefits both musical and linguistic processing? Native English speakers discriminated Norwegian tonal contrasts, non-linguistic pure-tone analogues, Norwegian vowels, and short tones differing in temporal, pitch and spectral characteristics. Musicality was measured using Gordon’s (1989) Advanced Measures of Musical Audiation (AMMA). After controlling for effects of sex, non-verbal IQ and previous language learning experience, the link between AMMA scores and tonal contour discrimination was partially mediated by pitch acuity. In addition, tonal contrast, pitch contour and vowel discrimination were predicted by temporal and spectral acuity. No independent effects of musical training were found. Thus, links between musicality and non-native speech sound processing appear to be mainly due to superior temporal, pitch or spectral acuity, which, in turn, may play somewhat different roles in processing different speech sounds.