Music traditions worldwide are subject to remarkable diversity but the origins of this variation are not well understood. Musical behaviour is the product of a multicomponent collection of abilities, some possibly evolved for music but most derived from traits serving nonmusical functions. Cultural evolution has stitched together these systems, generating variable normative practices across cultures and musical genres. Here, we describe the cultural evolution of musical distortion, a noisy manipulation of instrumental and vocal timbre that emulates nonlinear phenomena (NLP) present in the vocal signals of many animals. We suggest that listeners’ sensitivity to NLP has facilitated technological developments for altering musical instruments and singing with distortion, which continues to evolve culturally via the need for groups to both coordinate internally and differentiate themselves from other groups. To support this idea we present an agent-based model of norm evolution illustrating possible dynamics of continuous traits such as timbral distortion in music, dependent on i) a functional optimum, ii) intra-group cohesion and inter-group differentiation, and iii) groupishness for assortment and social learning. This account illustrates how cultural transmission dynamics can lead to diversity in musical sounds and genres, and also provides a more general explanation for the emergence of subgroup-differentiating norms.