Music making across cultures arguably involves a blend of innovation and adherence to established norms. This integration allows listeners to recognise a range of innovative, surprising, and functional elements in music, while also associating them to a certain tradition or style. In this light, musical creativity may be seen to involve the novel recombination of shared elements and rules, which can in itself give rise to new cultural conventions. Put simply, future norms rely on past knowledge and present action; this holds for music as it does for other cultural domains. A key process permeating this temporal transition, with regards to both music making and music listening, is prediction. Recent findings suggest that as we listen to music, our brain is constantly generating predictions based on prior knowledge acquired in a given enculturation context. Those predictions, in turn, can shape our appraisal of the music, in a continual perception-action loop. This dynamic process of predicting and calibrating expectations may enable shared musical realities, that is, sets of norms that are transmitted, with some modification, either vertically between generations of a given musical culture, or horizontally between peers of the same or different cultures. As music transforms through cultural evolution, so do the predictive models in our minds and the expectancy they give rise to, influenced by cultural exposure and individual experience. Thus, creativity and prediction are both fundamental and complementary to the transmission of cultural systems, including music, across generations and societies. For these reasons, prediction, creativity and cultural evolution were the central themes in a symposium we organised in 2022. The symposium aimed to study their interplay from an interdisciplinary perspective, guided by contemporary theories and methodologies. This special issue compiles research discussed during or inspired by that symposium, concluding with potential directions for the field of music cognition in that spirit.