Large cities are culturally diverse. Does this diversity stem from a mix of people with varied demographic backgrounds, or from each individual seeking a broader spectrum of cultural experiences? Due to the lack of data on individual behavioural patterns and demographics, previous research could not discern individuals' contributions to collective cultural outcomes. Leveraging data from over 2.5 million French, Brazilian, and German listeners, comprising 250 million real-world listening behaviours, we trace the mechanisms contributing to cultural diversity across regional populations within these countries. We assess the collective shared musical repertoire in each region, while concurrently measuring each individual's breadth of music engagement through their personal listening histories. Our analysis reveals that an increase in diversity at the collective scale is associated with the size of its population, aligning with previous research on cultural evolution and urban scaling law. We extend this understanding by demonstrating that an individual's cultural breadth also expands with population size, consistently across all three countries. Although demographic factors such as age, gender, income, immigration, education, and social connections mediate these trends, particularly in the most populated areas, they do not fully explain them. This potentially suggests that large cities are culturally diverse not only because they bring together people from varied backgrounds, but also due to the greater opportunities for cultural interaction and exchange that urban settings facilitate.