The role of population size in folk tune complexity

Demography, particularly population size, plays a key role in cultural complexity. However, the relationship between population size and complexity appears to vary across domains: while studies of technology typically find a positive correlation, the opposite is true for language, and the role of population size in complexity in the arts remains to be established. Here, we investigate the relationship between population size and complexity in music using Irish folk session tunes as a case study. Using analyses of a large online folk tune dataset, we show that popular tunes played by larger communities of musicians have diversified into a greater number of different versions which encompass more variation in melodic complexity compared with less popular tunes. However, popular tunes also tend to be intermediate in melodic complexity and variation in complexity is lower than expected given the increased number of tune versions. We also find that user preferences for individual tune versions are more skewed in popular tunes. Taken together, these results suggest that while larger populations create more frequent opportunities for musical innovation, they encourage convergence upon intermediate levels of melodic complexity due to a widespread inverse U-shaped relationship between complexity and aesthetic preference. We explore the assumptions underlying our empirical analyses further using simple simulations of tune diffusion through populations of different sizes, finding that a combination of biased copying and structured populations appears most consistent with our results. Our study demonstrates a unique relationship between population size and cultural complexity in the arts, confirming that the relationship between population size and cultural complexity is domain-dependent, rather than universal.