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.